Macroeconomics and Asset Markets: some Mutual Implications. · Harald Uhlig Fachbereich...

Macroeconomics and AssetMarkets: some Mutual

Implications.Harald Uhlig

Fachbereich Wirtschaftswissenschaften

Humboldt Universitat zu Berlin

Deutsche Bundesbank, CentER and CEPR

uhlig@wiwi.hu-berlin.de

Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 1/75

The Issue

• Economic Risks: unemployment, stock returns,business cycles. How much do they matter?

• Economic Policy: Risk Management.

• Macroeconomic Risks: not diversifiable.•

• Price of Risks: Asset Markets.

Asset Markets vs Macro

• Asset pricing literature: take economic choices asgiven, determine prices from preferences or viceversa.

• Macro literature: take preferences as given, solvefor economic choices.

• Each imposes discipline on the other.

Some literature• Mehra-Prescott. Cochrane’s book (2001),

Campbell’s survey (2004).

• Habit formation: Constantinides et al., Abel,Campbell-Cochrane. Risk av. vs intertemp.subst.: Epstein-Zin, Weil, Tallarini. Robustcontrol: Hansen-Sargent-Tallarini. Nonstandardpreferences: Kahnemann-Tversky,Backus-Routledge-Zin, many more .

• E[u′(ci)] 6= u′(E[ci])): Constantinides,Storesletten et al.. Taxes: McGrattan-Prescott.

• Joint explanation: Jermann, Boldrin - Christiano -Fisher, Lettau-Uhlig,Tallarini , Guvenen.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 4/75

Asset Market Facts.

• Campbell (2004)

• Equity premium: 7.2% annually. Volatility:15.5%. Sharpe Ratio: 0.46.

• Excess returns are forecastable, in particular atlonger horizons.

• Lettau-Ludvigson.cayt: consumption, assets andincome are cointegrated. Deviations predictcorrections in asset prices, not changes inconsumption.

• The safe rate is not very volatile: 1.7%annually.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 5/75

Macroeconomic Facts.

• Cooley and Prescott (1999)

• Labor, labor productivity, consumption are allprocyclical.

• Consumption fluctuates less than output,hours nearly as much, and investment muchmore.

The Question• What is needed to generate both the risk premium

on asset markets as well as the underlyingeconomic choices for consumption, leisure etc?

• Or: given that asset markets imply high riskaversion at the observed economic choices, whatis needed in general equilibrium to generate theseeconomic choices under such high risk aversion?

• Or: how can we keep risk bottled up in a macromodel in such a way that the risk premiumremains high?

Results• High risk aversion is not enough.

• Fix 1: non-separability between consumption andleisure. Does not work.

• Fix 2: frictions on labor markets, exogenouswages. This works. Plausible?

• Fix 3: heterogeneous agents. Does not work.

• Fix 4: Epstein-Zin preferences. This works.Another paper.

• “Generic” real business cycle model.

• Nonseparability: consumption vs leisure.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 8/75

A simple example• Imagine three periods.

1. given endowment, agent chooses capitalk1,portfolio of zero net supply assets, and thusconsumptionc1.

2. shocks to labor productivityγ2. ReturnsR2

on assets. Agent chooses laborn2, investmentx2, consumptionc2.

3. Agent receives returns from capitalinvestment, works, consumes.

A simple example continued

• Asset pricing:1 = βEt

u′(c2)u′(c1)

• Finance: c2 = γ2 + const.High u′′(c2)c2/u′(c2) and high correlation ofc2andR2 induce high risk premium.

• Macro: c2 = γ2n2 +Rkk1 − x2.High risk aversion means: agents wish to avoidfluctuations inc2, i.e. avoid risk.

• Escape hatches for risk:1. Investment.2. Labor.

A simple example continued• Closing the escape hatches for risk:

1. Investment: per adjustment costs to capital.Jermann, others. Extreme: fix capital.

2. • Labor: Literature fixes labor. Here: labor iscountercyclical.. Data: laborpro-cyclical,important feature of business cycles.

• Solution: wage rigidities. Extreme: fixwages,make labor fluctuationsdemanddriven. Now: highγ → highn2.

• Wage rigidities: Keynes, Hall-Shimer,Blanchard-Gali, others.

• Utility: nonseparability between consumptionand leisure?

Overview

1. Introduction•

2. Asset pricing•3. Macroeconomic consequences•

4. A two agent model.•

5. Conclusions.•

Overview: asset pricing.

