Embed Size (px)
Citation preview
Macroeconomics of
small open economies
Manuel Walti
Inauguraldissertation
zur Erlangung der Wurde eines
Doctor rerum oeconomicarum
der Wirtschafts- und Sozialwissenschaftlichen
Fakultat der Universitat Bern
Bern, October 2004
Wälti, Manuel: Macroeconomics of small open economies / Manuel Wälti. – Als Ms. gedr.. – Berlin : dissertation.de – Verlag im Internet GmbH, 2005 Zugl.: Bern, Univ., Diss., 2004 ISBN 3-89825-954-4 Die Fakultät hat diese Arbeit am 18. November 2004 auf Antrag der beiden Gutachter Prof. Dr. Harris Dellas und Prof. Dr. Klaus Neusser, als Dissertation angenommen, ohne damit zu den darin ausge-sprochenen Auffassungen Stellung nehmen zu wollen.
Bibliografische Information der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über <http://dnb.ddb.de> abrufbar. dissertation.de – Verlag im Internet GmbH 2005 Alle Rechte, auch das des auszugsweisen Nachdruckes, der auszugsweisen oder vollständigen Wiedergabe, der Speicherung in Datenverarbeitungsanlagen, auf Datenträgern oder im Internet und der Übersetzung, vorbehalten. Es wird ausschließlich chlorfrei gebleichtes Papier (TCF) nach DIN-ISO 9706 verwendet. Printed in Germany. dissertation.de - Verlag im Internet GmbH Pestalozzistraße 9 10 625 Berlin URL: http://www.dissertation.de
Preface
This thesis deals with topics in applied macroeconomics. Chapter 1 sur-
veys the strand of literature in the field of open-economy macroeconomics
which applies quantitative models to the issue of transmission properties
of economic disturbances and international policy. We discuss the genesis
of quantitative open-economy models, their ability to match the data, and
their use as a laboratory for policy analysis. In doing so, we concentrate on
studies dealing with the role of exchange rate stabilization in the conduct
of monetary policy and the choice of exchange rate arrangement.
In chapter 2, we compare Taylor type interest rules which differ in the
size of the reaction coefficient on the real exchange rate. The alternative
policy regimes are evaluated in terms of macroeconomic performance and
welfare within the framework of an artificial small-open economy with opti-
mizing agents, a moderate degree of nominal price rigidity, and five kinds of
shocks (domestic and foreign). We limit the consideration to feedback rules
which require only information which could plausibly be possessed by the
central bank. The results are discussed against the background of two nat-
ural benchmark policies: strict domestic inflation targeting and a credible
and unilateral peg toward the currency of the rest of the world. We find that
introducing a moderate form of real exchange rate targeting in the original
Taylor rule induces higher welfare with respect to shocks to productivity
and foreign demand and lower welfare with respect to shocks to govern-
ment consumption and the terms of trade. However, the outcome under
rules which, unlike the original Taylor rule, allow for a considerable degree
of interest smoothing, is robust regarding the inclusion of real exchange rate
targeting.
iv PREFACE
In an influential paper, Jordi Gali (1999)1 studies the effects of tech-
nology shocks on employment in the G7 countries using a structural vec-
tor autoregressive model (VAR) approach. Gali finds that the response of
employment to a positive technology shock is negative and persistent. In
chapter 3, we repeat his analysis with two important modifications. First,
we add an open-economy block to Gali’s five-variable framework. Second,
the use of structural vector error correction model (VECM) methods allows
us to investigate the effect of a productivity shock on employment based
on less restrictive assumptions than Gali does. His findings, however, are
largely confirmed.
1Technology, employment, and the business cycle: do technology shocks explain ag-
gregate fluctuations?, American Economic Review 1999, 89(1), 249-271.
Acknowledgement
When writing this thesis, I benefited from the input of many people. Above
all I wish to thank my advisor Harris Dellas for his constant attention and
guidance. I would like to thank Klaus Neusser for kindly taking the role of
a co-examiner and for giving many valuable hints.
I am very grateful to Carlos Lenz for providing me his method for esti-
mating structural VARs and crucial sections of the RATS code; the third
chapter of this book has also greatly benefited from discussions with him.
I thank the participants of the Wednesday seminar at the Economics De-
partment – Esther Brugger, Alain Egli, Armin Hartmann, Roland Hodler,
Simon Lortscher, and Michael Manz – as well as Kurt Schmidheiny for their
valuable comments and their friendship.
Finally, I would like to thank the Swiss National Bank (SNB) for sup-
porting this project in its final stage and Werner Hermann and Ulrich Kohli
for putting the necessary time at my disposal. Thanks also to Christoph
Meyer for his assistance in obtaining the OECD MEI and IMF data at a
time when I was not yet familiar with EASY, the SNB’s economic analysis
system.
Contents
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Quantitative open-economy NNS models 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Genesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 International RBC approach . . . . . . . . . . . . . . 3
1.2.2 Market incompleteness and the small country assump-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 New Neoclassical Synthesis . . . . . . . . . . . . . . . 7
1.3 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Laboratory for policy analysis . . . . . . . . . . . . . . . . . 13
1.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . 18
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 The role of exchange rate stabilization 25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Behavior of final good producers . . . . . . . . . . . . 29
2.2.2 Digression: Total demand for input factor i . . . . . 31
2.2.3 Behavior of intermediate good producer i . . . . . . . 32
2.2.4 Behavior of representative agent . . . . . . . . . . . . 37
2.2.5 Fiscal and monetary policy . . . . . . . . . . . . . . . 41
2.2.6 Market clearing . . . . . . . . . . . . . . . . . . . . . 42
2.2.7 Closing the model: International asset markets . . . . 43
2.3 Solution, parameterization, and diagnostic check . . . . . . . 44
2.3.1 Baseline parameterization . . . . . . . . . . . . . . . 45
2.3.2 Dynamic effects . . . . . . . . . . . . . . . . . . . . . 47
viii CONTENTS
2.4 The role of exchange rate stabilization . . . . . . . . . . . . 54
2.4.1 Interest-rate rules to be investigated . . . . . . . . . 56
2.4.2 Simulation results . . . . . . . . . . . . . . . . . . . . 60
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.A Stationary representation . . . . . . . . . . . . . . . . . . . . 68
2.A.1 Change in notation and useful simplifications . . . . 68
2.A.2 Equilibrium conditions . . . . . . . . . . . . . . . . . 70
2.A.3 Deflating the system . . . . . . . . . . . . . . . . . . 72
2.B Non-stochastic steady state . . . . . . . . . . . . . . . . . . 74
2.C First-order approximation . . . . . . . . . . . . . . . . . . . 77
2.C.1 Linear system . . . . . . . . . . . . . . . . . . . . . . 77
2.C.2 Digression: The New Phillips curve . . . . . . . . . . 80
2.D Exchange rate peg . . . . . . . . . . . . . . . . . . . . . . . 80
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3 Technology shocks and employment in open economies 87
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.2 Benchmark model . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2.1 Estimation method . . . . . . . . . . . . . . . . . . . 92
3.2.2 Two critical remarks . . . . . . . . . . . . . . . . . . 94
3.2.3 Replication results . . . . . . . . . . . . . . . . . . . 97
3.3 Nominal block . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.3.1 Estimation method . . . . . . . . . . . . . . . . . . . 100
3.3.2 Replication results . . . . . . . . . . . . . . . . . . . 102
3.4 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.4.1 Open-economy block . . . . . . . . . . . . . . . . . . 105
3.4.2 Structural VECM approach . . . . . . . . . . . . . . 109
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.A Univariate unit root tests . . . . . . . . . . . . . . . . . . . . 114
3.B Estimation of structural VARs and VECMs . . . . . . . . . 115
3.B.1 Non-cointegrated case . . . . . . . . . . . . . . . . . 115
3.B.2 Cointegrated case . . . . . . . . . . . . . . . . . . . . 121
3.C Bootstrap confidence intervals . . . . . . . . . . . . . . . . . 126
3.D Model specifications . . . . . . . . . . . . . . . . . . . . . . 128
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
CONTENTS ix
Tables and figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Chapter 1
Quantitative
new neoclassical synthesis
models of open economies
1.1 Introduction
The traditional framework for studying policy issues in international macroe-
conomics – such as the choice of optimal exchange rate arrangements –
has long been the Mundell-Fleming-Dornbusch model. Since the Mundell-
Fleming-Dornbusch model does not provide an internal welfare criterion,
it has, for the purpose of policy evaluation, typically been supplemented
with an ad hoc loss function depending on output and inflation variabil-
ity. In recent years, the same issues have increasingly been investigated in
frameworks which integrate monopolistic competition in goods and/or labor
markets and some form of nominal rigidity into dynamic general equilib-
rium (DGE) settings. Given its solid microfoundations, the new generation
of open-economy models is far better suitable for serious policy evaluation
exercises.
Broadly speaking, there are two strands of the new open-economy macroe-
conomics literature. Models following the approach initiated by Obstfeld
and Rogoff [26], on the one hand, possess an analytical solution.1 This
advantage, however, comes at a price: It involves the imposition of many
1For a survey of small analytical open-economy models, see Lane [26] and Sarno [34].
2 CHAPTER 1
simplifying assumptions such as that prices are predetermined rather than
sluggish, that physical capital is exogenous rather than endogenous, that
monetary policy is passive with money stock as the instrument rather than
following a Taylor-type interest rule, that changes in monetary policy are the
only kind of shocks rather than allowing for a reasonable number of struc-
tural driving forces (including supply shocks), and that the representative
agent’s momentary utility is separable between consumption and leisure
rather than nonseparable (as is typical in the real business cycle litera-
ture). Moreover, the small -open economy version typically abstracts from
the stability problems attached to a small open economy setting (an issue
to which we will return later). All these simplifications and abstractions
make Obstfeld and Rogoff [26] and its numerous successors too stylized for
the purpose of calibration or estimation and, thus, inappropriate for the
purpose of policy analysis.
Models in the real business cycle (RBC) tradition such as Kollmann [24]
and Chari et al. [9], on the other hand, do not admit a closed-form but have
to be (approximately) solved based on numerical methods. Due to their
richer structure, however, they can be brought to data. In other words, not
only the models’ ability to explain qualitative features of observed business
fluctuations can be tested, but also their ability to account for statistical
properties like the standard deviations and cross-correlations of observed
aggregate time series. It is this capability that in our view qualifies them
for the purpose of serious policy analysis.
The present paper selectively surveys recent studies in the field of new
open-economy macroeconomics which apply realistically quantitative mod-
els to the issue of transmission properties of economic disturbances and
international policy. The remainder of the paper is organized as follows.
Section 1.2 discusses the genesis of modern quantitative open-economy busi-
ness cycle models. Section 1.3 discusses these models’ ability to fit the data
and section 1.4 their use as a laboratory for policy analysis. Section 1.5
concludes.
1.2. GENESIS 3
1.2 Genesis of quantitative open-economy busi-
ness cycle models
The modern quantitative open-economy business cycle models have their
roots in the methodological advances of the RBC approach and elements
of the New Keynesian models of the 1980s. We begin this section with
a brief discussion of what we consider to be the main contribution of the
RBC literature, the demonstration of how general equilibrium models can
be taken to data. Then, we point to the stability problem related to the
neoclassical model of a small open economy and the remedies suggested in
the literature. Lastly, we give a brief summary of the emergence of the
so-called New Neoclassical Synthesis.
1.2.1 International RBC approach
Nowadays, most macroeconomists would agree that the main contribution
of the RBC literature to the profession has been in terms of methodology
(see e.g. Woodford [40]): First, the RBC literature has shown how general
equilibrium models can be made quantitative; this involves realistic numer-
ical parameter values and methods to compute numerical solutions to the
equations of a model. Second, the RBC literature has emphasized the as-
sessment of a model’s validity to fit the data by comparing quantitative
features of the theoretical economy such as the standard deviations, the
cross-correlations, and the autocorrelations for key variables of the model
to those of observed aggregate time series, using some informal distance
criterion.
Let us illustrate this point by means of an example taken from the in-
ternational RBC literature. The two-country model of Backus et al. [1],
section 5, is a typical exponent of this approach. Both countries specialize
in the production of a single, imperfect substitutable intermediate good,
which implies that all trade between the countries is in intermediate goods.
Intermediate goods producers use domestic physical capital and labor as
inputs; both capital and labor, are immobile internationally. Each country
also produces a non-tradable final good, which is used for consumption,
investment, and government spending. The final good is produced by as-
4 CHAPTER 1
sembling domestic and imported intermediate goods. In both countries, the
representative household owns domestic firms, the capital stock, and the
time endowment; the capital stock and the time devoted to labor are rented
to the intermediate good producer. The household has access to a com-
plete contingent-claims market. Needless to say, all markets are perfectly
competitive and prices are fully flexible.
Among the notable features of international macroeconomic data and
the economic connections among countries which received much attention at
the time, is the observation that the correlations of output across countries
are larger than the analogous correlations for consumption and productivity
and that the terms of trade of the individual countries are highly variable
and persistent (compare e.g. Backus et al.). How successful is the model of
Backus et al. in mimicking these properties? A first finding is that in the
theoretical economy the consumption correlation exceeds the productivity
and output correlations. A second finding is that the fluctuations in the
terms of trade are much less variable in the theoretical economy than in the
data. Since the two findings are robust to a number of reasonable changes
in the economy (in terms of parameter values and key assumptions), Backus
et al. label them, respectively, the consumption correlations and the terms
of trade anomaly. We conclude that while for the basic version of a closed-
economy RBC model the match between theory and observations (with
respect to real economic activity) is surprisingly well,2 the open-economy
counterpart is far less successful.
1.2.2 Market incompleteness and the small country
assumption
So far, we have been talking about extensions of the basic closed-economy
RBC model, which involves the existence of a complete contingent-claims
market, to a two-country setting. An alternative setting in international
macroeconomics, however, is the case of a small open economy, often in
combination with a bonds-only structure.
From the growth literature, it is known that modifying the basic neo-
classical growth model to allow for mobility of goods and international bor-
2For a critical assessment of this statement, see e.g. King and Rebelo [23].
1.2. GENESIS 5
rowing and lending features two undesirable properties (compare e.g. Barro
and Sala-i-Martin [3], chapter 3): The first is that the adjustment toward
the steady state is instantaneous. The second is that if the world interest
rate is not equal the small open economy’s rate of time preference, in the
long run consumption either approaches zero and net foreign assets reach
a negative lower bound, or both consumption and net foreign assets, grow
forever and get infinite (which would imply that the small open economy
finally gets a big player). However, if the two interest rates are equal, then
the steady state depends on the economy’s initial net foreign asset position.
Translated into a stochastic framework this means that transitory shocks
to the world interest rate induce permanent changes in the net foreign asset
position. This raises a problem since standard solution techniques rely on
the existence of a stationary steady state.3
Allowing for complete contingent-claims markets would be a way to over-
come the stability problem.4 The state-contingent claims protect the small
open economy against future contingencies and, thus, work as an insurance
against the shocks’ effects. For standard specifications of the utility func-
tion, deviations of domestic consumption from their steady state values are
proportional to their foreign counterpart. In this event, since the rest of the
world behaves as a (stationary) closed-economy, the same behavior must
apply for the small open economy.
An implication of the complete markets assumption is that there is
no current account surplus or deficit – which is the reason why anyone
who intends to study current account dynamics does not assume complete
3In the words of Ghironi [21], p. 3 [emphasize in original]: ”When the model is log-
linearized, one is actually approximating its dynamics around a ’moving steady state’.
(...) De facto, one cannot perform any stochastic analysis.”4Recall that we focus here on a stochastic setting. In a deterministic setting, however,
there is no point in modelling complete markets, since there are no risks to pool.
6 CHAPTER 1
contingent-claims markets in the first place.5, 6 Hence, whenever we want
to make predictions regarding the dynamics of the stock of external assets
minus liabilities (the net external position) or the change in the net external
position from one period to the next (the current account), we are bound
to assume that the only asset nations trade is a one-period bond that offers
a certain one-period return, i.e., that there is free borrowing and lending in
riskless one-period bonds but no trade in contingent claims.
The literature suggests various remedies to the notorious deficiencies
in the small-country, bonds-only version of the neoclassical growth model
mentioned above. The introduction of convex capital adjustment costs can
solve the problem of instantaneous adjustment toward the steady state.7
Making the steady state level of net foreign assets unique involves one of
the following strategies. A first alternative is letting the interest rate faced
by the small open economy equal the exogenous world interest rate plus a
spread that is an increasing function of the country’s aggregate net foreign
asset position. The intuition behind this is a country-specific risk premium.
A second alternative is allowing for time varying (Uzawa-type) preferences,
which implies that the agent becomes more impatient as he becomes richer.
Allowing for effects from finite horizons is a third alternative. Within a
so-called Blanchard-Yaari-type (stochastic) overlapping generations frame-
work, a household’s life ends according to a Poisson process (which implies
that households are heterogenous with respect to date of birth and age).
5To see this, suppose there is a permanent positive productivity shock in a small
open economy with inelastic labor supply. Resources are shifted from the rest of the
world to the small open economy since agents in the world economy ”make hay where
the sun shines”, as Backus et al. [1] put it. This means that in the beginning the small
open economy is running a trade deficit to finance the additional investment. While the
resulting increase in consumption is negligible for the rest of the world, the small open
economy effect is large, resulting in a trade surplus in the subsequent periods. However,
there is no accompanying increase in foreign indebtedness to the small open economy.
In the words of Baxter [4], p. 1825, this is because ”the trade surplus may be viewed as
representing payments in fulfillment of a contingent-claims contract that specified these
payments in the event that the home country experienced an increase in productivity”.6As we will argue below, in a monetary setting there are other good reasons to deviate
from the complete asset market assumption.7Alternatively, constraints in international credit can be imposed (see Barro and Sala-
i-Martin [3].
1.2. GENESIS 7
However, households can buy actuarially fair annuities to hedge against un-
certainty with respect to the length of their life: As long as a household
lives, the insurance company pays a constant sum; it gets the remaining
assets when a household ends life (i.e., there is no bequest). In effect, this
leads to steady state values for consumption and foreign debt which are
positive and finite. Introducing convex portfolio adjustment costs is a final
alternative to overcome the stability problem. It implies that holding assets
in quantities which are different from a long-run level is costly.
1.2.3 New Neoclassical Synthesis
We begin this subsection with a brief overview of the empirical evidence
on the response of real and nominal variables to monetary policy impulses.
We then ask to what extent the neoclassical model is compatible with these
facts. Which finally leads us to the emergence of a new paradigm in macroe-
conomics, the New Neoclassical Synthesis (NNS).
In the last couple of years, a consensus from the empirical literature
on the short-run monetary relationships has developed. A first voluminous
body of empirical literature provides evidence on the short-run effects of
monetary policy shocks on real and nominal variables. Christiano et al. [11],
for instance, find for their benchmark model – which measures the policy
instrument by the federal funds rate – that a contractionary policy shock
leads to significant, persistent non-neutralities, to a rather slow response
of prices, and to a strong liquidity effect. These findings are robust across
alternative identification schemes; moreover, there is a long list of other
papers which find similar results. A second body of literature has produced
evidence in favor of a positively sloped short-run Phillips curve (basically the
correlation between inflation and unemployment or an alternative measure
of excess capacity in the economy).
Those pieces of evidence are hard to reconcile with the basic one-good,
one-shock RBC model. First, and most obviously, since the basic RBC
model does not refer to money, it has nothing to say about the behavior of
nominal variables. Second, the basic RBC model explains macroeconomic
fluctuations only with technology shocks; that is, demand shocks are absent
– which contrasts to the econometric evidence which identifies money as an
important source of fluctuations. A related, rather controversial property of
8 CHAPTER 1
the basic RBC model is that since economic fluctuations are efficient, there
is no scope for any form of government intervention, including monetary
stabilization policy.
The one-good, one-shock RBC model has subsequently been modified
to allow for money; this with the objective of learning whether monetary
forces can be an important cause of business cycle fluctuations in a neoclas-
sical setting. Cooley and Hansen [15], for instance, focus on theories of the
short-run non-neutrality of money which are in line with New Classical eco-
nomics. The first treats money as a source of confusion (the Lucas imperfect
information model); in the second, inflation acts as a distorting tax on the
holding of nominal money (the cash-in-advance approach). They find that
the quantitative importance of monetary shocks is very small and, accord-
ingly, that the two monetary models do not provide a good description of
the associations between real and nominal variables.
In the first half of the 1990s, more and more researchers began to intro-
duce New Keynesian features such as imperfect competition and sluggish or
costly nominal price adjustment into otherwise standard neoclassical busi-
ness cycle models, thereby considerably improving the models’ match to
data (see e.g. Yun [42]).8 A typical feature of NNS models is that they in-
volve substantial market failures, so that government intervention is desir-
able, and that increases in demand (e.g., due to an expansionary monetary
policy shock) stimulate aggregate activity.9
Compared to the traditional IS/LM-Phillips curve framework, the new
generation of models of the monetary transmission mechanism has a number
of advantages. First, agents are intertemporally optimizing and forward-
looking, do not in equilibrium want to change what they are doing, and
have rational expectations. Second, there is an appropriate emphasis on
real disturbances as a source of short-run variations in economic activity.
Finally, the new approach permits formal welfare evaluation of alternative
policies.
8The models’ ability to match the data crucially depends on a sufficiently large degree
of nominal price staggering or a similar mechanism. For a survey of the field in a closed-
economy context, compare e.g. Walsh [35], chapter 5.9It is probably worth to mention that with sluggish prices the effects of supply shocks
are altered, too. This is because not all firms are able to lower prices in response to an
unexpected increase in productivity and the corresponding decrease in marginal costs.
1.3. MODEL EVALUATION 9
The development in closed-economy macroeconomics has rapidly spilled
over into international macroeconomics. Among the first who introduced
money, imperfect competition, and price rigidities into an otherwise stan-
dard neoclassical open-economy framework were Obstfeld and Rogoff [27].
A drawback of this prototypical open-economy NNS model, however, is that
it is highly stylized and only provides qualitative results.
1.3 How well do quantitative, open-economy
NNS models match the data?
The empirical regularities in post-war data on the international business
cycle which have been used as criteria for assessing international RBC mod-
els focused on real quantities and relative prices (compare above). Open-
economy NNS models, however, should also be able to account for the fol-
lowing facts which involve the nominal exchange rate and the choice of the
exchange rate regime: (a) Nominal and measured real exchange rates are
highly volatile and very persistent; (b) nominal and real exchange rates
are strongly positively correlated; (c) the behavior of exchange rates (nom-
inal and real) varies systematically with the exchange rate regime; (d) the
behavior of the other real macroeconomic variables appears to be roughly
independent of the exchange rate regime.10
In the following, we discuss four examples of quantitative open-economy
NNS models and see how well they can account for fact (a) through (d). We
begin our study with Chari et al. [9], who aim at explaining fact (a). The
model of Chari et al. shares many features with the previously discussed
model of Backus et al. The most important differences are as follows. Since
Chari et al. consider a monetary economy, they assume a complete finan-
cial asset market rather than a complete contingent-claims market. The
intermediate goods markets are monopolistically rather than perfectly com-
petitive (i.e., competitive final good producers in each country purchase
intermediate goods from monopolistically competitive intermediate good
10Fact (b) and (c) have typically been interpreted as evidence in favor of sticky prices,
since they can only be explained within frictionless flexible-price models when most
significant shocks buffeting the economy are real – a rather unrealistic assumption, as we
have argued above (for an opposite view compare Stockman [36]).
10 CHAPTER 1
producers). And, intermediate good producers set nominal prices in stag-
gered contracts a la Taylor [37], rather than optimally adjusting them in
every period.
In principle, in an open-economy setting, price rigidities can take various
forms. Traditionally, prices have been assumed to be fixed in the currency
of the producer (i.e., the exporter’s country). Under this assumption the
law of one price (LOP) holds, taking for granted that trade is costless.
As a corollary, the purchasing power parity (PPP) is always satisfied and
exchange rate changes immediately feed into import prices (complete pass-
through).
However, a large body of empirical studies for many countries show that
the LOP does, more often than not, not hold and the PPP is only satisfied
in the long run. Both pieces of evidence suggest that the pass-through into
import prices might be limited. One popular story assumes that due to
high costs of arbitrage, home and foreign markets are segmented and each
individual monopolist can price-discriminate across countries; in addition
to this, producers set prices in the currency of the buyer (so-called local
currency pricing, LCP). Under this form of price stickiness, exchange rate
changes lead to proportional deviations from the LOP and the pass-through
is nil. This is exactly what Chari et al. assume.
To close the model, Chari et al. have to specify monetary policy. In
their benchmark version, they assume a (stochastic) money growth rule in
combination with a floating exchange rate.11 The first of the two countries
is calibrated to the U.S., the other to a European aggregate. Their findings,
which are based on simulations for shocks to the monetary aggregate, can be
summarized as follows. If prices are held fixed one period (i.e., one quarter),
the persistence of the real exchange rate is nil. For six period stickiness, the
persistence is considerable but still smaller than in the data. Only for an
implausibly large contract length of twelve periods they get a persistence
11Two key characteristics of modern international financial markets are the market
determination of exchange rates among the major industrialized countries and the global
financial integration. It therefore makes sense to assume that financial capital is interna-
tionally mobile. In accordance with the open-economy trilemma, the monetary authority
can then choose between an independent policy within a floating exchange rate or nom-
inal exchange rate stability at the expense of monetary independence.
1.3. MODEL EVALUATION 11
that roughly coincides with that found in the data.12
Duarte [17] is another example of a quantitative open-economy NNS
model; she aims at explaining fact (c) and (d). In Duarte’s model – as
opposed to Chari et al. – imports enter as final rather than as intermedi-
ate goods. There are two categories of goods, domestic and foreign, both
produced by monopolistically competitive firms in Home and Foreign, re-
spectively. Both categories of goods are aggregated to a distinct composite
consumption good; the two composites (or bundles) are then nested in a
two-input argument CES function which gives an overall consumption bas-
ket.
Further differences compared to Chari et al. are: Duarte abstracts from
capital and investment; there are two country-specific, cross-correlated pro-
ductivity shocks in addition to the two country-specific money growth shocks;
momentary utility is nonseparable between leisure and consumption; and
prices are not sluggish but set one period in advance.13
Another difference lies in the specification of the asset market. While
Chari et al. assume a complete financial asset market, Duarte assumes mar-
ket incompleteness. The assumption of asset market incompleteness is often
motivated pragmatically with a better performance regarding the dimension
consumption and output correlation. As we have seen in section 1.2, models
with complete risk sharing generate cross-country consumption correlations
that are much higher than in the data. Yet models with a bonds-only struc-
ture produce correlations which roughly coincide with those found in the
data (compare e.g. Kollmann [23]). A second argument in favor of a bonds-
only structure can be seen in the empirical evidence of non-fundamental
exchange rate fluctuations and strong deviations from the uncovered inter-
est parity (UIP). In the short to medium run, exchange rates are mostly
exogenous, that is, cannot be explained from macroeconomic fundamentals
(the Meese and Rogoff evidence). Moreover, there exists a large body of
literature that identifies (and searches to explain) deviations from the UIP.
A bonds-only structure in combination with the addition of an error term to
12Chari et al. also investigate variants of the benchmark model, in particular incomplete
financial asset markets, sticky wages, and an active rather than a passive monetary policy.
The findings of the benchmark model are largely confirmed.13As Chari et al., Duarte assumes 100% LCP.
12 CHAPTER 1
the UIP relation allows to account for these facts. In Duarte [17], however,
the UIP always holds.
Duarte assumes that the two countries are perfectly symmetric and cali-
brates them to U.S. data. Her model successfully generates a sharp increase
in the volatility of the real exchange rate following a switch from fixed to
flexible rates, without a similar pattern for the volatilities of output, con-
sumption, or trade flows. As we will discuss below, the LCP assumption is
crucial in generating this pattern (since it implies – in the words of Duarte
– that changes in the nominal exchange rate are dissociated from allocation
decisions).
Yet another example of a quantitative open-economy NNS model is
Monacelli [25], who aims at explaining fact (c). In Monacelli, as in Duarte,
consumption goods are directly traded, asset markets are incomplete, and
the UIP always holds. The most important differences compared to Duarte
are as follows. Monacelli considers a small country, whereby he ignores
the stability problem discussed in Subsection 1.2.2; no monetary assets are
needed to facilitate transactions (i.e., a cashless economy is considered, see
e.g. Woodford [41]); utility is separable between leisure and consumption;
prices are staggered a la Calvo [8] and fixed in the currency of the producer
(100% producer currency pricing, PCP); moreover, the model incorporates
capital and capital adjustment costs.
Finally, Monacelli assumes that monetary policy follows an interest-rate
feedback rule (which includes a term that reacts to movements of the nom-
inal exchange rate about the parity). The model is parameterized for a
hypothetical economy (i.e., the parameter values are borrowed from the
literature). Monacelli finds that the model is consistent with Mussa’s evi-
dence: The real exchange rate is between four to five times more variable
under floating than under fixed rates, independent of the underlying source
of fluctuations.
As mentioned above, another classical finding in international macroe-
conomics is that traditional exchange rate models are unable to beat a
random walk in forecasting the nominal exchange rate. Bergin [5] asks
whether open-economy NNS models can better explain the exchange rate.
His two-country model shares many features with the benchmark version of
Chari et al. The most important differences are as follows. Staggered price
1.4. LABORATORY FOR POLICY ANALYSIS 13
adjustment a la Calvo is assumed. Both types of price stickiness, PCP and
LCP, are allowed to coexist where the share is a parameter to be estimated.
The model has a bonds-only structure. To the UIP, a country risk premium
to the net foreign asset position plus an error term (i.e., a shock to the risk
premium) is added. Monetary policy is assumed to be active: it follows a
contemporaneous-date Taylor rule with interest rate smoothing.
A few structural parameters are pinned down using information from
prior studies. But most parameters (among others the elasticity of substi-
tution between home and foreign composite goods and the constant fraction
of firm exhibiting LCP) are estimated by maximum likelihood methods.
Quarterly data for the U.S. and an aggregate of the remaining G7 countries
are used to this aim. Bergin finds that the model performs moderately well
in that it is able to beat a random walk model for in-sample predictions.
To sum up, there is no unified modelling framework which can account
for all discussed facts. However, specific specifications match specific key
moments in the data quite well. Price staggering a la Calvo seems to be
more capable than price staggering a la Taylor. The appropriate choice of
the pricing pattern (PCP or LCP) remains an unsettled issue.
1.4 Laboratory for policy analysis
So far, we have been asking the (positive) question of how successfully
quantitative open-economy NNS models can replicate statistical properties
observed in the data. We now turn to normative aspects in international
macroeconomics such as the question whether monetary authorities should
take account of the (nominal or real) exchange rate in the conduct of mon-
etary policy and if yes, to what extent. An extreme form of taking account
of the exchange rate is stabilizing it towards a foreign currency of choice.
A step beyond fixed exchange rates is for two countries to share a common
currency. Thus, a related question asks about the ranking of alternative
international monetary arrangements: a free float, an unilateral peg, and a
currency union.
The fact that the world is interdependent with government policy pos-
sibly being a major source of the transmission of economic disturbances
across countries leads to yet another topic, namely the question wether
14 CHAPTER 1
there are potential benefits from international macroeconomic policy coor-
dination. The work on strategic interaction between central banks utilizing
two-country NNS models has recently been surveyed by Bowman and Doyle
[7]. Here, we concentrate on the quantitative open-economy literature deal-
ing with the role the exchange rate should play in the conduct of monetary
policy and the choice of the exchange rate regime.
In the literature concerned with the design of monetary policy, two broad
branches can be distinguished. One strand aims at deriving the globally
optimal policy (under either commitment or discretion). This is relatively
straightforward when a number of simplifying assumptions is imposed re-
garding the size of the economy, the asset market structure, the capital
accumulation, and the number and kind of distortions present in the econ-
omy (compare e.g. Clarida et al. [10] and Gali and Monecelli [15], section
5). In more general settings, however, the derivation of the globally optimal
policy is more involved and often intractable. In this event, an alternative
is to restrict the instrument rule (typically the nominal interest rate) to lie
in a given class and at the same time to assume that the central bank can
commit, once and for all, to a given policy rule for all future periods.
Hence, in rather general open-economy frameworks the question about
how responsive monetary policy should be to the exchange rate comes down
to the question whether amending or altering the original Taylor rule im-
proves economic performance and welfare.14 The followed strategy for pol-
icy evaluation is concisely described in Taylor [38], pp. 263/4: One places a
particular modification of the original rule (allowing for a direct response of
the interest rate to the exchange rate) into a parameterized stochastic DGE
model of a small open economy with sticky prices, solves the model using
a numerical solution algorithm, examines the properties of the stochastic
behavior of those macroeconomic variables which reflect potential goals of
monetary policy, and/or examines the consequences on welfare. One proviso
is in order here. It concerns the abstraction from the possibility of specu-
lative attacks when the nominal exchange rate is pegged, which is actually
an important form of cost of fixing the exchange rate.
14The original Taylor rule makes the instrument depend on current domestic inflation
and output deviations from trend with reaction coefficients 1.5 and 0.5, respectively.
1.4. LABORATORY FOR POLICY ANALYSIS 15
Two-country models We now come to the synopsis of some recent find-
ings. We start our study with Collard and Dellas [13] who ask how changes
in international monetary arrangements affect the properties of the busi-
ness cycle in individual countries as well as globally. Three regimes are
considered: a perfect float, an unilateral peg, and a bilateral peg. Collard
and Dellas’ [13] two-country model shares many features with the bench-
mark version of Chari et al. The most important differences are as follows.
First, Collard and Dellas [13] assume staggered nominal wage contracts a
la Calvo; furthermore, there are five shocks in the model in addition to the
two country-specific monetary shocks, namely a common and two country-
specific supply shocks and two country-specific fiscal shocks; finally, mone-
tary policy is active and follows a forward-looking Taylor rule.
The model is calibrated to Germany and France. Collard and Dellas
[13] find that in France, macroeconomic volatility under a monetary union
is comparable to that under a flexible exchange rate system but consider-
ably lower than that under an unilateral peg (where the French franc is
fixed towards the Deutsch mark). In Germany, output volatility is signifi-
cantly higher under a peg – relative to the flexible regime – and increases
even further under a currency union, whereas inflation volatility becomes
smaller. The monetary union also induces a strong negative international
transmission of country specific supply shocks.
Milton Friedman’s classical conjecture that a floating exchange rate pro-
vides the needed relative price adjustment when nominal goods prices are
sluggish, is based on the complete pass-through assumption and the notion
that monetary policy is passive. In another piece of work, Collard and Del-
las [12] investigate how much rigidity is needed in order to make a difference
for the choice of exchange rate regime and whether Friedman’s case for a
flexible regime is consistent with an activistic policy. The model they utilize
is similar to the one in Collard and Dellas [13]. The most important dif-
ferences are as follows. Collard and Dellas [12] assume that nominal goods
prices rather than wages are sluggish; prices are set in the producer’s cur-
rency (100% PCP); and, monetary policy follows a contemporaneous-date
Taylor rule with interest rate smoothing.
The model is calibrated to the postwar U.S. economy, under the assump-
tion of perfect symmetry across countries. Welfare is computed based on a
16 CHAPTER 1
quadratic approximation to the utility function of the representative agent
(together with a first-order approximation to the equilibrium conditions).
Collard and Dellas [12] indeed find that a high degree of sluggishness tends
to favor the flexible system, while a low degree of sluggishness favors the
fixed regime. However, the differences across exchange rate regimes in terms
of performance and welfare tend to be small.
