
Volume 9, Issue 2, April 2008
The Research Agenda: Sydney Ludvigson on Empirical Evaluation of Economic Theories of Risk Premia
Sydney Ludvigson is the William R. Berkley Term Associate Professor at the Department of Economics, New York University. She is interested in asset valuation, equity premia and consumption smoothness.
Ludvigson's RePEc/IDEAS entry.
What explains the behavior of risk premia in stock and bond markets, both
over time and crosssectionally across classes of assets? For academic
researchers, the progression of empirical evidence on these questions has
presented a continuing challenge to asset pricing theory and an important
road map for future inquiry. For investment professionals, finding practical
answers to these questions is the fundamental purpose of financial
economics, as well as its principal reward.
To address these questions, economists need to develop theoretical models of
risk. Once such models have been developed, formal statistical analysis is
required to assess how well these models fit the data, and to provide
independent estimates of the theories' key parameters. In this essay, I
describe work that aims to build our understanding of the ways in which
modernday asset pricing theories are related to asset pricing facts
established from historical data, to estimate the models' key parameters,
and to formally evaluate the extent to which leading theories are successful
in explaining the facts. The general approach is a multifarious one that
involves both formal econometric estimation as well as simulation analyses
directed at particular questions of interest. The approach is summarized in
three articles, numbered below for ease of reference:
 [1] "Euler Equation Errors" (with
Martin Lettau).
 [2] "An Estimation of Economic Models with Recursive
Preferences" (with Xiaohong Chen and Jack Favilukis).
 [3] "Land of Addicts? An Empirical Investigation of
HabitBased Asset Pricing Models" (with Xiaohong Chen).
Relating Asset Pricing Theories to Asset Pricing Facts
Previous research shows that the standard, representative agent,
consumptionbased asset pricing theory based on constant relative risk
aversion utility fails to explain the average returns of risky assets. (For
example, Hansen and Singleton (1982); Ferson and Constantinides (1991); Hansen and Jagannathan (1991); Cochrane (1996); Kocherlakota (1996)) One
aspect of this failure, addressed in [1], is the large unconditional Euler
equation errors that the model generates when evaluated on crosssections of
stock returns. Euler equation errors are statistical discrepancies between a
theory's prediction about the dynamic behavior of expected discounted asset
returns and that implied by observable data. In [1], we present evidence on
the size of these errors and show that they remain economically large even
when preference parameters are freely chosen to maximize the model's chances
of fitting the data. Thus, unlike the equity premium puzzle of Mehra and Prescott (1985), the large Euler equation errors cannot be resolved with
high values of risk aversion.
To explain why the standard model fails, we need to develop alternative
models that can rationalize its large Euler equation errors. Yet
surprisingly little research has been devoted to assessing the extent to
which newer consumptionbased asset pricing theoriesthose specifically
developed to address empirical limitations of the standard consumptionbased
modelcan explain its large Euler equation errors. Unconditional Euler
equation errors can be interpreted economically as pricing errors; thus we
use the terms "Euler equation error" and
"pricing error" interchangeably.
The research in [1] makes three contributions. First, we show that leading
consumptionbased asset pricing theories resoundingly fail to explain the
mispricing of the standard consumptionbased model. Specifically, we
investigate four models at the vanguard of consumptionbased asset pricing
and show that the benchmark specification of each of these theories
counterfactually implies that the standard model has negligible Euler
equation errors when its parameters are freely chosen to fit the data. This
anomaly is striking because early empirical evidence that the standard
model's Euler equations were violated provided much of the original impetus
for developing the newer models we investigate here.
Second, we show that the leading asset pricing models we study fail to
explain the mispricing of the standard model because they fundamentally
mischaracterize the joint behavior of consumption and asset returns in
recessions, when aggregate consumption is falling. In the model economies,
realized excess returns on risky assets are negative when consumption is
falling, whereas in the data they are often positive.
Our third contribution is to suggest one specific direction along which the
current models can be improved, based on a timevarying, statedependent
correlation between stockholder and aggregate consumption growth.
Specifically, we show that a stylized model in which aggregate consumption
growth and stockholder consumption growth are highly correlated most of the
time, but have low or negative correlation in recessions, produces
violations of the standard model's Euler equations and departures from joint
lognormality of aggregate consumption growth and asset returns that are
remarkably similar to those found in the data.
Why should we care about the ability of leading consumptionbased asset
pricing models to explain the failure of the standard consumptionbased
model? To motivate the importance of these findings for consumptionbased
asset pricing theory, it is helpful to consider, by way of analogy, the
literature on the value premium puzzle in financial economics. In this
literature, the classic Capital Asset Pricing Model (CAPM) resoundingly
fails to explain the high average excess returns of value stocks, resulting
in a value premium puzzle (Fama and French (1992, 1993)). It is well accepted that a fully successful
theoretical resolution to this puzzle must accomplish two things: (i) it must
provide an alternative theory to the CAPM that explains the high average
returns of value stocks, and (ii) it must explain the failure of the CAPM to
rationalize those high returns.
Analogously, the large empirical Euler equation errors of the standard
consumptionbased model place additional restrictions on new
consumptionbased models: not only must such models have zero pricing
errors when the Euler equation is correctly specified according to the
model, they must also produce large pricing errors when the Euler equation
is incorrectly specified using power utility and aggregate consumption. To
understand why the classic consumptionbased model is wrong,
alternative theories must generate the same large Euler equation errors that
we observe in the data for this model.