1. Introduction•

2. Asset pricing(a) Theory(b) Data•(c) Preference implications•

3. Macroeconomic consequences•

5. Conclusions.•

Asset Pricing: theory•

1 = Et[βΛt+1

Rt+1] (1)

• Notation.λt+1 = log Λt+1, etc. No tilde:log-deviation.

0 = log β+log(

∆λt+1 + rt+1

• Assume joint log-normality

Asset Pricing: theory 2• Risk-free rate:

rft = − log β − Et[∆λt+1] −

λ,t (3)

• Define theSharpe Ratio

SRt =logEt[Rt+1] − rf

• Result:SRt = −ρλ,r,tσλ,t (4)

SRmaxt = σλ,t (5)

Utility function

∞∑

βtU(Ct, Lt)

, stationarity

ηcc = −UCC(C, L)C

UC(C, L)

ηcl,c =UCL(C, L)C

UL(C, L)

ηcl,l =UCL(C, L)L

UC(C, L)

ηll = −ULL(C, L)L

UL(C, L)Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 16/75

Utility function.

• From macro:

κ =ηcl,c

ηcl,l

=UC(C, L)C

UL(C, L)L

is the ratio of the expenditure shares forconsumption and leisure. We shall see:κ ≈ 0.58.

• Convexity:

ηll ≥ηcl,cηcl,l

η2cl,l

Asset pricing: theory 3•

λt = −ηccct + ηcl,llt

• For risk free rate:

Et[∆λt+1] = −ηccEt[∆ct+1] + ηcl,lEt[∆lt+1]

• Sharpe ratio with nonseparable utility:

SRt = ηccρc,r,tσc,t − ηcl,lρl,r,tσl,t (6)

• The Sharpe ratio also depends on thecross-derivative termηcl,l. Therefore, assetpricing facts can be explained with low cons. riskaversion, ifηcl,l etc. are chosen appropriately.

1. Introduction•

2. Asset pricing(a) Theory•(b) Data(c) Preference implications•

5. Conclusions.•

Asset pricing: data• Holding period:k quarters. Volatilities: of∆kct

etc.. Ignores predictable part exceptunconditional mean.

• Calculate correlations at various horizons.

• Data: log excess return of S&P 500 (withdividends reinvested) versus 1-year T-bill.

Asset pricing: data 2k std.dev. Sharpe Ann. Sharpe

(Quart.) of rt+1 ratio ratio,SR√

1 6.87 0.15 0.302 10.37 0.21 0.293 13.18 0.24 0.284 15.40 0.27 0.278 22.21 0.36 0.2612 26.75 0.47 0.2716 29.47 0.63 0.3120 31.41 0.82 0.37

Asset pricing: data 3k σl σc ρ(c, l) ρ(l, r) ρ(c, r)

(Quart.) (leis.) (cons.)1 0.45 0.67 -0.33 -0.07 0.272 0.80 1.04 -0.42 -0.08 0.343 1.11 1.33 -0.51 -0.15 0.374 1.36 1.64 -0.55 -0.21 0.398 2.10 2.42 -0.62 -0.39 0.4212 2.46 2.73 -0.62 -0.50 0.3416 2.49 3.01 -0.57 -0.58 0.3920 2.39 3.11 -0.48 -0.59 0.41

Asset pricing: data 4• Time variation in volatility: GARCH,

σ2l,t = (1 − φ)σ2

l,t−1 + φ(lt − lt−1 − E[lt − lt−1])2

• Assuming constant correlations,

∆SRt+1 = ηccρc,r∆σc,t+1 − ηcl,lρl,r∆σl,t+1 (7)

• Interpretation: surprise increases inmacroeconomic volatility (i.e rising businesscycle uncertainty) should lead to surprise falls instock prices. Data: they do for leisure.

Macroeconomic Volatility•

1970 1975 1980 1985 1990 1995 2000 20050

cons. std.dev.leisure std.dev.

Asset pricing: data 5k σ of σ of ρ(σc, σl) ρ(σl, r) ρ(σc, r)

σl,t σc,t

1 0 0.01 0.18 0.06 0.002 0.01 0.02 0.22 -0.01 -0.003 0.02 0.02 0.24 -0.13 -0.014 0.02 0.03 0.21 -0.23 -0.008 0.03 0.07 0.17 -0.46 0.0212 0.04 0.10 0.24 -0.53 -0.0716 0.05 0.11 0.38 -0.52 -0.1120 0.05 0.10 0.43 -0.52 -0.09

Leisure vol. and returns,k = 8.