A number of recent studies indicate that the amendment of a direct
exchange rate target (nominal or real) into an otherwise standard Taylor
rule does either not yield a greater improvement in performance or that
performance actually deteriorates (see e.g. Taylor [38]). In yet another piece
of work, Collard and Dellas [14] argue that this finding presents a challenge
for understanding actual monetary policy practices. To gain more insight,
they investigate the implication of direct exchange rate targeting within a
modelling framework which is identical to that of Collard and Dellas [12].
They find that real exchange rate targeting is indeed never a good idea
while nominal exchange rate targeting is likely to be irrelevant.
Small open economy models In a rather influential paper, Gali and
Monacelli [15] analyze within a small open economy setting the macroeco-
nomic implications of the three alternative policy regimes strict domestic
inflation targeting, strict consumer price index (CPI) inflation targeting,
and an unilateral peg. As in Duarte, consumption goods are directly traded.
The most important differences compared to Duarte are as follows. In Gali
and Monacelli, the home economy is small (while the rest of the world is
treated as a closed economy following an optimal policy); the related sta-
bility problem is overcome by assuming complete financial asset markets;
no monetary assets are needed to facilitate transactions (cashless economy);
utility of the representative household is assumed to be separable between
leisure and consumption; finally, staggered price adjustment a la Calvo and
100% PCP is assumed.
Gali and Monacelli report quantitative results for a parameterized ver-
sion of their model; parameter values are borrowed from the literature. They
find that a peg amplifies both output gap and inflation volatility, relative to
a strict domestic inflation targeting, with the strict CPI inflation targeting
regime lying somewhere in between.
1.4. LABORATORY FOR POLICY ANALYSIS 17
Ghironi [16] compares the performance of alternative monetary policy
rules for the (approximately) small open economy of Canada. The model
shares key features with Monacelli [25]. The most important differences
are as follows. Rather than ignoring the stability problem, Ghironi deals
with it by assuming Blanchard-Yaari-type overlapping generations; money
is incorporated; and, the household’s momentary utility is nonseparable be-
tween leisure and consumption. Ghironi estimates an extended Taylor-type
reaction function which is backward looking and comprises an exchange rate
target, a CPI inflation target (in addition to a domestic inflation target),
and interest rate smoothing.
The structural (or non-policy) parameters are estimated using quarterly
data from Canada and the U.S. Despite the simple structure of the exoge-
nous processes, the model matches several key moments in the data quite
well. According to the simulation results, the benchmark policy (the es-
timated extended Taylor-type rule) dominates the considered alternatives
(strict CPI targeting, an unilateral peg, and the original Taylor rule) in
terms of welfare, whereby risk diversification (the covariance between con-
sumption and leisure) is playing a crucial role.
A final example of a quantitative NNS model used for policy analysis is
Kollmann [24], who optimizes reaction coefficients for different variants of
Taylor-type interest rules. His model shares many features with Chari et al.
The most important differences are as follows. Kollmann considers a small
country within a bonds-only structure; he overcomes the stability problem
by adding to the UIP a risk premium to the net foreign asset position;
he assumes staggered price adjustment a la Calvo; and, he ignores direct
services provided by money.
In the benchmark case, in which the policy instrument only depends on
domestic inflation and the output gap, the optimized policy rule has infla-
tion and output coefficients of 3.01 and -0.01, respectively. Kollmann also
experiments with extended Taylor rules. Independent whether the nominal
exchange rate in growth rates or in levels is appended to the benchmark
rule, the optimized reaction coefficient is close to zero and the welfare gains
are minuscule. CPI targeting yields essentially the same welfare as domes-
tic inflation targeting. And, a peg greatly raises the variability of both
consumption and output.
18 CHAPTER 1
1.5 Concluding remarks
This paper selectively surveyed the strand of literature within open-economy
macroeconomics which applies quantitative business cycle models to the
issue of transmission properties of economic disturbances and international
policy. The discussion revealed that there is one major point of disagreement
over the appropriate specification of open-economy models: it concerns the
nature of price stickiness.
The assumption of LCP has been motivated by a number of well doc-
umented facts in the data: pervasive deviations from the LOP, persistent
deviations from the PPP, and a close to zero correlation between nominal
exchange-rate changes and inflation (at the business cycle frequency). As
indicated above, one interpretation of these facts is that exporters price-
discriminate across markets and in addition post prices in the buyer’s cur-
rency. Direct evidence on the choice of invoice currencies in international
trade, however, seems to contradict this interpretation.15 Moreover, there
are other reasons thinkable why consumer prices do not respond much to
exchange rates. There might be transportation or distribution costs; im-
ports may incorporate a substantial nontradable marketing input and/or
may be distributed through an imperfectly competitive retailing network;
finally, there might be true pricing to market.16 Each one of these reasons
might weaken the link between consumer and original price without assum-
ing LCP. We conclude that until additional (microeconometric) studies are
available we should be cautious in interpreting the existing evidence in favor
of one or the other policy regime (see Engel [18]).
To conclude, we would like to point to some recent developments in
closed-economy macroeconomics that might in the future spill over into in-
ternational finance. Most models discussed in this study assume that the
central bank can perfectly observe and react to current shocks. In reality,
however, disturbances (and possibly also steady state values) are not di-
rectly observable and policy makers as well as the private sector have to
solve complicated signal-extraction problems instead. In particular, central
15For an overview, see Engel [18] and Obstfeld [30].16True pricing to market means optimal price discrimination in the sense of monopo-
listic firms intentionally setting different prices in different markets because of different
market conditions (see Bergin and Feenstra [6]).
1.5. CONCLUDING REMARKS 19
bankers have only incomplete information regarding current values of the
output gap and the natural rate of interest. Some authors include devia-
tions from trend, lagged values of the gap or previous period’s conditional
expectations of the current gap, in lieu of the current gap itself. Yet the
lack of a learning process on the part of the monetary authority makes
these short-cuts unsatisfactory. A related issue is uncertainty about the
true structure of the economy: The decision makers at central banks have
only vague notions about the workings of the economy. It would be inter-
esting to explore both types of practical complications in an open-economy
setting and examine their implications for monetary policy.
Literally all models discussed in this study assume that the nominal
price or wage setting mechanism is time dependent. The reason for the per-
vasiveness of staggered price adjustment a la Calvo in particular, is a very
pragmatic one, namely tractability. However, the lack of a formal optimiza-
tion underpinning is a potential disadvantage. Recently, some research has
been devoted to price settings in which the nominal price rigidity is derived
as an endogenous result from microeconomic optimality conditions. Bakhshi
et al. [2], for instance, derive a closed-form solution for short-term inflation
in the NNS modelling framework of Dotsey et al. [16].17 The resulting
state-dependent New Phillips curve relates inflation not only to expected
future inflation and current and expected future real marginal costs (as the
New Phillips curve in standard Calvo models does) but – most interestingly
– also to lagged inflation, with fast decreasing weights. The number of leads
and the size of the coefficients are endogenous and depend on the level of
steady-state inflation and on firms’ beliefs about future adjustment costs.
Again, it would be interesting to investigate this alternative pricing scheme
in an open-economy context and examine implications for monetary policy.
17Dotsey et al. [16] assume that firms face stochastic menu costs which are i.i.d. across
firms and across time.
Bibliography
[1] Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1995),
International business cycles: theory and evidence, in: T. F. Cooley,
ed., Frontiers of Business Cycle Research, Princeton University Press
[2] Bakhshi, Hasan, Hashmat Khan, and Barbara Rudolf (2004), The
Phillips curve under state-dependent pricing, Working Paper, Swiss
National Bank
[3] Barro, Robert J., and Xavier Sala-i-Martin (1995), Economic Growth,
McGraw-Hill
[4] Baxter, Marianne (1995), International trade and business cycles, in:
G. Grossman and K. Rogoff, eds., Handbook of International Eco-
nomics, Vol. 3, Elsevier Science
[5] Bergin, Paul R. (2004), How well can the new open economy macroeco-
nomics explain the exchange rate and current account?, NBER Work-
ing Paper No. 10356
[6] Bergin, Paul R., and Robert C. Feenstra (2001), Pricing-to-market,
staggered contracts, and real exchange rate persistence, Journal of In-
ternational Economics 54(2), 333-359
[7] Bowman, David, and Brian Doyle (2003), New Keynesian, open-
economy models and their implications for monetary policy, Board of
Governors of the Federal Reserve System, International Finance Dis-
cussion Papers No. 762
[8] Calvo, Guillermo A. (1983), Staggered prices in a utility-maximizing
framework, Journal of Monetary Economics 12(3), 383-398
BIBLIOGRAPHY 21
[9] Chari, V.V., Patrick J. Kehoe, and Ellen R. McGrattan (2000), Can
sticky price models generate volatile and persistent real exchange
rates?, Federal Reserve Bank of Minneapolis, Research Department
Staff Report 277
[10] Clarida, Richard, Jordi Gali, and Mark Gertler (2001), Optimal mon-
etary policy in open versus closed economies: an integral approach,
American Economic Review, AEA Papers and Proceedings 91(2), 248-
252
[11] Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans
(1999), Monetary policy shocks: what have we learned and to what
end?, in: J. B. Taylor and M. Woodford, eds., Handbook of Macroeco-
nomics, Vol. 1A, Elsevier Science
[12] Collard, Fabrice, and Harris Dellas (2001), Price rigidity and the selec-
tion of the exchange rate regime, Mimeo
[13] Collard, Fabrice, and Harris Dellas (2002), Exchange rate systems and
macroeconomic stability, Journal of Monetary Economics 49(3), 571-
599
[14] Collard, Fabrice, and Harris Dellas (2002), Monetary policy rules and
exchange rate targeting, Mimeo
[15] Cooley, Thomas F., and Gary D. Hansen, (1995), Money and the busi-
ness cycle, in: T. Colley (ed.), Frontiers of business cycle research,
Princeton University Press
[16] Dotsey, Michael, Robert G. King, and Alexander L. Wolman (1999),
State-dependent pricing and the general equilibrium dynamics of
money and output, The Quarterly Journal of Economics 114(2), 655-
690
[17] Duarte, Margarida (2003), Why don’t macroeconomic quantities re-
spond to exchange rate volatility?, Journal of Monetary Economics
50(4), 889-913
22 CHAPTER 1
[18] Engel, Charles (2002), The responsiveness of consumer prices to ex-
change rates and the implications for exchange-rate policy: a survey of
a few recent new open-economy macro models, NBER Working Paper
No. 8725
[19] Gali, Jordi, and Tommaso Monacelli (2002), Monetary policy and ex-
change rate volatility in a small open economy, NBER Working Paper
No. 8905
[20] Ghironi, Fabio (2000), Alternative monetary rules for a small open
economy: the case of Canada, Working Paper, Boston College
[21] Ghironi, Fabio (2000), Towards new open economy macroeconomics,
Working Paper, Boston College
[22] King, Robert G., and Sergio T. Rebelo (1999), Rescuscitating real
business cycles, in: J. B. Taylor and M. Woodford, eds., Handbook
of Macroeconomics Vol. 1, Elsevier Science
[23] Kollmann, Robert (1996), Incomplete asset markets and the cross-
country consumption correlation puzzle, Journal of Economic Dynam-
ics and Control 20(5), 945-961
[24] Kollmann, Robert (1997), The exchange rate in a dynamic-optimizing
current account model with nominal rigidities: a quantitative investi-
gation, IMF Working Paper WP/97/7
[25] Kollmann, Robert (2002), Monetary policy rules in the open economy:
effects on welfare and busincess cycles, Journal of Monetary Economics
49(5), 989-1015
[26] Lane, Philip R. (2001), The new open economomy macroeconomics: a
survey, Journal of International Economics 54(2), 235-266
[27] McCallum, Bennett T., and Edward Nelson (2004), Timeless perspec-
tive vs. discretionary policy in forward-looking models, Federal Reserve
Bank of St. Louis Review 86(2), 43-56
[28] Mendoza, Enrique G. (1991), Real business cycles in a small open econ-
omy, American Economic Review 81(4), 797-818
BIBLIOGRAPHY 23
[29] Monacelli, Tommaso (2000), Into the Mussa puzzle: monetary policy
regimes and real exchange rate in a small open economy, Working Pa-
per, Boston College
[30] Obstfeld, Maurice (2002), Exchange rates and adjustment: perspec-
tives from the new open economy macroeconomics, CEPR Discussion
Paper Series No. 3533
[31] Obstfeld, Maurice, and Kenneth Rogoff (1995), Exchange rate dynam-
ics redux, Journal of Political Economy 103(3), 624-660
[32] Obstfeld, Maurice, and Kenneth Rogoff (1995), The mirage of fixed
exchange rates, Journal of Economic Perspectives 9(4), 73-96
[33] Obstfeld, Maurice, and Kenneth Rogoff (1996), Foundations of inter-
national macroeconomics, The MIT Press
[34] Sarno, Lucio (2001), Toward a new paradigm in open economy model-
ing: where do we stand?, Federal Reserve Bank of St. Louis
[35] Schmitt-Grohe, Stephanie, and Martin Uribe (2002), Closing small
open economy models, CEPR Discussion Paper No. 3096
[36] Stockman, Alan C. (1987), The equilibrium approach to ex-
change rates, Federal Reserve Bank of Richmond, Economic Review
March/April
[37] Taylor, John B. (1980), Aggregate dynamics and staggered contracts,
Journal of Political Economy 88(1), 1-23
[38] Taylor, John B. (2001), The role of the exchange-rate in monetary-
policy rules, American Economic Review, AEA Papers and Proceedings
91(2), 263-267
[39] Walsh, Carl E. (2003), Monetary theory and policy, second edition,
The MIT Press
[40] Woodford, Michael (forthcoming), Revolution and evolution in
twentieth-century macroeconomics, in: P. Gifford, ed., Frontiers of the
mind in the twenty-first century, Harvard University Press
24 CHAPTER 1
[41] Woodford, Michael (2003), Interest and prices: foundations of a theory
of monetary policy, Princeton University Press
[42] Yun, Tack (1996), Nominal price rigidity, money supply endogeneity,
and busincess cycles, Journal of Monetary Economics 37(2-3), 345-370
Chapter 2
On the role of exchange rate
stabilization in the conduct of
monetary policy of a small
open economy
2.1 Introduction
In the case of a small open economy (with free financial capital mobility)
whose policy is oriented towards domestic goals and for which shocks from
the rest of the world are important: What role should the stabilization of
the exchange rate play in the conduct of monetary policy? In the new open
economy macroeconomics literature concerned with the design of monetary
policy, two broad branches can be distinguished. One strand aims at de-
riving the globally optimal policy (under either commitment or discretion).
This is relatively straightforward when a number of simplifying assump-
tions are imposed regarding the size of the economy, the specification of the
preferences, the capital accumulation, and the number and kind of distor-
tions present in the economy (compare e.g. Clarida et al. [10] and Gali and
Monecelli [15], section 5).
In more general settings, however, the derivation of the globally optimal
policy is more involved and often intractable. In this event, an alternative
is to restrict the instrument rule (typically the nominal interest rate) to lie
26 CHAPTER 2
in a given class and at the same time to assume that the central bank can
commit, once and for all, to a given policy rule for all future periods. In
the rather general framework of quantitative open economy New Neoclassi-
cal Synthesis (NNS) models, the question about how responsive monetary
policy should be to the exchange rate, thus, comes down to the question
whether amending or altering the original Taylor rule improves economic
performance and welfare.1 A number of studies have recently appeared on
this subject (compare e.g. Ghironi [16], Monacelli [25], Collard and Dellas
[11], Gali and Monacelli [15], and Kollmann [22]).2 The typical result is
either that directly reacting to the exchange rate does not yield a greater
improvement in performance or welfare or that performance actually dete-
riorates (Taylor [34], p. 266). In Kollmann [22], for instance, the optimized
reaction coefficient is close to zero; the involved welfare gains are minuscule.
This finding, however, contrasts to actual monetary policy practices.
Casual observation reveals that central banks of small and semi-small open
economies often follow the rule of thumb – expressed in Obstfeld and Rogoff
[27], p. 93 – saying that a substantial appreciation of the real exchange rate
accompanied by slow output growth and low inflation furnishes a case for
cutting interest rates. To gain potential insights into the underpinnings
of actual policy practices, we add a terms-of-trade target to Taylor-type
interest rules as they have been proposed in the literature and evaluate them
in terms of their implications on the business cycles and welfare within a
variant of Kollmann’s [22] model of a small open economy.3
1The original Taylor [32] rule makes the instrument depend on current domestic infla-
tion and output deviations from trend with reaction coefficients 1.5 and 0.5, respectively.2Monacelli [25] presents qualitative results only, while the other studies conduct per-
formance and/or welfare analyzes as well; Collard and Dellas [11] investigate a two-
country model, while the other studies consider small open economies. – Two other
frequently cited examples which do not belong in the class of NNS models (in that they
are not fully microfounded but directly specify aggregate supply and demand curves) are
Ball [2] and Svensson [31]. Ball derives the optimal instrument rule assuming an ad hoc
loss function within a backward-looking framework; Svensson explores optimal reaction
functions for different variants of the loss function and two versions of the Taylor rule
within a forward-looking framework.3Collard and Dellas [11] do a similar exercise in a two-country setting. They find that
real exchange rate targeting is never a good idea while nominal exchange rate targeting
is likely to be irrelevant.
2.1. INTRODUCTION 27
We limit the consideration to operational feedback rules, that is, to pol-
icy rules which require only information which could plausibly be possessed
by the central bank. The results are discussed against the background of
two natural benchmark policies, namely strict (domestic) inflation target-
ing and a credible and unilateral peg of the domestic currency toward the
currency of the rest of the world. We find that introducing a moderate form
of terms-of-trade targeting in the original Taylor rule induces higher wel-
fare with respect to shocks to productivity and foreign demand and lower
welfare with respect to shocks to government consumption and the terms of
trade. The outcome under rules that allow for a considerable degree of in-
terest smoothing and a high relative weight on inflation, however, is robust
regarding the inclusion of terms-of-trade targeting.
In the remainder of this section, we briefly describe Kollmann’s [22]
original setting and then discuss our modifications. In Kollmann’s model,
the small open economy specializes in a continuum of tradable intermediate
goods and imports a continuum of foreign intermediate goods. Each differ-
entiated good, whether domestic or foreign, is produced by a monopolist.
Domestic intermediate goods producers use domestic (physical) capital and
labor as inputs; both inputs are immobile internationally.
The small open economy also produces a non-tradable final good, which
is used for consumption, investment, and government spending. The fi-
nal good is produced by assembling imperfectly substitutable domestic and
imported intermediate goods. While nominal prices in the perfectly com-
petitive final good and input markets are fully flexible, intermediate goods
producers set their prices for a stochastic number of periods as in Calvo
[5]. The representative household owns the firms of both sectors as well as
the capital stock and the time endowment; the capital stock and the time
devoted to labor are rented to the domestic intermediate goods producers.
Other distinguishing features of Kollmann’s model are: International
risk sharing is imperfect due to incomplete international financial markets;
to the uncovered interest parity, a country risk premium to the net foreign
asset position is added; the exchange rate pass-through is limited (100%
local-currency pricing); and, direct services provided by money are ignored
(a cashless economy). The model is calibrated to quarterly data for Japan,
Germany, and the U.K.
2.2. THE MODEL 29
a stationary representation of the system of equilibrium conditions. Ap-
pendix 2.B derives the non-stochastic steady state. Appendix 2.C presents
a first-order approximation to the equilibrium conditions, given that the
monetary policy obeys a Taylor-type feedback rule. Appendix 2.D describes
the implementation of an exchange rate peg.
2.2 The Model
2.2.1 Behavior of final good producers
There is a representative, competitive firm which produces a non-tradable,
homogenous consumption/investment good. To produce this good, the firm
has to purchase intermediate goods from domestic and foreign intermediate
goods producers. The country-specific, final good is assembled according to
a CRTS production technology
Y(st)
= F[Xd(st), Xf
(st)]
where st is one out of finitely many states the economy experiences in period
t (i.e., all variables in the model follow a discrete state stochastic process)
and the two input factors are CES-aggregators given by
Xd(st)
=
[∫ 1
0
Xd(i, st)θ
di
] 1
θ
Xf(st)
=
[∫ 1
0
Xf(i, st)θ
di
] 1
θ
where i stands for a differentiated intermediate good and θ ∈ (0, 1) is the
lower-level substitution parameter. In what follows, F [•] is specified to
F[Xd(st), Xf
(st)]
=[ω1−ρXd
(st)ρ
+ (1 − ω)1−ρ Xf(st)ρ]1/ρ
where ρ ∈ (−∞, 1) is the upper-level substitution parameter and ω ∈ (0, 1)
is a distribution parameter (in fact, one minus the import share).
The final good producer simultaneously solves two problems. First, the
firm minimizes costs of producing a given level of Xd (st); this yields condi-
tional factor demand functions Xd (i, st) for all i ∈ [0, 1]. Similarly, the firm
minimizes costs of producing a given level of Xf (st). Second, the firm mini-
mizes costs of producing a given level of Y (st); this yields conditional factor
demand functions Xd (st) and Xf (st). These are both static problems; to
simplify notation, we therefore skip the state-in-time-t label.
30 CHAPTER 2
Conditional factor demand functions Xd (i) and Xf (i) The problem
of minimizing costs of producing a given level of Xd can be stated as
minXd(i)
∫ 1
0
Px (i) Xd (i) di
subject to
Xd =
[∫ 1
0
Xd (i)θ di
] 1
θ
where Px (i) is the price of the domestic intermediate good i denoted in
domestic currency. From the FOC to this problem, we can derive the final
good producer’s conditional factor demand function
Xd (i) =
[Px (i)
Px
] 1
θ−1
Xd for all i ∈ [0, 1]
and an expression for the price index of the domestic intermediate goods,
the producer price index (PPI) in brief,
Px =
[∫ 1
0
Px (i)θ
θ−1 di
] θ−1
θ
.
There is an analogous problem for the foreign intermediate good i, from
which we get
Xf (i) =
[P ∗
x (i)
P ∗x
] 1
θ−1
Xf for all i ∈ [0, 1]
with
P ∗
x =
[∫ 1
0
P ∗
x (i)θ
θ−1 di
] θ−1
θ
.
Note that P ∗
x (i) (and, thus, the intermediate goods price index, P ∗
x ) is
denoted in terms of the currency of the seller, i.e., in foreign currency.
Conditional factor demand functions Xd and Xf The problem of
minimizing the costs of producing a given level of Y can be stated as
minXd, Xf
PxXd + eP ∗
xXf
2.2. THE MODEL 31
subject to
Y =[ω1−ρ
(Xd)ρ
+ (1 − ω)1−ρ (Xf)ρ]1/ρ
where e is the price of foreign money in units of domestic money (i.e., the
nominal exchange rate). From the FOCs to this problem, the following two
conditional factor demand functions can be derived
Xd = ω
(Px
P
) 1
ρ−1
Y Xf = (1 − ω)
(eP ∗
x
P
) 1
ρ−1
Y.
Assuming that the representative final good producer efficiently produces
one unit of Y provides us with an expression for the CPI as a function of
the domestic and foreign PPI
P =[ωP
ρρ−1
x + (1 − ω) (eP ∗
x )ρ
ρ−1
] ρ−1
ρ
Recall that all conditional factor demand functions derived in this subsec-
tion need to be satisfied in any state of the world.
2.2.2 Digression: Total demand for input factor i
To derive a function for total demand for input i, we start by noting that
intermediate good i is produced for the domestic final good sector and for
the export market
X(i, st)
= Xd(i, st)
+ Xd∗(i, st)
where Xd∗ (i, st) denotes the quantity of intermediate good i used in the rest
of the world. In step one of the domestic final good producer’s optimization
problem, we have derived a function for the domestic demand for good i,
Xd (i, st); we would like to come up with a similar expression for the export
demand for good i, Xd∗ (i, st).
Following Kollmann [22], we assume that the export demand function
resembles the domestic demand function
Xd∗(i, st)
=
[Px (i, st)
Px (st)
] 1
θ−1
Xd∗(st)
for all i ∈ [0, 1]
32 CHAPTER 2
where Xd∗ (st) is exogenous.5 We end up with the following total conditional
factor demand function
X(i, st)
=
[Px (i, st)
Px (st)
] 1
θ−1 [Xd(st)
+ Xd∗(st)]
︸ ︷︷ ︸X(st)
. (2.1)
Note that the elasticity of total demand for input factor i with respect to
input price Px (i, st), defined as
ε ≡ −∂X (i, st)
∂Px (i, st)
Px (i, st)
X (i, st),
is given by1
1 − θ.
In words: If the lower-level substitution parameter, θ, is close to 1, the price
elasticity of demand is large (in the limit +∞); if θ is much smaller than 1,
the price elasticity of demand is small (in the limit 0).
2.2.3 Behavior of intermediate good producer i
Each intermediate goods producer supplies a differentiated intermediate
good i and demands inputs in a competitive fashion. Thus, firm i has to
make two simultaneous decisions: how much capital and labor to lease in
each period (thereby acting as a price taker) and what output price to charge
for the differentiated intermediate good (thereby acting as a monopolist).
Input demand
Firm i combines capital K (i, st) and labor h (i, st) to produce intermediate
good i according to a CRTS production technology
X(i, st)
= F[K(i, st), h(i, st), A(st), Γt
]
where A (st) is an exogenous stationary stochastic technological shock and
Γt is deterministic technical progress. F [•], A (st), and Γt are identical for
5Recall that in contrast to Kollmann [22] we assume producer-currency pricing. This
explains the difference between his and our specification.
2.2. THE MODEL 33
all i. In what follows, F [•] is specified to as Cobb-Douglas
F[K(i, st), h(i, st), A(st), Γt
]= A
(st)K(i, st)α [
Γth(i, st)]1−α
(2.2)
where α ∈ [0, 1] is a positive constant.
In order to decide how much capital and labor to lease in each period,
intermediate good producer i solves the static cost minimizing problem
(again, we skip the state-in-time-t label)
minK(i),h(i)
PzK (i) + PWh (i)
subject to
X (i) = AK (i)α [Γh (i)]1−α
where z is the real rental rate and W is real wage. From the FOC to this
problem, we can derive the conditional demand functions for capital
K [X (i) ,W, z, ...] =
(α
1 − α
W
z
)1−α
A−1Γα−1X (i)
and for labor
h [X (i) ,W, z, ...] =
(α
1 − α
W
z
)−α
A−1Γα−1X (i) .
The value function to the cost minimizing problem is given by (in real
terms)
C [X (i) ,W, z, ...] = A−1χ−1zαW 1−αΓα−1X (i)
where χ−1 ≡ α−α (1 − α)α−1. Note that in the presence of a CRTS Cobb-
Douglas technology, (real) average costs, Ca (i) ≡ C (i) /X (i), equal (real)
marginal costs, Cm (i) ≡ ∂C (i) /∂X (i), i.e.,
Ca (i) = Cm (i) .
Moreover, note that Cm (i) and Ca (i) are the same for all i
Cm (i) = Cm = Ca (i) = Ca = A−1χ−1zαW 1−αΓα−1. (2.3)
34 CHAPTER 2
To get more economic insight – and for later reference – we derive the
inverse of the two conditional factor demands, thereby substituting Cm for
A−1χ−1zαW 1−αΓα−1. We end up with
z(st)
= Cm
(st)α
X (st)
K (st)︸ ︷︷ ︸MPK(st)
(2.4)
and
W(st)
= Cm
(st)(1 − α)
X (st)
h (st)︸ ︷︷ ︸MPh(st)
. (2.5)
In words: In the optimum, the real rental return is equated to the marginal
product of capital, MPK, times real marginal costs; similarly, the real wage
is equated to the marginal product of labor, MPh, times real marginal costs.
We will comment on this peculiarity further below.
Output supply: The flexible price case
To have a suitable reference point, we start by considering the case where
intermediate goods producers can adjust prices in every period. In this
instance, firm i solves the following static profit maximization problem
maxPx(i)
Πx (i) = [Px (i) − P Cm ] X (i)
such that
X (i) =
[Px (i)
Px
] 1
θ−1
X.
The FOC to this problem can be rearranged to the optimality condition
Px (i) =1
θP Cm.
In words: Monopolist i sells at a price which is greater than the socially
optimal price, which is its marginal costs (in nominal terms). As a conse-
quence, the monopolist’s optimal output must be below the socially optimal
(or competitive) output level. The price distortion in form of the markup,
1/θ, is larger when the representative final good producer, facing a price in-
crease, reduces its demand only slightly (that is, when the price elasticity of
demand is small). Note that all firms sell at the same price, i.e., Px(i) = Px.
2.2. THE MODEL 35
The inefficiency in the final good market has its mirror image in the two
input markets. To make this clear, consider the long-run equilibrium where
the relative price Px/P is assumed to be 1 and, thus, Cm = θ. From the two
conditions which implicitly define the factor demands, equation (2.4) and
(2.5), follows that on average there is a wedge between the marginal product
of labor and the real wage on the one hand and the marginal product of
capital and the real rental price on the other hand. Generally speaking, the
average firm pays a rental price which is smaller than the socially optimal
rental price, given by the marginal product. Again, the wedge (in the form
of θ) is larger when the price elasticity of demand is small.
Output supply: The sticky price case
We now turn to the situation where prices are sluggish. Apart from price
sluggishness we also allow for sustained (or steady state) inflation; that is,
the central bank manipulates its policy instrument such that the money
supply and the domestic price level are growing at a constant rate. This
assumption has to be seen as a means of preventing that in a calibrated
version of the model, large shocks affecting the economy lead to a nominal
interest rate which hits the zero lower bound.
Price change signal Let q be the probability that a firm gets a price-
change signal in a given period. Note that q does not depend on the duration
of the interval of price fixity. By visualizing an event tree, we immediately
see that (1 − q)j is the probability of being stuck in period t + j with the
price which was set at t and that (1 − q)j−1 q is the probability of adjusting
in period t + j (or, alternatively, of adjusting in j periods).
Imagine a monopolist who gets a price-change signal in period t. The
probability that firm i can adjust its price in period 1 is q; the probability
that firm i can adjust in period 2 is (1 − q) q; the probability that firm i
can adjust in period 3 is (1 − q)2 q, and so on. Thus, the time over which
a price is fixed can be considered as a discrete random variable with p.d.f.
(1 − q)t−1 q. The average time over which a price is fixed, thus, is given by
∞∑
t=1
t (1 − q)t−1 q = q[1 + 2 (1 − q) + 3 (1 − q)2 + ...
]=
1
q.
36 CHAPTER 2
Sustained inflation Monopolist i anticipates that on average the do-
mestic price level is growing at a constant rate. Therefore, the monopolist
chooses a ”deflated” price of the good as the choice variable and then multi-
plies the ”deflated” price by the steady-state growth factor of the domestic
price level to get the optimal nominal price of good i in time t.6 Formally,
Px
(i, st)
= Ξ · px
(i, st)
where px (i, st) is the ”deflated” price of good i and Ξ is the steady-state
growth factor of the PPI.
Firm i’s profit maximization behavior We are now in the position to
state firm i’s profit maximization problem in the presence of sticky prices.
A firm resetting the price of its good in period t chooses a price px (i, st) in
order to maximize
Πx
(i, st)+
∞∑
τ=1
∑
st+τ
P b(st+τ
∣∣ st)(1 − q)τ−1
[qΠx
(i, st+τ
)+ (1 − q) Πx
(i, st+τ
)]
(2.6)
where P b (st+τ | st) denotes the τ -step pricing kernel which is used to value
date t + τ profits,7 Πx (i, st+τ ) is the profit attained when the firm gets a
price-change signal in period t + τ (an event which occurs with probability
(1 − q)τ−1 q), given by
Πx
(i, st+τ
)=[Ξτpx
(i, st+τ
)− P
(st+τ
)Cm
(st+τ
)]X(i, st+τ
),
and Πx (i, st+τ ) is the profit attained when the firm gets no price-change
signal in period t + τ (an event which occurs with probability (1 − q)τ ),
given by
Πx
(i, st+τ
)=[Ξτ px
(i, st)− P
(st+τ
)Cm
(st+τ
)]X(i, st+τ
).
The maximization takes place subject to the sequence of total conditional
factor demand constraints (2.1) (expressed in terms of px (i, st)),
X(i, st+τ
)=
[Ξτ px (i, st)
Px (st)
] 1
θ−1
X(st+τ
)for all τ = 0, 1, ...
6Deflated is put in quotation marks because it only refers to the deterministic part of
PPI inflation.7 P b (st+τ | st) gives the value of an asset which pays exactly one unit of money in
state sj in period t + τ and zero otherwise.
2.2. THE MODEL 37
The expected profit is maximized at8
px
(st)
=1
θ
∑∞
τ=0
∑st+τ P b (st+τ | st) (1 − q)
τ(Ξτ )
1θ−1 Px (st)
11−θ P (st+τ ) Cm (st+τ ) X (st+τ )
∑∞
τ=0
∑st+τ P b (st+τ | st) (1 − q)
τ[Ξτ ]
θ
θ−1 Px (st)1
1−θ X (st+τ ).
(2.7)
PPI evolution under a Calvo price setting structure Given that
prices are set a la Calvo, how does the aggregate intermediate price index
evolve over time?
Recall that the PPI is given by (expressed in terms of px (i, st))
Px
(st)
=
∫ 1
0
[Ξ · px
(i, st)] θ
θ−1 di
θ−1
θ
.
The Calvo price setting structure allows us to make statements about the
price of every individual producer i. We know that in any period t some
producers are stuck with a price set t− j periods ago, where j goes toward
infinity (recall that all producers which set their price in the same period
will choose the same price). By visualizing ones more an event tree, it
becomes evident that in every period t a fraction of (1 − q)j−1 q of prices
from period t − j survives. The price index, thus, becomes
Px
(st)
=
q
∞∑
j=1
(1 − q)j−1 [Ξ · px
(st+1−j
)] θθ−1
θ−1
θ
.
This expression can be turned into the following non-linear difference equa-
tion
Px
(st)
=
qpx
(st) θ
θ−1 + (1 − q) Ξθ
θ−1 Px
(st−1
) θθ−1
θ−1
θ
. (2.8)
2.2.4 Behavior of representative agent
The representative household maximizes lifetime utility
∞∑
τ=0
∑
st+τ
βτπ(st+τ
∣∣ st)U
[C(st+τ
),M (st+τ )
P (st+τ ), l(st+τ
)]
8Due to the symmetry of producers, all firms which get a price-change signal in period
t will set the same price such that px (i, st) = px (st).
38 CHAPTER 2
where β ∈ (0, 1) is the constant discount factor and π (st+τ | st) is the (ob-
jectively known) probability of state st+τ conditional on being in state st in
period t.9 The arguments in the momentary (or period-by-period) utility
function are consumption, C (st), real balances, M (st) /P (st), and leisure,
l (st). In what follows, the momentary utility is specified to
U
[C(st),M (st)
P (st), l(st)]
=1
1 − σ
[Ψ(st)ν
l(st)1−ν
]1−σ
− 1
where
Ψ(st)≡
C(st)η
+ ζ
[M (st)
P (st)
]η 1
η
.
The parameters satisfy the conditions σ, η > 0 and ν, ζ ∈ (0, 1). For a
discussion of this kind of nonseparable preferences compare e.g. Chari et al.
[6].
Constraints
Budget constraint The agent’s maximization is subject to three con-
straints which are discussed in turn. The first is the budget constraint.