Our analysis employs simulated data from several contemporary
consumptionbased asset pricing theories expressly developed to address
empirical limitations of the standard consumptionbased model. Clearly, it
is not possible to study an exhaustive list of all models that fit this
description; thus we limit our analysis to four that both represent a range
of approaches to consumptionbased asset pricing, and have received
significant attention in the literature. These are: the representative agent
external habitpersistence paradigms of (i) Campbell and Cochrane (1999) and
(ii) Menzly, Santos and Veronesi (2004), (iii) the representative agent
longrun risk model based on recursive preferences of Bansal and Yaron (2004), and (iv) the limited participation model of Guvenen (2003). Each is an
explicitly parameterized economic model calibrated to accord with the data,
and each has proven remarkably successful in explaining a range of asset
pricing phenomena that the standard model fails to explain.
We show that some of these models can explain why we obtain
implausibly high estimates of risk aversion and the subjective rate of
timepreference when freely fitting aggregate data to the Euler equations of
the standard consumptionbased model. But, none can explain the large
unconditional Euler equation errors associated with such estimates for
plausibly calibrated sets of asset returns. Indeed, the asset pricing models
we consider counterfactually imply that parameter values can be found for
which the unconditional Euler equations of the standard consumptionbased
model are exactly satisfied.
The work in [1] diagnoses this result by showing that each of the four
models studied satisfy sufficient conditions under which parameter values
can always be found such that the Euler equations of the standard model will
be exactly satisfied. The economically important condition satisfied by each
model is that realized excess returns on risky assets are negative whenever
consumption growth is sufficiently negative. We show that such a condition
is violated in the data.
We close the paper by turning our attention to stylized models with limited
stockmarket participation. When limited participation is combined with a
timevarying, statedependent correlation between stockholder and aggregate
consumption, consumptionbased asset pricing theories come much closer to
rationalizing the large Euler equation errors of the standard paradigm that
in large part motivated the search for newer models in the first place.
Econometric Modeling of Asset Pricing Models
A large and growing body of theoretical work in macroeconomics and finance
models the preferences of economic agents using a recursive utility function
of the type explored by Epstein and Zin (1989, 1991) and Weil (1989) (See for example Campbell (1993, 1996); Tallarini (2000); Campbell and Viceira (2001); Bansal and Yaron (2004); Colacito and Croce (2005); Bansal, Dittmar and Kiku (2007); Campbell and Vuolteenaho (2004); Gomes and Michaelides (2005); Krueger and Kubler (2005); Hansen, Heaton and Li (2005); Kiku (2005); Malloy, Moskowitz and VissingJorgensen (2005); Campanale, Castro and Clementi (2007); Croce (2006); Bansal, Dittmar and Lundblad (2005); Croce, Lettau and Ludvigson (2007); Hansen and Sargent (2006), Piazzesi and Schneider (2006)). One reason for the
growing interest in such preferences is that they provide a potentially
important generalization of the standard power utility model discussed
above, first investigated in classic empirical studies by Hansen and
Singleton (1982, 1983). The salient feature of this generalization is a
greater degree of flexibility as regards attitudes towards risk and
intertemporal substitution. Specifically, under the recursive
representation, the coefficient of relative risk aversion need not equal the
inverse of the elasticity of intertemporal substitution (EIS), as it must in
timeseparable expected utility models with constant relative risk aversion.
This degree of flexibility is appealing in many applications because it is
unclear why an individual's willingness to substitute consumption across
random states of nature should be so tightly linked to her willingness to
substitute consumption deterministically over time, as it must in standard
models of preferences.
Despite the growing interest in recursive utility models, there has been a
relatively small amount econometric work aimed at estimating the relevant
preference parameters and assessing the model's fit with the data. As a
consequence, theoretical models are often calibrated with little econometric
guidance as to the value of key preference parameters, the extent to which
the model explains the data relative to competing specifications, or the
implications of the model's bestfitting specifications for other economic
variables of interest, such as the return to the aggregate wealth portfolio
or the return to human wealth. The purpose of [2] is to help fill this gap
in the literature by undertaking a formal econometric evaluation of the
EpsteinZinWeil (EZW) recursive utility model.
If recursive preferences are of growing interest, why has there been so
little formal econometric work evaluating these models? In its most general
form, the EZW model is extremely challenging to evaluate empirically. The
EZW recursive utility function is a constant elasticity of substitution
(CES) aggregator over current consumption and the expected discounted
utility of future consumption. This structure makes estimation of the
general model difficult because the intertemporal marginal rate of
substitution is a function of the unobservable continuation value of the
future consumption plan. The common approach in the literature is to make
one of a number of simplifying assumptions that effectively reduce the
continuation value function to an observable variable. For example, one
approach to this problem, based on the insight of Epstein and Zin (1989), is
to exploit the relation between the continuation value and the return on the
aggregate wealth portfolio. To the extent that the return on the aggregate
wealth portfolio can be measured or proxied, the unobservable continuation
value can be substituted out of the marginal rate of substitution and
estimation can proceed using only observable variables (e.g., Epstein and Zin (1991)).
Unfortunately, the aggregate wealth portfolio represents
a claim to future consumption and is itself unobservable. Moreover, given
the potential importance of human capital and other nontradable assets in
aggregate wealth, its return may not be well proxied by observable asset
market returns.