−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6−60

Leisure volatility change

1. Introduction•

2. Asset pricing(a) Theory•(b) Data•(c) Preference implications

5. Conclusions.•

Preference implications• Benchmark case:ηcl,l = 0. Campbell (2004).

ηcc =SR

ρc,rσc

1.64% ∗ 0.39= 42 for k = 4

• With ηcl,l 6= 0:

ηcl,l =SR− ηccρc,rσc

−ρl,rσl

• Desirable:ηll as low as possible. Thus,

ηll =κη2

Preference implications 2ηcc ηcll ηll

k=4 k=8 k=4 k=83.0 84.7 41.1 1389.2 327.55.0 80.4 38.7 749.8 173.510.0 69.5 32.5 280.0 61.215.0 58.5 26.3 132.6 26.720.0 47.6 20.1 65.8 11.730.0 25.8 7.7 12.9 1.140.0 4.0 -4.7 0.2 0.350.0 -17.9 -17.1 3.7 3.4

The cross-derivative termηcl,l.

0 10 20 30 40 50 60−40

η cl,l

k= 4k= 8

Leisure risk aversionηll.

0 10 20 30 40 50 600

k= 4k= 8

Overview

1. Introduction•

2. Asset pricing•

3. Macroeconomic consequences4. A two agent model.•

5. Conclusions.•

A generic model

∞∑

βtU(Ct, Lt)

Ct +Xt = Yt = ZtF (Kt−1, Nt)

Kt = (1 − δ)Kt−1 +G

Kt−1

1 = Nt + Lt

Ct:consumption.Lt: leisure.Xt: investment.Kt:capital.Yt: output.Nt: labor.Zt: TFP.U : utilityfunction.F : production function for output, const.ret. to scale.G: adjustment cost function for capital.

Utility function

ηcc = −UCC(C, L)C

UC(C, L)

ηcl,c =UCL(C, L)C

UL(C, L)

ηcl,l =UCL(C, L)L

UC(C, L)

ηll = −ULL(C, L)L

UL(C, L)≥

ηcl,c

ηcl,l

η2cl,l

Production function

θ =FK(K, N)K

F (K, N)

φkk = −FKK(K, N)K

FK(K, N)

φnn = −FNN(K, N)N

FN(K, N)

Production function 2

φkk =FKN(K, N)N

FK(K, N)

φnn =FKN(K, N)K

FN(K, N)

Cobb-Douglas:φkk = 1 − θ andφnn = θ

Adjustment cost function

• G(δ) = δ

• G′(δ) = 1

ξ = −1

G′′(δ)δ> 0

• ξ = ∞: no adj. cost.ξ = 0.23.

Loglinearization

feasib. yt = XYxt +

1 − XY

goods prod.: yt = θkt−1 + (1 − θ)nt

cap. prod.: kt = (1 − δ)kt−1 + δxt

wages: wt = zt + φnn(kt−1 − nt)

dividends: dt = zt − φkk(kt−1 − nt)

time: lt = − 1−LLnt

shadow v. of c: λt = −ηccct + ηcl,lltshadow v. of l:: λt + wt = ηcl,cct − ηllltadj. cost: ψt = 1

ξ(xt − kt−1)

ret. on cap.: rt = R−1+δR

dt − ψt−1 + 1Rψt

asset pric.: 0 = Et [λt+1 − λt + rt+1]

Free Parametersparameter econ. calibr.

θ cap. share 0.36δ deprec. 0.025R gross cap. ret. 1.01φnn elast. of w. θ (Cobb-Douglas)φkk elast. of d. 1 − θ (Cobb-Douglas)ξ ≥ 0 adj. cost 0.23 or∞L leis. share 2/3ηcc cons. risk. av. [1,∞)

ηcl,l cross der. (−∞,∞)

Parameter RestrictionsRestrictions

parameter theory econ. calibr.XY

= δθR−1+δ

inv. share 25.7%

κ =ηcl,c

ηcl,l= (1−L)

(1− XY )

(1−θ) rel. exp. sh. 0.58

ηll ≥κη2

ηccleis. risk. av. [0,∞)

Macroeconomic Implications• Exogenous process for technology:

zt = 0.95zt−1 + ǫt

• σǫ = 0.712.