We assume complete financial markets, that is, there is a world market in
one-period claims which completely spans the relevant uncertainty faced by
the households in the small open economy and the rest of the world about
future income, prices, etc. The payoff of these claims is assumed to be in
terms of domestic paper money.10 The period-by-period budget constraint
in nominal terms is given by∑
st+1
P b(st+1
∣∣ st)B(st+1
)+ M
(st)
+ P(st) [
C(st)
+ I(st)]
+ T(st)
≤ B(st)
+ M(st−1
)+ N
(st)
+ Π(st)
+ P(st) [
z(st)K(st−1
)+ W
(st)h(st)]
. (2.9)
Let us start the discussion of inequality (2.9) by considering the source of
funds. There are three assets in the economy. Of each asset, the household
9Given that the stochastic processes in the model are Markovian, π (st+τ | st) can be
derived via recursion (see e.g. Ljungqvist and Sargent [23]).10This is just for convenience; the claims could equally well be assumed to be denoted
in the world currency.
2.2. THE MODEL 39
brings a certain amount into period t. B (st) is the share of a claim which
is contingent on the state at t being st and pays out one unit of paper
money; hence, B (st) · 1 is the total amount of paper money paid out in
period t. M (st−1) is the agent’s holdings of nominal money balances and
K (st−1) is the amount of physical capital which is leased to the intermediate
goods producers at the nominal rental price P (st) z (st). Note that K (st)
is somehow split up in a continuum of differentiated capital supplies, such
that
K(st)
=
∫ 1
0
K(i, st)di.
Apart from the three assets carried over into period t, there are three
additional sources of funds. First, the agent sacrifices some leisure-time to
labor. The amount of hours worked, h (st), is leased to the intermediate
goods producers at the nominal wage rate P (st) W (st). Again, h (st) is
somehow split up in a continuum of differentiated labor supplies, such that
h(st)
=
∫ 1
0
h(i, st)di.
Second, the agent receives a nominal lump-sum transfer from the govern-
ment, N (st). Finally, the agent receives the nominal profits of the monop-
olistically competitive intermediate goods producers,
Π(st)
=
∫ 1
0
Π(i, st)di.
The household allocates its resources between investment in the three
assets, in consumption, and in taxes (the use of funds). P b (st+1| st) is
the one-step pricing kernel, B (st+1) is the amount of claims regarding a
particular state sj, I (st) is real investment expenditures, and T (st) is a
nominal lump-sum tax.
Time endowment and capital evolution Apart from the period-by-
period budget constraint in nominal terms, there are two additional con-
straints to the households maximization problem. First, time devoted to
labor and leisure is equal to total time endowment (normalized to 1)
l(st)
+ h(st)
= 1. (2.10)
40 CHAPTER 2
Second, the evolution of the capital stock follows
K(st)
= I(st)− Φ
[I(st)
+
, K(st−1
)
−
]+ (1 − δ) K
(st−1
)(2.11)
where δ ∈ (0, 1) is the rate of depreciation. In words: I (st) units of gross
investment involve adjustment costs which depend positively on the amount
of gross investment, I (st), and negatively on the amount of the capital
already in place, K (st−1). The Uzawa-type adjustment cost function in
equation (2.11) is specified to
Φ[I(st), K(st−1
)]≡
φ
2
[I (st)
K (st−1)− δ
]2
K(st−1
)
where φ > 0 is a cost parameter.
Digression: Real demand for money
To get some economic insight, we derive a function which implicitly defines
the real demand for money. Combining the FOC for C (st) and for M (st)
yields
ζ
[M (st)
P (st) C (st)
]η−1
= 1 − β
∑st+1 π (st+1| st) Λ1 (st+1)
Λ1 (st)(2.12)
where Λ1 (st) is the nominal shadow price on the first constraint to the
agent’s maximization problem. From the FOC for B (st+1), we get an ex-
pression for the one-step pricing kernel
P b(st+1
∣∣ st)
= βπ(st+1
∣∣ st) Λ1 (st+1)
Λ1 (st). (2.13)
The nominal gross return of an asset that yields one unit of money in state
st+1 with certainty is given by
R(st)
=1
P b (st+1| st).
Substituting for P b (st+1| st) from equation (2.13), provides us with
1
R (st)= β
∑
st+1
π(st+1
∣∣ st) Λ1 (st+1)
Λ1 (st)
2.2. THE MODEL 41
which can alternatively be written as
1 = β∑
st+1
π(st+1
∣∣ st) UC (st+1)
UC (st)
R (st) P (st)
P (st+1)
where UC (st) stands for ∂U(st)/∂C(st). The ratio R (st) P (st) /P (st+1) is,
of course, the gross real interest rate and the resulting condition the famous
Lucas asset pricing equation.
Finally, substituting Λ1 (st) /R (st) for β∑
st+1 π (st+1| st) Λ1 (st+1) in
equation (2.12) leads to the following condition which characterizes the de-
mand for real money balances as a function of the nominal rate of interest
and real consumption
ζ
[M (st)
P (st) C (st)
]η−1
=[1 − R
(st)−1].
2.2.5 Fiscal and monetary policy
The output of the final good production is either used as a consumption
good, a capital good, or it is absorbed by the public sector. It is assumed
that public services do neither provide utility to households nor are they
an input to (private) production. We further assume that the government
spends amount G (st) of the final good and that the cyclical component of
G (st) is determined exogenously. Since Ricardian equivalence holds in this
model, we can - without loss of generality - assume that the government
runs a balanced budget each period
P(st)G(st)
= T(st).
Monetary policy is assumed to be either active or passive. Active mon-
etary policy is implemented by means of a simple instrument rule. Granted
that the exchange rate is floating, the nominal interest rate, R(st), is a lin-
ear function of the lagged nominal rate, the long-run equilibrium nominal
rate and deviations of the actual values of output, inflation, and the terms
of trade from their respective target values
ln R(st) = ρr ln R(st−1) + (1 − ρr)ln R + φy
[ln Y (st) − ln Y
]
+ φπ
[ln πx(s
t) − ln πx
]+ φe
[ln etot(st) − ln etot
](2.14)
42 CHAPTER 2
where πx(st) is PPI inflation and etot(st) is the small open economy’s terms
of trade (the relative price of imports and exports), defined by
etot(st) ≡e(st)P ∗
x (st)
Px(st).
The policy parameters (or reaction coefficients) ρr, φy, φπ, and φe determine
how aggressively policy responds to the lagged interest rate and to devia-
tions of the target variables from their respective target values. Like the
target values Y , πx, and etot, they are chosen by the monetary authority. If
the (gross) nominal interest rate follows (2.14), money holdings are demand
determined, that is, the money supply is set so as to satisfy any money
demand that prevails at the ongoing interest rate.
A passive monetary policy can have two forms (within the present set-
ting). One alternative is that the growth process of the nominal money
supply is specified as follows
M(st+1
)= M
(st)µ(st)
(2.15)
where the variable µ (st) (one plus the money growth rate) is assumed to
follow a stochastic AR(1) process (to be specified) and the nominal exchange
rate is assumed to be completely flexible.11 A second alternative is that the
nominal exchange rate is fixed toward the currency of the rest of the world
at an arbitrary value. In this event, the nominal money supply is chosen
such that the exchange rate target is achieved to the full extent in every
period.
Under all three regimes, new money is introduced through lump-sum
transfers from the monetary authority to households:
M(st)− M
(st−1
)= N
(st).
2.2.6 Market clearing
The following market clearing conditions hold in equilibrium. Final good
market:
Y(st)
= C(st)
+ I(st)
+ G(st).
11Obviously, in the steady state µ = Ξ.
2.2. THE MODEL 43
Intermediate goods market i:12
X(i, st)
= Xd(i, st)
+ Xd∗(i, st)
from which follows that
X(st)
= Xd(st)
+ Xd∗(st).
Labor market:
h(st)
=
∫ 1
0
h(i, st)di.
Capital market:
K(st)
=
∫ 1
0
K(i, st)di.
Money market:13
Md(st)
= M s(st)
Since all these markets clear in equilibrium, by Walras law the market for
financial securities clears, too.
2.2.7 Closing the model: International asset markets
In order to close the model, the Euler equation of the representative agent
of the small open economy has to be linked to the international financial
asset market. From the expression for the one-step pricing kernel (2.13) and
the FOC for C (st), we get the following optimality condition
P b(st+1
∣∣ st)
= βπ(st+1
∣∣ st) UC (st+1) /P (st+1)
UC (st) /P (st).
In the rest of the world, agents have access to the same array of financial
assets as in the domestic economy. Thus, there is a similar condition for
12Note that since intermediate goods prices are eroded over time as inflation is above
average, intermediate goods producers do not charge the same output prices and, thus,
do not produce the same amount of output (this phenomenon is called price dispersion).
Since indirect demand functions depend on output (among others), conditional factor
demands are asymmetric, too.13In fact, we do not distinct between money demand and supply but just write M (st).
44 CHAPTER 2
the rest of the world14
P b(st+1
∣∣ st)
= βπ(st+1
∣∣ st) U∗
C (st+1) / [e (st+1) P ∗ (st+1)]
U∗
C (st) / [e (st) P ∗ (st)]
where we assume that domestic and foreign households share the same sub-
jective discount factor. Arbitrage implies that
UC (st+1)
UC (st)
P (st)
P (st+1)=
U∗
C (st+1)
U∗
C (st)
P ∗ (st)
P ∗ (st+1)
e (st)
e (st+1).
Iteration yields (compare e.g. Chari et al. [7], p. 14)
UC (st)
U∗
C (st)
P ∗ (st) e (st)
P (st)=
UC (s0)
U∗
C (s0)
P ∗ (s0) e (s0)
P (s0).
We end up with the following expression for the nominal exchange rate
e(st)
= κU∗
C (st)
UC (st)
P (st)
P ∗ (st)(2.16)
where κ ≡e(s0)UC(s0)P ∗(s0)
P (s0)U∗
C(s0)
and the ratio U∗
C (st) /P ∗ (st) is exogenous.
2.3 Solution, parameterization, and diagnos-
tic check
The equilibrium of this economy is a sequence of prices and quantities for
which the representative household’s problem and the firms’ problems are
solved and markets are cleared. In order to compute those sequences, the
optimality conditions for the representative household and the firms, the
government’s budget constraint, the central bank’s feedback rule, and the
market clearing conditions must be put together. The resulting system of
equations we call the (competitive) equilibrium conditions. We then ap-
ply the standard linear approximation method from the RBC literature
(compare e.g. King et al. [18] and King and Rebelo [20]), which involves
14Recall that the nominal price of a one-period claim that pays out one unit of paper
money if state st occurs and nothing otherwise, P b(st+1
∣∣ st), is denominated in home
currency; thus, the foreign price level has to be converted.
2.3. SOLUTION, PARAMETERIZATION, AND DIAGNOSTIC CHECK 45
determining the properties of the non-stochastic steady state (of the system
which describes the equilibrium) and taking a first-order Taylor expansion
of the equilibrium conditions around the steady state. The resulting linear
system of structural relations determine the prices and quantities (in terms
of percentage deviations from the steady state) in period t = 0, 1, 2, ...; it
can be solved by means of any computational algorithm for solving and
simulating linear rational expectations models.15
But before we can solve and simulate the model we have to assign values
to the structural parameters. Moreover, we undertake the following change
of notation: We write Yt for Y (st) etc. and let Et• be a function which
takes the expected value of the term inside the curly bracket, based on
information available in t.16
2.3.1 Baseline parameterization
Rather than assigning values to the structural parameters such that the
behavior of the model economy matches features of measured data for a
real-life economy, we borrow a set of plausible values from other studies, a
strategy which is not uncommon in the literature. Following Collard and
Dellas [10], we set the parameters to:17
15The one we make use of is a version of the classical solution algorithm developed by
King, Plosser, and Rebelo [18].16One may wonder why we did not do this from the beginning on. The reason is that
in our view, solving the representative household’s and the firms’ optimization problems
in terms of the states of the economy makes the underlying economics more transparent.17Collard and Dellas [10] investigate the role played by price sluggishness in the perfor-
mance of alternative exchange rate regimes in a two-country NNS model. Their model is
calibrated on the postwar US economy. For parameter values they heavily rely on Cooley
and Prescott [14] and Chari et al. [7]. Collard and Dellas find that a high degree of price
sluggishness tends to favor the flexible regime while a low degree favors the fixed regime.
46 CHAPTER 2
Category: Parameter: Value
Final good producer: ω (one minus import share) 0.8000
ρ (substitution parameter - upper level) 0.3333
θ (substitution parameter - lower level) 0.8000
Intermediate goods prod.: α (capital elasticity) 0.2813
Discount factor: β 0.9880
Momentary utility: σ (relative risk aversion) 1.5000
η (parameter in Ψ(•)) 1.5600
ζ (weight of money - liquidity service) 0.0649
Rate of depreciation: δ 0.0250
Adjustment costs: φ 10.000
Time devoted to labor: h (= 1 − l) 0.3100
Degree of price stickiness: q 0.2500
GDP devoted to govt. exp.: g 0.2200
Steady state inflation: Ξ 1.0260
Note that the discount factor is set so as to imply (approximately) a 5%
annual subjective discount rate, following the formula
β =
(1
1 + 0.05
)0.25
.
The degree of price stickiness is chosen such that the average duration prices
remain fixed is four years. The implied steady state values are given by:
C 0.3944
M/P 0.4910
l 0.6900
Y (= X) 0.6274
Xf 0.1255
Xd 0.5020
I 0.0950
G 0.1380
K 3.8012
R 1.0385
Cm 0.8000
z 0.0371
ν 0.3394
2.3. SOLUTION, PARAMETERIZATION, AND DIAGNOSTIC CHECK 47
The autoregressive parameters of the shocks are set to:
Parameter: Value
ρa (productivity) 0.9500
ρg (government expenditures) 0.9700
ρm (money growth) 0.4900
ρl (foreign lambda) 0.9500
ρp (foreign intermediate goods prices) 0.9500
ρx (foreign intermediate goods demand) 0.9500
Standard deviations are normalized to 0.01.
2.3.2 Dynamic effects
We are now in the position to compute the model’s equilibrium dynamics for
alternative specifications of monetary policy. For the time being, we focus on
three policy regimes: (i) constant money growth, (ii) an unilateral exchange
rate peg, and (iii) strict domestic inflation targeting. For each regime, the
impulse responses will be analyzed and the role of key parameters (like
the degree of price stickiness) investigated. The purpose of this exercise is
twofold. First, we want to gain some intuition on how the model works.
Second, given that we have no measure of fit, comparing the dynamics of
our model with the qualitative predictions of models of the same class and
with comparable parameterizations is a way to make sure that there are no
coding or other errors.18 The results are summarized in table 1.
Domestic technology shock
Fixed money supply The effect of sticky prices is best understood in
terms of variations in the markup of price over marginal costs. In the style
of King and Wolman [19] and Goodfriend and King [17] we define the time
varying, endogenous average markup as the ratio of the intermediate price
level to nominal marginal costs of production
υt ≡Px,t
PtCm,t
18We say ”to make sure” even though we are well aware of the fact that one can never
be virtually sure that ones code is faultless.
48 CHAPTER 2
or, alternatively, in terms of deflated variables (see appendix 2.A):
υt = (ptCm,t)−1
where pt = Pt/Px,t is the deflated PPI. In terms of percentage deviations
from the steady state we have
υt = −(pt + Cm,t
).
Suppose monetary policy follows a constant money growth rule. More-
over, suppose there are no capital adjustment costs (i.e., φ = 1). If prices
are fully flexible (which is implemented by letting q almost but not exactly
1), the markup is not affected by a positive technology shock; the elasticity
of υ with respect to a supply shock is literally zero. We conclude that the
responses of the real variables to the shocks are efficient.19 Not surprisingly,
the dynamics are in line with the predictions of the baseline RBC model
of a closed one-good, one-shock economy (compare e.g. King and Rebelo,
[20]).
The marginal product of labor increases above its steady state value and
stays there for a protracted period. This results in a rise of the real wage;
the elasticity of Wt is close to 0.8.20 Accordingly, there is a great incentive
to substitute intertemporally and to take less leisure now and in the near
future than in the far future. However, there is also an offsetting income
effect. Initially, the substitution effect outweighs the income effect and,
thus, work effort responses positively. The positive labor response amplifies
the productivity shock; the elasticity of Xdt is about 1.4. As long as the
domestic productivity is the only source of shocks, total output of domestic
intermediate goods production is given by Xt = ωXdt . And so, Xt moves
along with Xdt .
The rise in At together with the positive labor response lead to a marginal
product of capital which is higher than normal. The impact effect of the
real rental price, zt, is about 0.9. Most of the additional input therefore
19In the words of Rotemberg and Woodford [29], the average markup represents a
measure of if and how fluctuations in real variables are inefficient.20The impulse effect of Wt is not as large as the impulse effect on MPht. This is
because Wt = Cm,t + MPht and a gain in productivity leads to a reduction of real
marginal costs below the long-run level (the elasticity of Cm,t is about −0.2).
2.3. SOLUTION, PARAMETERIZATION, AND DIAGNOSTIC CHECK 49
is invested, which leads to a higher capital stock. As productivity decays
geometrically, the intertemporal substitution effect is outbalanced by the
offsetting income effect: work effort drops below its steady-state level. Also,
investment becomes lower than normal as the capital stock is reduced to its
stationary level.
How do international trade aspects come into play? An increase in
the supply of domestic intermediate goods, Xt, lowers the relative price
of domestic intermediate goods, i.e., induces a deterioration of the terms
of trade. As a consequence, the amount of intermediate inputs imported
by the representative final good producer, Xft , decreases while the amount
of inputs purchased from domestic intermediate goods producers, Xdt , in-
creases (expenditure-switching).
What about the nominal variables? The rise in consumption induced by
a positive supply shock tends to raise the demand for money. The fact that
nominal money growth remains constant gives rise to a decrease of the CPI,
Pt, (and, thus, an increase of (M/P )t) and an increase of the opportunity
costs of holding money, Rt.21 The nominal exchange rate, finally, increases
(i.e., the domestic currency depreciates).
The picture changes dramatically when prices are assumed to be sticky
(q = 0.25). To begin with, the dynamics now exhibit the hump-shaped
pattern typical for sticky-price economies. In addition to this, the elasticity
of the markup amounts to 2.3.22 Why this massive rise in the markup in the
presence of sticky prices? A sudden gain in productivity produces a shift in
the marginal cost schedule. But because prices do not fall immediately in
proportion to the decline in costs, markups rise. This is inevitable: Firms
would like to lower prices (thereby expanding output); but a large fraction
of firms does not receive a price adjustment signal and, thus, remains stuck
with the price from the previous period. Some prices, however, do fall
and thus output increases. The transitory rise in the markup – relative
to what would happen under flexible prices – lessens the output effect of
the technology shock; the elasticity of Xt is −0.5, compared to 1.1 in the
21When the weight for money in the utility function, ζ, is non-zero, changes in real
balances affect the marginal utility of consumption and labor and thereby Ct and ht; this
effect, however, is small.22Notice: υt falls back to normal rather quickly and approaches its long-run level just
after a few quarters.
50 CHAPTER 2
flex-price case.23
Since the increase of the markup is temporary, we observe a strong
substitution effect (see e.g. King and Wolman [19], p. 20): the supply of
labor is massively reduced; the same is true for investment. As the gap
returns to normal, the supply of labor expands and investment increases.
The response of the input factors is mirrored by the response of rental prices:
the impact effect of both Wt and zt now is negative (the elasticities are −0.9
and −2.9, respectively).
This result is standard in models of this type. For an illustration, con-
sider the baseline sticky price model of a closed economy as put forward by
Clarida et al. [9], with a comparable parameterization. In this model, the
output gap can only increase if the marginal costs increase or, alternatively,
if the markup falls. Moreover, there is a link between markup and inflation.
With fully flexible prices and a fixed money supply, the impact effect of the
markup to a positive technology shock is zero; the elasticity of the real wage
with respect to the supply shock is about 1.0. If prices are sticky, however,
the impact effect of the markup to a positive technology shock is significant
and the elasticity of the real wage with respect to the supply shock is about
−0.7.
What happens when we introduce capital adjustment costs (i.e., when
we set φ to its baseline value of 10) in the flex price environment? Recall
that some of the windfall associated with a productivity shock is consumed,
some is invested. (The third component of aggregate demand, government
consumption, is unaffected by a productivity shock.) In the presence of high
adjustment costs, investment will not increase by as much as in the previ-
ously discussed no-adjustment cost scenario. Given that the representative
agent has an incentive to smooth consumption (i.e., that the agent does
not just want to expand consumption by the same amount by which the
response of investment turns out to be smaller), the only way for aggregate
demand and aggregate supply to be equalized is that hours worked drop be-
low their long-run level. Hence, the most significant difference compared to
the no-adjustment cost scenario (besides the significantly smaller response
of investment) is the negative impact effect of work effort.24
23Notice: Xt lies above normal from period 2 onward.24Starting from the baseline parameterization, a way to provoke a positive impact effect
2.3. SOLUTION, PARAMETERIZATION, AND DIAGNOSTIC CHECK 51
Exchange rate peg Under the previously discussed floating regime with
constant money growth, et increases in response to a positive technology
shock, that is, the domestic currency depreciates. Accordingly, to keep
et = 0 for all t, monetary policy needs to be contractionary: Mt decreases
and returns to normal only slowly.25 The cost of stabilizing the nominal
exchange rate (in terms of a contractionary monetary policy), however, are
negligible if prices are flexible and still small if prices are sticky.
Strict domestic inflation targeting If prices are sticky and monetary
policy actively seeks to stabilize domestic inflation, the response of the real
variables to a positive domestic technology shock is pretty much the same
as under the previously discussed floating regime under flexible prices and
with a fixed money supply. The picture differs, however, with regard to the
nominal variables: Since monetary policy succeeds in stabilizing domestic
inflation around its long-run equilibrium level, the effect on πx,t (and, thus,
the markup) is zero. Given that prices are sticky, a deterioration of the
terms of trade (i.e., a rise in etott ) leads to a rise of the nominal exchange
rate; the domestic CPI becomes negative on impact and returns to normal
only gradually.
Domestic fiscal policy shock
With a constant money growth and flexible prices, a shock to government
expenditures produces the standard results (compare e.g. Baxter and King,
[3]). A persistent (but not permanent) shift in government consumption
financed by a lump-sum tax means higher future taxes, which induces a
moderate negative wealth effect. To this negative wealth effect the repre-
sentative household responds by decreasing consumption and leisure. As a
corollary, ht and Xt jump to positive values. Given the slowly adjusting
capital stock, the shift in ht leads to a marginal productivity of labor below
average which in turn leads to a negative percentage deviation of the real
wage from its steady state value.
of work effort other than setting φ to 1.0 is to let domestic and foreign inputs become
closer substitutes, i.e., to increase the parameter ρ (compare Collard and Dellas [10]).25Compare appendix 2.D to learn how we implement an exchange rate peg.
52 CHAPTER 2
The behavior of investment is influenced by two offsetting effects. On the
one hand, due to the increased government absorption of resources, there
are reduced opportunities for private uses of output, i.e., consumption and
investment.26 On the other hand, the increase in labor input shifts up the
marginal product for capital, a force which works in the direction of more
investment. Given the baseline parameterization, the first effect outweighs
the second and, hence, I becomes slightly negative for a protracted period.
In the long run, however, investment is above normal as the economy works
to rebuild the capital stock.
If intermediate prices are assumed to be sticky, the reaction of domestic
inflation is weakened and slowed down. The markup now is significantly
positive on impact and outweighs the negative marginal productivity of la-
bor, which brings about a positive impact effect of the real wage. Otherwise,
in qualitative terms the picture largely remains the same as under flexible
prices.
Foreign shocks
How does the economy respond to a shock to the nominal foreign shadow
price, Λ∗
1,t? Suppose money growth is constant, the exchange rate is flexible,
and intermediate prices are sticky (q = 0.25). Moreover, suppose the inter-
mediate goods produced in the small open economy represent a negligible
input into world final good production. Finally, suppose for a moment that
the world monetary authority succeeds in fully stabilizing the foreign inter-
mediate goods price level. The third together with the second assumption
imply that the foreign CPI coincides with the foreign PPI, which in turn is
constant.
To derive an expression for the terms of trade, note that the equilibrium
condition et = κΛ∗
1,t/Λ1,t can be extended to
etott
(=
etP∗
x,t
Px,t
)= κ
Λ∗
1,tP∗
x,t
Λ1,tPx,t
.
Taking into account our previously made assumptions (and the definition
of Λ∗
1,t = U∗
C,t/P∗
x,t), we end up with
etott = κU∗
C,t/λ1,t,
26Keep in mind that the negative wealth effect induces consumption to decrease.
2.3. SOLUTION, PARAMETERIZATION, AND DIAGNOSTIC CHECK 53
where κ = κ/P ∗
x and λ1,t = Λ1,tPx,t. In terms of percentage deviations from
the steady state, we have
etott = U∗
C,t − λ1,t.
Note that λ1,t is an endogenous variable which responds to the exogenous
forces in the model in much the same way as any other endogenous variable,
while U∗
C,t (which under the given assumptions equals Λ∗
1,t) is exogenous.
Now, consider a positive shock to Λ∗
1,t(= U∗
C,t). For the baseline (and in
fact for any reasonable alternative) parameterization, although λt is affected
too, by far the biggest part of the sudden increase in etott stems from the
change in Λ∗
1,t. In response to this unexpected deterioration of the terms of
trade, the final good producers substitute away from foreign inputs toward
domestic inputs. At the same time, the terms of trade deterioration induces
a negative wealth effect (the small open economy needs to export more in
order to purchase a given bundle of imports) and, thus, a drop of consump-
tion and leisure (which in turn leads to an increase in ht). The decrease
in consumption is smoothed by a cut in investment. The two price levels
(domestic and consumption) rise and the final good production declines.
The picture remains the same when we allow for changes in the foreign
PPI: A positive shock to P ∗
x,t has identical effects on the nominal and real
variables in the model as a positive shock to Λ∗
1,t – with the prominent
exception of the nominal exchange rate (compare table 1). Since within the
policy simulation exercise variations in et are of no concern for us, we will
further below refer to a so-called ”terms-of-trade shock”, where we mean a
temporary change in either Λ∗
1,t or P ∗
x,t.
Under the same scenario (constant money growth, flexible exchange rate,
sticky intermediate prices) and under the additional assumption that capital
is costless to adjust, the dynamics implied by a foreign demand shock in
favor of domestic intermediate inputs (that is, a unexpected increase in Xd∗t )
are consistent with the traditional Mundell-Fleming-Dornbusch model (as
described e.g. in Clarida and Gali [8]): the terms of trades improve and the
price levels and the final good production rise.
54 CHAPTER 2
Domestic money growth shock
Suppose money growth follows a stochastic process: What are the effects of
a shock to the money growth process, given that prices and exchange rates
are fully flexible? If ζ is non-zero, the model’s predictions are in line with
the standard money-in-the-utility-model of a closed one-sector economy as
described e.g. in Walsh [35], chapter 2. This is to say, the effects on real
variables (except real balances) are extremely small.
However small these effects are, where do they come from? Suppose
the growth rate of money follows the stochastic process µt = ρmµt−1 + εm,t
where ρm ∈ (0, 1) and εm,t is i.i.d. with zero mean. Now consider the
effect of a positive shock to µt. Since future money growth will be above
average for a protracted period, expectations of future inflation instantly
rise; both price levels jump to higher levels. How does this affect real
balances? Given the baseline parameterization, the CPI rises more than in
proportion to the rise in the nominal money stock and, thus, real money
balances decrease on impact. As both the nominal money stock and the CPI
gradually climb to their new steady state values, real money balances returns
to normal. The reduction of real money balances lowers the marginal utility
of consumption and - by affecting the ratio of the marginal utility of leisure
to the marginal utility of consumption - causes the agent to substitute away
from consumption towards leisure. As a consequence, work effort as well as
intermediate goods output fall.
If intermediate prices are sticky, the same mechanism is at work. Again,
the adjustment process of prices is now weakened and slowed down. Over-
all, the implied dynamics are in line with the traditional Mundell-Fleming-
Dornbusch model: A shock to the money growth rate results in a perma-
nent nominal depreciation, a permanent rise in the price level (both PPI
and CPI), a temporary rise of intermediate and final good production, and
a temporary deterioration of the terms of trades.
2.4 The role of exchange rate stabilization
The purpose of this section is to evaluate selected members of the family
of simple policy rules represented by equation (2.14). The chosen strategy
for policy evaluation follows the steps proposed by Taylor [34], pp. 263/4:
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 55
First, we place a particular specification of equation (2.14) into the pa-
rameterized model. Second, we solve the model using a numerical solution
algorithm. Third, we examine the properties of the stochastic behavior of
those macroeconomic variables which reflect potential goals of monetary
policy, in particular the variability of Yt, πx,t, πt, etott , and Rt.
27 Finally, we
examine the consequences on welfare, measured by means of a quadratic
approximation of the representative household’s lifetime utility, given by
W ≈ (1 − β)−1
[U +
C · UC
2(1 + ξC) σCC +
m · Um
2(1 + ξm) σmm
+l · Ul
2(1 + ξl) σll + C · m · UCm · σCm + C · l · UCl · σCl + m · l · Uml · σml
]
where U ≡ U [C, m, l] with m ≡ M/P , UC ≡ ∂U/∂C, ξC ≡ C ·UCC/UC , and
σCC = Corr(Ct, Ct) are functions of the structural parameters of the model.
Both performance and welfare are conditioned on the kind of disturbance
which hits the economy; this is because unless the model is calibrated we
cannot make predictions regarding the relative size of each kind of shock.
Why focusing on instrument rules such as (2.14)? A first argument given
in the literature refers to their simplicity : Taylor rules may serve as an in-
formative guideline for policy or as an aid in promoting policy transparency
(compare e.g. Walsh [35], p. 549). A second argument has been pointed out
by McCallum (compare e.g. [24]): the optimal policy rule determined by
solving an explicit policy design problem crucially depends on the form of
the model under consideration.28 The recommended research strategy is to
search for a policy rule which possesses robustness in the sense of yielding
a desirable outcome in policy simulation experiments in a wide variety of
models. A third argument can be seen in the fact that the derivation of the
(globally) optimal policy would be relatively straightforward if a number
of simplifying assumptions were imposed, but is much more involved and
in fact intractable in the rather general setting at hand. In this event, an
alternative is to restrict the instrument rule to lie in a given class and at
the same time to assume that the central bank can commit, once and for
all, to a given policy rule for all future periods.
27On the choice of Yt compare below.28In the words of Taylor [33], p. 11, ”[t]he optimal rule exploits properties of a model
which are specific to that model, and when the optimal rule is then simulated in another
model those properties are likely to be different and the optimal rule works poorly.”
56 CHAPTER 2
2.4.1 Interest-rate rules to be investigated
Given that we do not intend to systematically search the whole parameter
space of ρr, φy, φπ, φe as e.g. Kollmann [22] does (for a reasoning compare
above), the next question to answer is which configurations we want to look
at. We begin by defining two policies which represent suitable reference
points. These two policies are strict domestic inflation targeting and an
unilateral exchange rate peg. When monetary policy seeks to completely
stabilize PPI inflation, it does – obviously – not make allowance for variables
other than domestic inflation. Conversely, when the nominal interest rate
and the nominal money supply are set such that the nominal exchange rate
is fixed at an arbitrary value, monetary policy does not make allowance
for variables other than the exchange rate. In this sense the two reference
points are two (feasible) extreme cases; we call them benchmark policies.
Next, we consider three examples of simple instrument rules as they
have been proposed in the literature. Recall that when monetary policy is
assumed to be active, it follows the generalized Taylor type interest rule
(2.14). Suppose, the target values Y , πx, and etot coincide with the respec-
tive long-run equilibrium values. Rule (2.14) can then be written as
Rt = ρrRt+1 + (1 − ρr)[φyYt + φππx,t + φee
tott
]. (2.17)
In terms of equation (2.17), the baseline specifications of the three rules
are characterized by the parameter configurations ρr, φy, φπ, φe equal
to 0, 0.5, 1.5, 0, 1/3, 0.4, 1.5, 0, and 2/3, 0.1, 2, 0; we label them,
respectively, Rule 1, Rule 2, and Rule 3.29 They roughly correspond to,
respectively, Rule III, I and V in table 1 of Taylor [33].30 We compare the
29This kind of policies are often referred to as flexible inflation targeting. Flexible
inflation targeting gives, on the one hand, leeway to the central bank to respond to
economic shocks and, on the other hand, represents a strong commitment to keeping
inflation low and stable.30To see this, note that it is the relative size of the parameters that matter. Rule I in
table 1 of Taylor [33] e.g. is given by (in Taylor’s terminology)
3.0 · π + 0.8 · y + 1.0 · i−1
where i is the nominal interest rate. Multiplying by 1/3 yields
1.0 · π + 0.26 · y + 0.3 · i−1
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 57
achievement of these three rules with that of the two benchmark policies and
investigate the robustness of the findings. Finally, we modify the baseline
specifications of the three rules to allow for exchange rate targeting and
explore the consequences of this modification on welfare and performance;
and again, we perform robustness checks.
Output targeting Specification (2.17) assumes that the target values of
output, inflation etc. are equivalent to their respective steady state values.
Note that in the absence of secular growth, the long-run equilibrium output
coincides with the deterministic trend in output. The general rule (2.17),
thus, can be interpreted as describing a reaction to deviations of actual
output from trend.
In the recent literature on policy rules, however, output is typically not
stabilized around trend but around the contemporaneous potential output,
defined as the period t level of output which would obtain under flexible
prices. If we want this to be the case, Rule 1 (in log form) is modified to
ln Rt = ln R + 0.5 · ln Yt + 1.5 · (ln πx,t − ln πx)
where ln Yt ≡ ln Yt − ln Y pott denotes the (log) output gap. In terms of
percentage deviations from the steady-state, we have
Rt = 0.5 · Yt + 1.5 · πx,t.
Note that independent of whether prices are flexible or not, long-run output
remains the same. Hence,
Yt = (ln Yt − ln Y ) −(ln Y pot
t − ln Y)
= Yt − Y pott
where Y pott is the percentage deviation of actual potential output from its
steady state value.31
which is equivalent to
0.6 (1.5 · π + 0.4 · y) + 0.3 · i−1.
31Given a particular state of the economy, what output would obtain under flexible
prices? Suppose, in terms of the linear rational expectations modelling framework utilized
to solve the model, Y pott is a function of exactly the same state variables as Yt. Then,
to compute potential output, we need to import the elasticity values of Yt for q ' 1 and
the policy regime under consideration. Moreover, we set φy = 0 (if prices are flexible,
the output gap is zero for all t anyway).
58 CHAPTER 2
In our policy simulation experiments, we will consider interest rate rules
which involve deviations of actual output from trend as realistic and oper-
ational specifications:32 The central bank takes the fitted trend as a proxy
for the potential output not because it does not know better, but because it
lacks an appropriate current-period measure for the potential output.33 In
this sense, our choice represents a short-cut for allowing for imperfect ob-
servability. The central bank does not have all relevant information available
about the state of the economy and, thus, potential output is measured (or
estimated) with an error. Conversely, we consider it plausible that data on
inflation is readily available and is measured with sufficient accuracy.
