Macroeconomics and AssetMarkets: some Mutual
Implications.Harald Uhlig
Fachbereich Wirtschaftswissenschaften
Humboldt Universitat zu Berlin
Deutsche Bundesbank, CentER and CEPR
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 2/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 3/75
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. [email protected] – 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. [email protected] – 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 6/75
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?
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 7/75
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. [email protected] – 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 9/75
A simple example continued
• Asset pricing:1 = βEt
[
u′(c2)u′(c1)
R2
]
• 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 10/75
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?
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 11/75
Overview
1. Introduction•
2. Asset pricing•3. Macroeconomic consequences•
4. A two agent model.•
5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 12/75
Overview: asset pricing.
1. Introduction•
2. Asset pricing(a) Theory(b) Data•(c) Preference implications•
3. Macroeconomic consequences•
4. A two agent model.•
5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 13/75
Asset Pricing: theory•
1 = Et[βΛt+1
Λt
Rt+1] (1)
• Notation.λt+1 = log Λt+1, etc. No tilde:log-deviation.
•
0 = log β+log(
Et
[
exp(
∆λt+1 + rt+1
)])
(2)
• Assume joint log-normality
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 14/75
Asset Pricing: theory 2• Risk-free rate:
rft = − log β − Et[∆λt+1] −
1
2σ2
λ,t (3)
• Define theSharpe Ratio
SRt =logEt[Rt+1] − rf
t
σr,t
• Result:SRt = −ρλ,r,tσλ,t (4)
SRmaxt = σλ,t (5)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 15/75
Utility function
U = E
[
∞∑
t=0
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. [email protected] – 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
ηcc
= κ
(
η2cl,l
ηcc
)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 17/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 18/75
Overview: asset pricing.
1. Introduction•
2. Asset pricing(a) Theory•(b) Data(c) Preference implications•
3. Macroeconomic consequences•
4. A two agent model.•
5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 19/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 20/75
Asset pricing: data 2k std.dev. Sharpe Ann. Sharpe
(Quart.) of rt+1 ratio ratio,SR√
4/j
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 21/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 22/75
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
etc.
• 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 23/75
Macroeconomic Volatility•
1970 1975 1980 1985 1990 1995 2000 20050
0.2
0.4
0.6
0.8
1
1.2
1.4
Date
Per
cent
cons. std.dev.leisure std.dev.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 24/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 25/75
Leisure vol. and returns,k = 8.
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6−60
−40
−20
0
20
40
60
Leisure volatility change
Exc
ess
Ret
urn
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 26/75
Overview: asset pricing.
1. Introduction•
2. Asset pricing(a) Theory•(b) Data•(c) Preference implications
3. Macroeconomic consequences•
4. A two agent model.•
5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 27/75
Preference implications• Benchmark case:ηcl,l = 0. Campbell (2004).
ηcc =SR
ρc,rσc
=0.27
1.64% ∗ 0.39= 42 for k = 4
(8)
• With ηcl,l 6= 0:
ηcl,l =SR− ηccρc,rσc
−ρl,rσl
(9)
• Desirable:ηll as low as possible. Thus,
ηll =κη2
cl,l
ηcc
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 28/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 29/75
The cross-derivative termηcl,l.
0 10 20 30 40 50 60−40
−20
0
20
40
60
80
100
ηcc
η cl,l
k= 4k= 8
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 30/75
Leisure risk aversionηll.