The benchmark model• A representative agent. Fixηcc = 40. Vary the

adjustment costs to capitalξ.

One agent, no frictions,ηcc = 40.ξ−1 σy σn ρn,y σc ρc,y σx ρx,y SR σrf

0 0.88 0.38 -0.13 0.03 0.92 3.46 1.000.01 0.10

1 0.21 1.12 -1.00 0.03 1.00 0.74 1.000.02 0.15

2 0.13 1.24 -1.00 0.03 1.00 0.43 1.000.02 0.16

3 0.10 1.28 -1.00 0.03 1.00 0.31 1.000.02 0.16

4 0.09 1.31 -1.00 0.04 1.00 0.24 1.000.02 0.17

5 0.08 1.33 -1.00 0.04 1.00 0.20 1.000.02 0.18

U.S.: 2.13 1.79 0.86 1.30 0.82 8.07 0.860.26 1.7

The benchmark model• Verdict: A failure. High risk aversion alone does

not do the trick. Agents find ways to avoid risk,e.g. per countercyclical labor. The Sharpe ratio istoo low.

Fix 1: nonseparable preferences• A representative agent. UseU(C,L).

• Vary ηcc. Calculate the impliedηcl,c, ηcl,l, ηll,using the asset market equations, theleisure-to-consumption ratio and the convexitycondition.

• Vary ξ.

One agent, no frictions,U(C,L)

ηcc σy σn ρn,y σc ρc,y σx ρx,y SR σrf

ξ = ∞, ξ−1 = 0:

1 1.30 0.32 0.28 7.01 -0.27 22.99 0.470.00 0.01

5 1.29 0.63 0.58 2.44 -0.57 11.12 0.840.00 0.04

20 1.08 0.46 0.48 0.23 -0.37 4.60 0.990.01 0.08

40 0.85 0.39 -0.24 0.02 0.85 3.34 1.000.02 0.11

U.S.: 2.13 1.79 0.86 1.30 0.82 8.07 0.860.26 1.7

ξ = 0.5, ξ−1 = 4:

1 0.89 0.05 -1.00 1.11 1.00 0.24 1.000.00 0.00

5 0.77 0.24 -1.00 0.95 1.00 0.26 1.000.00 0.02

20 0.41 0.80 -1.00 0.44 1.00 0.33 1.000.01 0.08

40 0.08 1.31 -1.00 0.04 -1.00 0.46 1.000.02 0.17

U.S.: 2.13 1.79 0.86 1.30 0.82 8.07 0.860.26 1.7

ξ = 0.25, ξ−1 = 2:

1 0.89 0.05 -1.00 1.15 1.00 0.13 1.000.00 0.00

5 0.77 0.24 -1.00 0.98 1.00 0.14 1.000.00 0.02

20 0.39 0.84 -1.00 0.46 1.00 0.18 1.000.01 0.09

40 0.03 1.40 -0.99 0.04 -0.99 0.26 1.000.02 0.18

U.S.: 2.13 1.79 0.86 1.30 0.82 8.07 0.860.26 1.7

Fix 1: nonseparable preferences• Verdict: A failure. Risk aversion is not really

gone. Agents shift risk to where it hurts the least,but still avoid risk. The Sharpe ratio is too low.

Fix 2: sluggish wages.• Replace FOC wrt leisure with

wt = µwt−1 + (1 − µ)wft (10)

and the definition of the frictionless wage,

wft = −λt + ηcl,cct − ηlllt (11)

• Hall, Shimer, others. This specification:Blanchard-Gali.

• Includes frictionless case atµ = 0.

frictions, ηcc = 40, ξ = 0.5

µ σy σn ρn,y σc ρc,y σx σw ρw,y SR σrf

0.00 0.08 1.31 -1.00 0.04 -1.00 0.46 1.40 1.000.02 0.17

0.50 0.20 1.24 -0.63 0.04 0.09 0.78 1.37 0.710.04 1.01

0.80 0.52 1.16 -0.08 0.11 0.88 1.81 1.31 0.470.09 2.57

0.90 0.90 1.23 0.36 0.20 0.96 3.03 1.24 0.370.13 3.54

0.95 1.37 1.48 0.69 0.31 0.98 4.56 1.12 0.310.18 3.97

0.96 1.53 1.59 0.77 0.35 0.99 5.09 1.07 0.290.19 4.04

0.97 1.74 1.75 0.84 0.41 0.99 5.75 0.98 0.270.21 3.96

0.98 2.00 1.96 0.91 0.47 0.99 6.57 0.84 0.250.23 3.61

0.99 2.28 2.23 0.97 0.57 1.00 7.43 0.57 0.220.27 3.20

* U.S.: 2.13 1.79 0.86 1.30 0.82 8.07 0.89 0.140.26 1.7Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 51/75

Fix 2: sluggish wages.• Verdict: This works! Surprisingly reasonable

numbers forµ = 0.97.