These difficulties can be overcome in specific cases of the EZW recursive
utility model. For example, if the EIS is restricted to unity and
consumption follows a loglinear timeseries process, the continuation value
has an analytical solution and is a function of observable consumption data
(e.g., Hansen, Heaton and Li (2005)). Alternatively, if consumption and asset
returns are assumed to be jointly lognormally distributed and homoskedastic
(or if a secondorder linearization is applied to the Euler equation), the
risk premium of any asset can be expressed as a function of covariances of
the asset's return with current consumption growth and with news about
future consumption growth (e.g., Restoy and Weil (1998), Campbell (2003)).
In this case, the model's crosssectional asset pricing implications can be
evaluated using observable consumption data and a model for expectations of
future consumption.
While the study of these specific cases has yielded a number of important
insights, there are several reasons why it may be desirable to allow for
more general representations of the model, free from tight parametric or
distributional assumptions. First, an EIS of unity implies that the
consumptionwealth ratio is constant, contradicting statistical evidence
that it varies considerably over time. Lettau and Ludvigson (2001a) argue
that a cointegrating residual for log consumption, log asset wealth, and log
labor income should be correlated with the unobservable log
consumptionaggregate wealth ratio, and find evidence that this residual
varies considerably over time and forecasts future stock market returns. See
also recent evidence on the consumptionwealth ratio in
Hansen, Heaton, Roussanov and Lee (2007) and Lustig, Van Nieuwerburgh and Verdelhan (2008). Moreover, even firstorder expansions of the EZW model around an EIS of
unity may not capture the magnitude of variability of the consumptionwealth
ratio (Hansen, Heaton, Roussanov and Lee (2007)). Second, although aggregate
consumption growth itself appears to be well described by a lognormal
process, empirical evidence suggests that the joint distribution of
consumption and asset returns exhibits significant departures from
lognormality (Lettau and Ludvigson (2005)). Third, Kocherlakota (1990)
points out that joint lognormality is inconsistent with an individual
maximizing a utility function that satisfies the recursive representation
used by Epstein and Zin (1989, 1991) and Weil (1989).
To overcome these issues, in [2] we employ a semiparametric estimation
technique that allows us to conduct estimation and testing of the EZW
recursive utility model without the need to find a proxy for the
unobservable aggregate wealth return, without linearizing the model, and
without placing tight parametric restrictions on either the law of motion or
joint distribution of consumption and asset returns, or on the value of key
preference parameters such as the EIS. We present estimates of all the
preference parameters of the EZW model, evaluate the model's ability to fit
asset return data relative to competing asset pricing models, and
investigate the implications of such estimates for the unobservable
aggregate wealth return and human wealth return.
To avoid having to find a proxy for the return on the aggregate wealth
portfolio, we explicitly estimate the unobservable continuation value of the
future consumption plan. By assuming that consumption growth falls within a
general class of stationary, dynamic models, we may identify the state
variables over which the continuation value is defined. However, without
placing tight parametric restrictions on the model, the continuation value
is still an unknown function of the relevant state variables. Thus the key
to our approach is that the unknown continuation value function is estimated
nonparametrically, in effect allowing the data to dictate the shape of the
function. The resulting empirical specification for investor utility is
semiparametric in the sense that it contains both the finite dimensional
unknown parameters that are part of the CES utility function (risk aversion,
EIS, and subjective timediscount factor), as well as the infinite
dimensional unknown continuation value function.
Using quarterly data on consumption growth, assets returns and instruments,
our empirical results indicate that the estimated relative risk aversion
parameter is high, ranging from 1760, with higher values for the
representative agent version of the model than the representative
stockholder version. The estimated elasticity of intertemporal substitution
is typically above one, and differs considerably from the inverse of the
coefficient of relative risk aversion. In addition, the estimated aggregate
wealth return is found to be weakly correlated with the CRSP valueweighted
stock market return and much less volatile, implying that the return to
human capital is negatively correlated with the aggregate stock market
return. This later finding is consistent with results in Lustig and
Van Nieuwerburgh (2005), discussed further below. In data from 1952 to
2005, we find that an SMD estimated EZW recursive utility model can explain
a crosssection of size and bookmarket sorted portfolio equity returns
better than the timeseparable, constant relative risk aversion power
utility model and better than the Lettau and Ludvigson (2001b) scaled
consumption CAPM model, but not as well as purely empirical models based on
financial factors such as the Fama and French (1993) threefactor model.
These results are encouraging for the recursive utility framework, because
they suggest that the model's ability to fit the data is in a comparable
range with other models that have shown particular success in explaining the
crosssection of expected stock returns.
A similar semiparameteric approach is taken in [3] to study an entirely
different class of asset pricing models, namely those in which investors
are presumed to have a consumption "habit." According to these theories of aggregate stock
market behavior, assets are priced as if there were a representative
investor whose utility is a power function of the difference between
aggregate consumption and a "habit"
level, where the habit is some function of lagged and (possibly)
contemporaneous consumption. Unfortunately, theory does not provide precise
guidelines about the parametric functional relationship between the habit
and aggregate consumption. As a consequence, there is substantial divergence
across theoretical models in how the habit stock is specified to
vary with aggregate consumption. As for the EZW model, the fundamental
problem is the unobservability of some function that is crucial to the
success of the model, in this case the habit function. [3] both develops and
applies the formal econometric techniques required to estimate the habit
function and to formally test important aspects of habitbased models. While
many theoretical papers have offered calibrated versions of the habit, the
econometric estimation and testing of these models that we propose is new.