0 10 20 30 40 50 600
200
400
600
800
1000
1200
1400
ηcc
η ll
k= 4k= 8
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 31/75
Overview
1. Introduction•
2. Asset pricing•
3. Macroeconomic consequences4. A two agent model.•
5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 32/75
A generic model
maxE
[
∞∑
t=0
βtU(Ct, Lt)
]
Ct +Xt = Yt = ZtF (Kt−1, Nt)
Kt = (1 − δ)Kt−1 +G
(
Xt
Kt−1
)
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 33/75
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
ηcc
)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 34/75
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)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 35/75
Production function 2
Thus,
φkk =FKN(K, N)N
FK(K, N)
φnn =FKN(K, N)K
FN(K, N)
Cobb-Douglas:φkk = 1 − θ andφnn = θ
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 36/75
Adjustment cost function
• G(δ) = δ
• G′(δ) = 1
•
ξ = −1
G′′(δ)δ> 0
• ξ = ∞: no adj. cost.ξ = 0.23.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 37/75
Loglinearization
feasib. yt = XYxt +
(
1 − XY
)
ct
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]
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 38/75
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. (−∞,∞)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 39/75
Parameter RestrictionsRestrictions
parameter theory econ. calibr.XY
= δθR−1+δ
inv. share 25.7%
κ =ηcl,c
ηcl,l= (1−L)
L
(1− XY )
(1−θ) rel. exp. sh. 0.58
ηll ≥κη2
cl,l
ηccleis. risk. av. [0,∞)
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 40/75
Macroeconomic Implications• Exogenous process for technology:
zt = 0.95zt−1 + ǫt
• σǫ = 0.712.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 41/75
The benchmark model• A representative agent. Fixηcc = 40. Vary the
adjustment costs to capitalξ.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 42/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 43/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 44/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 45/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 46/75
One agent, no frictions,U(C,L)
ηcc σy σn ρn,y σc ρc,y σx ρx,y SR σrf
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 47/75
One agent, no frictions,U(C,L)
ηcc σy σn ρn,y σc ρc,y σx ρx,y SR σrf
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 48/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 49/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 50/75
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. [email protected] – 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?
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 52/75
Overview
1. Introduction•
2. Asset pricing•
3. Macroeconomic consequences•
4. A two agent model.5. Conclusions.•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 53/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 54/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 55/75
The capitalist.
maxE
[
∞∑
t=0
βtU (C)(C(C)t )
]
C(C)t +Bt +Xt = DtKt−1 +Rf
t−1Bt−1
Kt = (1 − δ)Kt−1 +G
(
Xt
Kt−1
)
Kt−1
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 56/75
The worker.
maxE
[
∞∑
t=0
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. [email protected] – 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
(C)t
C(W )
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
t
]
0 = Et
[
λ(W )t+1 − λ
(W )t + rf
t
]
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 58/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 59/75
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%
C(C)
Y1 − X
Y− C(C)
Ycons. share (C) 14.3%
κ =η(W )cl,c
η(W )cl,l
= (1−L)L
C(W )
Y
(1−θ) rel.exp.shares 0.5
η(W )ll ≥
κ(η(W )cl,l )
2
ηccleis.risk.av. 0,∞ or CD
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 60/75
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 ≥
SR
η(C)cc
=0.27
2= 13.5% for k = 4
• Plausible? Evidence on luxury goods, seeAït-Sahalia - Parker - Yogo (2002).
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 61/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 62/75
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. [email protected] – 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 64/75
Overview
1. Introduction•
2. Asset pricing•
3. Macroeconomic consequences•
4. A two agent model.•
5. Conclusions.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 65/75
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. [email protected] – 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!
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 67/75
Campbell-Cochrane. •
•
E0
[
∞∑
t=0
δt (Ct −Xt)1−γ
− 1
1 − γ
]
• Surplus consumption ratio
Sat ≡ (Ca
t −Xt)/Cat
• Use lower-case to denote logs.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 68/75
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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 69/75
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
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 70/75
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%.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 71/75
Welfare gains
0 1 2 3 4 5 6 7 8 9 10−8
−6
−4
−2
0
2
4
6
8
10
Percent endowment destruction
Wel
fare
in p
erce
nt c
onsu
mpt
ion
incr
ease
... from a one-time endowment destruction.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – 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.
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 73/75
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
0
0.05
Consumption deviation in percent from steady state
Nex
t per
iods
hab
it de
viat
ion
from
ste
ady
stat
e in
per
cent
Next-period habit as function of consumption.Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 74/75
Decision rule for consumption•
Macroeconomics and Asset Markets: some Mutual Implications. Harald Uhlig, Humboldt Universitat zu Berlin. [email protected] – p. 75/75