Interest smoothing The general rule (2.17) has a dynamic form, that is,
the current interest rate is a weighted average of some desired value which
depends on the state of the economy and the lagged interest rate, where the
relative weights depend on the parameter ρr. The baseline specifications of
Rule 2 and 3 have interest smoothing parameters of 1/3 and 2/3, respec-
tively, whereas there is no interest smoothing in the baseline specification
of Rule 1. One rationale for interest smoothing can be seen in the fact that
whenever the steady state net growth factor of the domestic price level is
larger than minus the steady state net real interest rate, there is a monetary
distortion present in the model.34 This distortion could be eliminated by
following the Friedman rule, which in turn calls for a perfect stabilization
of Rt at 1 (i.e., Rt = 0 for all t). Another rationale can be seen in the
32Another example of a realistic and operational specification would be the prede-
termination of Yt and πx,t, i.e., the assumption that the current inflation and output
deviation from trend cannot be influence by current monetary policy decisions (compare
e.g. Woodford [37], chapter 5).33Rotemberg and Woodford [28], p. 93: ”There are two reasons why such variables [like
the current potential output] may simply be unobservable by the central bank. These
are that some important economic data are collected retrospectively and that even the
data that are collected concurrently need to be processed before their message about the
economy as a whole can be distilled.”34In terms of our model, the condition reads: whenever Ξ > β there is a monetary
distortion present in the model. To make the link to the informal statement, let us define
β ≡ 1/(1 + r) where r ∈ (0,∞] is the agent’s rate of time preference and Ξ ≡ (1 + x)
where x is the net rate of steady state PPI inflation. The inequality Ξ > β approximately
implies x > −r.
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 59
argument, that in a rather general NNS framework an inertial (or history-
dependent) dynamic response of interest-rate policy to disturbances would
be preferable to a purely forward-looking approach (see e.g. Woodford [37],
chapter 7).
Exchange rate targeting The rule of thumb – expressed in Obstfeld and
Rogoff [27], p. 93, and taken up in Taylor [34] – saying that a substantial
appreciation of the real exchange rate,
erealt ≡
etP∗
t
Pt
,
accompanied by slow output growth and low inflation furnishes a case for
cutting interest rates, represents a concise description of actual monetary
policy behavior of many small and semi-small open economies.
Since only intermediate goods are traded in our model, it might be a
sensible starting point to assume that the central bank targets the terms
of trade, rather than the real exchange rate. In this instance, Rule 1 is
modified to
Rt = 0.5 · Yt + 1.5 · πx,t + φeetott (2.18)
where the parameter on the terms of trade, φe, is negative. Rule 2 and 3
are amended accordingly.35
CPI inflation targeting In the baseline specifications of Rule 1 to 3, the
nominal interest rate reacts to deviations of PPI inflation from its steady
state value. Since it is the intermediate sector where price rigidities and the
implied distortions occur, this might be a sensible starting point. However,
35Given our assumption that P ∗
t = P ∗
x,t, the real exchange rate can be rewritten as
erealt =
etP∗
x,t
pt
=etott
pt
where et ≡ et/Px,t and pt ≡ Pt/Px,t. In terms of percentage deviations from the steady-
state, we have
erealt = et − pt + P ∗
x,t = etott − pt.
For examples of studies which make allowance for the real exchange rate instead of (or
as an alternative to) the terms of trade, compare e.g. Taylor [34] and Kollmann [22].
60 CHAPTER 2
the central bank might prefer to make allowance for CPI inflation rather
than PPI inflation. Why this? Recall that the CPI, defined as
Pt =[ωP
ρρ−1
x,t + (1 − ω)[etP
∗
x,t
] ρρ−1
] ρ−1
ρ
,
includes the price for foreign intermediate goods expressed in the domestic
currency and, consequently, the nominal exchange rate, et. Therefore, tar-
geting CPI inflation can be considered as a way for monetary policy to take
changes in the nominal exchange rate into account. Rule 1 is modified to
Rt = 0.5 · Yt + 1.5 · πt;
Rule 2 and 3 are amended accordingly.
2.4.2 Simulation results
The simulation results are summarized in table 2. In what follows, the
trend output specification for a policy rule is called TREND, the potential
output specification is called GAP, PPI (or domestic) inflation targeting is
abbreviated by DIT, the exchange rate peg is called PEG, CPI inflation
targeting is called CIT, the standard deviation of a variable is denoted by
Std(•), shocks to technology, government consumption, terms of trade, and
foreign demand, respectively, are labelled A-, G-, TOT-, and FD-shocks.
Throughout, the parameter Ξ is set to 1.0.36 Moreover, we focus on reac-
tion coefficient configurations for which a rational expectations equilibrium
exists.37
Benchmark policies
Performance We start by discussing the findings for the two benchmark
policies strict DIT and PEG for the flexible price case. Compared to strict
DIT, the PEG raises output and inflation volatility with respect to all four
36We are safe to make this assumption since at this stage of the work the model is not
calibrated and we may restrict it to small enough shocks.37Determinacy of equilibrium cannot be taken for granted in NNS models; this holds
particularly true when monetary policy is defined in terms of interest-rate rules (see e.g.
Woodford [36]).
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 61
shocks. Regarding the terms of trade variability, the relative performance is
rather mixed: under the PEG, Std(etot) is clearly raised in the presence of
A-shocks, whereas it is slightly reduced in the presence of G-shocks. With
respect to TOT- and FD-shocks, the differences are negligible. Note that in
the presence of TOT-shocks strict DIT tends to stabilize the interest rate
almost as well as the PEG (the active policy actually performs better). This
is because under a PEG, the gross domestic interest rate is directly propor-
tional to Λ∗
1-shocks and in this sense Λ∗
1-disturbances can be interpreted as
shocks to the world nominal interest rate – to which the domestic nominal
interest rate is equated under the PEG.
Changing the degree of price flexibility from q ' 1 to 0.25 has the
following consequences on the outcome under the PEG. With respect to
all four shocks the volatility of inflation and the terms of trade improves
whereas the volatility of output deteriorates. The increase in Std(Y ) is
particularly significant with respect to TOT-shocks. In contrast, under
strict DIT there are hardly any differences distinguishable as the degree of
price flexibility varies. Note that despite the lower inflation volatility under
sticky prices, Std(π) is still higher under the PEG.
Welfare Given that prices are flexible, moving from strict DIT to the PEG
affects the variances and the respective covariances of C, m, and l, which in
turn affect welfare. However, the differences in terms of welfare are rather
small – from which we conclude that the welfare function is quite flat in
the neighborhood of the set of points we are evaluating it.38 If anything,
the PEG is dominated by strict DIT. The dominance of strict DIT becomes
somewhat more pronounced when prices are sticky: While under strict DIT
welfare is hardly affected as the degree of price flexibility varies, we observe
an albeit small deterioration in welfare under the PEG. This is particularly
true with respect to TOT-shocks.
Baseline rules
Flexible prices Next, we compare the three baseline specifications of
Rule 1, 2, and 3 with each other. If prices are flexible, then, in terms
38As a matter of fact, the differences in terms of welfare are minuscule for all policy
alternatives considered here; this finding is notorious for that kind of studies.
62 CHAPTER 2
of welfare, Rule 1 is invariably dominated by Rule 2 and 3 whereas the
differences between Rule 2 and 3 are small.39 This pronounced discrepancy
in the outcome for Rule 1 on the one hand and Rule 2 and 3 on the other
hand disappears for the GAP-specification. Only regarding A-shocks, Rule
1 yields minimally lower welfare than the two other rules.
A similar pattern emerges from comparing the three simple policy rules
with the two benchmark policies strict DIT and PEG. For the TREND-
specification, Rule 3 delivers virtually the same level of welfare as strict DIT,
Rule 2 yields somewhat higher welfare with respect to A- and G-shocks, and
Rule 1 clearly and invariably involves welfare losses. This pattern practically
disappears for the GAP-specification.
The differences between the TREND-specification of Rule 1 and strict
DIT in terms of volatilities are invariably significant, while the performances
under Rule 2 and 3 (again, the TREND-specifications) come relatively close
to the one under strict DIT. Rule 3 e.g. differs from strict DIT only insofar
as (and this finding does not surprise) the variability of πx is higher; the
variability of π, on the other hand, is slightly smaller with respect to A- and
FD-shocks and slightly higher for G- and TOT-shocks. From the differences
in terms of performance between Rule 1 on the one side and Rule 2 and 3
on the other side, we conclude that under flexible prices interest smoothing
in combination with a more aggressive reaction to inflation pays off in terms
of both inflation and output variability.
Sticky prices If prices are sticky, the differences across the rules in terms
of welfare decrease by about one half to two thirds. But still, Rule 1 is
dominated by Rule 2 and 3. Interestingly, the ranking between Rule 2 and
3 gets now reversed: Rule 2 yields slightly more welfare with respect to all
shocks but FD-shocks.
In terms of volatilities, Rule 1 performs better in the sticky price case
compared to the flex price case, and this with respect to all shocks;40 the
only exception is Std(etot) for which we observe a move in the opposite
39Rule 3 yields a little bit more welfare with respect to A-shocks and insignificantly
less welfare with respect to TOT-shocks.40This does not come at a surprise to us since the original Taylor [32] rule has been
proposed for a sticky price environment.
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 63
direction in the case of G- and TOT-shocks. Under all three rules output
variability with respect to A-shocks is smaller than under strict DIT. Rule
2 invariably performs better than strict DIT in terms of Std(Yt). The same
is true for Rule 3 in terms of Std(πt). In comparison to Rule 2 and 3, an
adoption of Rule 1 induces higher inflation variability (both PPI and CPI
inflation). With respect to output variability, however, Rule 1 outperforms
Rule 3.
Varying the parameter φy A weaker response to output deviations from
trend in Rule 1 relative to the respective baseline value invariably leads to
higher welfare, whereby the biggest benefits arise with respect to A-shocks.
Rule 2 and 3 are less sensitive to lowering φy; the observed welfare gains
or losses are negligible. In terms of performance, a smaller φy-parameter in
Rule 1 brings about somewhat more variability in output deviations from
trend and significantly less volatility in inflation as well as in the interest
rate.
A stronger response to output from trend in Rule 1 leads to welfare losses
with respect to all four shocks (the biggest losses can be observed regarding
A-shocks). In the case of Rule 2, a higher φy leads to welfare losses with
respect to A-shocks while the outcome regarding the remaining three shocks
is mainly unaffected. In the case of Rule 3, raising φy seems to have no
effect whatsoever. If output is measured with respect to deviations from
its potential level, Rule 1 gets fairly robust in that varying the parameter
φy has very little consequences for welfare and performance. If anything, a
higher φy leads to modest welfare gains.
Varying the parameter ρr A modest rise in the smoothness parame-
ter ρr of Rule 1 leads to substantial gains in welfare. In fact, introducing
smoothing in Rule 1 leads to the largest welfare gains we have found among
all investigated modifications. In terms of performance, a smoothing pa-
rameter of 1/3 brings about less variability not only for inflation but also
for output – and this with respect to all types of shocks – with the only
exception that with respect to TOT-shocks, Std(Y ) increases. Again, this
pattern disappears when it is assumed that the current potential output
level is observable or can be measured accurately. In this event, the only
64 CHAPTER 2
gains in terms of welfare from interest smoothing can be observed with
respect to A-shocks. However, these gains are much smaller than for the
TREND-specification.
We conclude that the differences in terms of welfare and performance
between the baseline specifications of Rule 1 on the one hand and Rule 2
and 3 on the other hand mainly stem from the absence of interest smoothing
in Rule 1.
Terms of trade targeting
Suppose, the central bank targets the terms of trade (in addition to devi-
ations of PPI inflation and output from trend). Lowering φe to −0.1 and
further to −0.2 and finally to −0.3 in Rule 1 yields increasingly higher wel-
fare compared to the baseline specification with respect to A-shocks and
(to a much lower extent) FD-shocks. The same experiment leads to welfare
losses with respect to G- and TOT-shocks. Without knowing more about
the relative size of each type of shock we cannot decide how much terms of
trade targeting the welfare maximizing central bank should opt for.
In the case of Rule 2 and 3, lowering φe (relative to the baseline value)
leads to shifts in welfare of much smaller magnitudes. In particular, going
from φe = 0 to -0.1 has barely any effects on welfare. Only with respect
to A-shocks we can detect a minor shift (for Rule 2 a small gain and for
Rule 3 a small loss; note that the small gain turns into a loss for the GAP-
specification).
In the case of Rule 1, a moderate form of terms of trade targeting leads
to lower inflation and interest rate volatilities with respect to A- and FD-
shocks, while the same volatilities are higher with respect to G- and TOT-
shocks. Output variability practically remains unaffected with respect to
A-, G-, and FD-shocks and improves somewhat with respect to TOT-shocks.
In the case of Rule 2, the same experiment leads to a similar pattern – with
the difference that output variability now is clearly negatively affected and
that the effects on Std(R) are much smaller. Letting Rule 3 respond to
the terms of trade leads to moderate effects on output volatility (Std(Y )
improves with respect to A- and FD-shocks and deteriorates with respect to
G- and TOT-shocks) while the effects on inflation volatility are negligible.
2.4. THE ROLE OF EXCHANGE RATE STABILIZATION 65
Varying the parameter φy How are the numerical results under terms of
trade targeting affected by decreasing the coefficient on deviations of output
from trend? When we compare Rule 1 for the parameter configuration
ρr, φy, φπ, φe = 0, 0.1, 1.5, − 0.3 with 0, 0.5, 1.5, − 0.3 we observe
a deterioration in terms of welfare with respect to A-shocks (considerably)
and FD-shocks (marginally) and an improvement with respect to G-shocks
(considerably) and TOT-shocks (marginally). Output volatility is hardly
affected by lowering φy (we only observe a small increase with regard to
A-shocks). However, we observe a pronounced effect on inflation volatility
with respect to A-shocks (deterioration) and G-shocks (improvement). The
effects of lowering φy on Rule 2 and 3 in terms of welfare are small.41 If
anything, we observe a moderate loss in the case of Rule 2 and with respect
to A-shocks.
How are the numerical results affected by increasing the coefficient on
deviations of output from trend? In the case of Rule 1, the parameter con-
figuration 0, 1.5, 1.5, − 0.3 leads to indeterminacy. One way to get rid
of indeterminacy is to raise the smoothness parameter from 0 to 0.1 (which
admittedly biases the outcome towards welfare gains). We observe welfare
gains with respect to A-shocks (considerably) and FD-shocks (marginally).
The outcome for Rule 2, again, seems to be fairly stable regarding shifts
in φy, while the outcome for Rule 3 is slightly improved with respect to A-
and G-shocks and barely affected with respect to TOT- and FD-shocks.42
Increasing the φy-parameter in Rule 3 in conjunction with a very mod-
est terms of trade targeting also pays off in terms of output and inflation
volatility.
CPI inflation targeting
Suppose the central bank targets CPI inflation rather than PPI inflation.
For all three rules, the CIT outcome is going to be compared to the outcome
41For Rule 2, we compare the parameter configuration 1/3, 0.1, 1.5, − 0.1
with 1/3, 0.4, 1.5, − 0.1. For Rule 3, we compare the parameter configuration
2/3, 0, 2, − 0.1 with 2/3, 0.1, 2, − 0.1.42For Rule 2, we compare the parameter configuration 1/3, 1.5, 1.5, − 0.1
with 1/3, 0.4, 1.5, − 0.1. For Rule 3, we compare the parameter configuration
2/3, 0.5, 2, − 0.1 with 2/3, 0.1, 2, − 0.1.
66 CHAPTER 2
for the respective baseline specification (which involves DIT). In the case
of Rule 1, CIT leads to modest welfare gains with respect to A- and FD-
shocks and brings about losses (modest as well) with respect to G- and
TOT-shocks. Welfare is invariably lower in the case of Rule 2 and 3, albeit
these differences are minuscule. Lowering φy in Rule 1 invariably improves
welfare in almost the same manner as allowing for modest interest smoothing
does, while nothing is gained by raising φy. As for the case of PPI targeting,
the results for Rule 2 and 3 are fairly robust regarding moderate shifts in
φy. If anything, we can observe welfare gains with respect to A-shocks when
lowering the parameter on output in Rule 2 and when increasing the same
parameter in Rule 3.
In the case of Rule 1, CIT leads to a modest improvement of output
and inflation volatility with respect to A- and FD-shocks and an equally
modest deterioration with respect to G- and TOT-shocks. For Rule 2 and
3 the differences in terms of performance are even smaller (and in fact
negligible).
Strict CTI Finally, we undertake an assessment of strict CTI. If prices
are flexible, there is hardly any difference in terms of welfare between strict
DIT and strict CIT, respectively; both versions of active policies dominate
the PEG. The only difference we are aware of is that with respect to A-
shocks, strict CIT achieves slightly more welfare. However, if prices are
sticky, strict CIT invariably yields less welfare than strict DIT targeting.
The biggest differences can be observed with respect to TOT-shocks.
2.5 Conclusions
In this paper, we have compared simple monetary policy rules in the frame-
work of a hypothetical small open economy with optimizing agents and
monopolistic competition in intermediate product markets. The role the
exchange rate is playing in manipulating the policy instrument has been
explored in the presence of a moderate degree of price stickiness, perfect
exchange rate pass-through into import prices, and a small number of do-
mestic and foreign structural shocks. We found that a moderate form of
exchange rate targeting in the original Taylor rule induces higher perfor-
2.5. CONCLUSIONS 67
mance with respect to productivity and foreign demand shocks and lower
performance with respect to government and terms-of-trade shocks; without
knowing more about the relative size of each type of shock we cannot decide
whether directly reacting to the exchange rate is preferable. For rules with
a moderate to considerable degree of persistence and a larger relative weight
on inflation, the outcome was practically unaffected by the inclusion of an
exchange rate target.
There are some obvious limitations to the analysis conducted in this
paper which may indicate directions for future work. Some investigation
of the robustness of the findings was presented here, but more needs to be
done. One may want to vary key parameters of the model (such as the
trade elasticity and the degree of openness) and/or key assumptions such
as the degree of exchange rate pass-through – and assess the numerical
sensitivity of the results. One may also want to calibrate the model (or
an extended version of it) to quarterly data of a real-world, approximately
small open economy like the one of Switzerland – an exercise which would
involve, among others, getting an idea of the relative size of the structural
shocks. Together with the adoption of Sims’ [30] non-linear solution method
this would, after all, allow one to evaluate unconditional welfare and make
policy recommendations.
68 CHAPTER 2
2.A Stationary representation
2.A.1 Change in notation and useful simplifications
Before presenting the system of equations which describes the equilibrium
of the economy, we undertake a change in notation and some useful sim-
plifications. In what follows, we write Yt for Y (st) etc. Moreover, we let
Et • be a function which takes the expected value of the term inside the
curly bracket, based on information available in t. The optimal pricing rule
can then be rewritten as follows43
px,t =1
θ
∑∞
τ=0 βτ (1 − q)τ (Ξτ )1
θ−1 Et
Λ1,t+τ
Λ1,tP
1
1−θ
x,t+τPt+τCm,t+τXt+τ
∑∞
τ=0 βτ (1 − q)τ (Ξτ )θ
θ−1 Et
Λ1,t+τ
Λ1,tP
1
1−θ
x,t+τXt+τ
.
Both the nominator and the denominator of the pricing rule can be ex-
pressed in terms of expectational difference equations. We end up with the
following rather compact expression for the optimal price
px,t =1
θ
S1,t
S2,t
where
S1,t ≡ P1
1−θ
x,t PtCm,tXt + β (1 − q) Ξ1
θ−1 Et
Λ1,t+1
Λ1,t
S1,t+1
and
S2,t ≡ P1
1−θ
x,t Xt + β (1 − q) Ξθ
θ−1 Et
Λ1,t+1
Λ1,t
S2,t+1
.
Next, the FOC for lt from the household’s maximization problem44
(1 − ν) Ψν(1−σ)t l
(1−ν)(1−σ)−1t = Λ2,t,
43Before changing notation we multiply the nominator and the denominator of equa-
tion (2.7) by π(st+1
∣∣ st)/π(st+1
∣∣ st)
and then substitute P b(st+1
∣∣ st)/π(st+1
∣∣ st)
for
βΛ1
(st+1
)/Λ1 (st).
44The variables Λ1,t, Λ2,t and Λ3,t are the (nominal) shadow prices on the first, sec-
ond, and third constraint to the household’s maximization problem (compare Subsection
2.2.4).
2.A. STATIONARY REPRESENTATION 69
and for ht,
Λ1,tPtWt = Λ2,t,
are combined to
Λ1,tPtWt = (1 − ν) Ψν(1−σ)t l
(1−ν)(1−σ)−1t .
Also, the FOC for It,
Λ3,t = Λ1,tPt
[1 − φ
(It
Kt−1
− δ
)]−1
,
and for Kt,45
Λ3,t = βEt Λ1,t+1Pt+1zt+1
+Λ3,t+1
[φ
2
(It+1
Kt
)2
−φ
2δ2 + 1 − δ
],
are combined to
Λ1,tPtΦ−1t = βEt
Λ1,t+1Pt+1
(zt+1 + Φ−1
t+1
[φ
2
(It+1
Kt
)2
−φ
2δ2 + 1 − δ
])
where
Φt = 1 − φ
(It
Kt−1
− δ
).
Finally, we take notice of the fact that variable Bt shows up in exactly one
optimality condition, namely the FOC for the shadow price Λ1,t. Since this
would have been the equation which determined Bt, that particular FOC
(i.e., the budget constraint) can be dropped from the system of equilibrium
conditions (compare Subsection 2.2.6).
45Observe that
φ
(It+1
Kt
− δ
)It+1
Kt
−φ
2
(It+1
Kt
− δ
)2
+ (1 − δ) =φ
2
(It+1
Kt
)2
−φ
2δ2 + 1 − δ.
70 CHAPTER 2
2.A.2 Equilibrium conditions
We end up with a system of 22 equations plus policy rule (2.14) which simul-
taneously hold at all points in time, in a total of 23 endogenous variables:46
Final good producers:
Y : Yt =[ω1−ρ
(Xd
t
)ρ+ (1 − ω)1−ρ
(Xf
t
)ρ]1/ρ
(2.19)
Xd : Xdt = ω
(Px,t
Pt
) 1
ρ−1
Yt (2.20)
Xf : Xft = (1 − ω)
(etP
∗
x,t
Pt
) 1
ρ−1
Yt (2.21)
Intermediate goods producers:
h : Xt = AtKαt l1−α
t (2.22)
Cm : ztKt = αCm,tXt (2.23)
W : Wtht = (1 − α) Cm,tXt (2.24)
p : px,t =1
θ
S1,t
S2,t
(2.25)
S1 : S1,t = P1
1−θ
x,t PtCm,tXt + β (1 − q) Ξ1
θ−1 Et
Λ1,t+1
Λ1,t
S1,t+1
(2.26)
S2 : S2,t = P1
1−θ
x,t Xt + β (1 − q) Ξθ
θ−1 Et
Λ1,t+1
Λ1,t
S2,t+1
(2.27)
Evolution of PPI:
Px : Pθ
θ−1
x,t = qpθ
θ−1
x,t + (1 − q) Ξθ
θ−1
t−1 Pθ
θ−1
x,t−1 (2.28)
46There are fifteen endogenous quantities (C , l, h, I, K, M , Y , X, Xd, Xf , Cm, Ψ,
Φ, S1, S2) and eight endogenous prices – including the policy variable and the shadow
price in the household’s budget constraint (z, W , P , Px, px, e, R, Λ1).
2.A. STATIONARY REPRESENTATION 71
Representative household:
C : Λ1,tPt = νCη−1t Ψ
ν(1−σ)−ηt l
(1−ν)(1−σ)t (2.29)
Ψ : Ψt =
[Cη
t + ζ
(Mt
Pt
)η] 1
η
(2.30)
M : ζ
(Mt
PtCt
)η−1
=(1 − R−1
t
)(2.31)
P : Λ1,tPtWt = (1 − ν) Ψν(1−σ)t l
(1−ν)(1−σ)−1t (2.32)
Λ :Λ1,t
Rt
= βEt Λ1,t+1 (2.33)
z : Λ1,tPtΦ−1t = (2.34)
βEt
Λ1,t+1Pt+1
(zt+1 + Φ−1
t+1
[φ
2
(It+1
Kt
)2
−φ
2δ2 + 1 − δ
])
Φ : Φt = 1 − φ
(It
Kt−1
− δ
)(2.35)
K : Kt = It −φ
2
(It
Kt−1
− δ
)2
Kt−1 + (1 − δ) Kt−1 (2.36)
l : 1 = lt + ht (2.37)
Explicit market clearing conditions:
X : Xt = Xdt + Xd∗
t (2.38)
I : Yt = Ct + It + Gt (2.39)
International asset market:
e : et = κΛ∗
1,t
Λ1,t
. (2.40)
Notice: At, Gt, U∗
C,t, P ∗
x,t, and Xd∗t are exogenous variables. Moreover,
equations (2.19), (2.20), and (2.21) together ensure that
Pt =[ωP
ρρ−1
x,t + (1 − ω)(etP
∗
x,t
) ρρ−1
] ρ−1
ρ
.
72 CHAPTER 2
2.A.3 Deflating the system
In the presence of sustained inflation (Ξ > 1), the nominal variables in
the system of equilibrium conditions are non-stationary. We can get rid of
this non-stationarity by deflating the system appropriately.47 The choice of
the deflator is arbitrary; we prefer Px. We end up with the following 23
equations plus policy rule (2.14) in 24 endogenous variables:
Final good producers:
Y : Yt =[ω1−ρ
(Xd
t
)ρ+ (1 − ω)1−ρ
(Xf
t
)ρ]1/ρ
Xd : Xdt = ω
(1
pt
) 1
ρ−1
Yt
Xf : Xft = (1 − ω)
(etP
∗
x,t
pt
) 1
ρ−1
Yt
where pt ≡ Pt/Px,t and et ≡ et/Px,t.
Intermediate goods producers:
h : Xt = AtKαt h1−α
t
Cm : ztKt = αCm,tXt
W : Wtht = (1 − α) Cm,tXt
px : px,t =1
θ
s1,t
s2,t
s1 : s1,t = ptCm,tXt + β (1 − q) Ξ1
θ−1 Et
λ1,t+1
λ1,t
π1
1−θ
x,t+1s1,t+1
s2 : s2,t = Xt + β (1 − q) Ξθ
θ−1 Et
λ1,t+1
λ1,t
πθ
1−θ
x,t+1s2,t+1
where px,t ≡ px,t/Px,t, s1,t ≡ S1,tP−
2−θ1−θ
x,t , s2,t ≡ S2,t/P1
1−θ
x,t , and λ1,t ≡ Λ1,tPx,t.
47Note that equations (2.35), (2.37), (2.36), ( 2.19), (2.20), (2.38), (2.23), (2.24), and
( 2.39) are stated in terms of either (stationary) real variables or (likewise stationary)
relative prices.
2.A. STATIONARY REPRESENTATION 73
Representative household:
C : λ1,tpt = νCη−1t Ψ
ν(1−σ)−ηt l
(1−ν)(1−σ)t
Ψ : Ψt =
[Cη
t + ζ
(mt
pt
)η] 1
η
m : ζ
(mt
ptCt
)η−1
=(1 − R−1
t
)
p : λ1,tptWt = (1 − ν) Ψν(1−σ)t l
(1−ν)(1−σ)−1t
λ1 : λ1,t = βRtEt
λ1,t+1
πx,t+1
z : λ1,tpt1
Φt
= βEt
λ1,t+1pt+1
(zt+1 +
1
Φt+1
[φ
2
(It+1
Kt
)2
−φ
2δ2 + 1 − δ
])
Φ : Φt = 1 − φ
(It
Kt−1
− δ
)
K : Kt = It −φ
2
(It
Kt−1
− δ
)2
Kt−1 + (1 − δ) Kt−1
l : lt = 1 − ht
where mt ≡ Mt/Px,t.
Explicit market clearing conditions:
I : Yt = Ct + It + Gt
X : Xt = Xdt + Xd∗
t
International asset market:
e : κΛ∗
1,t
λ1,t
= et
74 CHAPTER 2
PPI and CPI inflation:
πx : 1 = qpθ
θ−1
x,t + (1 − q) Ξθ
θ−1
(1
πx,t
) θθ−1
π : πx,t+1 =pt
pt+1
πt+1
where πx,t+1 ≡ Px,t+1/Px,t and πt+1 ≡ Pt+1/Pt.
Note that equation (2.28) (the evolution of the PPI) now is expressed in
terms of PPI inflation, πx,t. Moreover, πx,t now shows up in the equations
which determine s1,t, s2,t, and λi,t. Finally, PPI inflation and CPI inflation
are related by πx,t+1 = (pt/pt+1)πt+1.
2.B Non-stochastic steady state
In the non-stochastic steady state we have sustained inflation (π = πx = Ξ)
and, thus, all prices grow at the same rate. It follows that (P/Px =) p =
(p/Px =) px = 1.
From λ1 = βRλ1π−1x , we get
R =Ξ
β.
From pρ
1−ρ = ω + (1 − ω) eρ
ρ−1
x P∗
ρρ−1
x , we get
e =1
P ∗x
.
From s1 = pCmX + β (1 − q) Ξ1
θ−1λ1
λ1π
1
1−θx s1, we get
CmX
s1
= 1 − β (1 − q) .
Similarly, from s2 = X + β (1 − q) Ξθ
θ−1λ1
λ1π
θ1−θx s2, we get
X
s2
= 1 − β (1 − q) .
2.B. NON-STOCHASTIC STEADY STATE 75
It follows thats1
s2
= Cm.
From px = 1θ
s1
s2together with the previous results, we get
Cm = θ
which is the expected result.
Transforming K = I− φ2
(IK− δ)2
K+(1 − δ) K yields a quadratic equation
in I/K, given by
0 = −1
2φ
(I
K
)2
+ (1 + δφ)I
K−
1
2δ2φ − δ.
The two solutions for the ratio I/K are δ and δφ+2φ
, respectively. Here, we
focus on the first oneI
K= δ.
It follows that
z =1 − β (1 − δ)
β.
From z = CmαXK
, we get
K
h=( z
αθ
) 1
α−1
=
(1 − β (1 − δ)
αβθ
) 1
α−1
.
Let us assume that Y = X and that A = 1. It follows that
Y
K=
1 − β (1 − δ)
αβθ
and, consequently, that
Y =
(Y
K
) αα−1
h.
We are now in the position to derive an expression for C/Y
C
Y= 1 −
I
Y−
G
Y
76 CHAPTER 2
where G/Y is steady state government expenditures in percent of steady
state output and whereI
Y=
I
K
K
Y.
From Xf = (1 − ω) e1
ρ−1
(P ∗
x
) 1
ρ−1 p−1
ρ−1 Y and previous results, we get
Xf = (1 − ω) Y.
Also, from Xd = ω(
1p
) 1
ρ−1
Y , we get
Xd = ωY.
From the assumption that Y = X and previous results, we get
Xd∗
Y
(=
Xd∗
X
)= 1 − ω.
Also,ωY
Y
(=
Xd
X
)= ω.
From ζ(
mC
)η−1= 1 − R−1, we get
m
Y=
C
Y
(R − 1
ζR
) 1
η−1
.
And, from Ψη = Cη + ζmη we get
Ψ
Y=
C
Y
[1 + ζ
(m/Y
C/Y
)η] 1
η
.
Suppose the time devoted to labor as a fraction of total endowment is given.
The implied CES weight ν can be computed as follows. Dividing the FOC
for C,
νCη−1Ψν(1−σ)−η (1 − h)(1−ν)(1−σ) = λ1,
by the FOC for h,
(1 − ν) Ψν(1−σ) (1 − h)(1−ν)(1−σ)−1 = λ1W,
2.C. FIRST-ORDER APPROXIMATION 77
provides us withνCη−1Ψ−η
(1 − ν) (1 − h)−1 =1
W.
Substituting out for Ψ = (Cη + ζmη)1
η yields
ν
1 − ν
Cη(1 − h)
C(Cη + ζmη)=
1
W.
An expression for W can be found from the condition
W =(1 − α) θY
h.
Substituting out for W yields
Y
C
1
h
(1 − h)θ (1 − α)[1 + ζ
(mC
)η] =1 − ν
ν.
Substituting out for m/C taking the inverse yields
ν =
(1 − h)θ (1 − α)[
1 + ζ1
1−η
(R−1
R
) ηη−1
]CY
h+ 1
−1
.
2.C First-order approximation
2.C.1 Linear system
Sofar, we have presented the system of equations which describes the equilib-
rium and have found the non-stochastic steady state of that system. Next,
we consider the first-order approximation to the equilibrium conditions (in
terms of percentage deviations from the steady state):
Final good producers:
Y : Yt = ωXdt + (1 − ω) Xf
t
Xd : Xdt = −
(1
ρ − 1
)pt + Yt
Xf : Xft =
(1
ρ − 1
)et +
(1
ρ − 1
)P ∗
x,t −
(1
ρ − 1
)pt + Yt
78 CHAPTER 2
Intermediate goods producers:
h : Xt = At + αKt + (1 − α) ht
Cm : zt = Cm,t + Xt − Kt
W : Wt = Cm,t + Xt − ht
px : px,t = s1,t − s2,t
s1 : s1,t =CmX
s1
[Cm,t + Xt
]
+β (1 − q)
[Et
λ1,t+1
− λ1,t +
(1
1 − θ
)Et πx,t+1 + Et s1,t+1
]
s2 : s2,t =X
s2
Xt
+β (1 − q)
[Et
λ1,t+1
− λ1,t +
(θ
1 − θ
)Et πx,t+1 + Et s2,t+1
]
Representative household:
C : λ1,t + pt = (η − 1) Ct + [ν (1 − σ) − η] Ψt + (1 − ν) (1 − σ) lt
Ψ :
(Ψ
Y
)η
Ψt =
(C
Y
)η
Ct + ζ(m
Y
)η
mt − ζ(m
Y
)η
pt
m : (R − 1) (η − 1)[mt − pt − Ct
]= Rt
p : λ1,t + pt + Wt = ν (1 − σ) Ψt + [(1 − ν) (1 − σ) − 1] lt
λ1 : λ1,t − Et
λ1,t+1
= Rt − Et πx,t+1
z : λ1,t + pt − Φt = Et
λ1,t+1
+ Et pt+1 + [1 − β (1 − δ)] Et zt+1
−β (1 − δ) Et
Φt+1
+ βφδ2Et
It+1
− βφδ2Kt
Φ : Φt = −φδIt + φδKt−1
K : Kt = δIt + (1 − δ) Kt−1
l : lt = −h
lht
2.C. FIRST-ORDER APPROXIMATION 79
Explicit market clearing conditions:
I : Yt =C
YCt +
I
YIt +
G
YGt
X : Xt = ωXdt + (1 − ω) Xd∗
t
International capital markets:
e : Λ∗
1,t − λ1,t = et
PPI and CPI inflation:
πx : πx,t =q
(1 − q)px,t
π : πx,t = pt−1 − pt + πt.
Policy rule: If monetary policy is assumed to be active, it follows the
generalized Taylor type interest rule (2.14). Suppose, the target values Y ,
πx, and etot coincide with the respective long-run equilibrium values. Rule
(2.14) can then be rewritten as
Rt = ρrRt+1 + (1 − ρr)[φyYt + φππx,t + φee
tott
]
where
etott = et + P ∗
x,t.