If habit formation is actually present in the manner suggested by these many
influential theoretical papers, then estimating it freely should produce a
theoretically plausible functional form. [3] studies the ability of a
general class of habitbased asset pricing models to match the conditional
moment restrictions implied by asset pricing theory. Instead of testing a
particular model of habit formation, our semiparameteric approach allows us
to treat the functional form of the habit as unknown, and to estimate it
along with the rest of the model's parameters. This approach allows us to
empirically evaluate a number of interesting hypotheses about the
specification of habitbased asset pricing models that have not been
previously investigated, and to formally test the framework's ability to
explain stock return data relative to other models that have proven
empirically successful.
Using this methodology, we empirically investigate a number of hypotheses
about the specification of habitbased asset pricing models that have not
been previously investigated. One hypothesis concerns whether the habit is
better described as a linear or nonlinear function. We develop a statistical
test of the hypothesis of linearity and find that the functional form of the
habit is better described as nonlinear rather than linear.
A second hypothesis concerns the distinction between
"internal" and
"external" habit formation. About half of the theoretical
papers cited above investigate models of internal habit formation,
in which the habit is a function of the agent's own past consumption. The
rest investigate models of external habit formation, in which the habit
depends on the consumption of some exterior reference group, typically per
capita aggregate consumption. Abel (1990) calls external habit formation
"catching up with the Joneses."
Determining which form of habit formation is more empirically plausible is
important because the two specifications can have dramatically different
implications for optimal tax policy and welfare analysis (Ljungqvist and
Uhlig (2000)), and for whether habit models can explain
longstanding assetallocation puzzles in the international finance
literature (Shore and White (2002)). To address this issue, we derive a
conditional moment restriction that nests the internal and external
nonlinear habit function, under the assumption that both functions are
specified over current and lagged consumption with the same finite lag
length. Our empirical results indicate that the data are better described by
internal habit formation than external habit formation.
The SMD approach also allows us to assess the quantitative importance of the
habit in the power utility specification. Our empirical results suggest that
the habit is a substantial fraction of current consumptionabout 97 percent
on averageechoing the specification of Campbell and Cochrane (1999) in
which the steadystate habitconsumption ratio exceeds 94 percent. The SMD
estimated habit function is concave and generates positive intertemporal
marginal rate of substitution in consumption. The SMD estimated subjective
timediscount factor is around 0.99 and the estimated power utility
curvature parameter is about 0.80 for three different combinations of
instruments and asset returns.
Finally, we undertake a statistical model comparison analysis. Because our
habitbased asset pricing model makes some parametric assumptions that may
not be fully accurate (e.g., it maintains the power utility specification),
and because the SMDestimated nonparametric habit function contains lagged
consumption of only finite lag length, the implied Stochastic Discount
Factor (SDF) should be best viewed as a proxy to the true unknown SDF.
Thus, we evaluate the SMDestimated habit model and several competing asset
pricing models by employing the model comparison distance metrics
recommended in Hansen and Jagannathan (1997) (the socalled HJ distance and
the HJ^{+} distance), where all the models are treated as SDF proxies to
the unknown truth. In particular, the SMDestimated internal habit model is
compared to (i) the SMDestimated external habit model, (ii) the
threefactor asset pricing model of Fama and French (1993), (iii) the
"scaled" consumption Capital Asset
Pricing Model (CAPM) of Lettau and Ludvigson (2001b), (iv) the classic
CAPM of Sharpe (1964) and Lintner (1965), and (v) the classic
consumption CAPM of Breeden (1979) and Breeden and Litzenberger (1978).
Doing so, we find that a SMDestimated internal habit model can better
explain a crosssection of size and bookmarket sorted equity returns, both
economically and in a statistically significant way, than the other five
competing models. These results are particularly encouraging for the
internal habit specification, since the Fama and French (1993) threefactor
model and the Lettau and Ludvigson (2001b) scaled consumption CAPM have
previously displayed relative success in explaining the crosssection of
stock market portfolio returns.
The Future Research Agenda
I am currently working on several projects that extend the analyses on
equity markets described above to study housing markets, risk premia in
housing assets, and the relationship of these variables to aggregate
consumer spending. One line of work (joint with Christopher Mayer of
Columbia University) concerns the role of risk premia in U.S. housing
markets. Existing empirical work in the housing literature has assumed that
housing risk premia are constant. Yet there are plenty of reasons to
investigate whether this assumption is plausible. Indeed, the unprecedented
surge in U.S. house prices that preceded the recent mortgage crisis appears,
anecdotally, to have been driven by a decline in market participants'
assessment of the riskiness of these assets. We are currently investigating
whether risk premia in the U.S. housing market vary across metropolitan
areas and assessing the extent to which particular models of risk can
account for that variation.
