Asset Pricing with Countercyclical Household Consumption Risk

• Author: GEORGE M. CONSTANTINIDES,ANISHA GHOSH
• Published date: 01 February 2017
• Date: 01 February 2017
• DOI: http://doi.org/10.1111/jofi.12471

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 1 •FEBRUARY 2017

Asset Pricing with Countercyclical Household

Consumption Risk

GEORGE M. CONSTANTINIDES and ANISHA GHOSH∗

ABSTRACT

We show that shocks to household consumption growth are negatively skewed, per-

sistent, countercyclical, and drive asset prices. We construct a parsimonious model

where heterogeneous households have recursive preferences. A single state variable

drives the conditional cross-sectional moments of household consumption growth. The

estimated model fits well the unconditional cross-sectional moments of household

consumption growth and the moments of the risk-free rate, equity premium, price-

dividend ratio, and aggregate dividend and consumption growth. The model-implied

risk-free rate and price-dividend ratio are procyclical, while the market return has

countercyclical mean and variance. Finally,household consumption risk explains the

cross section of excess returns.

CONSIDERABLE EMPIRICAL EVIDENCE DOCUMENTS that households face a substan-

tial amount of uninsurable idiosyncratic labor income risk. The time variation

in idiosyncratic labor income risk plays a central role in understanding several

observed phenomena in macroeconomics and finance. Earlier studies focus on

the cross-sectional variance of idiosyncratic shocks, arguing that they are coun-

tercyclical (e.g., Storesletten, Telmer, and Yaron (2004)) and can, in principle,

account for the high historically observed level of the equity premium (e.g., Con-

stantinides and Duffie (1996)). More recently, using a very large data set from

the U.S. Social Security Administration, Guvenen, Ozkan, and Song (2014) find

that the left skewness of the idiosyncratic shocks is strongly countercyclical.

∗George M. Constantinides is at the University of Chicago and NBER. Anisha Ghosh is at

Carnegie-Mellon University. We thank Lorenzo Garlappi, the late Rick Green, Burton Hollifield,

Hanno Lustig, Stijn Van Nieuwerburgh, Thomas Philippon, Bryan Routledge, Ken Singleton (the

Editor), Chris Telmer, Sheridan Titman, two anonymous referees, and seminar participants at

Carnegie-Mellon University, Concordia University, the EFA 2015 Annual Meeting in Vienna, the

ESSFM 2015 conference in Gerzensee, the NBER 2015 summer institute, Georgetown University,

New York University, the 2015 Annual Meeting of the SED, the University of British Columbia,

the University of California at Los Angeles, the University of Chicago, the University of Miami,

the University of Michigan, the University of Southern California, and the University of Texas at

Austin for their helpful advice and feedback. Constantinides received financial support from the

Center for Research in Security Prices, the University of Chicago, as trustee/director of the DFA

group of funds, SW7 Holdings, and Cook County Illinois Investment Policy Committee, and as a

member of the advisory board of FTSE-Russell. Ghosh did not receive financial support from any

interested party and does not hold paid or unpaid positions in relevant nonprofit organizations or

profit-making entities.

DOI: 10.1111/jofi.12471

415

416 The Journal of Finance R

Further, contrary to prior research, they find that the cross-sectional variance

is not countercyclical but rather remains mostly flat over the business cycle

even after controlling for observable characteristics like age and average past

earnings. Krebs (2007) argues that higher job displacement risk in recessions

gives rise to the countercyclical left skewness of earnings shocks and that this

can generate a substantial cost of business cycles.

In this paper, we study the implications of countercyclical left skewness in

the cross-sectional distribution of household consumption growth on aggregate

asset prices.1We construct a parsimonious dynamic equilibrium model with

two key ingredients. First, the economy is inhabited by a continuum of hetero-

geneous households with identical Epstein-Zin (1989) recursive preferences.

Second, the heterogeneity among households arises from their labor income

processes that are modeled as an exponential function of a Poisson mixture

of normal distributions. This specification generates higher order moments in

the cross-sectional distribution of household consumption growth in a tractable

fashion. In fact, the parameter driving the Poisson process is the single state

variable—hereafter referred to as household consumption risk—that drives

the conditional cross-sectional third central moment of household consump-

tion growth. Aggregate consumption growth is modeled as an i.i.d. process to

emphasize that the explanatory power of the model does not derive from such

predictability.

We demonstrate that, under certain conditions, there exists a no-trade equi-

librium. To our knowledge, this is the first paper to establish the existence of

equilibrium in a heterogeneous-agent, incomplete-markets economy where in-

vestors have recursive preferences. For the log-linearized version of the model,

we obtain in closed form the equilibrium risk-free rate, expected market return,

and price-dividend ratio as functions of the single state variable, household

consumption risk.

We estimate the model using the generalized method of moments (GMMs) ap-

proach, targeting not only the model-implied moments of the market return, the

risk-free rate, and the market-wide price-dividend ratio, but also the first three

central moments of the cross-sectional distribution of household consumption

growth. The estimated model provides a good fit for the time-series averages

of the moments of household consumption growth. It also matches well the un-

conditional mean, volatility, and autocorrelation of the risk-free rate, thereby

addressing the risk-free rate puzzle; provides a good fit for the unconditional

mean, volatility, and autocorrelation of the market return, thereby address-

ing the equity premium and excess volatility puzzles; and it matches well the

mean, volatility, and autocorrelation of the market price-dividend ratio and

aggregate dividend growth, targets that challenge a number of other models.

1In a different context, in particular, relying on a nonparametric relative entropy minimizing

approach to filter the most likely stochastic discount factor (SDF), Ghosh, Julliard, and Taylor

(2016) highlight the importance of higher moments of the SDF, especially skewness, in pricing

assets. In particular, they show that about a quarter of the overall entropy of the most likely SDF

is generated by its third-order and higher order moments, with the third central moment alone

accounting for about 18% of the entropy.

Asset Pricing with Countercyclical Household Consumption Risk 417

Consistent with empirical evidence, the model implies that the risk-free rate

and price-dividend ratio are procyclical, while the expected market return, its

variance, and the equity premium are countercyclical. The model is also consis-

tent with the salient features of aggregate consumption growth observed in the

data: realistic mean and variance, and lack of predictability. Furthermore, the

third central moment of the cross-sectional distribution of household consump-

tion growth explains the cross section of excess returns of size-, book-to-market

equity-, and industry-sorted portfolios as well as the three Fama and French

(1993) factors do.

Uninsurable idiosyncratic income shocks is a new paradigm in asset pric-

ing that does not rely on a predictable component in aggregate consumption

growth, as in the long-run risks paradigm, time-varying and generally high

levels of risk aversion, as in the external habit paradigm, and both large and

frequent aggregate macroeconomic disasters, as in the rare disasters paradigm.

This paper is the first to empirically establish that observed uninsurable id-

iosyncratic consumption shocks can explain several observed time-series and

cross-sectional patterns in asset market data as well as several aspects of the

cross-sectional distribution of household consumption growth.

Figure 1displays the time series of the skewness in the cross-sectional dis-

tribution of quarterly household consumption growth over the period 1982:Q1

to 2009:Q4. The third central moment is mostly negative and countercyclical,

1985 1990 1995 2000 2005 2010

4 3 2 1 01

Time Period

Skewness

Jan Tranche

All Tranches

Figure 1. Time series of the cross-sectional skewness, quarterly data 1982:Q1 to 2009:Q4.