Exogenous variables: The variable At is assumed to follow the stochas-
tic AR(1) process
ln At = ρa ln At−1 + (1 − ρa) ln A + εa,t
where ρa ∈ [0, 1), A denotes the unconditional mean of At, and εa,t is
i.i.d.(0, σ2
εa
). This process can be rearranged as follows
(ln At − ln A
)= ρa
(ln At−1 − ln A
)+ εa,t
80 CHAPTER 2
from which we get
A : At = ρaAt−1 + εa,t.
Similarly, we have
G : Gt = ρgGt−1 + εg,t
Λ∗ : Λ∗
1,t = ρlΛ∗
1,t−1 + εl,t
Xd∗ : Xd∗t = ρxX
d∗t−1 + εx,t
P ∗
x : P ∗
x,t = ρpP∗
x,t−1 + εp,t
where ρg, ρµ, ρl, ρp, ρx ∈ [0, 1). All driving forces are i.i.d. with zero mean
and constant variance (and uncorrelated among each others, of course).
2.C.2 Digression: The New Phillips curve
Substituting out for s1 and s2 in the equation for px yields the following
expectational difference-equation
px,t = [1 − β (1 − q)] Cm,t + β (1 − q) Et πx,t+1 + β (1 − q) Et px,t+1 .
Replacing px,t by 1−qq
πx,t provides us with the familiar New Phillips curve
πx : πx,t = [1 − β (1 − q)]q
1 − qCm,t + βEt πx,t+1 .
2.D Exchange rate peg
Suppose the central bank pegs the domestic currency unilaterally and cred-
ibly to the world currency. There is just one way for the central bank of
the small open economy to effectively fix the nominal exchange rate: it has
to choose the same steady state inflation rate as the monetary authority of
the rest of the world does, that is, it has to choose Ξ = Ξ∗.
For Ξ = Ξ∗ > 1, the asset market equilibrium condition can be rewritten as
et = κΛ∗
t
Λ1,t
= κλ∗
t
λ1,t
Px,t
P ∗x,t
2.D. EXCHANGE RATE PEG 81
where the ratio Px,t/P∗
x,t is stationary; the original system of equations has
then to be deflated in a meaningful way.
However, things get simpler when we assume that Ξ = Ξ∗ = 1 (which
is the reason why we prefer this alternative). In this event, the original
(non-deflated) system of equilibrium conditions becomes stationary. The
non-deflated linearized system can then be modified as follows: We skip the
Taylor rule (since monetary policy becomes passive) and let et = 0 for all t
(since et is fixed at an arbitrary value). It follows that Λ1 becomes a control
variable, given by Λ1,t = Λ∗
1,t. R and M adjust endogenously. Moreover,
equation
Λ1,t − Et
Λ1,t+1
= (1 − ρl) Λ∗
1,t = Rt
determines R while M is determined via the money demand equation. Note
that when the Λ∗
1-shock is silent, Rt = et = 0.
Bibliography
[1] Backus, David K., Patrick J. Kehoe, and Finn E. Kydland (1995),
International business cycles: Theory and evidence, in: Thomas F.
Cooley, ed., Frontiers of Business Cycle Research, Princeton University
Press
[2] Ball, Laurance (1999), Policy rules for open economies, in: John B.
Taylor, ed., Monetary policy rules, NBER Studies in Business Cycles
[3] Baxter, Marianne, and Robert G. King (1993), Fiscal policy in general
equilibrium, American Economic Review 83(3), 315-334
[4] Blanchard, Olivier J., and Charles M. Kahn (1980), The solution of lin-
ear difference models under rational expectations, Econometrica 48(5),
1305-1312
[5] Calvo, Guillermo A. (1983), Staggered prices in a utility-maximizing
framework, Journal of Monetary Economics 12(3), 383-398
[6] Chari, V.V., Patrick J. Kehoe, and Ellen R. McGrattan (2000), Sticky
price models of the business cycle: can the contract multiplier solve
the persistence problem?, Econometrica 68(5), 1151-1179
[7] Chari, V.V., Patrick J. Kehoe, and Ellen R. McGrattan (2000), Can
sticky price models generate volatile and persistent real exchange
rates?, NBER Working Paper No. w7869
[8] Clarida, Richard, and Jordi Gali (1994), Sources of real exchange-rate
fluctuations: how important are nominal shocks?, Carnegie-Rochester
Conference Series on Public Policy 41, 1-65
BIBLIOGRAPHY 83
[9] Clarida, Richard, Jordi Gali, and Mark Gertler (1999), The science of
monetary policy: a New Keynesian perspective, Journal of Economic
Literature 37(4), 1661-1707
[10] Collard, Fabrice, and Harris Dellas (2001), Price rigidity and the selec-
tion of the exchange rate regime, Mimeo
[11] Collard, Fabrice, and Harris Dellas (2002), Monetary policy rules and
exchange rate targeting, Mimeo
[12] Collard, Fabrice, and Harris Dellas (2002), Technology shocks and em-
ployment, CEPR Discussion Paper No. 3680
[13] Collard, Fabrice, and Harris Dellas (2003), Inflation targeting, Mimeo
[14] Cooley, Thomas F., and Edward C. Prescott (1995), Economic growth
and business cycles, in: Thomas F. Cooley, ed., Frontiers of Business
Cycle Research, Princeton University Press
[15] Gali, Jordi, and Tommaso Monacelli (2002), Monetary policy and ex-
change rate volatility in a small open economy, NBER Working Paper
No. 8905
[16] Ghironi, Fabio (2000), Alternative monetary rules for a small open
economy: the case of Canada, Working Paper, Boston College
[17] Goodfriend, Marvin, and Robert G. King (1997), The new neoclassical
synthesis and the role of monetary policy, in: Ben S. Bernanke and
Julio Rotemberg, NBER Macroeconomics Annual 1997
[18] King, Robert G., Charles I. Plosser, and Sergio T. Rebelo (1988), Pro-
duction, growth, and business cycles, Journal of Monetary Economics
21, 195-232 and 309-341
[19] King, Robert G., and Alexander L. Wolman (1996), Inflation targeting
in a St. Louis model of the 21st century, NBER Working Paper No.
5507
[20] King, Robert G., and Sergio T. Rebelo (1999), Rescuscitating real busi-
ness cycles, in: John B. Taylor and Michael Woodford, eds., Handbook
of Macroeconomics Vol. 1, Elsevier Science
84 CHAPTER 2
[21] Kollmann, Robert (1997), The exchange rate in a dynamic-optimizing
current account model with nominal rigidities: aA quantitative inves-
tigation, IMF Working Paper WP/97/7
[22] Kollmann, Robert (2002), Monetary policy rules in the open economy:
effects on welfare and business cycles, Journal of Monetary Economics
49(5), 989-1015
[23] Ljunqvist, Lars, and Thomas J. Sargent (2000), Recursive macroeco-
nomic theory, The MIT Press
[24] McCallum, Bennett T. (1999), Issues in the design of monetary policy
rules, in: John B. Taylor and Michael Woodford, eds., Handbook of
Macroeconomics Vol. 1, Elsevier Science
[25] Monacelli, Tommaso (2000), Into the Mussa puzzle: monetary policy
regimes and real exchange rate in a small open economy, Working Pa-
per, Boston College
[26] Obstfeld, Maurice, and Kenneth Rogoff (1995), Exchange rate dynam-
ics redux, Journal of Political Economy 103(3), 624-660
[27] Obstfeld, Maurice, and Kenneth Rogoff (1995), The mirage of fixed
exchange rates, Journal of Economic Perspectives 9(4), 73-96
[28] Rotemberg, Julio J., and Michael Woodford (1999), Interest rate rules
in an estimated sticky price model, in: John B. Taylor, ed., Monetary
policy rules, NBER Studies in Business Cycles
[29] Rotemberg, Julio J., and Michael Woodford (1999), The cyclical be-
havior of prices and costs, in: John B. Taylor and Michael Woodford,
eds., Handbook of Macroeconomics Vol. 1, Elsevier Science
[30] Sims, Christopher A. (2003), Second order accurate solution of discrete
time dynamic equilibrium models, Working paper
[31] Svensson, Lars E.O. (2000), Open-economy inflation targeting, Journal
of International Economics 50(1), 155-183
BIBLIOGRAPHY 85
[32] Taylor, John B. (1993), Discretion versus policy rules in practice,
Carnegie-Rochester Conference Series on Public Policy 39, 195-214
[33] Taylor, John B. (1999), Introduction, in: John B. Taylor, ed., Monetary
policy rules, NBER Studies in Business Cycles
[34] Taylor, John B. (2001), The role of the exchange-rate in monetary-
policy rules, American Economic Review, AEA Papers and Proceedings
91(2), 263-267
[35] Walsh, Carl E. (2003), Monetary theory and policy, second edition,
The MIT Press
[36] Woodford, Michael (2001), The Taylor rule and optimal monetary pol-
icy, American Economic Review, AEA Papers and Proceedings 91(2),
232-237
[37] Woodford, Michael (2003), Interest and prices: foundations of a theory
of monetary policy, Princeton University Press
86 TABLES CHAPTER 2
Tables Chapter 2
Table 1a+b: Elasticities of key variables
Table 2a-e: Performance and welfare of alternative policy regimes
Policy regime: Constant money growth rate
Flexible prices (q =1), no capital adjustment costs (φ =1)
A G µ Λ* Xd* Px*Y 1.133 0.182 -0.036 -0.299 -0.064 -0.299C 0.673 -0.083 -0.082 -0.189 -0.085 -0.189 I 4.687 0.096 0.100 -1.190 -0.072 -1.190h 0.187 0.153 -0.038 -0.008 0.156 -0.008πx -0.848 0.122 1.650 -0.006 0.127 -0.006π -0.658 0.092 1.652 0.189 0.096 0.189e 0.102 -0.027 1.658 0.968 -0.025 -0.032etot 0.950 -0.149 0.008 0.975 -0.152 0.975
Sticky prices (q =0.25), no capital adjustment costs (φ =1)
A G µ Λ* Xd* Px*Y -0.729 0.464 3.425 -0.341 0.228 -0.341C 0.079 0.007 1.020 -0.203 0.009 -0.203 I -5.142 1.582 18.377 -1.412 1.471 -1.412h -2.042 0.490 4.106 -0.058 0.506 -0.058πx -0.366 0.049 0.754 0.005 0.051 0.005π -0.270 0.034 0.930 0.197 0.035 0.197e 0.114 -0.028 1.634 0.968 -0.027 -0.032etot 0.480 -0.078 0.880 0.964 -0.078 0.964
Flexible prices (q =1), capital adjustment costs (φ =10)
A G µ Λ* Xd* Px*Y 0.831 0.177 -0.044 -0.223 -0.059 -0.223C 0.812 -0.080 -0.078 -0.225 -0.087 -0.225 I 2.120 0.046 0.034 -0.538 -0.033 -0.538h -0.067 0.148 -0.044 0.057 0.160 0.057πx -1.083 0.118 1.644 0.053 0.130 0.053π -0.843 0.089 1.647 0.236 0.099 0.236e 0.114 -0.026 1.658 0.965 -0.025 -0.035etot 1.196 -0.144 0.014 0.912 -0.156 0.912
Table 1a: Elasticities of key variables
Policy regime: Exchange rate peg
Flexible prices (q =1), no capital adjustment costs (φ =1)
A G Λ* Xd* Px*Y 1.133 0.183 -0.316 -0.064 -0.299C 0.673 -0.082 -0.213 -0.084 -0.189 I 4.684 0.097 -1.202 -0.072 -1.189h 0.187 0.154 -0.024 0.157 -0.008πx -0.950 0.149 -0.981 0.152 0.025π -0.760 0.119 -0.785 0.122 0.220e 0.000 0.000 0.000 0.000 0.000etot 0.950 -0.149 0.981 -0.152 0.975
Sticky prices (q =0.25), no capital adjustment costs (φ =1)
A G Λ* Xd* Px*Y -1.018 0.536 -2.695 0.298 -0.269C -0.023 0.032 -0.984 0.033 -0.180 I -6.628 1.954 -13.705 1.828 -1.030h -2.388 0.577 -2.872 0.589 0.028πx -0.409 0.060 -0.382 0.061 0.018π -0.327 0.048 -0.306 0.049 0.215e 0.000 0.000 0.000 0.000 0.000etot 0.409 -0.060 0.382 -0.061 0.982
Policy regime: Strict domestic inflation targeting
Sticky prices (q =0.25), no capital adjustment costs (φ =1)
A G Λ* Xd* Px*Y 1.131 0.181 -0.295 -0.066 -0.295C 0.664 -0.085 -0.182 -0.087 -0.182 I 4.711 0.095 -1.193 -0.074 -1.193h 0.184 0.152 -0.003 0.154 -0.003πx 0.000 0.000 0.000 0.000 0.000π 0.190 -0.030 0.195 -0.030 0.195e 0.950 -0.148 0.973 -0.151 -0.027etot 0.949 -0.148 0.973 -0.151 0.973
Table 1b: Elasticities of key variables (Cont.)
Benchmark policies:
Strict domestic inflation targeting (strict DIT) - Reaction coeff.: ρr =0.0, φy =0.0, φπ =1000, φe =0.0
Sticky prices (q =0.25) Flexibel prices (q =1)Shocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.2915 0.0729 0.0766 0.0200 0.2905 0.0728 0.0765 0.0198std (πx ) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000std (π ) 0.0240 0.0029 0.0185 0.0031 0.0240 0.0029 0.0185 0.0031std (etot ) 0.4758 0.0561 0.2721 0.0509 0.4751 0.0561 0.2721 0.0508std (R ) 0.0152 0.0019 0.0010 0.0024 0.0152 0.0019 0.0010 0.0024
welfare -114.9880 -114.9854 -114.9852 -114.9853 -114.9880 -114.9854 -114.9852 -114.9853
PegSticky prices Flexibel pricesShocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.3147 0.0951 0.3129 0.0354 0.3531 0.0749 0.0988 0.0203std (πx ) 0.0468 0.0065 0.0415 0.0066 0.0958 0.0150 0.0998 0.0154std (π ) 0.0374 0.0052 0.0332 0.0053 0.0766 0.0120 0.0799 0.0123std (etot ) 0.4209 0.0424 0.1748 0.0369 0.5048 0.0558 0.2726 0.0514std (R ) 0.0000 0.0000 0.0160 0.0000 0.0000 0.0000 0.0160 0.0000
welfare -114.9967 -114.9861 -115.0068 -114.9860 -114.9887 -114.9854 -114.9858 -114.9853
Rule 1:
Baseline specification: flexible DIT - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =0.0
Sticky prices Flexibel pricesShocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.2690 0.0735 0.0714 0.0173 0.4243 0.1044 0.1086 0.0298std (πx ) 0.2684 0.0647 0.0648 0.0195 0.4159 0.0945 0.1003 0.0312std (π ) 0.2661 0.0654 0.0704 0.0193 0.4129 0.0949 0.1042 0.0309std (etot ) 0.3247 0.0866 0.3056 0.0393 0.4356 0.0652 0.2824 0.0477std (R ) 0.2683 0.0604 0.0616 0.0206 0.4117 0.0895 0.0961 0.0320
welfare -115.1059 -114.9916 -114.9914 -114.9860 -115.2905 -115.0002 -115.0015 -114.9868
Flexible domestic inflation plus terms of trade targeting - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =-0.1
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2715 0.0743 0.0630 0.0184std (πx ) 0.2060 0.0831 0.1163 0.0129std (π ) 0.2035 0.0838 0.1216 0.0128std (etot ) 0.3570 0.0947 0.3373 0.0434std (R ) 0.2087 0.0782 0.1094 0.0145
welfare -115.0592 -114.9957 -115.0046 -114.9856
Table 2a: Performance and welfare of alternative policy regimes
Rule 1 (Cont.):
Flexible domestic inflation plus terms of trade targeting - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =-0.2
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2721 0.0757 0.0555 0.0195std (πx ) 0.1283 0.1058 0.1830 0.0044std (π ) 0.1257 0.1065 0.1882 0.0049std (etot ) 0.3955 0.1043 0.3754 0.0483std (R ) 0.1341 0.1002 0.1719 0.0065
welfare -115.0169 -115.0023 -115.0332 -114.9854
Flexible domestic inflation plus terms of trade targeting - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =-0.3
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2699 0.0781 0.0503 0.0203std (πx ) 0.0424 0.1340 0.2703 0.0068std (π ) 0.0406 0.1348 0.2754 0.0080std (etot ) 0.4416 0.1158 0.4217 0.0543std (R ) 0.0468 0.1277 0.2545 0.0041
welfare -114.9902 -115.0127 -115.0905 -114.9854
Flexible domestic inflation plus terms of trade targeting - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =-0.4
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2632 0.0818 0.0493 0.0207std (πx ) 0.1172 0.1697 0.3863 0.0218std (π ) 0.1196 0.1705 0.3915 0.0226std (etot ) 0.4977 0.1295 0.4787 0.0617std (R ) 0.1029 0.1626 0.3653 0.0184
welfare -115.0028 -115.0296 -115.2023 -114.9859
Flexible CPI inflation targeting (flexible CIT) - Reaction coeff.: ρr =0.0, φy =0.5, φπ =1.5, φe =0.0
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2635 0.0749 0.0795 0.0167std (πx ) 0.2624 0.0660 0.0721 0.0186std (π ) 0.2597 0.0666 0.0761 0.0182std (etot ) 0.3227 0.0861 0.3035 0.0391std (R ) 0.2580 0.0626 0.0745 0.0191
welfare -115.0966 -114.9921 -114.9946 -114.9859
Table 2b: Performance and welfare of alternative policy regimes (Cont.)
Rule 2:
Baseline specification: flexible DIT - Reaction coeff.: ρr =0.3333, φy =0.4, φπ =1.5, φe =0.0
Sticky prices Flexibel pricesShocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.2520 0.0691 0.0759 0.0162 0.2905 0.0727 0.0764 0.0199std (πx ) 0.0337 0.0034 0.0007 0.0032 0.0577 0.0063 0.0042 0.0056std (π ) 0.0232 0.0066 0.0195 0.0022 0.0386 0.0091 0.0219 0.0034std (etot ) 0.4303 0.0613 0.2729 0.0459 0.4758 0.0561 0.2720 0.0509std (R ) 0.0157 0.0026 0.0045 0.0023 0.0292 0.0029 0.0029 0.0035
welfare -114.9869 -114.9853 -114.9852 -114.9854 -114.9890 -114.9854 -114.9852 -114.9853
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr =0.3333, φy =0.4, φπ =1.5, φe =-0.1
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2595 0.0680 0.0688 0.0171std (πx ) 0.0264 0.0045 0.0059 0.0023std (π ) 0.0170 0.0079 0.0256 0.0019std (etot ) 0.4395 0.0632 0.2831 0.0473std (R ) 0.0142 0.0030 0.0046 0.0023
welfare -114.9868 -114.9853 -114.9852 -114.9854
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr =0.3333, φy =0.4, φπ =1.5, φe =-0.2
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2681 0.0668 0.0631 0.0183std (πx ) 0.0187 0.0057 0.0121 0.0014std (π ) 0.0134 0.0094 0.0327 0.0022std (etot ) 0.4497 0.0653 0.2947 0.0488std (R ) 0.0137 0.0033 0.0061 0.0024
welfare -114.9868 -114.9853 -114.9855 -114.9854
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr =0.3333, φy =0.4, φπ =1.5, φe =-0.3
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2783 0.0656 0.0606 0.0197std (πx ) 0.0104 0.0070 0.0188 0.0003std (π ) 0.0159 0.0110 0.0409 0.0030std (etot ) 0.4613 0.0677 0.3079 0.0505std (R ) 0.0144 0.0038 0.0086 0.0027
welfare -114.9872 -114.9853 -114.9861 -114.9853
Table 2c: Performance and welfare of alternative policy regimes (Cont.)
Rule 2 (Cont.):
Flexible CIT - Reaction coeff.: ρr = 0.3333, φy=0.4, φπ = 1.5, φe = 0.0
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2500 0.0695 0.0791 0.0161std (πx ) 0.0345 0.0034 0.0014 0.0033std (π ) 0.0230 0.0062 0.0164 0.0019std (etot ) 0.4280 0.0609 0.2706 0.0456std (R ) 0.0089 0.0031 0.0078 0.0015
welfare -114.9870 -114.9854 -114.9854 -114.9854
Rule 3:
Baseline specification: flexible DIT - Reaction coeff.: ρr =0.6666, φy =0.1, φπ =2.0, φe =0.0
Sticky prices Flexibel pricesShocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.2703 0.0744 0.0885 0.0173 0.2908 0.0729 0.0770 0.0199std (πx ) 0.0154 0.0012 0.0074 0.0020 0.0246 0.0019 0.0117 0.0033std (π ) 0.0103 0.0018 0.0118 0.0013 0.0099 0.0019 0.0122 0.0013std (etot ) 0.4526 0.0543 0.2589 0.0475 0.4759 0.0561 0.2722 0.0509std (R ) 0.0114 0.0018 0.0070 0.0017 0.0161 0.0021 0.0073 0.0024
welfare -114.9869 -114.9854 -114.9855 -114.9854 -114.9880 -114.9854 -114.9853 -114.9853
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr = 0.6666, φy =0.1, φπ =2.0, φe =-0.1
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2739 0.0739 0.0848 0.0177std (πx ) 0.0128 0.0009 0.0055 0.0017std (π ) 0.0122 0.0022 0.0139 0.0016std (etot ) 0.4566 0.0548 0.2626 0.0481std (R ) 0.0129 0.0021 0.0077 0.0019
welfare -114.9870 -114.9854 -114.9854 -114.9854
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr =0.6666, φy =0.1, φπ =2.0, φe =-0.2
Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2778 0.0734 0.0812 0.0181std (πx ) 0.0101 0.0006 0.0036 0.0013std (π ) 0.0148 0.0026 0.0164 0.0019std (etot ) 0.4608 0.0554 0.2665 0.0486std (R ) 0.0148 0.0023 0.0090 0.0022
welfare -114.9872 -114.9854 -114.9854 -114.9854
Table 2d: Performance and welfare of alternative policy regimes (Cont.)
Rule 3 (Cont.):
Flexible domestic inflation plus terms of trade targeting - R. coeff.: ρr =0.6666, φy =0.1, φπ =2.0, φe =-0.3Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2820 0.0730 0.0779 0.0187std (πx ) 0.0073 0.0003 0.0018 0.0010std (π ) 0.0180 0.0030 0.0191 0.0023std (etot ) 0.4652 0.0559 0.2706 0.0493std (R ) 0.0170 0.0027 0.0108 0.0025
welfare -114.9875 -114.9854 -114.9854 -114.9853
Flexible CIT - Reaction coeff.: ρr =0.6666, φy =0.1, φπ =2.0, φe =0.0Sticky pricesShocks to:
A G TOT FDstd (Y ) 0.2684 0.0747 0.0915 0.0172std (πx ) 0.0160 0.0013 0.0076 0.0020std (π ) 0.0067 0.0013 0.0089 0.0009std (etot ) 0.4509 0.0541 0.2574 0.0473std (R ) 0.0102 0.0013 0.0062 0.0015
welfare -114.9871 -114.9855 -114.9857 -114.9854
Strict CPI inflation targeting (strict CIT):
Strict CIT - Reaction coeff.: ρr =0.0, φy =0.0, φπ =1000, φe =0.0
Sticky prices Flexibel pricesShocks to: Shocks to:
A G TOT FD A G TOT FDstd (Y ) 0.2688 0.0761 0.1078 0.0177 0.2905 0.0730 0.0776 0.0199std (πx ) 0.0153 0.0018 0.0115 0.0020 0.0241 0.0029 0.0185 0.0031std (π ) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000std (etot ) 0.4510 0.0531 0.2496 0.0473 0.4761 0.0562 0.2725 0.0510std (R ) 0.0232 0.0028 0.0210 0.0029 0.0122 0.0015 0.0035 0.0019
welfare -114.9887 -114.9855 -114.9876 -114.9854 -114.988 -114.985 -114.985 -114.985
Table 2e: Performance and welfare of alternative policy regimes (Cont.)
Chapter 3
Technology shocks and
employment in open economies
3.1 Introduction
The one-good, one-shock RBC model as described e.g. in King and Rebelo
[23] features a strongly positive correlation between labor input and mea-
sured labor productivity, and this regardless whether technology shocks are
considered to be highly persistent or permanent.1 This prediction contra-
dicts the facts. Hansen and Wright [18] e.g. report estimates of the correla-
tion between total hours worked and measured labor productivity (output
divided by total hours) for quarterly U.S. data. They consider two measures
of total hours (and, thus, productivity) and several sample periods. Their
point estimates are near zero or slightly negative while the individual series
for total hours and productivity are, respectively, strongly and moderately
procyclical.
This anomaly has spurred a vast literature. To illustrate the problem,
consider a labor-supply/labor-demand graph with labor on the abscissa and
real wage on the ordinate. Under perfect competition the real wage equals
the marginal product of labor which – under standard assumptions – is di-
1King and Rebelo [23] discuss the effects of both shocks that have a highly persistent
but not permanent and shocks that have a permanent effect on total factor productivity.
In the case of a permanent positive productivity shock, the long-run effect on labor is
nil. In the short and medium run, however, the effect on labor is strongly positive.
88 CHAPTER 3
rectly proportional to average labor productivity.2 Productivity shocks –
i.e., shifts of the labor demand curve – imply a positive correlation between
labor and the real wage. To get a roughly zero correlation between labor
and real wage, shifts of the supply curve have somehow to be introduced. If
both labor demand and labor supply shocks are active, then the predicted
correlation might be close to zero. This can be achieved, among others, by
augmenting the basic one-good, one-shock RBC model to allow for govern-
ment consumption (compare e.g. Christiano and Eichenbaum [5]).
Modifying the basic one-good, one-shock RBC model to allow for gov-
ernment consumption may improve the model’s ability to produce uncon-
ditional correlations between labor input and average labor productivity
similar to those found in the data. Yet the predicted correlation condi-
tional on an exogenous productivity shock – regardless whether assumed to
be highly persistent or permanent – remains positive and high.
In an influential paper, Gali [13] studies the effects of technology shocks
on labor input in the G7 countries using a bivariate structural vector au-
toregressive model (VAR) approach. Gali’s results can be summarized as
follows: (i) The estimated conditional correlations between the proxy for
labor input and measured labor productivity are negative for technology
shocks and positive for non-technology shocks.3 (ii) The labor proxy shows a
persistent decline in response to a positive technology shock. (iii) Measured
productivity increases temporarily in response to a positive non-technology
shock. Given that standard labor proxies are (strongly) procyclical, Gali
concludes that shocks other than technology shocks must play the dominant
role in business cycles.
In the sense of a robustness check, Gali also estimates a higher dimen-
sional extension of the bivariate VAR including – in addition to labor input
and productivity – real money balances, inflation, and a real interest rate;
the findings for the bivariate VAR are largely confirmed.
The impact of Gali’s work on the profession was rather big, all the more
as independent studies published at about the same time found similar ev-
2For the CRTS Cobb-Douglas production function Yt = ZtNχt K1−χ
t where Yt is out-
put, Zt is total factor productivity, Nt is labor, Kt is capital, and χ ∈ [0, 1] is a parameter,
we have ∂Yt/∂Nt = χYt/Nt.3Examples of non-technology shocks are tax rate changes, demographic changes in
the labor force, and shocks to government spending or the nominal money supply.
3.1. INTRODUCTION 89
idence.4 The subsequent work went into two directions. One route was to
check whether the measured response of labor input on a productivity shock
depends on (or can be explained by) an incorrect specification of the utilized
structural VAR framework. Gali’s identification strategy – which goes back
to Blanchard and Quah [4] – relies on the assumption that only technology
shocks have a permanent effect on measured labor productivity. Uhlig [32]
challenges the theoretical foundations for this assumption and presents a
neoclassical business cycle model in which there are two shocks which may
influence labor productivity in the long run apart from technology shocks,
namely changes to the dividend tax rate and shifts in the preferences. A
second critical point within Gali’s econometric framework is the choice of
the proxy for labor input and its treatment as either a level-stationary or
a difference-stationary variable. Altig et al. [1] estimate a full-fledged New
Neoclassical Synthesis (NNS) model with eight structural shocks; the mon-
etary shock is identified by strategies which are standard in the literature,
the productivity shock is identified as in Gali, and the remaining six shocks
are identified by means of what they call model-based strategies. They
employ average weekly hours worked per person rather than total hours or
employment series as Gali does. If average hours enter the VAR in levels
rather than in first differences, Altig et al. find that labor input rises in
response to a positive technology shock.5
A second route was to accept the Gali evidence but to question the con-
clusion that exogenous variations in technology play a very limited role, if
any, as sources of the business cycle. Collard and Dellas [7], for instance,
argue that the predictions of an RBC model are fairly sensitive to the de-
gree of openness to trade and to the trade elasticity. They underpin their
conjecture by presenting an international RBC model that produces – for
plausible parameter values – conditional correlations between labor input
and productivity of the same sign and magnitude as those estimated by Gali.
Francis and Ramey [12] attain the same goal by modifying a standard RBC
model of a closed economy to allow for habit formation in consumption.
4Basu et al. [2] and Shea [31] investigate Solow-residual based measures of technolog-
ical shocks.5Christiano et al. [6] take up the issue of whether the specification of average hours
worked in levels or in first-differences is more adequate and provide additional evidence.
90 CHAPTER 3
Adding to this body of literature, we extend the discussion in two direc-
tions. First, we add an open-economy block to Gali’s five-variable VAR and
then repeat his analysis. Second, we use – alongside with standard struc-
tural VAR methods – structural vector error correction model (VECM)
methods and then, again, repeat his analysis.
Let us briefly elaborate on the two modifications. As mentioned above,
Uhlig [32] and others argue that there might be sources of long-run stochas-
tic movements in labor productivity other than technology shocks; perma-
nent changes in the capital income tax rate and shifts in preferences are
frequently cited candidates.6 We suggest that within an international con-
text there is yet another potential source of shifts in labor productivity,
which has (to our knowledge) not received much attention in the literature
sofar, namely permanent terms-of-trade shocks. Whatever the empirical
importance of each of these sources might be,7 we cannot exclude that the
shocks identified by Gali are contaminated in that they capture disturbances
other than genuine technological changes. A structural modelling frame-
work which allowed one to disentangle the alternative potential origins of
long-run shifts in labor productivity would therefore be highly desirable.
As a first step towards that end we suggest to repeat Gali’s exercise with
the difference that we include a set of openness variables and then to inves-
tigate whether this modification has an effect on the estimated dynamics
and conditional correlations. In principle, the inclusion of additional vari-
ables allows a more precise identification of the shocks that do not have a
permanent effect on measured productivity (we call them ”non-technology
shocks”). This in turn leads to a more precise identification of the conglom-
erate which – the methodological flaws of the utilized method notwithstand-
ing – we continue to call ”technology shocks”. While Gali in his robustness
6As usual in a business cycle context, we abstract from the possibility of endogenous
technological progress.7In a recent attempt to provide evidence in support of his identification scheme, Gali
[14] compares the co-movement between ”his” shocks and measures of dividend tax rates
(both for the U.S.). He finds that the two series are uncorrelated whereas the very same
shocks are significantly positively correlated with independent measures of technological
change (in particular, those provided by Basu et al. [2]). Gali takes this as evidence in
favor of the view that technology changes are the only empirically relevant kind of shocks
which plausibly induce a permanent shift in measured labor productivity.
3.1. INTRODUCTION 91
check adds variables which make allowance for monetary aspects, we focus
here on variables that capture aspects of international trade and finance
such as net exports and the terms of trade.
In the specification of his higher dimensional VAR, Gali incorporates
two cointegrating relations, one between money and the price level (both in
first differences) and another between the interest rate and changes in the
price level. Although from a theoretical point of view such a proceeding
certainly is justifiable, one can argue that by specifying the number and the
form of the cointegrating relations present in the VAR, more restrictions
are imposed than absolutely necessary.8 Any estimation method which gets
by with less restrictive assumptions should be favored. This is particularly
true when we plan to estimate models for which no priors regarding the
number and the form of the cointegrating relations exist (e.g. the models
including an open-economy block). Therefore, our second modification is
the use of structural VECM rather than standard structural VAR methods.
The estimations are conducted with quarterly data for the G7 countries
(minus Germany) plus Australia, Canada, Switzerland, Spain, and New
Zealand. We utilize employment in manufacturing as a proxy for labor in-
put; all variables are treated as integrated of order one. In a few cases,
the inclusion of openness variables indeed lead to an estimated correlation
between labor input growth and measured labor productivity growth con-
ditional on a positive ”technology shock” which is either close to zero or
negative but not significantly different from zero. However, we cannot dis-
cern a systematic pattern that would indicate a relationship between the
incorporation of international trade aspects and the size of the conditional
correlation coefficient. Moreover, we find that extending the standard struc-
tural VAR framework to the cointegrated case with an arbitrary number of
cointegrating relations and general linear restrictions on the cointegration
space does not alter the Gali evidence.
The remainder of this paper is organized as follows. In section 3.2, we
discuss Gali’s bivariate structural VAR and present our replication results.
In section 3.3, we discuss Gali’s robustness check and present replication
8In Gali [13], the relations are embedded despite the fact that in most cases for-
mal tests indicate that the presumed relations do not belong to the cointegrating space
(compare the technical appendix to Gali’s article).
92 CHAPTER 3
results. In section 3.4, we repeat Gali’s analysis with the two modifications
discussed above and report the main findings. Section 3.5 concludes and
gives directions for future work. Most technicalities are postponed to the
appendices. Appendix 3.A sketches our estimation strategy in connection
with univariate unit root tests. Appendix 3.B contains the applied method
for estimating structural VARs and VECMs and for computing dynamics
and conditional correlations. Appendix 3.C describes the computation of
percentile confidence intervals for the estimated impulse-response functions
and conditional correlation coefficients and appendix 3.D, finally, contains
the model specifications (VAR and VECM).
3.2 Benchmark model
3.2.1 Estimation method
Suppose the economic variables of interest can be expressed as a distributed
lag of some unobserved exogenous shocks, whereby the number of shocks
equals the number of endogenous variables and the shocks are uncorrelated
at all leads and lags. Let xt be a n × 1 covariance-stationary vector of
economic variables. The structural vector moving average (VMA) represen-
tation for xt is given by
xt = A (L) ut (3.1)
where A (L) is a matrix infinite-order lag polynomial and ut is a n×1 vector
of white noise disturbances
E (ut) = 0
E (utu′
τ ) =
Σu for t = τ
0 otherwise
where Σu is a symmetric positive definite matrix.
In Gali’s [13] bivariate model, the first variable is average labor pro-
ductivity in first differences, denoted by ∆(yt − nt) where yt is the natural
logarithm of real GDP and nt is the log of labor input; the second vari-
able is a detrended measure of the log of labor input. The first structural
disturbance is labelled ”technology shock” and the second ”non-technology
shock”. Gali continues by imposing two identifying restrictions. First, the
3.2. BENCHMARK MODEL 93
structural shocks are mutually uncorrelated and their variances are nor-
malized to one (i.e., Σu = In). Second, only technology shocks have a
permanent effect on the (log) level of labor productivity. The latter restric-
tion corresponds to the assumption that the cumulative impulse-response
of the non-technology shock on ∆(yt − nt) must equal to zero, that is, in
[x1,t
x2,t
]=
[A11(L) A12(L)
A21(L) A22(L)
] [u1,t
u2,t
](3.2)
A12(1) is set to 0.9 This sort of long-run identifying restriction requires that
the level of the endogenous variable on which the restriction is imposed
(here: (yt − nt)) is non-stationary but not cointegrated with any of the
other non-stationary endogenous variables in the system (in case the proxy
for labor input turns out to be I(1): with nt). In the case at hand, there
is every reason to believe that (yt − nt) is non-stationary and that it is not
cointegrated with nt.