A closely related theoretical project with Stijn Van Nieuwerburgh of the
Stern School at NYU and Jack Favilukis of London School of Economics
explores the effects of changing collateral constraints from housing assets
on aggregate consumer spending. It is often presumed that changes in such
collateral constraints will have a large affect on aggregate consumer
spending, especially if financial markets are incomplete and agents cannot
perfectly insure idiosyncratic shocks to their labor income or housing
wealth. In this work we show that, even when markets are incomplete, the
theoretical basis for such a large and direct linkage between consumer
spending and housing wealth is unclear. Although fluctuations in housing
collateral constraints do affect some household's ability to borrow and
consume, in general equilibrium fluctuations in housing collateral affect
households' ability to share risks with one another, and therefore affect
the crosssectional distribution of consumption, but may have very little
affect on the size of the overall consumption pie, that is on aggregate
consumption. We develop and solve a general equilibrium model to measure the
theoretical marginal propensity to consume out of housing wealth and to
assess the impact of changing collateral constraints on aggregate
consumption. One important question we intend to address is to what extent
risk premia adjust versus quantities (aggregate consumption). We solve for
optimal portfolio decisions of such heterogeneous households who face
housing collateral constraints, and determine the equilibrium housing
returns they give rise to.
References
Andrew Abel, 1990.
" Asset Prices under Habit Formation and Catching Up with the Joneses,"
American Economic Review,
v. 80(2), p. 3842.
Ravi Bansal & Amir Yaron, 2004.
" Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles,"
Journal of Finance,
v. 59(4), p. 14811509.
Ravi Bansal, Robert Dittmar & Christian Lundblad, 2005.
" Consumption, Dividends, and the Cross Section of Equity Returns,"
Journal of Finance, v. 60(4), p. 16391672.
Ravi Bansal, Robert Dittmar & Dana Kiku, 2007.
" Cointegration and Consumption Risks in Asset Returns,"
NBER Working Paper
13108.
Douglas Breeden, 1979.
" An intertemporal asset pricing model with stochastic consumption and investment opportunities,"
Journal of Financial Economics,
v. 7(3), p. 265296.
Douglas Breeden & Robert Litzenberger, 1978.
" Prices of Statecontingent Claims Implicit in Option Prices,"
Journal of Business,
v. 51(4), p. 62151.
Claudio Campanale, Rui Castro & Gian Luca Clementi, 2007.
" Asset Pricing in a Production Economy with ChewDekel Preferences,"
Working Paper
0707, Rimini Centre for Economic Analysis.
John Campbell, 1993.
" Intertemporal Asset Pricing without Consumption Data,"
American Economic Review, v. 83(3), p. 487512.
John Campbell, 1996.
" Understanding Risk and Return,"
Journal of Political Economy, v. 104(2), p. 298345.
John Campbell, 2003.
" Consumptionbased asset pricing,"
in: G. Constantinides, M. Harris & R. Stulz (ed.), Handbook of the Economics of Finance, volume 1, chapter 13, p. 803887,
Elsevier.
John Campbell & John Cochrane, 1999.
" Force of Habit: A ConsumptionBased Explanation of Aggregate Stock Market Behavior,"
Journal of Political Economy, v. 107(2), p. 205251.
John Campbell & Luis Viceira, 2001. "Strategic Asset Allocation: Portfolio Choice for LongTerm Investers," London, UK: Oxford University Press.
John Campbell & Tuomo Vuolteenaho, 2004.
" Bad Beta, Good Beta,"
American Economic Review, v. 94(5), p. 12491275.
John Cochrane, 1996.
" A CrossSectional Test of an InvestmentBased Asset Pricing Model,"
Journal of Political Economy, v. 104(3), p. 572621.
Riccardo Colacito & Mariano Croce, 2005.
" Risks For The Long Run And The Real Exchange Rate,"
2005 Meeting Papers,
794, Society for Economic Dynamics.
Mariano Croce, 2006.
" Welfare Costs, Long Run Consumption Risk, and a Production Economy,"
2006 Meeting Papers,
582, Society for Economic Dynamics.
Mariano Croce, Martin Lettau & Sydney Ludvigson, 2007.
" Investor Information, LongRun Risk, and the Duration of Risky CashFlows,"
NBER Working Paper 12912.
Larry Epstein & Stanley Zin, 1989.
" Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework,"
Econometrica, v. 57(4), p. 93769.
Larry Epstein & Stanley Zin, 1991.
" Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis,"
Journal of Political Economy, v. 99(2), p. 26386.
Eugene Fama & Kenneth French, 1992.
" The CrossSection of Expected Stock Returns,"
Journal of Finance, v. 47(2), p. 42765.
Eugene Fama & Kenneth French, 1993.
" Common risk factors in the returns on stocks and bonds,"
Journal of Financial Economics, v. 33(1), p. 356.
Wayne Ferson & George Constantinides, 1991.
" Habit persistence and durability in aggregate consumption: Empirical tests,"
Journal of Financial Economics, v. 29(2), p. 199240.
Francisco Gomes & Alexander Michaelides, 2005.
" Optimal LifeCycle Asset Allocation: Understanding the Empirical Evidence,"
Journal of Finance, v. 60(2), p. 869904.
Fatih Guvenen, 2003.
" A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation or Crosssectional Heterogeneity?,"
RCER Working Paper
499, University of Rochester.
Lars Peter Hansen & Kenneth Singleton, 1982.
" Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models,"
Econometrica, v. 50(5), p. 126986.
Lars Peter Hansen & Kenneth Singleton, 1983.
" Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns,"
Journal of Political Economy, v. 91(2), p. 24965.