• Are wages now too sluggish?

• Agents wish to avoid risk, but cannot, due tolabor market rigidities. Is this reasonable?Welfare costs?

Overview

1. Introduction•

2. Asset pricing•

4. A two agent model.5. Conclusions.•

Fix 3: A two-agent economy.• Campbell-Cochrane (1999): highly nonlinear,

external habit explain asset pricing observations.

• Ljungqvist-Uhlig (2003): endogenizingconsumption choices with CC preferences hasunusual consequences. E.g., an agent issignificantly better off by periodically destroyingparts of a constant stream of endowment. Reason:utility has local and global nonconcavities.• •

• Guvenen (2003): habit stock = consumption of“poor”. Asset pricing in terms of consumption ofparticipating agents. Proposes two-agenteconomy.

A two-agent economy.• “Capitalist”: owns capital, does not work, trades

in the riskless bond. Risk aversion = 2.

• “Worker”: owns time, does not trade in capital.Trades in the riskless bond. Risk aversion = 10.

• Guvenen (2003): emphasizes nonlinearities, etc..Here: extend benchmark model and study theloglinearized dynamics. Easier to understand.

• Guvnenen (2003) fixes labor,ηll = ∞.Guvenen-Kuruscu (2006): Cobb-Douglaspreferences. Large volatility of tech. shock.

• We considerηll = ∞, ηll = 0, Cobb-Douglasutility versus sluggish wages.

The capitalist.

∞∑

βtU (C)(C(C)t )

C(C)t +Bt +Xt = DtKt−1 +Rf

t−1Bt−1

Kt = (1 − δ)Kt−1 +G

Kt−1

The worker.

∞∑

βtU (W )(C(W )t , Lt)

C(W )t −Bt = WtNt −Rf

t−1Bt−1

1 = Nt + Lt

Four Possibilities:

• η(W )ll = ∞: Guvenen 2003.

• U(C,L) Cobb-Douglas: Guvenen-Kuruscu 2006.

• η(W )ll = 0.

• Sluggish wages.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 57/75

Loglinearization: the changes.

yt = XYxt + C(C)

Yc(C)t + C(W )

Yc(W )t

λ(W )t = −η

(W )cc c

(W )t + η

(W )cl,l lt

λ(W )t + wt = η

(W )cl,c ct − η

(W )ll lt

λ(C)t = −η

(C)cc c

Yc(W )t − bt = (1 − θ)(wt + nt) − R B

Yrft−1 − Rbt−1

0 = Et

λ(C)t+1 − λ

(C)t + rt+1

0 = Et

λ(C)t+1 − λ

(C)t + rf

0 = Et

λ(W )t+1 − λ

(W )t + rf

Free parametersparam. econ. calibr.θ capital share 0.4δ deprec. rate 0.02R gross cap. return 1.01φnn elast. of wages θ

φkk elast. of div. 1 − θ

ξ ≥ 0 adj. cost 0.23L leisure share 2/3

η(C)cc cons. risk. avers. cap. 2

η(W )cc cons. risk. avers. worker10 or CD

η(W )cl,l cross derivative 0 or CDB/Y debt-to-GDP ratio 0

Parameter restrictionsRestrictions

param. theory econ. calibr.XY

= δθR−1+δ

inv. share 25.7%C(W )

Y1 − θ − (R− 1) B

Ycons. share (W) 60%

Y1 − X

Y− C(C)

Ycons. share (C) 14.3%

κ =η(W )cl,c

η(W )cl,l

= (1−L)L

(1−θ) rel.exp.shares 0.5

η(W )ll ≥

κ(η(W )cl,l )

ηccleis.risk.av. 0,∞ or CD

Cons. volatility of capitalist:• To nail the Sharpe ratio with this model and a

relative risk aversion of two, the consumption ofthe capitalist must be quite volatile,

σ(C)c ≥

η(C)cc

2= 13.5% for k = 4

• Plausible? Evidence on luxury goods, seeAït-Sahalia - Parker - Yogo (2002).