Gali employs the following series. For the U.S. (sample period: 1948:1-
1994:4), he makes use of real GDP and either total employee-hours in nona-
gricultural establishments or employed civilian labor force. All three series
9To see this, consider the following univariate process (in first-differences)
∆xt = θ (L) εt
where θ (L) is an infinite-order lag polynomial and εt is a white noise variable. The effect
of εt on ∆xt+j is given by∂∆xt+j
∂εt
= θj .
Now, note that
xt+j = xt+j − xt+j−1 + xt+j−1 − xt+j−2 + xt+j−2 − ...
= ∆xt+j + ∆xt+j−1 + ...
Thus, the effect of εt on xt+j (the level) is given by
∂xt+j
∂εt
=∂∆xt+j
∂εt
+∂∆xt+j−1
∂εt
+ ... +∂∆xt
∂εt
+ ...
= θj + θj−1 + ... + θ0
=∑j
i=0θi.
For ε to have no effect on x in the long run, we must have that∑j
i=0θi = 0.
94 CHAPTER 3
are drawn from Citibase. For the remaining G7 OECD countries Canada,
United Kingdom, Germany, France, Italy and Japan (sample periods are
country specific and depend on data availability), he makes use of GDP
(drawn from the OECD Quarterly National Accounts) and employed civil-
ian labor force (drawn from the OECD Quarterly Labor Force statistics).
Gali detrends the measure of labor input in two alternative ways: either
he takes first differences or he removes a fitted linear time-trend from the
original series.
Estimating the bivariate VAR by means of a method similar to the
one described in appendix 3.B provides Gali with estimates of the MA-
coefficients of model (3.1). Based on the estimated MA-coefficients, point
estimates for the impulse response functions (IRF) and the conditional co-
variances and correlations can be computed. The standard errors for the
conditional correlations and the confidence intervals for the IRF are gener-
ated using a Monte Carlo method.
3.2.2 Two critical remarks
Before proceeding by replicating Gali’s results for the bivariate VAR, we
critically assess two key ingredients of the econometric framework.
Sources of long-run stochastic movements in labor productivity
In the basic one-good, one-shock RBC model, there is (as the name says)
only one source of shocks, namely changes in the production function.10 In
richer frameworks, however, there might be sources of long-run stochastic
movements in labor productivity other than technology shocks, from which
we conclude that the assumption upon which Gali’s identification strategy
relies may not be valid and that the identified shocks may contain things
other than genuine technological changes.
Two candidates suggested in the literature are permanent changes in the
dividend tax rate and shifts in preferences (see e.g. Uhlig [32]).11 A further
10While productivity is typically assumed to follow a highly persistent but not per-
manent autoregressive process, the model can readily be extended to the case where
productivity follows a random walk with a positive drift - a typical homework assign-
ment for graduate students.11Note that in the presence of non-distorting taxation, permanent shocks to govern-
3.2. BENCHMARK MODEL 95
source which has not (to our knowledge) received much attention so far
are permanent terms-of-trade shocks. Consider a standard NNS model of a
small open economy such as Kollmann [24]. To simplify matters, suppose
money growth is constant, the exchange rate is flexible, and asset markets
are complete. Moreover, domestic intermediate goods prices are supposed
to be moderately sticky. In response to an unexpected, permanent im-
provement of the terms of trade, final good producers substitute away from
domestic inputs toward foreign inputs, a force, which works in the direction
of a contraction of the domestic intermediate goods production. At the same
time, the terms-of-trade improvement induces a positive permanent wealth
effect (the small open economy needs to export less in order to purchase a
given bundle of imports) and, thus, a permanent rise in consumption and
leisure. The rise in consumption is smoothed by an increase in investment,
which leads in the long run to a higher capital stock. Altogether, the model
predicts a lasting shift of measured labor productivity.
Removing trends from macroeconomic time series Good economet-
ric practice requires that the specification of an econometric model is based
on theory whenever this is feasible. This is particularly true for the choice of
the number and kind of endogenous (an possibly exogenous) variables and
the identification scheme. When theory offers no clear guidelines as is the
case for the choice of the number of lags to be included in a VAR, then our
decision is usually based on statistical inference. Finally, for some aspects
of the empirical model we have no choice other than accepting what the
real world offers us; this is typically true for the choice of the data range.
A related issue is the question about the appropriate way of removing
trends from macroeconomic time series. In principle, macroeconomic time
series may be level stationary, difference stationary, or trend stationary. In
the last two cases, the time trend may be either common or series specific
and it may have structural breaks. It is a well-known fact that the amount
of macroeconomic data is not large enough to get precise information about
the true data generating process; in other words, there is no reliable method
for distinguishing among the alternatives listed above. As a way to cope
with this ambiguity, we follow a rather pragmatic approach, partly based
ment consumption do not belong in this category; see e.g. Baxter and King [3].
96 CHAPTER 3
on empirical evidence, partly based on common sense.
To illustrate our approach, let us have a closer look at the labor proxy
we choose. In the basic RBC model, all of the variation in aggregate hours
arises due to movements in hours per worker (the ”intensive margin”). Yet
movements of individuals in and out of employment (the ”extensive mar-
gin”) seems to be important for understanding aggregate labor supply (see
e.g. Hansen’s [17] seminal study). We are therefore convinced that an ac-
curate proxy for labor input should incorporate the extensive margin.
What we actually would like to have is a measure of total hours worked
in the non-farm business sector.12 However, if we had the choice between a
measure of people with jobs in an economy (the extensive margin only) and a
measure of the individual choice of the number of hours worked for the same
economy (the intensive margin only), we would go for the employment series.
In the case of the OECD MEI data base – the widely accessible data base
we are making use of – this is exactly the situation: There is either a series
of employment or a series of average weekly hours, both in manufacturing.13
We, thus, decide to restrict our investigation on employment.
It remains to be decided how the trend should be removed from the
chosen labor proxy. In principle, there is no theoretical reason against a
time trend in employment in manufacturing. This trend component may
stem from long-run developments on the demand and the supply side of the
labor market, such as changes in the demographic composition (immigration
or a long-run drop in the birth-rate), a rise in real income (and the related
substitution and income effects), shifts in the production structure, etc.
However, in what follows we assume – and here the common sense comes in
– that all time series employed in this study are I(1), including the nominal
12To be more precise, we would like to have a measure of labor services in the non-farm
business sector. But since such a measure is not available, we prefer the proxy total hours
worked. Suppose we knew of each individual in the labor force how many hours he or
she works during a given period. In the aggregate, this gives total hours worked.13Average weekly hours series are available only for a subset of the countries included
in our study; moreover, only the series for the U.S. is of an acceptable quality. When we
experimented with a version of the benchmark model for the USA which involves average
hours series in levels, we got the same result as reported in Altig et al. [1] and others:
The response of hours to a technology shock is positive at all dates; also, the correlation
between measured productivity growth and hours is positive (and significant).
3.2. BENCHMARK MODEL 97
and real variables that might be added to the bivariate VAR in an attempt
to get a more precise measure of what we term technology shocks . It goes
without saying that we conduct standard (univariate) unit root tests, and
in most cases the analysis indeed indicates that the series at hand contain a
random walk component. But we would like to stress that we consider our
basic assumption to hold independent of those test results.
3.2.3 Replication results
In order to replicate Gali’s results for the bivariate VAR, we proceed as
follows:
• Step 1: Data. We obtain data on gross domestic output and employ-
ment in manufacturing for the G7 countries plus Australia, Canada,
Switzerland, Spain, and New Zealand (in what follows abbreviated by
AUS for Australia etc.). The data bases are OECD MEI (mostly) and
IMF (partly). All series (except interest rates) are seasonally adjusted
(where necessary, we apply Census X12).
• Step 2: Univariate analysis. The series (yt − nt) and nt are pretested
in order to assess their order of integration. A description of the test-
ing strategy we follow is given in appendix 3.A. There is only one
country for which the evidence regarding (yt − nt) is mixed, namely
AUS. There is only one country for which the hypothesis that nt is
I(1) has to be rejected, namely ESP.
• Step 3: Model specification. Regardless of the findings of step
2 and as a matter of principle we consider both (yt − nt) and nt as
I(1)-variables. Accordingly, our benchmark model is a VAR in first
differences given by
∆xt = D1∆xt−1 + D2∆xt−2 + ... + Dp∆xt−p + εt
with
xt =[
(yt − nt) nt
]′
where p is the number of lags in the model, and εt is an 2 × 1 vector
containing the reduced form residuals which are assumed to be white
98 CHAPTER 3
noise. In order to determine the number of lags, we follow Enders [10],
p. 396, and estimate the reduced form VAR using the undifferenced
(non-stationary) data.14 We then apply a classical LR test (or pairing
down lag length strategy).15 The sample period, finally, is country
specific and depends on data availability. In some cases, data avail-
ability is limited in such a way that we have to do without a particular
series or a particular country. For instance, the time series for GER
only start with the reunification and in our view are too short for the
purpose of model estimation.
• Step 4a: Estimating impulse response functions (IRF) and
the conditional correlations (CC) – the former in terms of levels,
the latter in terms of growth rates. For a description of the applied
estimation method see appendix 3.B.
• Step 4b: Computing bootstrap confidence intervals (CI) for
the IRF and the CC. In our view it is not meaningful to display
standard errors for the CC. A correlation has a lower and an upper
bound (i.e., a truncated distribution). For this reason we prefer to
display percentile confidence bands (for a description of the applied
bootstrap method see appendix 3.C). However, to ensure compara-
bleness between Gali’s results and ours we will also display standard
errors.
Let us now turn to the replication results for the benchmark specifica-
tion (figure 1 and table 1). For each country investigated, we report the
dynamic response of employment to a technology shock (in terms of per-
centage deviations from average) with 5 and 95% confidence bands over
almost 5 years (beginning with t = 0) and the correlation between labor
productivity growth and employment growth conditional on a technology
shock with 5 and 95% percentile points. For each model specification, we
start with a rather detailed discussion of the results for the USA. We then
go on by discussing the rest of the G7 OECD countries minus Germany
14This procedure is standard in the univariate case (compare e.g. Hamilton [16], p. 553
or table 17.3). The argumentation carries over to the vector case.15We are careful and use a rather small size of tests (since the type one error cumulates).
3.2. BENCHMARK MODEL 99
(CAN, FRA, GBR, ITA, JPN) and, finally, the additionally investigated
OECD countries (AUS, CHE, ESP, NZL).
USA For the USA, both the estimated dynamics and the value for the
correlation between measured labor productivity growth and employment
growth conditional on a technology shock (CC), are pretty much in line with
the corresponding results reported in Gali [13] and in the technical appendix
that comes along with the article. A positive technology shock leads to a
negative and significant response in period 0 and 1. The response remains
negative but gets insignificant from period 2 after the shock onwards. The
estimated CC is negative and significant (-.82 compared to -.84 in Gali).
Note that the CI does not cover the point estimate; for an explanation and
a possible remedy compare appendix 3.C.
FRA, GBR, and ITA For FRA, we observe a j-shaped response of em-
ployment to a technology shock.16 After a weakly negative impact effect,
employment decreases for a couple of periods, then begins to rise, returns
to its average, and eventually gets positive (after about 3 years). For GBR
and ITA, on the other hand, the response of employment remains nega-
tive over the entire horizon. This general picture corresponds to the results
reported in Gali. Since our bootstrapped confidence bands are somewhat
narrower than those computed by Gali, the responses for FRA and GBR
are significant not only on impact and for the subsequent two periods but
for the first three to four periods. For ITA, the negative effect is significant
even over the entire horizon.
For GBR, the estimated CC is close to the corresponding value reported
by Gali (-0.87 compared to -0.91). For FRA, our point estimate is higher
(-0.31 compared to -0.81) while it is lower for ITA (-0.96 compared to -0.41).
In all three cases, the point estimates are significantly different from zero
(in the case of FRA where the 0.95 percentile point is -0.01 rather narrowly,
though). Note that the bootstrapped standard deviations are significantly
lower than those reported by Gali.
16FRA is the only country for which Gali utilizes detrended employment rather than
employment in first differences. Preliminary experiments lead us to follow suit; however,
unlike Gali we use the Hodrick-Prescott filter to remove the trend.
100 CHAPTER 3
CAN and JPN For all the investigated countries except CAN and JPN,
Gali finds a significantly negative response, at least on impact. We therefore
prefer to discuss the two countries CAN and JPN separately within the G7-
block. For both countries, the impact effect is negative but insignificant.
Employment rises quickly and turns positive in period 1 or 2; it remains
so in the medium and long run. In the case of JPN, the positive long-run
effect is actually significant.
For CAN, the estimated CC is higher than the corresponding value re-
ported by Gali (-0.27 compared to -0.59) and insignificant. For JPN, the
CC is somewhat lower than the value reported by Gali (-0.12 compared to
-0.07) but still insignificant. Note that for JPN the bootstrapped standard
deviation is clearly larger than the value reported by Gali (0.28 compared
to 0.08).
AUS, CHE, ESP, and NZL The response of employment for AUS and
CHE is similar to the one for FRA and GBR; the dynamics for ESP and
NZL are comparable to the one for ITA. In all four cases, the estimated
CCs are significantly negative. The variability is rather small for AUS and
ESP (about the same size as for GBR) and somewhat larger for CHE and
NZL (about the same size as for the USA).
Summary The replication results for the benchmark specification largely
confirm Gali’s findings. For the USA and GBR, the estimated dynamics
and the CC are in line with the corresponding point estimates reported by
Gali. For CAN, FRA, ITA, and JPN, the results coincide in qualitative
terms.
3.3 Nominal block
3.3.1 Estimation method
In order to check robustness, Gali augments the basic VAR by a nominal
block consisting of log nominal money (e.g. M1), the log price index (e.g. the
GDP deflator), and a nominal interest rate (e.g. the 90-day money market
rate) – denoted by mt, pt, and rt, respectively.
3.3. NOMINAL BLOCK 101
The extension of model (3.2) to the case of more than two variables is
straightforward. In this event, x2,t is no longer a scalar but an (n − 1) × 1
vector of variables which enter the model for theoretical or empirical rea-
sons. The n×1 vector xt of endogenous variables is still driven by the same
two structural disturbances. Matrices A21(L) and A22(L) have the appro-
priate dimensions. To identify the extended VAR, Gali makes the following
assumptions: (i) The conglomerate we term technology shock is orthogonal
to each of the n − 1 non-technology shocks; (ii) only the technology shock
has a long-run effect on (yt − nt); (iii) the n − 1 non-technology shocks
are orthogonal to each other. Given this set of assumptions, the structural
representation (3.2) can be recovered from the reduced form VAR to be
described below.
Note that assumption (iii) is completely arbitrary. This poses no prob-
lem as long as the (squared) MA-coefficients are finally added up – which
is the case in the process of computing the correlation conditional on an
aggregated non-technology shock (the sum of the components driven by
the n − 1 individual non-technology shocks). The response function to the
aggregated non-technology shock, however, is sensitive regarding alterna-
tive identification schemes. For instance, it makes a difference whether the
individual non-technology shocks are identified by means of an arbitrary
short-run identifying assumption (as is the case here) or an equally arbi-
trary long-run identifying assumption. But since in this study we entirely
focus on the IRF to and the correlation conditional on a technology shock,
this issue is not a concern for us.
According to the technical appendix that comes with Gali’s paper, uni-
variate analysis of the data on ∆pt, ∆mt, and rt indicates that all three series
can be characterized as I(1) variables. Further univariate analysis lead Gali
to the conclusion that ∆mt and ∆pt as well as rt and ∆pt+1 are cointe-
grated with cointegrating vectors [1,−1] (implying stationary processes for
∆ (mt − pt) and (rt − ∆pt+1), respectively).
As further reported in the technical appendix to Gali, cointegration tests
(Johansen procedure based on the trace statistic) on the five variable vector
xt = [(yt − nt) , nt, ∆mt, ∆pt, rt]′
point to the presence of a cointegration rank equal to 2 (which is consistent
102 CHAPTER 3
with the previous conjecture).17 However, tests of the joint hypothesis that
the vectors [0, 0, 1,−1, 0] and [0, 0, 0, 1,−1] belong to the cointegration space
are rejected.18 Nevertheless, Gali continues by estimating a reduced form
VAR with
xt =[
∆ (yt − nt) ∆nt ∆ (mt − pt) ∆2pt rt − ∆pt+1
]′.
3.3.2 Replication results
In order to replicate Gali’s results for the higher-dimensional structural
VAR, we proceed as follows.
• Step 1: Data. We come up with series for the GDP deflator, narrow
nominal money (mostly M1, in some cases M0), and the nominal
interest rate (3 month money market rate and 10-year government
bonds) for the OECD countries included in our study.
• Step 2: Univariate analysis. The series ∆pt, (rt − ∆pt+1), and
(mt − pt) are pretested. There is only one country for which the hy-
pothesis that (mt − pt) has a unit root and a drift has to be rejected,
namely ESP. The hypothesis that ∆pt has a unit root has to be re-
jected (or at least the evidence is mixed) for CAN, ITA, and NZL. And
finally, the hypothesis that (rt − ∆pt+1) is I(1) cannot be rejected for
AUS, FRA, JPN, and USA.
• Step 3: Model specification. Regardless of the findings of step 2
and as a matter of principle we consider ∆pt, (mt − pt), and rt as
17The reported test results refer to U.S. data; labor input is measured by total hours
worked. Note that (rt − ∆pt) is not precisely equal to (rt − ∆pt+1).18In terms of the VECM specification
∆xt = Πxt−1 +∑p−1
i=1Γi∆xt−i + εt
Gali imposes the restriction
Π =
[0 0 1 −1 0
0 0 0 −1 1
].
3.3. NOMINAL BLOCK 103
I(1)-variables. The reduced form VAR(p) is given by
xt = D1xt−1 + D2xt−2 + ... + Dpxt−p + εt
with
xt =[
∆ (yt − nt) ∆nt ∆ (mt − pt) ∆2pt rt − ∆pt+1
]′
where εt is assumed to be white noise. Lag-length is tested for
xt =[
(yt − nt) nt (mt − pt) ∆pt rt
]′.
The sample period is country specific and depends on data availability.
• Step 4: Estimating IRF and CC and computing bootstrap
CI. For a description of the applied estimation method see appendix
3.B. A description of the applied bootstrap method can be found in
appendix 3.C.
The results for the original five-variable VAR (hereafter ”VAR 0”) are
contained in figure 2 and table 1.
USA Again, we start by discussing the results for the USA. When looking
at the response of employment to a technology shock for ”VAR 0” reported
by Gali, the first thing which catches ones eye is that the confidence band is
clearly narrower compared to the benchmark specification. Moreover, the
response has a pronounced j-shaped form: After a modest negative impact
effect, employment continues to drop in period 1, then returns to its average,
and eventually turns positive (from period 7 onwards).
We observe a similar pattern. After a negative impact effect, employ-
ment further declines in period 1 and 2 and then rises and eventually turns
positive, but not as much as in Gali.19 In the long run (from 2 to 3 years
after the shock onwards), employment falls back below average on a level
that is less negative than in the case of the benchmark model. (We suppose
this is also the case for Gali’s estimation but we cannot tell since he chooses
19The negative effect on employment is significant for periods 0 to 2, as in the bench-
mark model.
104 CHAPTER 3
a horizon of just 3 years.) Also, the confidence band is somewhat narrower
than for the benchmark specification.
According to Gali, there is barely a difference between the CC estimates
for the two model specifications (-.82 for ”VAR 0” compared to -.84 for the
benchmark model). As far as our replication results are concerned, the point
estimate for CC is less negative compared to the benchmark specification
(-.66 compared to -.82), but still significant. The width of the bootstrapped
CI for the two model specifications differ only slightly. Note that the boot-
strapped standard deviation of .21 is rather large compared to the (very
small) .08 reported by Gali.
FRA, GBR, and ITA In the case of FRA, going from the bivariate to
the five-variable VAR gives rise to a widening of the confidence band, in
particular in the short run. As a consequence, the negative impact effect is
not significant any more. Moreover, the j-shaped response which we have
observed for the benchmark specification disappears. The medium- and
long-run effect on employment now is negative, albeit insignificantly. In the
case of GBR, the inclusion of additional variables gives rise to a j-shaped
response. While in the benchmark specification employment was below
average over the entire horizon, it now begins to rise in the medium run
and becomes positive in the long run. The positive long-run effect is not
significant, though. In the case of ITA, the inclusion of additional variables
seems to have no effect on the response of employment.
In the cases of GBR and ITA, the estimated CCs are close to the respec-
tive point estimates for the benchmark model and highly significant. The
variability gets somewhat bigger for GBR whereas for ITA it remains rather
small. For FRA, the point estimate is lower (i.e., more negative) compared
to the benchmark model; at the same time, the CI becomes wider such that
the CC is not significantly different from zero any more.
CAN and JPN For CAN, the impact effect is still insignificant. The
subsequent rise is less pronounced; so is the (insignificant) positive long-run
effect. The estimated CC is somewhat lower than for the benchmark model
but remains insignificant. For JPN, the only effect from augmenting the
VAR which we can discern is that the estimated CC now is positive (while
3.4. EXTENSIONS 105
it was weakly negative for the benchmark specification).
AUS, CHE, ESP, and NZL In the case of the remaining OECD coun-
tries investigated, the CC estimates are close to those for the respective
benchmark models. In the case of CHE, the confidence bands tend to be-
come narrower compared to the benchmark specification, while in the cases
of AUS and NZL they tend to become wider. (In the case of ESP, there is
no effect observable with respect to the bootstrapped confidence bands.)
Summary The findings for the bivariate VAR are largely confirmed. In
the case of the USA, the estimated CC is somewhat less negative than both
the value we got for the benchmark model and the corresponding value
reported by Gali, but still significant.
3.4 Extensions
3.4.1 Open-economy block
In the introduction, we argued that – despite the methodological flaws of
the utilized identification strategy and in the sense of an explorative study
– we want to check the robustness of the Gali evidence to the inclusion
of variables that capture aspects of international trade and finance. Our
choice of openness variables is partly based on theoretical models of small
open economies such as Kollmann [24]; it involves the current account bal-
ance (cat) and the terms of trade (tott).20 Unfortunately, for a number of
countries the series cat is too short for the purpose of model estimation
(this is the case for ESP, FRA, and ITA). Apart from that, for some of the
countries for which the series cat is available, its quality is questionable.
Therefore, we utilize the main component of the current account, the trade
balance (or net exports, nxt), in addition or as a proxy to the series cat.
This, and the fact that we are interested in the effect of the inclusion of
each individual international trade and finance variable lead us to estimating
a number of different model specifications (for a detailed description see
20We say ”partly” since a pure model-based approach would include the world interest
rate and possibly the world price level as an exogenous variable.
106 CHAPTER 3
appendix 3.D). Note that in some of these specifications we omit money from
the model. In our view, this is justifiable as most central banks nowadays
use a short-term nominal interest rate as their policy instrument. Therefore,
monetary aggregates such as M1 have lost some of their importance for the
conduct of (and the measurement of exogenous shocks to) monetary policy.
Adding an open economy block to Gali’s extended VAR involves the
following steps:
• Step 1: Data. We come up with series for the real effective exchange
rate,21 net exports, and the current account balance for the OECD
countries included in the set.
• Step 2: Univariate analysis. The series tott, nxt, and cat are
pretested. There is no country for which the hypothesis that tott fol-
lows a random walk (with or without drift) has to be rejected. There
are a few countries for which the hypothesis that nxt follows a ran-
dom walk without drift can be rejected (or at least the evidence is
mixed), namely AUS, GBR, JPN, and NZL. There are a few coun-
tries for which the hypothesis that cat follows a random walk without
drift can be rejected (or at least the evidence is mixed), namely AUS,
GBR, and NZL.
• Step 3: Model specification. Regardless of the findings of step 2 and
as a matter of principle we consider tott, nxt, and cat as I(1)-variables.
Moreover, we assume (for the time being) that ∆mt and ∆pt on the
one hand and rt and ∆pt+1 on the other hand are cointegrated with
cointegrating vectors [1,−1].
• Step 4: Estimating IRF and CC and computing bootstrap CI.
Same as in subsection 3.3.2.
The results for the structural VAR specifications including international
trade and finance variables (”VAR 1” to ”VAR 7”) are contained in figure
3 and 4 and in table 1. For details on the specifications compare appendix
3.D.
21As a matter of fact, the ratio of the import deflator to the export deflator would
have been the better proxy.
3.4. EXTENSIONS 107
USA As usual we start with reporting the results for the USA. Above,
we have pointed to the j-shaped response of employment which we observed
for Gali’s five-variable specification (”VAR 0”). This general pattern is not
preserved for the VARs including international trade and finance variables,
at least not for the larger ones. We make the following observations. First,
the inclusion of more variables leads to an upward shift of the impact effect.
Since the width of the confidence bands remains almost unaltered across
the alternative VAR specifications, we conclude that the more variables
are incorporated in the model the more likely it is that the impact effect
is insignificant. Second, while for ”VAR 0” the response of employment
to a technology shock gets positive after about 3 years, employment does
never hit the zero-line in the case of the seven specifications incorporating
openness variables. Finally, the negative (and insignificant) long-run effect
is more pronounced than it was for ”VAR 0”.
What about the CC estimates? For the models which do not include the
variable tott (i.e., ”VAR 1”, and ”VAR 2”), the CC remains clearly negative.
Since the CI is only moderately wider compared to the benchmark case, the
point estimates are significant, albeit narrowly. The inclusion of the variable
tott, however, leads to a significant widening of the CI such that for ”VAR
3” through ”VAR 7” the point estimates get insignificant. Moreover, for
the larger models, the CC is less negative and reaches values of about -0.2
to -0.3.
FRA, GBR, and ITA In the case of FRA, the inclusion of tott brings the
j-shaped response back (which we observed for the benchmark specification
and which got lost for ”VAR 0”). At the same time, the confidence bands
tend to become wider the larger the VAR is. For GBR, we observe no such
widening of the confidence bands. Interestingly, the inclusion of either cat
or nxt leads to a significant (negative) long-run effect, while in the medium
run the (negative) response is insignificant; incorporating tott brings about
a reversion of this pattern. In the case of ITA, the permanent (negative)
effect is a little bit less pronounced for the extended VARs and in some
cases the effect is barely significant (the width of the confidence band is
stable across the specifications).
In the case of FRA, the estimated CC for ”VAR 4” and ”VAR 6” is about
108 CHAPTER 3
as weakly negative as for ”VAR 0”; the point estimates are insignificant for
all considered specifications. In the cases of GBR and ITA, the findings for
CC are robust to the inclusions of openness variables.
CAN and JPN In the case of CAN, the inclusion of cat (or nxt) together
with tott in ”VAR 0” gives rise to a positive (albeit insignificant) impact
effect. Moreover, we observe a positive and significant medium to long-run
effect for ”VAR 1” and for the model versions which include tott but omit
∆mt. The weakly negative CC is insignificant for all seven specifications.
In the case of JPN, we observe no effect whatsoever.
AUS, CHE, ESP, and NLZ In the case of AUS, CHE, and ESP the
inclusion of international trade and finance variables does not affect the
response of employment, whereas in the case of NZL the inclusion of both
tott and cat lifts the impulse response considerably over the entire horizon.
While we have observed a pronounced and significant negative long-run
effect for the benchmark model and ”VAR 0”, the long-run effect now is
much weaker and not different from zero any more.
In the cases of AUS, CHE, and ESP, we hardly observe any effect on the
CC estimates whereas in the case of NZL the same value becomes narrowly
significant when tott is included (”VAR 3”) and – due to a pronounced
widening of the CI – insignificant for specifications which include cat (”VAR
2”, ”VAR 5”, and ”VAR 7”).
Summary In case of the USA, we observe for models which do not include
the variable tott a CC which is clearly negative and (narrowly) significant.
The inclusion of the variable tott leads to a pronounced widening of the
CI; the point estimates (which are less negative for the larger models) get
insignificant. For most of the remaining OECD countries included in our
set, the CC is negative and significant across all alternative specifications.
The only exceptions are CAN, JPN and FRA, for which the estimated CC
is insignificant across all alternative specifications and NZL, for which we
get an insignificant point estimate for models which include cat.
3.4. EXTENSIONS 109
3.4.2 Structural VECM approach
In a last step, we extend the previous two robustness checks (which involved
the addition of a nominal and an open-economy block) to the cointegrated
case with an arbitrary number of cointegrating relations and general linear
restrictions on the cointegration space. So far, we have (for all specifica-
tions) assumed that there are exactly two cointegrating relations with a
very specific form (see subsection 3.3.1). This restriction is now going to
be relaxed. To this aim, we apply a two stage procedure which involves the
following modifications:
• Step 3: Model specification. Consider the VECM
∆xt = Πxt−1 +∑p−1
i=1Γi∆xt−i + εt. (3.3)
where εt is assumed to be Gaussian white noise. All variables that
enter xt are assumed to be I(1). For lag-lenth determination we esti-
mate a VAR using the non-stationary xt (compare above). Then, in
a first stage, we perform a rank test (for details regarding the testing
strategy compare appendix 3.D).
• Step 4: Estimating IRF and CC and computing bootstrap CI.
In a second stage, we set the rank of Π in model (3.3) according to
the test results of the modified step 3 (the vectors are normalized
reasonably) and estimate the VECM with the estimation method for
structural VARs extended to the cointegrated case (compare appendix
3.B). This provides us with estimates of the MA-coefficients in model
(3.2), on the base of which we can compute point estimates of the IRF
and the CC and, finally, a measure for the estimation variability.
The findings for the VECM version of Gali’s five-variable specification
(henceforth ”VECM 0”) and for the various extensions (”VECM 1” through
”VECM 7”) can be found in figure 5 to 6 and in table 2. For half of the
countries investigated, the test results do not point out to the presence of
a cointegration rank equal to 2; these countries include AUS, ESP, FRA,
GBR, NZL, and the USA. For the countries for which the hypothesis of
rank 2 cannot be rejected, there is virtually no case for which the joint
hypothesis that the vectors [0, 0, 1,−1, 0] and [0, 0, 0,−1, 1] belong to the
cointegration space cannot be rejected.
110 CHAPTER 3
USA In the case of the USA, the response of employment to a technology
shock for ”VECM 0” can be summarized as follows. Compared to both the
benchmark model and the restricted counterpart ”VAR 0”, the decrease
after the (moderately) negative impact effect is more pronounced and more
prolonged. In the medium to long run, employment reverses as in ”VAR
0”, but then remains negative. The confidence band is rather wide. For
”VECM 1” the response is similar to the one for ”VECM 0”, while for
”VECM 2” (which involves cat) we observe a long-run response which is
somewhat more negative and a confidence band which is wider than for
”VECM 0”.
For ”VECM 3” and ”VECM 5” (which include, respectively, tott and
tott in combination with cat) we observe something like an inverted j-shaped
response in that the effect is positive on impact, then rises over the medium
run, and eventually gets negative. However, for both specifications the
dynamic response features a weak negative trend, which suggests that the
growth rate rather than the level of the series is affected by the shock. This
anomaly makes us suspicious and in what follows we disregard the evidence
for the concerned specifications.22
For ”VECM 4” and ”VECM 6” (which contain tott in combination with
nxt) the negative impact effect is less pronounced than for ”VECM 0”.
Moreover, we observe no subsequent decline in employment. For both spec-
ifications, only the impact effect is (narrowly) significant. For ”VECM 7”
(which involves mt in addition to tott and cat), we observe the same inverted
j-shaped response as for ”VECM 3” and ”VECM 5”; but now, the dynamic
response on employment converges in the very long-run to an admittedly
rather low value (-0.9).
What about the CC estimates? As can be read off the relevant table,
relaxing the number and kind of cointegrating relationships alone (”VECM
0”) leads to a modest widening of the CI. At the same time, the point
estimate rises to -.42 (compared to -.66 for the unrestricted version ”VAR
0”). Together this implies that the CC is not significantly different from
zero any more. Adding either nxt or cat and omitting mt (”VECM 1” and
”VECM 2”) brings about a further increase in the point estimate, while
22We would like to stress here that within the entire set of countries and model speci-
fications these are the only two cases where such a problem arises.
3.4. EXTENSIONS 111
the width of the CI is comparable to the one for ”VECM 0”. Adding tott(”VECM 4” and ”VECM 6”), however, leads to a significant decrease of the
point estimate to a value in the neighborhood of the one observed for the
benchmark model, while the CI still remains unaltered. Accordingly, the
negative correlations for ”VECM 4” and ”VECM 6” are only marginally
insignificant.
Remaining OECD countries in the set In the case of FRA, the impact
effect for ”VECM 0” is zero; thereafter, the response gets positive and sig-
nificant (even in the long run). Skipping mt and adding openness variables
leads to a moderately negative impact effect. The estimated CC is positive
for ”VECM 0” and weakly negative for the other VECM specifications; none
of the point estimates is significant. In the case of GBR, the response of
employment for ”VECM 0” is similar to the one for the benchmark model.
Within the specifications which include tott, employment gradually returns
to the long-run equilibrium. The CCs are significantly negative for all spec-
ifications.
In the case of CAN, the employment response estimated for ”VECM
0” is moderately negative on impact – as for ”VAR 0” –, but then quickly
gets positive and remains so in the long run. The inclusion of tott together
with either cat or nxt leads to a pronounced upward shift of the short-
run response. For the remaining countries (AUS, CHE, ESP, ITA, JPN,
NZL), the effect of relaxing the rank assumption and introducing additional
variables is modest (if anything).23
What about the estimated CCs? In the case of AUS, CHE and ITA, the
CCs are significantly negative for all specifications, as for CAN and JPN
the CCs (some of which are positive) are always insignificant. In the case
of NZL, the inclusion of nxt leads to a moderate widening of the CI; for
those specifications, the point estimates are not significantly different from
zero. Note that the pronounced widening of the CI which we observed for
the VAR specifications involving cat is not apparent anymore.
23Within this subset of countries, there is exactly one specification for which we observe
a j-shaped response, namely ESP ”VECM 1”, rank 3.
112 CHAPTER 3
Summary In the case of the USA, relaxing the number and kind of cointe-
grating relationships and including international trade and finance variables
leads for the smaller models (which do not include tott) to an estimated CC
which is close to zero. For the larger models (which include tott) the point
estimate is in the neighborhood of the one reported for the benchmark
specification, while the CI is wider compared to the benchmark case such
that the estimated negative correlation are marginally significant. For the
majority of the investigated countries, however, the finding that the CC is
negative and significant is robust across the alternative specifications. Only
for CAN, FRA, and JPN we find nonsignificant point estimates; but this
finding too is robust across the alternative specifications.
3.5 Conclusions
In this paper, we raised the question whether the negative response of em-
ployment to productivity shocks estimated by Gali [13] is robust to the
inclusion of international trade and finance variables and to relaxing the
restrictions on the number and kind of cointegrating relationships imposed
in Gali’s higher-dimensional VAR framework. Results based on quarterly
data for a set of 10 OECD countries suggest that there is no systematic
relationship between the provision for variables that catch openness aspects
and the size of the conditional correlation coefficient. Also, we find that
going from a standard structural VAR approach to a two stage procedure
within a VECM framework does not alter Gali’s evidence.