Lars Peter Hansen & Ravi Jagannathan, 1997.
" Assessing Specification Errors in Stochastic Discount Factor Models,"
Journal of Finance, v. 52(2), p. 55790.
Lars Peter Hansen & Ravi Jagannathan, 1991.
" Implications of Security Market Data for Models of Dynamic Economies,"
Journal of Political Economy, v. 99(2), p. 22562.
Lars Peter Hansen & Thomas Sargent, 2006. "Fragile Beliefs and the Price of Model Uncertainty." Unpublished mimeo, New York University.
Lars Peter Hansen, John Heaton & Nan Li, 2005.
" Consumption Strikes Back?: Measuring LongRun Risk,"
NBER Working Paper 11476.
Lars Peter Hansen, John Heaton, Junghoon Lee & Nikolai Roussanov, 2007.
" Intertemporal Substitution and Risk Aversion,"
in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, volume 6, chapter 61, Elsevier.
Dana Kiku, 2005. "Is the Value Premium a Puzzle?" Unpublished mimeo, Duke University.
Narayana Kocherlakota, 1990.
" Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result,"
Journal of Finance, v. 45(1), p. 17590.
Narayana Kocherlakota, 1996.
" The Equity Premium: It's Still a Puzzle,"
Journal of Economic Literature, v. 34(1), p. 4271.
Dirk Krueger & Felix Kubler, 2006.
" ParetoImproving Social Security Reform when Financial Markets are Incomplete!?,"
American Economic Review, v. 96(3), p. 737755.
Martin Lettau & Sydney Ludvigson, 2001.
" Consumption, Aggregate Wealth, and Expected Stock Returns,"
Journal of Finance, v. 56(3), p. 815849.
Martin Lettau & Sydney Ludvigson, 2001.
" Resurrecting the (C)CAPM: A CrossSectional Test When Risk Premia Are TimeVarying,"
Journal of Political Economy, v. 109(6), p. 12381287.
Martin Lettau & Sydney Ludvigson, 2005.
" Euler Equation Errors,"
NBER Working Paper 11606.
John Lintner, 1965. "Security Prices, Risk and Maximal Gains from Diversification," Journal of Finance, v. 20, p. 587615.
Lars Ljungqvist & Harald Uhlig, 2000.
" Tax Policy and Aggregate Demand Management under Catching Up with the Joneses,"
American Economic Review, v. 90(3), p. 356366.
Hanno Lustig & Stijn Van Nieuwerburgh, 2005.
" The Returns on Human Capital: Good News on Wall Street is Bad News on Main Street,"
NBER Working Paper 11564.
Hanno Lustig, Stijn Van Nieuwerburgh & Adrien Verdelhan, 2008.
" The WealthConsumption Ratio,"
NBER Working Paper 13896.
Christopher Malloy, Tobias Moskowitz & Annette VissingJorgensen, 2005. "LongRun Stockholder Consumption Risk and Asset Returns," unpublished mimeo, University of Chicago, Graduate School of Business.
Rajnish Mehra & Edward Prescott, 1985.
" The equity premium: A puzzle,"
Journal of Monetary Economics, v. 15(2), p. 145161.
Lior Menzly, Tano Santos & Pietro Veronesi, 2004.
" Understanding Predictability,"
Journal of Political Economy, v. 112(1), p. 147.
Monika Piazzesi & Martin Schneider, 2006.
" Equilibrium Yield Curves,"
NBER Working Paper 12609.
Fernando Restoy & Philippe Weil, 1998.
" Approximate Equilibrium Asset Prices,"
NBER Working Paper 6611.
William F. Sharpe, 1964. "Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk," Journal of Finance, v. 19, p. 425444.
Stephen H. Shore & Joshua S. White, 2002. "External Habit Formation and the Home Bias Puzzle." Unpublished mimeo, Harvard University.
Tallarini Jr., Thomas D., 2000.
" Risksensitive real business cycles,"
Journal of Monetary Economics, v. 45(3), p. 507532.
Weil, Philippe, 1989.
" The equity premium puzzle and the riskfree rate puzzle,"
Journal of Monetary Economics, v. 24(3), p. 401421.
EconomicDynamics Interviews James Heckman and Flávio Cunha on Skill Formation and Returns to Schooling
James Heckman is the Henry Schultz Distinguished Service Professor of Economics at The University of Chicago. His recent research deals with such issues as evaluation of social programs, econometric models of discrete choice and longitudinal data, the economics of the labor market, and alternative models of the distribution of income. Flávio Cunha is Assistant Professor of Economics at the University of Pennsylvania. He is interested in inequality and skill formation.
Heckman's RePEc/IDEAS entry, Cunha's RePEc/IDEAS entry.

EconomicDynamics: In recent work, you highlight that it is essential to understand skill formation in childhood as a multiperiod problem. Why is it so?

James Heckman, Flavio Cunha: There are different reasons. First, different types of skills are produced at different periods of childhood. Economists, social scientists, and policy makers alike tend to focus on cognitive skill. Although it is necessary for success in life, it is not enough for many aspects of performance in social life. Furthermore, the evidence shows that cognitive skills crystallize early in life, so it is difficult to change them at later stages. Until recently,
few economists considered non cognitive skills although Marxist economists
considered them very early on. Of course, psychologists have studied them,
in addition to some work by sociologists. These skills play an important role in determining many socioeconomic measures, as shown in Heckman, Stixrud and Urzua (2006). They affect crime participation, teenage pregnancy, education, and many others important outcomes. More importantly, there is ample evidence from neuroscience showing that the prefrontal cortex, which is believed to be the neural focal point for noncognitive skills, matures later. This is consistent with the view that the way we motivate ourselves, the way we control our impulses, are malleable into later ages.
