Lars Peter Hansen Prize Lecture: Uncertainty Outside and Inside Economic Models

418 

The Nobel Prizes

the aversion of the decision maker to consumption risk. Applied researchers 

have only been too happy to explore this channel. A fully solved out stochastic 

equilibrium model represents C and V as part of the model solution. For in-

stance log C might have an evolution with the same form as log G as specified 

in (9) along a balanced stochastic growth trajectory. Representing S as in (8) 

presumes a solution for V

t

 or more conveniently 

V

t

C

t

 as a function of X

t

 along 

with a risk adjusted counterpart to V

t

 and these require a full specification of 

investor information.

For early macro-finance applications highlighting the computation of 

continuation values in equilibrium models, see Hansen et al. (1999) and Tal-

larini (2000). The subsequent work of Bansal and Yaron (2004) showed how 

these preferences in conjunction with forward looking beliefs about stochastic 

growth and volatility have a potentially important impact on even one-period 

(in discrete time) or instantaneous (in continuous time) risk prices through the 

forward-looking channel. Hansen (2011) and Borovička et al. (2011) show that 

the prices of growth rate shocks are large for all payoff horizons with recursive 

utility and when γ is much larger than ρ. By contrast, for power utility models 

with large values of ρ = γ, the growth rate shock prices start off small and only 

eventually become large as the payoff horizon increases. The analyses in Han-

sen et al. (2008) and Restoy and Weil (2011) also presume that one solves for 

the continuation values of consumption plans or their equivalent. This general 

approach to the use of recursive utility for investor preferences makes explicit 

use of the information available to investors and hence does not allow for the 

robustness that I discussed in section 3.

26

Sometimes there is a way around this sensitivity to the information structure 

when conducting an econometric analysis. The empirical approach of Epstein 

and Zin (1991) assumes that an aggregate equity return measures the return 

on an aggregate wealth portfolio. In this case the continuation value relative 

to a risk-adjusted counterpart that appears in formula (11) is revealed by the 

return on the wealth portfolio for alternative choices of the preference param-

eters. Thus there is no need for an econometrician to compute continuation 

values provided that data are available on the wealth portfolio return. Epstein 

and Zin (1991) applied GMM methods to estimate preference parameters and 

test model restrictions by altering appropriately the approach in Hansen and 

26 

Similarly, many models with heterogenous consumers/investors and incomplete mar-

kets imply pricing relation (1) for marginal agents defined as those who participate in the 

market over the relevant investment period. Such models require either microeconomic 

data and/or equilibria solutions computed using numerical methods.

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Uncertainty Outside and Inside Economic Models 419

Singleton (1982). Given that the one-period SDF can be constructed from con-

sumption and return data, the full investor information set does not have to 

be used in the econometric implementation.

27

 Campbell (1993) and Campbell 

and Vuolteenaho (2004) explored a related approach using a log-linear approxi-

mation, but this research allowed for market segmentation. Full participation 

in financial markets is not required because the econometric specification that 

is used to study the risk-return relation avoids having to use aggregate con-

sumption. Like Epstein and Zin (1991), this approach features the return on the 

wealth portfolio as measured by an aggregate equity return, but now prospective 

beliefs about that return also contribute to the (approximate) SDF.

4.3  a Continuing Role for GMM-based Testing

Even when fully specified stochastic equilibria are formulated and used as the 

basis for estimation, there remains the important task of assessing the perfor-

mance of the pricing implications remains. SDFs constructed from fully speci-

fied and estimated stochastic equilibrium models can be constructed ex post and 

used in testing the pricing implications for a variety of security returns. These 

tests can be implemented formally using direct extensions of the methods that 

I described in section 3. Thus the SDF specification remains an interesting way 

to explore empirical implications, and GMM-style statistical tests of pricing re-

strictions remain an attractive and viable way to analyze models.

In the remainder of this essay I will speculate on the merits of one produc-

tive approach to addressing empirical challenges based in part on promising 

recent research.

5  MiSSPeCiFied belieFS

So far I have focused primarily on uncertainty outside the model by exploring 

econometric challenges, while letting risk averse agents inside the model have 

rational expectations. Recall that rational expectations uses the model to con-

struct beliefs about the future.

28

 I now consider the consequences of altering 

27 

In contrast to recursive utility models with ρ ≠ γ, often GMM-type methods can be 

applied to habit persistence models of the type analyzed by Sundaresan (1989), Constan-

tinides (1990) and Heaton (1995) without having to specify the full set of information 

available to investors.

28 

A subtle distinction exists between two efforts to implement rational expectations 

in econometric models. When the rational expectations hypothis is imposed in a fully 

specified stochastic equilibrium model, this imposion is part of an internally consistent 

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