On several occasions we have pointed to the fact that, since the shock we
identify is in principle a conglomerate of disturbances which permanently
affect measured labor productivity, any inference referring to an accurately
measured, genuine technology shock is likely to be distorted. In a follow-
up project to this study, we plan to disentangle the potential sources of
long-term shifts in average productivity, with particular emphasis on the
discrimination between technological and terms-of-trade disturbances. This
will require incorporating openness variables (as we did in this study) and
making additional identifying assumptions.
We have also pointed to the fact that employment in manufacturing, the
series which we made use of, is not an ideal proxy for overall labor input.
3.5. CONCLUSIONS 113
Drawing on more specific data bases should allow us to repeat the exercise
with total hours in non-farm business activities, at least for the subset of
the countries investigated in our study for which such a series exist. In the
case of Switzerland, for instance, we are aware of two (inofficial) estimates
of total hours, whereas in the case of the U.S. we could utilize the same
series as Gali [13] does (drawn from Citibase).
114 CHAPTER 3
3.A Univariate unit root tests
In practice, the specification of a time series process is carried out empir-
ically by means of unit root tests. As it is well known, the asymptotic
distributions of statistics from regressions involving unit roots are sensitive
to the presence of deterministic regressors. It matters whether we include
an intercept, an intercept plus a time trend, or neither an intercept nor
a time trend (see e.g. Hamilton [16]. As a consequence, one has to fol-
low a full-fledged estimation strategy rather than computing a single test
statistic. The testing strategy we apply is a pragmatic one and provides an
alternative to more involved (but in our view more error prone) strategies
as proposed e.g. by Enders [10]; it is largely based on Elder and Kennedy
[9].24
A crucial element of Elder and Kennedy’s testing strategy is making use of
prior knowledge regarding the growth status of a series based on theory.25 In
the case at hand, we presume that (yt −nt) is growing, that the status of nt
(measured by employment) is unknown, and that HP-filtered employment
is by definition not growing. Our priors for the other series are: (i) mt,
(mt − pt): growing, (ii) nxt, cat, ∆pt, (rt − ∆pt+1): not growing, (iii) tott:
unknown status (that is – as with employment – we cannot rule out that
there is some kind of growth, either positive or negative).
Another well-known fact is that in the presence of structural breaks, the
ADF and PP test statistics are biased toward the nonrejection of a unit
root (compare e.g. Enders [10], pp. 243-251). We suspect that some of the
series might indeed exhibit trend breaks. However, unit root tests that allow
for the presence of structural breaks assume that we know something about
when the break occurs (either on theoretical or on empirical grounds), but
in the case at hand we have no clue. Similar reasoning holds in the presence
of heteroscedasticity. We conclude that our test results might be biased
24We have to extend Elder and Kennedy [9] in some respects, among others in order
to permit the case where a series is integrated of higher order. A detailed description of
the applied testing strategy is available upon request.25Elder and Kennedy [9] also mention inspecting the data as a source of prior knowl-
edge. However, we trust more in theory than in visual checks.
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 115
toward the nonrejection of a unit root.
3.B Estimation of structural VARs and
VECMs
Lenz [26] proposes a rather flexible method for estimating structural VARs
with a wide range of identification schemes. In subsection 3.B.1, we present
Lenz’s original estimation method for the non-cointegrated case. In subsec-
tion 3.B.2, we extend the method to the cointegrated case, thereby drawing
on results provided by Hoffmann [20] and Johansen [21].
3.B.1 Non-cointegrated case
Notation
Consider the covariance-stationary reduced form VAR(p)
D (L) xt = εt (3.4)(I − D1L − D2L
2 − ... − DpLp)xt = εt
xt = D1xt−1 + D2xt−2 + ... + Dpxt−p + εt
where xt is a n × 1 vector of economic variables, D (L) is a matrix finite-
order lag polynomial, and εt is a n × 1 vector of reduced form disturbances
which is characterized as follows
E (εt) = 0
E (εtε′
τ ) =
Σ for t = τ
0 otherwise
where Σ is a symmetric positive definite matrix.26 If |D (L) | has all its
characteristic roots greater than one in modulus, it is invertible and there
26In practice, of course, we allow for deterministic variables.
116 CHAPTER 3
exists a reduced form VMA representation
xt = C (L) εt
xt =(I + C1L + C2L
2 + ...)εt
where C (L) = D (L)−1.
Also, consider the structural VAR (p)
B (L) xt = ut(B0 − B1L − B2L
2 − ... − BpLp)xt = ut
B0xt = B1xt−1 + B2xt−2 + ... + Bpxt−p + ut
where E (utu′
t) = In. If B (L) is invertible there exists a structural VMA
representation
xt = A (L) ut
xt =(A0 + A1L + A2L
2 + ...)ut
where A (L) = B (L)−1.
Some useful corollaries
Substituting A (L) ut for xt in B (L) xt = ut yields ut = B (L) A (L) ut. It
follows that27
B0A0 = I.
Moreover, from A (L) = B (L)−1 follows that
A (1) = B (1)−1 .
Combining xt = C (L) εt and xt = A (L) ut yields
A (L) ut = C (L) εt. (3.5)
27From the fact that there are no lags on the right hand side of
ut =(B0 − B1L − B2L
2 − ... − BpLp) (
A0 + A1L + A2L2 + ...
)ut,
we conclude that B0A0 = I while the other terms equal zero.
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 117
As (3.5) must hold for all t (and C0 = I), we have
A0ut = εt.
Substituting A0ut for εt in (3.5) yields
A (L) ut = C (L) A0ut
from which follows that A (1) = C (1) A0. Moreover, as A (L) ut = C (L) A0ut
must hold for all t, we have
Ai = CiA0 for i = 1, 2, ...
Key idea
The key idea of Lenz’s estimation method is to perform an orthogonal de-
composition of the observed residuals based on a total of n (n − 1) /2 re-
strictions on A0, B0, A (1), and B (1). This decomposition is accomplished
in two steps.
Step 1: Defining and computing S and defining Q
Let S be the lower triangular Cholesky decomposition of Σ, i.e., a lower
triangular matrix satisfying
Σ = SS ′.
Moreover, let Q be an arbitrary orthogonal matrix, i.e., a matrix satisfying28
Q′Q (= QQ′) = I and Q−1 = Q′.
From A0ut = εt follows that
E (εtε′
t) = E (A0utu′
tA′
0)
Σ = A0A′
0.
28In step 2, it will be shown that Q is uniquely determined – up to the sign of the
diagonal elements.
118 CHAPTER 3
Making use of the two matrices S and Q, we can derive a new expression
for A0 as follows
A0A′
0 = SQ (SQ)′ .
We end up with
A0 = SQ.
Step 2: Computing Q
In general, restrictions can be imposed on each of the four matrices A0,
B0, A (1), and B (1). We begin by expressing each of these four matrices
in terms of S, Q, and C (1). First, recall that A0 = SQ. Second, from
B0A0 = I we obtain
B′
0 = (S ′)−1
Q.
Third, from A (1) = C (1) A0 we immediately get
A (1) = C (1) SQ.
Finally, from B (1) = A (1)−1 we get
B (1)′ =[[C (1) S]′
]−1Q.
Let H be an n× 4n selection matrix whose function is to choose the appro-
priate restrictions on A0, B′
0, A (1), and B (1)′ (what is meant by ”choosing
the appropriate restrictions” will become clear further below), that is
H
S
(S ′)−1
C (1) S[[C (1) S]′
]−1
Q
︸ ︷︷ ︸matrix of restrictions
.
Then, we define
Z ≡ H
S
(S ′)−1
C (1) S[[C (1) S]′
]−1
.
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 119
In order to solve for Q, all we need to do is re-ordering the endogenous
variables (and the associated shocks) of the VAR such that H times the
matrix of restrictions can be written in a lower triangular form.29 Let us
denote this lower triangular matrix by R
R ≡ H
S
(S ′)−1
C (1) S[[C (1) S]′
]−1
Q.
Since R = ZQ is lower triangular, it follows that
R′ = Q′Z ′
is upper triangular.30 Premultiplying the above equation by Q yields an
expression for Z ′
Z ′ = QR′.
Under the assumption that Z has full rank, the QR-decomposition of Z ′
yields Q. As the QR-decomposition is unique only up to the sign of the
diagonal elements of R′, the columns of R′ and Q can now be appropriately
normalized so that the IRF of the ith variable to the ith shock has the
desired sign.
Computing the structural VMA coefficients in practice
In practice, we start by re-ordering the variables in the system and defining
H to make sure that R equals a lower triangular matrix. Next, estimating
the reduced form VAR provides us with estimates of the reduced form VAR
coefficients Di for i = 1, 2, ..., p and Σ. Once we have estimates of Di
for i = 1, 2, ..., p, we can compute estimates of the VMA representation
coefficients Ci for i = 1, 2, ... (the necessary computations are carried out
automatically in econometric packages like RATS), and, thus, of C (1) (in
29We do not claim that the proposed method can handle all existing combinations of
short-run and long-run restrictions on the structural form of a model.30In general, if U is lower triangular, then U−1 is lower triangular, too, while U ′ is
upper triangular.
120 CHAPTER 3
fact a truncated version of it). Also, the Cholesky decomposition of Σ,
labelled S, can be computed. From H, S, and C (1), we can compute
Z. The QR-decomposition of Z ′ yields Q. A0 = SQ and Ai = CiA0 for
i = 1, 2, ... can be computed, in turn.
Illustrative example
Consider Gali’s [13] five-variable VAR. Suppose ∆(yt−nt) is the first variable
in vector xt. We assume that the technology shock is orthogonal to the
four non-technology shocks and only the technology shock has a long-run
effect on the level of yt − nt. We also assume that non-technology shocks
are orthogonal to each other and that they have an arbitrary recursive
structure. We end up with 10 additional restrictions (in addition to the
restriction that all shocks are orthogonal to each other). In terms of the
previously discussed framework, the matrix of restrictions is given by
A0
B′
0
A (1)
B (1)′
=
· · · · ·
· · 0 0 0
· · · 0 0
· · · · 0
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· 0 0 0 0
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
· · · · ·
.
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 121
And, the matrix which picks out the appropriate rows of the matrix ofrestrictions is equal to
H =
0 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
1 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
.
3.B.2 Cointegrated case
Notation and key idea
So far, the vector process xt has been assumed to be covariance-stationary.
Now, suppose all components of xt are I (1). If all components of xt are
I (1), the D (L)-polynomial in the reduced form VAR(p) given in equation
(3.4) has roots equal to one and is therefore not invertible. Model (3.4) can
be re-parameterized as follows
∆xt =∑p−1
i=1Γi∆xt−i + Πxt−1 + εt (3.6)
where Π = D (1) has rank 0 ≤ r ≤ n and εt is Gaussian white noise.
Suppose we know r (in practice, the rank of Π is determined empirically by
means of rank tests). Moreover, suppose 0 < r < n (the interesting case).
In this event, Π can be factorized as Π ≡ αβ′ where β and α are n × r
matrices, each with rank r. In addition, xt is cointegrated such that β′xt is
I (0). System (3.6) is then called a Vector Error Correction Model (VECM),
that is, a VAR that incorporates cointegrating restrictions.
From the VECM, it is possible to derive a VMA representation
∆xt = C (L) εt
where C (1) has rank (n − r). Since D (L) is not invertible, the derivation
of the C (L)-polynomial is not completely straightforward (compare e.g.
Watson [33], subsection 3.2). In practice, however, the computation of Ci
for i = 1, 2, ... can readily be implemented in standard software packages like
RATS. Note that Ci is restricted by the assumption regarding the number
of cointegrating relations.
122 CHAPTER 3
The extension of Lenz’s [26] estimation method to the non-stationary, coin-
tegrated case involves an additional step. The purpose of this step is to dis-
tinguish innovations which have permanent effects from those which have
transitory effects. This goal is accomplished by a transformation of the
residuals using information that are available from the VECM estimation
(i.e., from the Johansen procedure; compare Hoffmann [20]).
Step 1: Distinguishing innovations that have permanent effects
from those that have transitory effects
Johansen [21] has shown that in the cointegrated case, the long-run impact
matrix C (1) can be given by the following representation
C (1) = β⊥ (α′
⊥Γ (1) β⊥)
−1α′
⊥
where α⊥, β⊥ are the orthogonal complements of α and β. Notice: α′
⊥α = 0
and α′
⊥is (n − r) × n. Moreover, Johansen has shown that the vector of
permanent and transitory disturbances is given by
ηt =
[η1,t
η2,t
]=
[α′
⊥
α′Ω−1
]
n×n
εt
where subvector η1t contains the disturbances that have permanent effects on
the components of xt (the levels!), subvector η2,t contains the disturbances
that have temporary effects, and Ω is the variance-covariance matrix of the
reduced form disturbances.
Let us define
P−1 ≡
[α′
⊥
α′Ω−1
]
from which we get ηt = P−1εt. For any initial choice of α⊥ and α, we have
P =[
Ωα⊥ (α′
⊥Ωα⊥)−1 α (α′Ωα)−1
].
Moreover, we have
Σ ≡ E (ηtη′
t) = P−1Ω(P−1
)′=
[α′
⊥Ωα⊥ 0(n−r)×r
0r×(n−r) α′Ω−1α
].
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 123
Note that Σ is positive definite.
This completes step 1, the orthogonalization of permanent and transitory
disturbances. However, permanent shocks among themselves and transitory
shocks among themselves are not yet orthogonal. This will be accomplished
within step 2 and 3.
Step 2 + 3: Orthogonalizing the previously distinguished shocks
among themselves
We are now in the position to re-formulate our problem such that it becomes
almost equivalent to the non-cointegrated case. We are looking at two
models. The first model is a reduced form VMA representation given by
∆xt = C (L) Pηt
∆xt =(I + C1L + C2L
2 + ...)Pηt.
It is computationally straightforward to get the matrix of long-run multi-
pliers to this model
C (1) P =[
β⊥ (α⊥Γ (1) β⊥)−1 0n×r
].
The first block with the dimension n × (n − r) corresponds to the long-run
multipliers for η1,t; the second block with the dimension of n× r corresponds
to the long-run multipliers for η2,t (a matrix of zeros). Let us define
Ψn×(n−r) ≡ β⊥ (α⊥Γ (1) β⊥)−1
from which we get
C (1) P =[
Ψn×(n−r) 0n×r
].
Note that Ψ can be partitioned into two blocks
Ψn×(n−r) =
[Ψ1 (n−r)×(n−r)
Ψ2 r×r
]
where Ψ1 corresponds to the long-run effects on the first n − r components
of xt (in levels).
124 CHAPTER 3
The second model is a structural VMA representation given by
∆xt = A (L) ut
∆xt =(A0 + A1L + A2L
2 + ...)ut
where E (utu′
t) = In.
Combining ∆xt = C (L) Pηt and ∆xt = A (L) ut yields
A (L) ut = C (L) Pηt. (3.7)
As (3.7) must hold for all t (and C0 = I), we have
A0ut = Pηt.
Substituting P−1A0ut for ηt in (3.7) yields
A (L) ut = C (L) A0ut
from which follows that A (1) = C (1) A0. Moreover, as A (L) ut = C (L) A0ut
must hold for all t, we have
Ai = CiA0 for i = 1, 2, ...
As in the stationary case, we are going to perform an orthogonal decompo-
sition of the η-residuals based on a total of n (n − 1) /2 restrictions on A0
and A (1). Let S be the Cholesky decomposition of Σ
Σ = SS ′.
Note that because Σ is block diagonal, its Cholesky decomposition is block
diagonal too
SS ′ =
[SuS
′
u (n−r)×(n−r) 0(n−r)×r
0r×(n−r) SlS′
l r×r
]
whereby each block consists of a lower triangular matrix. Moreover, let Q
be an arbitrary orthogonal matrix.
From A0ut = Pηt follows that
E (A0utu′
tA′
0) = E (Pηtη′
tP′)
A0A′
0 = PΣP ′.
3.B. ESTIMATION OF STRUCTURAL VARS AND VECMS 125
Making use of the two matrices S and Q, we can derive a new expression
for A0 as follows
P−1A0A′
0(P′)−1 = SQ (SQ)′
A0 = PSQ.
This represents the first of two conditions relating the two models. The
second one follows directly from A (1) = C (1) A0 and is given by
A(1) = C(1)PSQ.
In analogy to the non-cointegrated case, let H be an n×2n selection matrix
whose function is to choose the appropriate restrictions on A0 and A (1),
that is
H
[PS
C(1)PS
]Q.
We define
Z ≡ H
[PS
C (1) PS
].
In order to solve for Q, all we need to do is re-ordering the endogenous
variables (and the associated shocks) of the VAR such that H times the
matrix of restrictions can be written in a lower triangular form; let us
denote this matrix by R
R ≡ H
[PS
C (1) PS
]Q = ZQ.
Note that the range of specifications of H is restricted by the fact that
C (1) P =[
Ψn×(n−r)
∣∣ 0n×r
]; as a consequence, long-run restrictions on
A(1) can only be imposed on the first n − r variables. Moreover, note that
since S is block diagonal, Z is block diagonal, too
Z =
[Zu (n−r)×(n−r) 0(n−r)×r
0r×(n−r) Zl r×r
].
Under the assumption that both Zu and Zl, have full rank, the QR-decomposition
of Z ′
u yields Qu and similarly Z ′
l yields Ql, from which we finally get
Q =
[Qu (n−r)×(n−r) 0(n−r)×r
0r×(n−r) Ql r×r
].
126 CHAPTER 3
Computing the structural VMA coefficients in practice
In practice, we start by re-ordering the variables in the system and defining
H to make sure that R equals a lower triangular matrix. Next, estimating
the VECM (based on a rank assumption) provides us with estimates of
Π, Γi for i = 1, 2, ..., p − 1, and Ω. We can then compute P . From this
we get estimates of the VMA representation coefficients Ci for i = 1, 2, ...
and ηt, from which we get estimates of Σ in turn. Then, the Cholesky
decomposition of Σ, labelled S, can be computed. From H, S, P , and
C (1), we can compute Z. With the QR-decompositions of Zu′
and Zl′
at
our disposal, we get Q. A0 = P SQ and Ai = CiA0 for i = 1, 2, ... can be
computed, in turn.
3.C Bootstrap confidence intervals
Estimating a structural VAR or VECM by means of the estimation method
presented in appendix 3.B provides us with point estimates of the impulse
response functions (IRF) and conditional correlations (CC). Next, we would
like to come up with a measure for the estimation variability. We find
that percentile confidence intervals (CI) are particularly well suited for this
purpose. The chosen strategy is based on bootstrapping the VAR and was
originally proposed by Runkle [30].
Consider a covariance-stationary, reduced form VAR(p)
xt = γ + D1xt−1 + D2xt−2 + ... + Dpxt−p + εt (3.8)
where γ is a vector of constant terms. By estimating this VAR, we get the
coefficient estimates γ and the stacking matrix
D ≡[D′
1, D′
2, ..., D′
p
]
as well as the series of the estimated residuals, εtTt=1.
In the words of Runkle [30], pp. 438/9, ”[t]he basic insight behind the
bootstrap is that since the estimated residuals of the model are a represen-
tative sample of the true disturbances [i.e., they are i.i.d.], it should not
3.C. BOOTSTRAP CONFIDENCE INTERVALS 127
matter in what order the disturbances occur. This means that the distri-
bution of the estimator can be determined by generating large numbers of
artificial observations from the actual data and the estimated residuals.”
To guarantee that the (empirical) distribution function of the ε’s has mean
zero, we subtract ε = 1T
∑Tt=1 εt from every single εt. With draws (without
replacement) from the shaken, mean adjusted estimated residuals and the
coefficient estimates γ and D we generate 1000 artificial series
x∗
t = γ + D1x∗
t−1 + D2x∗
t−2 + ... + Dpx∗
t−p + (ε∗t − ε)
where x∗
t is the simulated value (the first p observations are taken as initial
conditions) and ε∗t is a draw from the shaken estimated residuals, ε.
We end up with 1000 simulated series x∗
tTt=1. For each individual series, we
estimate D∗ =[D∗′
1 , D∗′
2 , ..., D∗′
p
]; in each round, we compute – based on D∗
and the previously discussed identifying assumptions – the structural VMA
coefficients,[A∗′
1 , A∗′
2 , ..., A∗′
k
]where k is the chosen horizon. Finally, we can
compute the (empirical) relative distribution function for each element in
A∗
k.
We use the α/2 and (1 − α) /2 percentile points of the distribution functions
as confidence intervals. An example should make this point clearer. Note
that the empirical relative distribution function is computed for every single
element in A, that is every
aij,k =∂xi,t+k
∂uj,t
for i, j = 1, 2, ..., n and k = 1, 2, ..., k. In the case of a 0.90 confidence, the
interval is given by element 1000 ∗ 0.10/2 = 50 and element 1000 ∗ (1 −
0.10/2) = 950.
Runkle’s method has been criticized for being affected by a small sample
bias. The small sample bias distorts the initial VAR coefficient estimates;
the bootstrapped estimates are then biased again - usually towards the sta-
tionary region (compare Kursteiner [25]). As a consequence, it can happen
that the confidence bands constructed in this way do not contain the orig-
inal parameter estimates. To overcome this problem, Kilian [22] suggests
128 CHAPTER 3
a small-sample bias correction. The planned follow-up study will contain
Kilian’s algorithm.31
3.D Model specifications
VAR models
Gali’s bivariate VAR in first differences is given by
∆xt = D1∆xt−1 + D2∆xt−2 + ... + Dp∆xt−p + εt
where
xt =[
(yt − nt) nt
]′.
We term it the ”benchmark model”. Lag-length is tested for the VAR in
levels.
Gali’s five-variable VAR has the form
xt = D1xt−1 + D2xt−2 + ... + Dpxt−p + εt
where
xt =[
∆ (yt − nt) ∆nt ∆ (mt − pt) ∆2pt rt − ∆pt+1
]′.
We term it ”VAR 0”. Lag-length is tested for
xt =[
(yt − nt) nt mt − pt ∆pt rt
]′.
We consider a number of modifications of ”VAR 0”. The data vectors of
the estimated VARs are listed below. The models are numbered from 1 to
7. Lag length determination is analogous to that for ”VAR 0”.
1.
xt =[
∆ (yt − nt) ∆nt ∆2pt rt − ∆pt+1 ∆nxt
]′
31A detailed description of the strategy to be applied and its implementation is available
upon request.
3.D. MODEL SPECIFICATIONS 129
2.
xt =[
∆ (yt − nt) ∆nt ∆2pt rt − ∆pt+1 ∆cat
]′
3.
xt =[
∆ (yt − nt) ∆nt ∆2pt rt − ∆pt+1 ∆tott]′
4.
xt =[
∆ (yt − nt) ∆nt ∆2pt rt − ∆pt+1 ∆nxt ∆tott]′
5.
xt =[
∆ (yt − nt) ∆nt ∆2pt rt − ∆pt+1 ∆cat ∆tott]′
6.
xt =[
∆ (yt − nt) ∆nt ∆ (mt − pt) ∆2pt rt − ∆pt+1 ∆nxt ∆tott]′
7.
xt =[
∆ (yt − nt) ∆nt ∆ (mt − pt) ∆2pt rt − ∆pt+1 ∆cat ∆tott]′
VECM models
Data vectors Consider the following VECM
∆xt = Πxt−1 +∑p−1
i=1Γi∆xt−i + εt
where all variables entering xt are supposed to be I(1). The data vectors
of the estimated VECMs are listed below. The models are again numbered
from 0 to 7. Lag length determination is analogous to that for ”VAR 0”.
0.
xt =[
(yt − nt) nt ∆mt ∆pt rt
]′
1.
xt =[
(yt − nt) nt ∆pt rt nxt
]′
130 CHAPTER 3
2.
xt =[
(yt − nt) nt ∆pt rt cat
]′
3.
xt =[
(yt − nt) nt ∆pt rt tott]′
4.
xt =[
(yt − nt) nt ∆pt rt nxt tott]′
5.
xt =[
(yt − nt) nt ∆pt rt cat tott]′
6.
xt =[
(yt − nt) nt ∆mt ∆pt rt nxt tott]′
7.
xt =[
(yt − nt) nt ∆mt ∆pt rt cat tott]′
Rank tests For each VECM, rank tests are performed. Thereby, we
proceed as follows. We begin by running CATS in RATS. Then, we check
the adequacy of the model regarding time independence of the residuals,
etc. (for a motivation compare Johansen [21], pp. 20/1). This includes:
• A visual check of the autocorrelation and the cross-correlation func-
tions for the individual residual series.
• A visual check of the standardized residuals and the histograms.
• A formal analysis of the residuals: (i) LM test for residual auto-
correlation of order 1 and 4, respectively. (ii) For each individual
residual series descriptive statistics are computed (like standard de-
viation, skewness, excess kurtosis) and a normality test is performed
(Shenton-Brownman test, known as Jarque-Bera test). (iii) More-
over, a modified version of the Shenton-Brownman test for normality
of the individual series is performed (for a description see Hansen and
Juselius [19], p. 27 and p. 73).
• A visual check of the eigenvalues of the companion matrix.
3.D. MODEL SPECIFICATIONS 131
The correlogram together with the (uni- and multivariate) normality test
statistics are our main criteria for assessing the adequacy of the model. If
the residuals are far from white noise, the number of lags is augmented.
However, we do not do this mechanically but look for a compromise be-
tween white noise criterium and degrees-of-freedom considerations.32 For
the smaller models, we consider 8 lags as being a rather large number; in
the case of ”VECM 6” and ”VECM 7” we try not to go beyond 4 lags.
If there is no hint of misspecification, we perform rank tests (table 1 in
Osterwald-Lenum [29]). We work with 90% critical values. Then, we set the
rank of Π according to the test result and normalize the vectors reasonably.
Finally, we perform some checks to see whether the supposed number of
cointegrating relationships is valid. Criteria: same as above; in addition to
this: visual check of the cointegrating relationships.
Testing restrictions on the β-vector An informal visual check allows
us to see whether a specified structural relation is contained in the space
spanned by β. Moreover, the α coefficient indicate which cointegrating
relationship is important for a variable. To make these statements more
precise we perform a series of formal tests. The testing strategy depends
on the specification of a model (number of endogenous variables and of
cointegrating relationships):
• Model 0: If the test points out to the presence of a cointegration
rank > 2, we directly go on by estimating a structural VECM. If
r = 2, we test the joint hypothesis that the vectors [0, 0, 1,−1, 0] and
[0, 0, 0,−1, 1] belong to the cointegration space. If r = 1, we test the
two hypothesis individually. If the matrix Π is the null matrix, the
model can be estimated as a VAR in first-differences.
• Model 1-3: If r > 1, we directly go on by estimating a structural
VECM. If r = 1, we test the hypothesis that the vector [0, 0,−1, 1, 0]
32Johansen [21], p. 21: ”It is our experience that if a long lag length is required to get
white noise residuals then it often pays to reconsider the choice of variables, and look
around for another important explanatory variable to include in the information set.”
132 CHAPTER 3
belongs to the cointegration space. If the matrix Π is the null matrix,
the model can be estimated as a VAR in first-differences.
• Model 4+5: If r > 1 we directly go on by estimating a structural
VECM. If r = 1, we test the hypothesis that the vector [0, 0,−1, 1, 0, 0]
belongs to the cointegration space. If the matrix Π is the null matrix,
the model can be estimated as a VAR in first-differences.
• Model 6+7: If r > 2, we directly go on by estimating a structural
VECM. If r = 2, we test the joint hypothesis that the vectors
[0, 0, 1,−1, 0, 0, 0] and [0, 0, 0,−1, 1, 0, 0]
belong to the cointegration space. If r = 1, we test the two hypothesis
individually. If the matrix Π is the null matrix, the model can be
estimated as a VAR in first-differences.
Bibliography
[1] Altig, David, Laurence J. Christiano, Martin Eichenbaum, and Jesper
Linde (2002), Technology shocks and aggregate fluctuations, Working
paper (preliminary and incomplete), Federal Reserve Bank of Cleveland
[2] Basu, Susanto, John G. Fernald, and Miles Kimball (1998), Are tech-
nology improvements contractionary?, Board of Governors of the Fed-
eral Reserve System, International Finance Discussion Paper 625
[3] Baxter, Marianne, and Rober G. King (1993), Fiscal policy in general
equilibrium, The American Economic Review 83(3), 315-34
[4] Blanchard, Olivier J., and Danny Quah (1989), The dynamic effects of
aggregate demand and supply disturbances, American Economic Re-
view 79(4), 655-673
[5] Christiano, Lawrence J., and Martin Eichenbaum (1992), Current real
business cycle theories and aggregate labor market fluctuations, Amer-
ican Economic Review 82(3), 430-450
[6] Christiano, Laurance J., Martin Eichenbaum, and Robert Vigfusson
(2003), What happens after a technology shock?, NBER Working Pa-
per No. 9819
[7] Collard, Fabrice, and Harris Dellas (2002), Technology shocks and em-
ployment, CEPR Discussion Paper No. 3680
[8] Cooley, Thomas F., and Edward C. Prescott (1995), Economic growth
and business cycles, in: Thomas F. Cooley, ed., Frontiers of Business
Cycle Research, Princeton University Press
134 CHAPTER 3
[9] Elder, John, and Peter E. Kennedy (2001), Testing for unit roots: what
should students be taught?, Journal of Economic Education 32(2), 137-
146
[10] Enders, Walter (1995), Applied econometric times series, Wiley Text
Books
[11] Fisher, Jonas D.M. (2003), Technology shocks matter, Federal Reserve
Bank of Chicago, Working Paper No. 2002-14
[12] Francis, Neville, and Valerie A. Ramey (2002), Is the technology-driven
real business cycle hypothesis dead? Shocks and aggregate fluctuations
revisited, NBER Working Paper No. 8726
[13] Gali, Jordi (1999), Technology, employment, and the business cycle: do
technology shocks explain aggregate fluctuations?, American Economic
Review 89(1), 249-271
[14] Gali, Jordi (2003), On the role of technology shocks as a source of
business cycles: Some new evidence, Mimeo
[15] Gonzalo, Jesus, and Serena Ng (2001), A systematic framework for ana-
lyzing the dynamic effects of permanent and transitory shocks, Journal
of Economic Dynamics and Control 25, 1527-1546
[16] Hamilton, James D. (1994), Time series analysis, Princeton University
Press
[17] Hansen, Gary D. (1985), Indivisible labor and the business cycle, Jour-
nal of Monetary Econonomics 16(3), 309-327
[18] Hansen, Gary D., and Randall Wright (1992), The labor market in real
business cycle theory, Federal Reserve Bank of Minneapolis Quarterly
Review (Spring), 2-12
[19] Hansen, Henrik, and Katarina Juselius (1995), CATS in RATS: Coin-
tegration analysis of time series
[20] Hoffmann, Mathias (2001), Long run recursive VAR models and QR
decompositions, Economics Letters 73(1), 15-20
BIBLIOGRAPHY 135
[21] Johansen, Soren (1995), Likelihood-based inference in cointegrated vec-
tor autoregressive models, Oxford University Press
[22] Kilian, Lutz (1998), Small-sample confidence intervals for impulse re-
sponse functions, Review of Economics and Statistics 80(2), 218-230
[23] King, Robert G., and Sergio T. Rebelo (1999), Rescuscitating real busi-
ness cycles, in: John B. Taylor and Michael Woodford, eds., Handbook
of Macroeconomics Vol. 1, Elsevier Science
[24] Kollmann, Robert (2002), Monetary policy rules in the open economy:
effects on welfare and busincess cycles, Journal of Monetary Economics
49(5), 989-1015
[25] Kuersteiner, Guido (undated manuscript), Lecture 6: Additional re-
sults for VAR’s, Department of Economics, MIT
[26] Lenz, Carlos (forthcoming), A simple method for identifying structural
VAR models using combinations of short- and long-run restrictions,
Mimeo, University of Basel.
[27] Lutkepohl, Helmut (1991), Introduction to multiple time series analy-
sis, Springer-Verlag
[28] McCallum, Bennett T. (1993), Unit roots in macroeconomic time se-
ries: some critical issues, Federal Reserve Bank of Richmond Economic
Quarterly 79(2), 13-43
[29] Osterwald-Lenum, Michael (1992), A note with quantiles of the asymp-
totic distribution of the maximum likelihood cointegration rank test
statistics, Oxford Bulletin of Economics and Statistics 54(3), 461-472
[30] Runkle, David E. (1987), Vector autoregressions and reality, Journal
of Business and Economics Statistics 5(4), 437-454
[31] Shea, John (1998), What do technology shocks do?, NBER Working
Paper No. 6632
[32] Uhlig, Harald (2003), Do technology shocks lead to a fall in total hours
worked?, Mimeo
136 CHAPTER 3
[33] Watson, Mark W. (1994), Vector autoregressions and cointegration, in:
Robert F. Engle and Daniel L. McFadden, Handbook of Econometrics
Vol. 4, Elsevier Science
TABLES AND FIGURES CHAPTER 3 137
Tables and figures chapter 3
Table 1a-e: Structural VAR
Table 2a-j: Structural VECM
Figure 1a-c: Benchmark model
Figure 2a-c: VAR 0
Figure 3a+b: USA, VAR 1-7
Figure 4a-c: VECM 0
Figure 5a+b: USA, VECM 1-7
Figure 6a-i: Remaining countries in the set, VECM 1-7
FRA
Nbe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T88
8179
-79
79-
79-
ES:
FR
OM
1980
.219
78.4
1979
.2-
1979
.219
79.2
-19
79.2
-
TO20
02.1
1998
.419
98.4
-19
98.4
1998
.4-
1998
.4-
L8
24
44
4
CC
-0.3
05-0
.528
-0.3
91-
-0.4
14-0
.285
--0
.263
-St
d0.
141
0.31
30.
281
-0.
279
0.26
7-
0.28
7-
UpB
-0.0
120.
159
0.22
3-
0.18
80.
234
-0.
228
-Lo
B-0
.467
-0.8
37-0
.630
--0
.637
-0.5
80-
-0.6
42-
¦ Lo
B - U
pB ¦
0.45
50.
996
0.85
3-
0.82
50.
814
-0.
870
-
Gal
i (19
99)
CC
-0.8
1-
Std
0.27
-
GB
Rbe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T16
373
158
158
115
117
115
7575
ES:
FR
OM
1961
.219
83.4
1962
.319
62.3
1973
.219
72.4
1973
.219
83.2
1983
.2
TO20
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
L4
48
84
24
22
CC
-0.8
71-0
.799
-0.7
96-0
.813
-0.7
31-0
.738
-0.7
32-0
.911
-0.8
94St
d0.
092
0.20
90.
173
0.17
40.
140
0.22
30.
142
0.14
70.
113
UpB
-0.6
71-0
.415
-0.2
44-0
.250
-0.4
20-0
.162
-0.3
97-0
.599
-0.6
18Lo
B-0
.930
-0.9
00-0
.783
-0.7
95-0
.840
-0.8
76-0
.826
-0.9
58-0
.958
¦ Lo
B - U
pB ¦
0.25
90.
485
0.53
90.
545
0.42
00.
714
0.42
90.
359
0.34
0
Gal
i (19
99)
CC
-0.9
1-
(UK
)St
d.0.
16-
Not
es: I
n th
e ca
se o
f FR
Ai,
n(t
) is p
roxi
ed b
y H
P fil
tere
d em
ploy
men
t and
r(t
) by
a sh
ort-t
erm
inte
rest
rate
(3-m
onth
PIB
OR
).In
the
case
of G
BR
, r(t)
is p
roxi
ed b
y a
long
-term
rate
(10-
year
gov
ernm
ent b
onds
).Th
e #
of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en #
of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
CC
for t
he c
orre
latio
n be
twee
n
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
n a
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Sta
ndar
d de
viat
ions
(Std
) are
incl
uded
in o
rder
to m
ake
our f
indi
ngs c
ompa
rabl
e to
thos
e of
Gal
i (19
99).