Second, early advantages reinforce each other. Skills that are developed at one stage of life serve as an input to produce skills at other stages of life. For example, if we are given a paragraph that describes an algebra problem, it is necessary to know how to read so we can construct the correct equations from the description in the text. Once we have written down the equations, we can use our algebra skills to solve the equation and get the correct answer. Children who cannot read will have a hard time developing their algebra skills, because they will fail in the first stage of this task, namely decoding the information from the text into equations. This example supports our work on Job Training Programs. Public job training programs try to improve dropouts. Many do not know how to read or write well. These programs reflect the current view of public policy that it is possible to make up for 17 years of neglect. Our work in this area has shown that the success rate is really low. Creating the foundation of early skills is important.
Based on this evidence, we developed models of skill formation allowing for investments at different stages to complement each other. The multiple periods formulation is a crucial feature of the models because (1) some skills may be formed more easily at certain given periods, (2) some skills produced at earlier stages may serve as an input in the production of later skills.

ED: In related work, you argue that a substantial fraction of ex post
returns to schooling are predictable by the agents, but not necessarily
by the econometrician. Market structure is important here to identify
deep parameters. How is it then possible that you obtain similar results
across different market structures?

JH, FC: In Cunha, Heckman, and Navarro (2005) we developed a framework that can be used by economists to separate heterogeneity from uncertainty in life cycle earnings by looking at economic choices made by agents. Given preferences and market structure, we show how one can use an educational choice model to generate restrictions that allow one to recover the distributions of predictable heterogeneity and uncertainty separately. In that paper, we specified a completemarket environment and we found that almost 50% of the variance of unobservable components in returns to schooling are known and acted on by individuals when making schooling choices. This framework was extended in Cunha and Heckman (2007) where we showed that a large fraction of the increase in inequality in recent years is due to the increase in the variance of unforecastable components. Cunha, Heckman, and Navarro (2004) and Navarro (2005) extended the model to an incompletemarket environment. These papers also consider assets accumulation data, which, given a market structure, imposes identifying assumptions on preferences.
There is an open question: if we have data on choices (education decisions, consumption, etc...), outcomes of choices (earnings in a given education group), and assets accumulation, how far can we go in nonparametrically identifying information sets, preferences, and market structures? This is a question we first stated in the original Cunha, Heckman, and Navarro (2005) paper and the literature has not yet settled on a definite answer.
The question you raise is a good one. But remember  only one market structure generates the data. If for example, a full insurance model characterized the data, an econometric model that allowed for constraints on transfers across states would show that the constraints are not binding, and would reproduce the complete markets model. Some version of this story seems to be at work in our estimates.

ED: Given your results, where should the policy focus be? In particular, how
does your work distinguish itself in this regard from other work in
macroeconomics?

JH, FC: The current work in economics emphasizes the importance of market
incompleteness with regards to shocks agents experience while they are
already adults: for example, there are many theoretical and applied papers
discussing the allocation and welfare loss with respect to uninsurable
shocks in income agents face during their adulthood. In the type of Bewley
economies, Huggett (1993) and Aiyagari (1994) show that the inability of
agents to transfer resources across states of nature and over periods of
time distorts allocations and generates welfare losses that tend to be
larger the higher the persistence of these shocks.
In our work (see Cunha and Heckman, 2007), we have tried to point out to the
profession the lifetime importance of the shock represented by the accident
of birth. It is clearly a very persistent shock since children who are born
in a disadvantaged family will spend many years in a disadvantaged
environment, with terrible consequences for their skill acquisition and
opportunities in life, as we show in Cunha, Heckman, and Schennach (2008).
If markets were complete, children would be able to buy insurance against
those shocks and they would use the resources to improve the environment in
the family they grow up. Clearly, this is not feasible: at the very least,
such markets would require children to start making allocation decisions as
soon as they are born, something they clearly are not ready to do. It
becomes
imperative for our society to devise mechanisms or policies that will
implement an allocation as close as possible to the first best even if
markets are incomplete. This intervention can be justified on efficiency or
fairness grounds, as is laid out in Heckman and Masterov (2007). Our work
shows that a possible answer to the policy question is present in early
childhood intervention programs. Recent work by Heckman, Moon, Pinto, and
Yavitz (2008) shows that these programs are successful in a number of
dimensions: they promote education; they reduce participation in crime for
boys and reduce teenage pregnancy for girls all of which represent large
costs to society. The basic idea underlying these programs is to provide
children with an environment that would resemble the children's environments
if they were not born in disadvantaged families.
It is important to emphasize that our work does not mean that early
intervention programs are sufficient. The intertemporal complementarity of
investments that we estimate in our joint work with Susanne Schennach states
that early investments must be followed up with late investments:
highquality early programs, such as the Perry preschool, do not replace
the importance of having good schools and prepared teachers. At the same
time, the complementarity indicates that children from very disadvantaged
households will not be able to extract the full benefits from school unless
they receive early investments that make them school ready.