Parameters• E.g. Cobb Douglas preferences:

U(Ct, Lt) =(Cν

t (1 − Lt)1−ν)1−αi

1 − αi

whereν = 0.64 for both types of agents, andαi = 2 for capital holders, butαi = 10 forworkers.

• As in Guvenen:ξ = 0.23.

• Guvenen (2003):σǫ = 2. Here:σǫ = 0.712. Thisreduces the Sharpe ratio by nearly a factor ofthree compared to Guvenen.

Two-agent economy.σy σn σc σx ρn,y ρc,y ρx,y SR σrf

Fixed labor:

0.91 0.00 0.90 0.93 -1.00 1.00 1.00 0.06 0.58

Flexible labor:

0.22 1.16 0.21 0.24 -1.00 1.00 1.00 0.02 0.16

Cobb-Douglas utility:

0.99 0.14 1.05 0.83 1.00 1.00 1.00 0.06 0.52

Slow adjustment of wages,µ = 0.97:

1.70 1.68 1.57 2.04 0.89 1.00 1.00 0.15 2.77

U.S. data:

2.13 1.79 1.30 8.07 0.86 0.82 0.86 0.26 1.7Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 63/75

Fix 3: two agents.• Verdict: This does not do much. Agents share

and shift risk to where it hurts the least, ...

• ... unless wages are sluggish. But for that, onedoes not need a two-agent model.

• In fact, the representative agent model looksbetter, if anything.

Overview

1. Introduction•

2. Asset pricing•

5. Conclusions.

Conclusions• High risk aversion is not enough.

• Fix 1: non-separability between consumption andleisure. Does not work.

• Fix 2: frictions on labor markets, exogenouswages. This works. Plausible?

• Fix 3: heterogeneous agents. Does not work.

• (Fix 4: Epstein-Zin preferences. This works.Another paper.)

• “Generic” real business cycle model.

• Nonseparability: consumption vs leisure.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 66/75

Conclusions 2.

• Mutual discipline of asset market observationsand macroeconomic observations:• Economic choicessuch as consumption and

leisure ...• are taken asexogenousin asset pricing

literature and suggest preferencespecifications, ...

• which in turn may have undesirablemacroeconomic consequences, once theseeconomic choices are endogenized.

• Key: alternative labor market paradigm.Exogenous law for wage movement does thetrick!

Campbell-Cochrane. •

∞∑

δt (Ct −Xt)1−γ

1 − γ

• Surplus consumption ratio

Sat ≡ (Ca

t −Xt)/Cat

• Use lower-case to denote logs.

Campbell-Cochrane 2.

• Assumption:

sat+1 = (1 − φ)s+ φsa

t + λ(sat ) (cat+1 − cat − g) ,

whereφ ∈ [0, 1), g ands are parameters, and

λ(sa) =

S−1√

1 − 2(sa − s) − 1, sa ≤ smax;

0, sa ≥ smax;

• Campbell-Cochrane: assume consumption to bean exogenous random walk.

• Explains lots of asset pricing facts.

Ljungqvist-Uhlig

• Ljungqvist-Uhlig: consider an economy with aconstant stream of endowment. Let an agent withCC-preferences choose consumption, subject toconsumption≤ endowment.

• Analyze the social planners problem

Ljungqvist-Uhlig, 2

• A one-time destruction of consumption orperiodic destruction of consumption vastlyincreases welfare.

• Optimal decision rule look bizarre. Resultspreliminary.

• CC preferences are nonconcave.

• Habit decreases in consumption when increasingconsumption by more than 20%.

Welfare gains

0 1 2 3 4 5 6 7 8 9 10−8

Percent endowment destruction

... from a one-time endowment destruction.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 72/75

Welfare gainsk 1% 5% 10% 15%2 4.89 8.36 13.66 8.686 2.48 9.08 15.45 9.6512 1.37 9.03 15.91 9.8624 0.72 8.52 15.89 9.89120 0.24 4.95 13.40 8.51

... from periodic destruction everyk periods.

Habit function.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

Consumption deviation in percent from steady state

Next-period habit as function of consumption.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. uhlig@wiwi.hu-berlin.de – p. 74/75

Decision rule for consumption•

Macroeconomics and Asset Markets: some Mutual Implications. · Harald Uhlig Fachbereich...

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