Tabl
e 1a
: Stru
ctur
al V
AR
ITA
benc
hmar
kV
AR
0V
AR
1V
AR
2V
AR
3V
AR
4V
AR
5V
AR
6V
AR
7T
120
7777
-79
79-
79-
ES:
FR
OM
1972
.219
79.4
1979
.4-
1979
.219
79.2
-19
79.2
-
TO20
02.1
1998
.419
98.4
-19
98.4
1998
.4-
1998
.4-
L8
44
-2
2-
2-
CC
-0.9
61-0
.955
-0.9
39-
-0.9
75-0
.972
--0
.977
-St
d0.
082
0.09
70.
148
-0.
097
0.15
2-
0.13
5-
UpB
-0.7
40-0
.732
-0.5
95-
-0.7
54-0
.670
--0
.685
-Lo
B-0
.969
-0.9
65-0
.966
--0
.989
-0.9
85-
-0.9
86-
¦ Lo
B - U
pB ¦
0.22
90.
233
0.37
1-
0.23
50.
315
-0.
301
-
Gal
i (19
99)
CC
-0.4
7-
Std.
0.12
-
USA
benc
hmar
kV
AR
0V
AR
1V
AR
2V
AR
3V
AR
4V
AR
5V
AR
6V
AR
7T
156
162
162
162
115
115
115
115
115
ES:
FR
OM
1963
.219
61.3
1961
.319
61.3
1973
.219
73.2
1973
.219
73.2
1973
.2
TO20
02.1
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
L12
44
44
44
44
CC
-0.8
20-0
.658
-0.7
70-0
.763
-0.6
82-0
.622
-0.5
41-0
.288
-0.1
87St
d0.
161
0.21
20.
260
0.25
60.
319
0.29
40.
297
0.32
60.
342
UpB
-0.2
71-0
.105
-0.0
46-0
.055
0.30
60.
242
0.26
10.
500
0.57
6Lo
B-0
.789
-0.7
94-0
.891
-0.8
87-0
.735
-0.7
27-0
.697
-0.5
89-0
.577
¦ Lo
B - U
pB ¦
0.51
80.
689
0.84
50.
832
1.04
10.
969
0.95
81.
089
1.15
3
Gal
i (19
99)
CC
-0.8
4-0
.82
Std.
0.26
0.08
Not
es: I
n th
e ca
se o
f ITA
, r(t
) is p
roxi
ed b
y a
shor
t-ter
m in
tere
st ra
te, i
n th
e ca
se o
f the
USA
by
a lo
ng-te
rm ra
te.
The
# of
obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
# o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e, C
C fo
r the
cor
rela
tion
betw
een
av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t),an
d Lo
B fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t). S
tand
ard
devi
atio
ns (S
td) a
re in
clud
ed in
ord
er to
mak
e ou
r fin
ding
s com
para
ble
to th
ose
of G
ali (
1999
).
Tabl
e 1b
: Stru
ctur
al V
AR
(Con
t.)
CA
Nbe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T80
7981
7981
8181
8181
ES:
FR
OM
1982
.219
82.2
1981
.419
82.2
1981
.419
81.4
1981
.419
81.4
1981
.4
TO20
02.1
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
L4
42
42
22
22
CC
-0.2
65-0
.537
-0.0
08-0
.042
-0.0
36-0
.055
-0.0
670.
330
0.22
3St
d0.
277
0.35
20.
315
0.41
60.
329
0.32
20.
327
0.34
80.
340
UpB
0.19
80.
419
0.46
90.
679
0.47
30.
467
0.43
90.
736
0.65
7Lo
B-0
.720
-0.7
30-0
.582
-0.7
02-0
.628
-0.6
01-0
.671
-0.4
48-0
.525
¦ Lo
B - U
pB ¦
0.91
81.
149
1.05
11.
381
1.10
11.
068
1.11
01.
184
1.18
2
Gal
i (19
99)
CC
-0.5
9-
Std.
0.32
-
JPN
benc
hmar
kV
AR
0V
AR
1V
AR
2V
AR
3V
AR
4V
AR
5V
AR
6V
AR
7T
8483
8363
8385
6585
65ES
: F
RO
M19
81.2
1981
.219
81.2
1986
.219
81.2
1980
.419
85.4
1980
.419
85.4
TO
2002
.120
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.4L
44
44
42
22
2
CC
-0.1
220.
355
0.28
60.
190
0.02
40.
285
0.53
50.
498
0.61
6St
d0.
281
0.39
00.
404
0.33
60.
372
0.43
30.
381
0.47
20.
426
UpB
0.22
60.
563
0.79
10.
619
0.52
20.
735
0.80
10.
781
0.84
2Lo
B-0
.696
-0.6
85-0
.628
-0.4
98-0
.717
-0.7
08-0
.449
-0.7
66-0
.515
¦ Lo
B - U
pB ¦
0.92
21.
248
1.41
91.
117
1.23
91.
443
1.25
01.
547
1.35
7
Gal
i (19
99)
CC
-0.0
7-
Std.
0.08
-N
otes
: In
the
case
of b
oth
CA
N a
nd JP
N, r
(t) i
s pro
xied
by
a sh
ort-t
erm
inte
rest
rate
.Th
e #
of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en #
of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
CC
for t
he c
orre
latio
n be
twee
n
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
n a
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Sta
ndar
d de
viat
ions
(Std
) are
incl
uded
in o
rder
to m
ake
our f
indi
ngs c
ompa
rabl
e to
thos
e of
Gal
i (19
99).
Tabl
e 1c
: Stru
ctur
al V
AR
(Con
t.)
AU
Sbe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T15
010
312
812
811
111
511
710
310
3ES
: F
RO
M19
64.4
1976
.219
70.1
1970
.119
74.2
1973
.219
72.4
1976
.219
76.2
TO
2002
.120
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.4L
24
88
84
24
4
CC
-0.9
53-0
.900
-0.7
74-0
.763
-0.8
23-0
.929
-0.9
27-0
.898
-0.8
79St
d0.
095
0.10
50.
123
0.12
00.
136
0.13
80.
121
0.11
30.
132
UpB
-0.7
40-0
.614
-0.4
20-0
.412
-0.4
08-0
.577
-0.7
25-0
.576
-0.5
38Lo
B-0
.991
-0.9
31-0
.791
-0.7
85-0
.831
-0.9
33-0
.979
-0.9
13-0
.912
¦ Lo
B - U
pB ¦
0.25
10.
317
0.37
10.
373
0.42
30.
356
0.25
40.
337
0.37
4
CH
Ebe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T80
8484
8484
8484
8484
ES:
FR
OM
1982
.219
81.2
1981
.219
81.2
1981
.219
81.2
1981
.219
81.2
1981
.2
TO20
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
L8
44
44
44
44
CC
-0.9
51-0
.874
-0.8
79-0
.855
-0.8
46-0
.857
-0.8
03-0
.845
-0.7
89St
d0.
238
0.20
40.
170
0.18
40.
202
0.16
90.
194
0.19
40.
233
UpB
-0.1
94-0
.317
-0.4
20-0
.401
-0.3
30-0
.421
-0.2
90-0
.327
-0.1
97Lo
B-0
.960
-0.9
44-0
.950
-0.9
51-0
.935
-0.9
30-0
.909
-0.9
20-0
.909
¦ Lo
B - U
pB ¦
0.76
60.
627
0.53
00.
550
0.60
50.
509
0.61
90.
593
0.71
2N
otes
: In
the
case
of b
oth
AU
S an
d C
HE,
r(t
) is p
roxi
ed b
y a
shor
t-ter
m in
tere
st ra
te.
The
# of
obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
# o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e, C
C fo
r the
cor
rela
tion
betw
een
av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t),an
d Lo
B fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t). S
tand
ard
devi
atio
ns (S
td) a
re in
clud
ed in
ord
er to
mak
e ou
r fin
ding
s com
para
ble
to th
ose
of G
ali (
1999
).
Tabl
e 1d
: Stru
ctur
al V
AR
(Con
t.)
ESP
benc
hmar
kV
AR
0V
AR
1V
AR
2V
AR
3V
AR
4V
AR
5V
AR
6V
AR
7T
8672
73-
7373
-72
-ES
: F
RO
M19
80.4
1980
.419
80.4
-19
80.4
1980
.4-
1980
.4-
TO
2002
.119
98.3
1998
.4-
1998
.419
98.4
-19
98.3
-L
22
2-
22
-2
-
CC
-0.9
13-0
.827
-0.8
78-
-0.8
85-0
.883
--0
.823
-St
d0.
082
0.17
40.
184
-0.
144
0.18
9-
0.18
2-
UpB
-0.7
19-0
.442
-0.4
19-0
.487
-0.4
25-0
.429
LoB
-0.9
84-0
.939
-0.9
31-0
.937
-0.9
43-0
.926
¦ Lo
B - U
pB ¦
0.26
50.
497
0.51
2-
0.45
00.
518
-0.
497
-
NZ
Lbe
nchm
ark
VA
R 0
VA
R 1
VA
R 2
VA
R 3
VA
R 4
VA
R 5
VA
R 6
VA
R 7
T75
7474
5776
7657
7657
ES:
FR
OM
1983
.319
83.3
1983
.319
87.4
1983
.119
83.1
1987
.419
83.1
1987
.4
TO20
02.1
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
L4
44
22
22
22
CC
-0.7
30-0
.836
-0.6
29-0
.522
-0.5
97-0
.744
-0.4
03-0
.864
-0.5
46St
d0.
185
0.19
20.
201
0.38
00.
253
0.22
00.
430
0.18
70.
382
UpB
-0.3
66-0
.237
-0.1
600.
311
-0.0
16-0
.214
0.51
5-0
.424
0.39
6Lo
B-0
.886
-0.8
39-0
.818
-0.8
95-0
.856
-0.8
91-0
.862
-0.9
15-0
.857
¦ Lo
B - U
pB ¦
0.52
00.
602
0.65
81.
206
0.84
00.
677
1.37
70.
491
1.25
3N
otes
: In
the
case
of b
oth
ESP
and
NZL
, r(t
) is p
roxi
ed b
y a
shor
t-ter
m in
tere
st ra
te.
The
# of
obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
# o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e, C
C fo
r the
cor
rela
tion
betw
een
av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t),an
d Lo
B fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t). S
tand
ard
devi
atio
ns (S
td) a
re in
clud
ed in
ord
er to
mak
e ou
r fin
ding
s com
para
ble
to th
ose
of G
ali (
1999
).
Tabl
e 1e
: Stru
ctur
al V
AR
(Con
t.)
FRA
NV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T79
77-
7979
-79
ES:
FR
OM
1979
.219
79.4
-19
79.2
1979
.2-
1979
.2
TO19
98.4
1998
.4-
1998
.419
98.4
-19
98.4
T - N
OV
7946
-58
54-
50L
46
-4
4-
4
Ran
k1
2-
24
-4
CC
0.37
8-0
.033
--0
.138
-0.3
64-
-0.0
30U
pB0.
727
0.47
0-
0.67
90.
245
-0.
442
LoB
-0.2
45-0
.483
--0
.576
0.55
5-
-0.4
23 ¦
LoB
- UpB
¦0.
972
0.95
3-
1.25
50.
310
-0.
865
Ran
k2
CC
0.31
1U
pB0.
699
LoB
-0.4
49¦ L
oB -
UpB
¦1.
148
Not
es: I
n th
e ca
se o
f FR
Ai,
n(t
) is p
roxi
ed b
y H
P fil
tere
d em
ploy
men
t and
r(t
) by
a sh
ort t
erm
inte
rest
rate
(3-m
onth
PIB
OR
).Th
e nu
mbe
r of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en n
umbe
r of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
NO
V fo
r num
ber o
f var
iabl
es, C
C fo
r cor
rela
tion
betw
een
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
na
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Ran
k 0
is e
quiv
alen
t to
a V
AR
in fi
rst-d
iffer
ence
s.
Tabl
e 2a
: Stru
ctur
al V
ECM
GB
RV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T73
158
158
113
111
111
7373
ES:
FR
OM
1983
.419
62.3
1962
.319
73.4
1974
.219
74.2
1983
.419
83.4
TO20
01.4
2001
.420
01.4
2001
.420
01.4
2001
.420
01.4
2001
.4T
- NO
V52
117
117
8262
6244
44L
48
86
88
44
Ran
k1
10
10
14
4C
C-0
.930
-0.7
45-0
.849
-0.7
67-0
.717
-0.7
13-0
.727
-0.7
98U
pB-0
.560
-0.3
19-0
.560
-0.1
77-0
.201
-0.2
39-0
.267
-0.2
30Lo
B-0
.959
-0.7
80-0
.862
-0.7
95-0
.689
-0.7
09-0
.840
-0.8
92 ¦
LoB
- UpB
¦0.
399
0.46
10.
302
0.61
80.
488
0.47
00.
573
0.66
2
Ran
k2
11
3C
C-0
.792
-0.7
87-0
.611
-0.8
00U
pB-0
.402
-0.3
64-0
.205
-0.2
38Lo
B-0
.905
-0.8
16-0
.640
-0.8
86¦ L
oB -
UpB
¦0.
503
0.45
20.
435
0.64
8
Not
es: I
n th
e ca
se o
f GB
R, r
(t) is
pro
xied
by
a lo
ng te
rm ra
te (1
0-ye
ar g
over
nmen
t bon
ds).
The
num
ber o
f obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
num
ber o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e,N
OV
for n
umbe
r of v
aria
bles
, CC
for c
orre
latio
n be
twee
n av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t), a
nd L
oB fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t).R
ank
0 is
equ
ival
ent t
o a
VA
R in
firs
t-diff
eren
ces.
Gre
y st
ands
for:
num
ber o
f ran
ks n
ot b
ased
on
test
resu
lts (r
obus
tnes
s che
ck).
Tabl
e 2b
: Stru
ctur
al V
ECM
(Con
t.)
ITA
VE
CM
0V
ECM
1V
ECM
2V
ECM
3V
ECM
4V
ECM
5V
ECM
6V
ECM
7T
7676
-76
76-
76ES
: F
RO
M19
80.1
1980
.1-
1980
.119
80.1
-19
80.1
TO19
98.4
1998
.4-
1998
.419
98.4
-19
98.4
T - N
OV
5555
-55
51-
47L
44
-4
4-
4
Ran
k1
2-
33
-2
CC
-0.9
48-0
.958
--0
.920
-0.9
25-
-0.9
53U
pB-0
.525
-0.6
49-
-0.5
06-0
.522
--0
.704
LoB
-0.9
76-0
.970
--0
.941
-0.9
42-
-0.9
46 ¦
LoB
- UpB
¦0.
451
0.32
1-
0.43
50.
420
-0.
242
Ran
k2
CC
-0.9
52U
pB-0
.634
LoB
-0.9
68¦ L
oB -
UpB
¦0.
334
Not
es: I
n th
e ca
se o
f ITA
, r(t
) is p
roxi
ed b
y a
shor
t ter
m in
tere
st ra
te.
The
num
ber o
f obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
num
ber o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e,N
OV
for n
umbe
r of v
aria
bles
, CC
for c
orre
latio
n be
twee
n av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t), a
nd L
oB fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t).R
ank
0 is
equ
ival
ent t
o a
VA
R in
firs
t-diff
eren
ces.
Tabl
e 2c
: Stru
ctur
al V
ECM
(Con
t.)
USA
VE
CM
0V
ECM
1V
ECM
2V
ECM
3V
ECM
4V
ECM
5V
ECM
6V
ECM
7T
159
159
159
114
116
114
116
116
ES:
FR
OM
1962
.319
62.3
1962
.319
73.4
1973
.219
73.4
1973
.219
73.2
TO20
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.1T
- NO
V11
811
811
883
9177
8787
L8
88
64
64
4
Ran
k1
12
21
32
3C
C-0
.417
0.06
2-0
.053
-0.5
08-0
.844
0.19
6-0
.749
-0.0
32U
pB0.
173
0.35
20.
309
0.42
30.
001
0.53
90.
047
0.49
6Lo
B-0
.664
-0.5
21-0
.519
-1.0
00-0
.849
-0.9
87-0
.745
-0.6
15 ¦
LoB
- UpB
¦0.
837
0.87
30.
828
1.42
30.
850
1.52
60.
792
1.11
1
Ran
k2
CC
-0.6
02U
pB0.
246
LoB
-0.6
42¦ L
oB -
UpB
¦0.
888
Not
es: I
n th
e ca
se o
f the
USA
, r(t)
is p
roxi
ed b
y a
long
term
inte
rest
rate
.Th
e nu
mbe
r of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en n
umbe
r of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
NO
V fo
r num
ber o
f var
iabl
es, C
C fo
r cor
rela
tion
betw
een
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
na
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Ran
k 0
is e
quiv
alen
t to
a V
AR
in fi
rst-d
iffer
ence
s.G
rey
stan
ds fo
r: nu
mbe
r of r
anks
not
bas
ed o
n te
st re
sults
(rob
ustn
ess c
heck
).Li
ght g
rey
stan
ds fo
r: m
odel
spec
ifica
tion
unst
able
(gro
wth
rate
rath
er th
an le
vel o
f ser
ies s
eem
s to
be sh
ocke
d).
Tabl
e 2d
: Stru
ctur
al V
ECM
(Con
t.)
CA
NV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T80
8080
8082
8282
82ES
: F
RO
M19
82.2
1982
.219
82.2
1982
.219
81.4
1981
.419
81.4
1981
.4TO
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
T - N
OV
5959
5959
6969
6767
L4
44
42
22
2
Ran
k0
01
23
33
3C
C-0
.381
-0.3
17-0
.214
-0.3
24-0
.372
0.04
9-0
.101
0.20
9U
pB0.
185
0.24
10.
266
0.30
60.
521
0.64
80.
592
0.69
2Lo
B-0
.734
-0.7
3-0
.638
-0.5
87-0
.851
-0.7
62-0
.754
-0.5
82 ¦
LoB
- UpB
¦0.
919
0.97
10.
904
0.89
31.
372
1.41
01.
346
1.27
4
Ran
k2
32
34
CC
-0.0
06-0
.266
-0.2
34-0
.580
-0.2
48U
pB0.
463
0.43
60.
544
0.36
30.
447
LoB
-0.5
50-0
.582
-0.6
71-0
.665
-0.6
35¦ L
oB -
UpB
¦1.
013
1.01
81.
215
1.02
81.
082
Not
es: I
n th
e ca
se o
f CA
N, r
(t) i
s pro
xied
by
a sh
ort t
erm
inte
rest
rate
.Th
e nu
mbe
r of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en n
umbe
r of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
NO
V fo
r num
ber o
f var
iabl
es, C
C fo
r cor
rela
tion
betw
een
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
na
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Ran
k 0
is e
quiv
alen
t to
a V
AR
in fi
rst-d
iffer
ence
s.
Tabl
e 2e
: Stru
ctur
al V
ECM
(Con
t.)
JPN
VE
CM
0V
ECM
1V
ECM
2V
ECM
3V
ECM
4V
ECM
5V
ECM
6V
ECM
7T
8484
6484
8464
8666
ES:
FR
OM
1981
.219
81.2
1986
.219
81.2
1981
.219
86.2
1980
.419
85.4
TO20
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.1T
- NO
V63
6343
6359
3971
51L
44
44
44
22
Ran
k0
12
12
44
2C
C-0
.154
0.18
10.
268
0.20
20.
222
0.38
50.
583
0.24
5U
pB0.
230
0.55
60.
591
0.58
60.
626
0.78
70.
857
0.72
8Lo
B-0
.703
-0.6
41-0
.446
-0.6
39-0
.638
-0.5
96-0
.870
-0.7
26 ¦
LoB
- UpB
¦0.
933
1.19
71.
037
1.22
51.
264
1.38
31.
727
1.45
4
Ran
k2
CC
0.65
0U
pB0.
775
LoB
-0.5
90¦ L
oB -
UpB
¦1.
365
Not
es: I
n th
e ca
se o
f JPN
, r(t
) is p
roxi
ed b
y a
shor
t ter
m in
tere
st ra
te.
The
num
ber o
f obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
num
ber o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e,N
OV
for n
umbe
r of v
aria
bles
, CC
for c
orre
latio
n be
twee
n av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t), a
nd L
oB fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t).R
ank
0 is
equ
ival
ent t
o a
VA
R in
firs
t-diff
eren
ces.
Tabl
e 2f
: Stru
ctur
al V
ECM
(Con
t.)
AU
SV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T10
113
113
111
411
411
410
310
3ES
: F
RO
M19
77.1
1969
.319
69.3
1973
.419
73.4
1973
.419
76.3
1976
.3TO
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
T - N
OV
7010
010
083
7777
7474
L6
66
66
64
4
Ran
k1
11
11
12
2C
C-0
.817
-0.8
78-0
.869
-0.7
81-0
.785
-0.7
85-0
.924
-0.9
03U
pB-0
.454
-0.5
89-0
.615
-0.5
66-0
.518
-0.5
42-0
.598
-0.5
38Lo
B-0
.864
-0.9
04-0
.906
-0.8
45-0
.848
-0.8
47-0
.934
-0.9
13 ¦
LoB
- UpB
¦0.
410
0.31
50.
291
0.27
90.
330
0.30
50.
336
0.37
5
Ran
k2
3C
C-0
.772
-0.6
21U
pB-0
.252
-0.0
59Lo
B-0
.817
-0.8
79¦ L
oB -
UpB
¦0.
565
0.82
0
Not
es: I
n th
e ca
se o
f AU
S, r
(t) i
s pro
xied
by
a sh
ort t
erm
inte
rest
rate
.Th
e nu
mbe
r of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en n
umbe
r of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
NO
V fo
r num
ber o
f var
iabl
es, C
C fo
r cor
rela
tion
betw
een
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
na
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Ran
k 0
is e
quiv
alen
t to
a V
AR
in fi
rst-d
iffer
ence
s.G
rey
stan
ds fo
r: nu
mbe
r of r
anks
not
bas
ed o
n te
st re
sults
(rob
ustn
ess c
heck
).
Tabl
e 2g
: Stru
ctur
al V
ECM
(Con
t.)
CH
EV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T82
8484
8484
8484
84ES
: F
RO
M19
81.4
1981
.219
81.2
1981
.219
81.2
1981
.219
81.2
1981
.2TO
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
T - N
OV
5163
6363
5959
5555
L6
44
44
44
4
Ran
k1
22
12
23
4C
C-0
.915
-0.9
50-0
.886
-0.7
42-0
.727
-0.8
58-0
.770
-0.9
15U
pB-0
.400
-0.1
60-0
.275
-0.1
45-0
.021
-0.1
90-0
.113
-0.3
53Lo
B-0
.943
-0.9
56-0
.959
-0.8
92-0
.886
-0.9
42-0
.888
-0.9
22 ¦
LoB
- UpB
¦0.
543
0.79
60.
684
0.74
70.
865
0.75
20.
775
0.56
9
Ran
k2
33
4C
C-0
.763
-0.9
02-0
.890
-0.9
19U
pB-0
.366
-0.4
46-0
.314
-0.4
82Lo
B-0
.908
-0.9
43-0
.924
-0.9
32¦ L
oB -
UpB
¦0.
542
0.49
70.
610
0.45
0
Not
es: I
n th
e ca
se o
f CH
E, r
(t) i
s pro
xied
by
a sh
ort t
erm
inte
rest
rate
.Th
e nu
mbe
r of o
bser
vatio
ns (T
) dep
ends
on
the
chos
en n
umbe
r of l
ags (
L) a
nd o
n da
ta a
vaila
bilit
y. E
S st
ands
for e
ffec
tive
sam
ple,
NO
V fo
r num
ber o
f var
iabl
es, C
C fo
r cor
rela
tion
betw
een
aver
age
labo
r pro
duct
ivity
gro
wth
and
em
ploy
men
t gro
wth
con
ditio
nal o
na
posi
tive
tech
nolo
gy sh
ock,
UpB
for u
pper
bou
nd (0
.95
perc
entil
e po
int),
and
LoB
for l
ower
bou
nd (0
.05
perc
entil
e po
int).
Ran
k 0
is e
quiv
alen
t to
a V
AR
in fi
rst-d
iffer
ence
s.
Tabl
e 2h
: Stru
ctur
al V
ECM
(Con
t.)
ESP
VE
CM
0V
ECM
1V
ECM
2V
ECM
3V
ECM
4V
ECM
5V
ECM
6V
ECM
7T
6971
-71
71-
71ES
: F
RO
M19
81.3
1981
.2-
1981
.219
81.2
-19
81.1
TO19
98.3
1998
.4-
1998
.419
98.4
-19
98.3
T - N
OV
4850
-50
46-
56L
44
-4
4-
2
Ran
k1
0-
00
-3
CC
-0.7
84-0
.760
--0
.765
-0.7
62-
-0.7
67U
pB-0
.488
-0.4
69-
-0.4
77-0
.475
--0
.544
LoB
-0.9
01-0
.896
--0
.900
-0.8
98-
-0.9
33 ¦
LoB
- UpB
¦0.
413
0.42
7-
0.42
30.
423
-0.
389
Ran
k2
31
1C
C-0
.736
-0.5
31-0
.923
-0.9
69U
pB-0
.418
0.14
4-0
.512
-0.5
41Lo
B-0
.890
-0.8
27-0
.928
-0.9
39 ¦
LoB
- UpB
¦0.
472
0.97
10.
416
0.39
8
Ran
k3
CC
-0.5
80U
pB0.
140
LoB
-0.8
55¦ L
oB -
UpB
¦0.
995
Not
es: I
n th
e ca
se o
f ESP
, r(t
) is p
roxi
ed b
y a
shor
t ter
m in
tere
st ra
te.
The
num
ber o
f obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
num
ber o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e,N
OV
for n
umbe
r of v
aria
bles
, CC
for c
orre
latio
n be
twee
n av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t), a
nd L
oB fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t).R
ank
0 is
equ
ival
ent t
o a
VA
R in
firs
t-diff
eren
ces.
Gre
y st
ands
for:
num
ber o
f ran
ks n
ot b
ased
on
test
resu
lts (r
obus
tnes
s che
ck).
Tabl
e 2i
: Stru
ctur
al V
ECM
(Con
t.)
NZ
LV
EC
M 0
VEC
M 1
VEC
M 2
VEC
M 3
VEC
M 4
VEC
M 5
VEC
M 6
VEC
M 7
T75
7558
7375
5875
58ES
: F
RO
M19
83.3
1983
.319
87.4
1984
.119
83.3
1987
.419
83.3
1987
.4TO
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
2002
.120
02.1
T - N
OV
5454
4742
5045
4643
L4
42
64
24
2
Ran
k2
31
22
14
1C
C-0
.861
-0.7
57-0
.783
-0.5
30-0
.689
-0.8
01-0
.408
-0.7
88U
pB-0
.447
-0.1
65-0
.521
-0.1
33-0
.095
-0.4
620.
127
-0.3
32Lo
B-0
.896
-0.8
76-0
.957
-0.6
83-0
.823
-0.9
64-0
.738
-0.9
65 ¦
LoB
- UpB
¦0.
449
0.71
10.
436
0.55
00.
728
0.50
20.
865
0.63
3
Ran
k3
2C
C-0
.410
-0.6
85U
pB0.
018
0.13
6Lo
B-0
.754
-0.9
07¦ L
oB -
UpB
¦0.
772
1.04
3
Not
es: I
n th
e ca
se o
f NZL
, r(t
) is p
roxi
ed b
y a
shor
t ter
m in
tere
st ra
te.
The
num
ber o
f obs
erva
tions
(T) d
epen
ds o
n th
e ch
osen
num
ber o
f lag
s (L)
and
on
data
ava
ilabi
lity.
ES
stan
ds fo
r eff
ectiv
e sa
mpl
e,N
OV
for n
umbe
r of v
aria
bles
, CC
for c
orre
latio
n be
twee
n av
erag
e la
bor p
rodu
ctiv
ity g
row
th a
nd e
mpl
oym
ent g
row
th c
ondi
tiona
l on
a po
sitiv
e te
chno
logy
shoc
k, U
pB fo
r upp
er b
ound
(0.9
5 pe
rcen
tile
poin
t), a
nd L
oB fo
r low
er b
ound
(0.0
5 pe
rcen
tile
poin
t).R
ank
0 is
equ
ival
ent t
o a
VA
R in
firs
t-diff
eren
ces.
Tabl
e 2j
: Stru
ctur
al V
ECM
(Con
t.)
Figure 1a: Benchmark model FRA:
response of n to T-shock
5 10 15 20-2
-1
0
1
GBR:
response of n to T-shock
5 10 15 20-2
-1
0
1
ITA:
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
USA:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
Figure 1b: Benchmark model (Cont.) CAN:
response of n to T-shock
5 10 15 20-1
0
1
2
JPN:
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
AUS:
response of n to T-shock
5 10 15 20-1.2
-0.8
-0.4
-0.0
0.4
CHE:
response of n to T-shock
5 10 15 20-2
-1
0
1
Figure 1c: Benchmark model (Cont.) ESP:
response of n to T-shock
5 10 15 20-4
-2
0
2
NLZ:
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
Figure 2a: VAR 0 FRA:
response of n to T-shock
5 10 15 20-2
-1
0
1
GBR:
response of n to T-shock
5 10 15 20-2
-1
0
1
ITA:
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
USA:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
Figure 2b: VAR 0 (Cont.) CAN:
response of n to T-shock
5 10 15 20-1
0
1
2
JPN:
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
AUS:
response of n to T-shock
5 10 15 20-1.2
-0.8
-0.4
-0.0
0.4
CHE:
response of n to T-shock
5 10 15 20-2
-1
0
1
Figure 2c: VAR 0 (Cont.) ESP:
response of n to T-shock
5 10 15 20-4
-2
0
2
NLZ:
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
Figure 3a: USA, VAR 1-7 VAR 1:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VAR 2:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VAR 3:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VAR 4:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
Figure 3b: USA, VAR 1-7 (Cont.) VAR 5:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VAR 6:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VAR 7:
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
Figure 4a: VECM 0 FRA: Rank 1
response of n to T-shock
5 10 15 20-0.50
-0.25
0.00
0.25
0.50
GBR: Rank 1
response of n to T-shock
5 10 15 20-1.6
-0.8
0.0
0.8
ITA: Rank 2
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
USA: Rank 1
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
Figure 4b: VECM 0 (Cont.) CAN: Rank 2
response of n to T-shock
5 10 15 20-0.8
0.0
0.8
1.6
JPN: Rank 2
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
AUS: Rank 1
response of n to T-shock
5 10 15 20-1.2
-0.8
-0.4
-0.0
0.4
CHE: Rank 1
response of n to T-shock
5 10 15 20-2
-1
0
1
Figure 4c: VECM 0 (Cont.) ESP: Rank 1
response of n to T-shock
5 10 15 20-4
-2
0
2
NLZ: Rank 2
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
Figure 5a: USA, VECM 1-7 VECM 1: Rank 1
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VECM 2: Rank 2
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VECM 3: Rank 2
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
1.0
VECM 4: Rank 1
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
1.0
Figure 5b: USA, VECM 1-7 (Cont.) VECM 5: Rank 3
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
1.0
VECM 6: Rank 2
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
VECM 7: Rank 3
response of n to T-shock
5 10 15 20-1.0
-0.5
0.0
0.5
1.0
Figure 6a: FRA, VECM 1-7 VECM 1: Rank 2
response of n to T-shock
5 10 15 20-0.50
-0.25
0.00
0.25
0.50
VECM 3: Rank 2
response of n to T-shock
5 10 15 20-0.50
-0.25
0.00
0.25
0.50
VECM 4: Rank 4
response of n to T-shock
5 10 15 20-0.50
-0.25
0.00
0.25
0.50
VECM 6: Rank 4
response of n to T-shock
5 10 15 20-0.50
-0.25
0.00
0.25
0.50
Figure 6b: GBR, VECM 1-7 VECM 1: Rank 1
response of n to T-shock
5 10 15 20-1.6
-0.8
0.0
0.8
VECM 3: Rank 1
response of n to T-shock
5 10 15 20-1.6
-0.8
0.0
0.8
VECM 4: Rank 1
response of n to T-shock
5 10 15 20-1.6
-0.8
0.0
0.8
VECM 6: Rank 3
response of n to T-shock
5 10 15 20-2
-1
0
1
Figure 6c: ITA, VECM 1-7 VECM 1: Rank 2
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
VECM 3: Rank 3
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
VECM 4: Rank 3
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
VECM 6: Rank 2
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
Figure 6d: CAN, VECM 1-7 VECM 2: Rank 1
response of n to T-shock
5 10 15 20-0.8
0.0
0.8
1.6
VECM 2: Rank 2
response of n to T-shock
5 10 15 20-0.8
0.0
0.8
1.6
VECM 6: Rank 3
response of n to T-shock
5 10 15 20-0.8
0.0
0.8
1.6
VECM 7: Rank 3
response of n to T-shock
5 10 15 20-0.8
0.0
0.8
1.6
Figure 6e: JPN, VECM 1-7 VECM 1: Rank 1
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
VECM 2: Rank 2
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
VECM 4: Rank 2
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
VECM 7: Rank 2
response of n to T-shock
5 10 15 20-0.5
0.0
0.5
1.0
1.5
Figure 6f: AUS, VECM 1-7 VECM 1: Rank 1
response of n to T-shock
5 10 15 20-1.2
-0.8
-0.4
-0.0
0.4
VECM 2: Rank 1
response of n to T-shock
5 10 15 20-1.2
-0.8
-0.4
-0.0
0.4
VECM 6: Rank 2
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
VECM 7: Rank 2
response of n to T-shock
5 10 15 20-1.5
-1.0
-0.5
0.0
0.5
Figure 6g: CHE, VECM 1-7 VECM 1: Rank 2
response of n to T-shock
5 10 15 20-2
-1
0
1
VECM 2: Rank 2
response of n to T-shock
5 10 15 20-2
-1
0
1
VECM 6: Rank 3
response of n to T-shock
5 10 15 20-2
-1
0
1
VECM 7: Rank 4
response of n to T-shock
5 10 15 20-2
-1
0
1
Figure 6h: ESP, VECM 1-7 VECM 1: Rank 3
response of n to T-shock
5 10 15 20-4
-2
0
2
VECM 3: Rank 1
response of n to T-shock
5 10 15 20-4
-2
0
2
VECM 4: Rank 1
response of n to T-shock
5 10 15 20-5.0
-2.5
0.0
2.5
VECM 6: Rank 3
response of n to T-shock
5 10 15 20-4
-2
0
2
Figure 6i: NZL, VECM 1-7 VECM 1: Rank 3
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
VECM 2: Rank 1
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
VECM 3: Rank 2
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
VECM 7: Rank 2
response of n to T-shock
5 10 15 20-2.7
-1.8
-0.9
-0.0
0.9
![Neue Bücher in der Volkswirtschaftlichen Bibliothek I ... · and macroeconomics in a rigorous but easy to follow manner ... Macroeconomics / Manfred Gärtner. - 3. ed. - Harlow [u.a.]](https://img.pdfslide.org/doc/110x75/5b805db97f8b9a2a088d2a89/neue-buecher-in-der-volkswirtschaftlichen-bibliothek-i-and-macroeconomics.jpg)