References
S. Rao Aiyagari, 1994.
" Uninsured Idiosyncratic Risk and Aggregate Saving,"
The Quarterly Journal of Economics,
MIT Press, vol. 109(3), pages 65984, August.
Flavio Cunha & James Heckman, 2007.
" The Technology of Skill Formation,"
American Economic Review,
American Economic Association, v. 97(2), p. 3147, May.
Flavio Cunha & James Heckman, 2008.
"Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formation," Journal of Human Resources, forthcoming.
Flavio Cunha, James Heckman & Salvador Navarro, 2005.
" Separating uncertainty from heterogeneity in life cycle earnings,"
Oxford Economic Papers,
Oxford University Press, v. 57(2), p. 191261, April.
Flavio Cunha, James Heckman & Susanne Schennach, 2008. "Estimating the Elasticity of Intertemporal Substitution in the Formation of Cognitive and NonCognitive Skills", unpublished mimeo, University of Chicago.
James Heckman & Dimitriy Masterov, 2007.
" The Productivity Argument for Investing in Young Children", Review of Agricultural Economics, v. 29(3), p. 446493
James Heckman, Jora Stixrud & Sergio Urzua, 2006.
" The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior,"
Journal of Labor Economics,
University of Chicago Press, v. 24(3), p. 411482, July.
James Heckman, Seong Hyeok Moon, Rodrigo Pinto & Adam Yavitz, 2008. "A Reanalysis of The Perry
Preschool Program", unpublished mimeo, University of Chicago, first draft 2006, revised 2008.
Mark Huggett, 1993.
" The riskfree rate in heterogeneousagent incompleteinsurance economies,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 17(56), pages 953969.
Salvador Navarro, 2005. "Understanding Schooling: Using Observed Choices to Infer Agent's Information in a Dynamic Model of Schooling Choice when Consumption
Allocation is Subject to Borrowing Constraints," PhD dissertation, University of Chicago.
Society for Economic Dynamics: Letter from the President
Dear SED Members and Friends:
We continue the process of streamlining the organization. We have a new
server for the website, and are systematizing the software used for
registration and so forth. Much thanks is due to our Secretary, Christian,
who has put in a great deal of hard work to make this all happen. Hopefully
this means that we will continue to have a smooth process with minimal fuss.
The big news, of course, is the upcoming SED conference in Cambridge July
1012. Our organizers, Marios Angeletos, Arial Burstein, Mike Golosov, and
Christian Hellwig have done a fabulous job of pulling things together. We've
had an exceptionally strong set of submissions  1020 in all, a new record.
The quality of papers was enormously high  so good work everyone, and also
an apology to those who made strong submissions that didn't make the
program.
If you are coming to the meetings, we have great plenary talks lines up.
James Poterba, José Scheinkman and Per Krusell will be our speakers. The
Boston Federal Reserve Bank has kindly agreed to sponsor our reception.
Next year we are going to Istanbul  dates to be announced soon.
Sincerely,
David Levine, President
Society for Economic Dynamics
Review: Robustness
Robustness
by Lars Peter Hansen and Thomas Sargent
Modelling, especially under rational expectations, assumes that agents know the true underlying structure of the economy, including the parameter values. So does the researcher. What if the research is wrong, and he knows that he could be wrong? Model misspecification is a recognized, but often neglected problem in econometrics. It is mostly ignored in theoretical work. But it becomes particularly important if policy prescriptions differ significantly according to model specifications.
Hansen and Sargent tackle this "fear of model misspecification" by using recent advances in control theory: robust control. This book is not only an introduction to robust control for economists, it also extends robust control to areas particularly relevant to economic theory, for instance discounting, multiple agents, calibration of fear of misspecification.
The basic principle is based in relative entropy, a measure of distance with the true model. One represents misspecification as a set of perturbations to an approximating model. Hansen and Sargent apply this to a standard linearquadratic dynamic programming problem with a maximin objective: while the agent maximizes over strategies, the researcher minimizes over entropy.
This is an incredibly rich book. It covers a lot of material with plenty of examples.
Obviously, as for any pioneering work, disgesting it is somewhat challenging, but with high returns.
"Robustness" is published by Princeton University Press.
Impressum
The EconomicDynamics Newsletter is a free supplement
to
the Review of Economic
Dynamics
(RED). It is distributed through the
EconomicDynamics
mailing list and archived at http://www.EconomicDynamics.org/newsletter/. The
responsible
editors are Christian
Zimmermann (RED associate editor)
and Narayana Kocherlakota (RED coordinating editor).
The EconomicDynamics Newsletter is published twice a
year
in April and November.
Subscribing/Unsubscribing/Address change
To
subscribe to the EconomicDynamics mailing list,
send
a message to jiscmail@jiscmail.ac.uk with
the
following
message body:
join economicdynamics myfirstname mylastname
stop
To unsubscribe to the EconomicDynamics mailing
list, send
a message to jiscmail@jiscmail.ac.uk with the
following
message body:
leave economicdynamics
stop
To change a subscription address, please first
unsubscribe
and then subscribe. In case of problems, contact
economicdynamicsrequest@jiscmail.ac.uk.
The EconomicDynamics mailing list has very low
traffic,
less that 8 messages a year. For weekly
announcements
about online papers in Dynamic General
Equilibrium, you may to subscribe to
nepdge, following instructions in the link.

