The Returns on Human Capital - New York...

The Returns on Human Capital

H. Lustig and S. Van Nieuwerburgh

Sept 18, 2007

H. Lustig and S. Van Nieuwerburgh The Returns on Human Capital

Introduction

Many asset pricing models try to relate consumption growthto asset returns

Lustig and Van Nieuwerburgh ask the question: Whatrestrictions does the single agent framework impose on thejoint distribution of aggregate consumption growth andmarket returns?

Market returns are a weighted average of the returns onfinancial and human wealth

Instead of making assumptions directly on the unobservedhuman wealth return process, Lustig and Van Nieuwerburghimpute consumption innovations not attributed to news aboutcurrent or future financial returns to the returns on humanwealth


Results

Other models cannot match certain moments of their impliedconsumption growth

Innovations in financial asset returns are negatively correlatedwith innovations in human capital returns, for any EIS

Implied total market return is negatively correlated withreturns on financial wealth if EIS < 1

Hedging component of the risk premium is positive, unlikemost models


Consumption Volatility and Correlation Puzzle

In the data, the volatility of financial asset returns is muchhigher than that of aggregate consumption and the series areonly weakly correlated

If an agents portfolio contains only financial wealth, the modelimplied volatility of consumption is 5 times too high, and thecorrelation of innovations with financial assets is four timestoo high, regardless of the EIS


Epstein-Zin Preferences

Agents maximize:

Ut = ((1− β)C(1−γ)/θt + β(EtU

1−γt+1 )1/θ)θ/(1−γ)

Subject toWt = Rm

t+1(Wt − Ct)

Where

Ct is consumptionRm

t+1 is return on market portfolio

θ = 1−γ1−(1/σ)

γ is relative risk aversionσ is EIS


Distribution of Consumption and Asset returns

Following Campbell (1993), linearize the budget constraintand Euler Equation and assume that consumption and returnsare conditionally homoskedastic and jointly log normal to get:

ct+1−Etct+1 = rmt+1−Etr

mt+1 +(1−σ)(Et+1−Et)

∞∑j=1

ρj rmt+1+j

Rest of the paper: study the properties of aggregate impliedby this relationship between aggregate consumption and themarket return process

How to measure market returns?


Measuring the Market Return

Return on the Market Portfolio:

rmt = (1− νt−1)ra

t + νt−1ryt

rmt is the log return on the market portfolio

rat is the return on financial wealth

r yt is the return on human wealth

νt is the ratio of human wealth to total wealth

Only rat is observed, need to model r y

t and νt


Measuring Financial Asset Returns: 2 ways

1 CRSP Value Weighted Returns

2 ”Firm Value”


Cointegration

Following Lettau and Ludvigson (2001), a cointegratingrelationship exists between consumption and aggregatewealth, proxied by cayt = λct − (1− ν)at − νyt

λ = 1.0395, ν = 0.7761

Imposes restrictions on the transitions of ∆ct ,∆at ,∆yt


Computing Innovations: VAR

State Vector zt = (∆at ,∆yt , dpat , reltbt , yspt , st ,∆ct)′

Estimate VECM:

zt+1 = Azt + Γcayt + εt+1

Re-write this as a VAR:

zt+1 = Azt + εt


Notation

(c)t = ct − Et−1[ct ] = ∆ct − Et−1[∆ct ] = e ′7εt

DRat = ra

t − Et−1[rat ]

DRa∞ = (Et − Et−1)

∑∞j=1 ρ

j rat+j

CF yt = ∆yt − Et−1[∆yt ]

CF yt,∞ = (Et − Et−1)

∑∞j=0 ρ

j∆yt+j

CF at = ∆dt − Et−1[∆dt ]

CF at,∞ = (Et − Et−1)

∑∞j=0 ρ

j∆dt+j


Stylized Facts

Return innovations are much more volatile than consumptiondeviations (13.5% vs 0.8%)

Consumption innovations are only weakly correlated withreturn innovations Corr((c)t ,DRa

t ) = 0.21

News about future financial returns is volatile, St.dev = 14.3%

Current return innovations are negatively correlated with newsabout future expected returns, Corr(DRa

t ,DRa∞) = −0.86


Stylized Facts, Cont

Current and future dividend growth and labor income growthare negatively correlated, Corr(CF a

t,∞,CF yt,∞) = −.423

Periods with good news about current financial asset returnstend to be periods with good news about current and futurelabor income growth, Corr(CF y

t,∞,DRat ) = .493

Periods with good news about future financial asset returnstend to be periods with bad news about current and futurelabor income growth, Corr(CF y

t,∞,DRat,∞) = −.633

Current and future labor income growth is not very volatile,St.Dev(CF y

t,∞) = .030


Modeling Human Capital Returns

Campbell (1991) framework gives;

r yt −Et−1[r y

t ] = (Et−Et−1)∞∑j=0

ρj∆yt+j−(Et−Et−1)∞∑j=1

ρj r yt+j

Equivalently write: DRyt = CF y

t,∞ − DRy∞

Only CF yt,∞ is observed

How to model Et [r yt+1]?



Model 1: Only financial wealth, νt = 0∀t

Model 2 (Campbell 1996): Et−1[r yt ] = Et−1[ra

t ]

Model 3 (Shiller 1995): Et−1[r yt ] = 0

Model 4 (Jagannathan and Wang 1996):r yt − Et−1[r y

t ] = ∆yt − Et−1∆yt



All of these can be written as Et [r yt+1] = C ′zt for the

appropriate choice of C.

Once we have C, can compute:

DRy∞ = C ′ρ(I − ρA)−1εt

DRyt = CF y

t,∞ − DRy∞ = (e ′2 − C ′ρ)(I − ρA)−1εt



Lustig and Van Nieuwerburgh: All of the above models implyaggregate consumption is too volatile and too highlycorrelated with financial returns

Model 5: Choose the vector C which minimizes the distancebetween the model-implied consumption volatility andcorrelation and the same moments in the data.


Constant Wealth Shares

Suppose we had an estimate of ν, then:

(c)t = (1− ν)DRat + νCF y

t,∞ − σνDRy∞ + (1− σ)(1− ν)DRa

∞

Lustig and Van Nieuwerburgh choose C so that the momentsof this equation match those in the data.


Time Varying Wealth Shares (Sketch)

Under some conditions, we can write

νt =1

1 + exp(dpyt − dpa

t + log(1−stst

))

The consumption innovations become:

(c)t = (1− νt−1)DRat + νt−1CF y

t,∞− (νt−1 + (σ− 1)ν)DRy∞

+ (1− σ)(1− ν)DRa∞ − (1− σ)(DRw ,a

t − DRw ,yt ) (1)

DRw ,at = (Et − Et−1)

∑∞j=1 ρ

j(νt−1+j − ν)rat+j

DRw ,yt = (Et − Et−1)

∑∞j=1 ρ

j(νt−1+j − ν)r yt+j


Results


Why does Model 5 work?

Large negative correlation between human and financialwealth returns, Corr(DRy

t ,DRat ) < 0

Corr(DRyt ,DRa

t ) = Cov [CF yt,∞,CF a

t,∞]− Cov [CF yt,∞,DRa

∞]

− Cov(DRy∞,CF a

t,∞) + Cov(DRy∞,DRa

∞) (2)

Good news about current and future cash flows on humanwealth coincides with bad news about current and future cashflows for financial assets as well as lower future risk premia onfinancial assets

Discount rates on human wealth are high when expectedfuture dividend growth is high and future risk premia onfinancial assets are low.


Implications for Market Returns


Sensitivity to EIS


Implications for asset pricing

From Campbell (1996)

Etrat+1−r f +1/2Vaa,t = γCov(DRa

t ,DRmt )+(γ−1)Cov(DRa

t ,DRm∞)

Model 5 delivers positive hedging risk premia for all EIS,negative myopic risk premia for low EIS, else positive

Models 1-4 exactly the opposite


Title


Other Explanations

Innovations in aggregate consumption growth not accountedfor by innovations in financial returns was attributed tohuman wealth returns

Other models explored include habit formation, addinghousing wealth, heteroskedastic market returns, andheterogeneity

None can explain the volatility and correlation puzzles


Conclusion

Consumption volatility and correlation puzzles are hard toreconcile in other asset pricing models

The returns to human wealth needs to be negativelycorrelated with returns on financial assets in order to generatea consumption process that is consistent with the data,contrary to standard theoretical models.


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