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

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The Nobel Prizes

of unconditional expectations. It is mathematically straightforward to study a 

conditional counterpart, but the statistical implementation is more challenging. 

Application of the Law of Iterated Expectations still permits an econometrician 

to condition on less information than investors, so there continues to be scope 

for robustness in the implementation. By omitting information, however, the 

bounds are weakened.

By design, this approach allows for the SDF to be misspecified, but in a way 

captured by distorted beliefs. If the SDF S̃ depends on unknown parameters, say 

subjective discount rates, intertemporal elasticities of substitution or risk aver-

sion parameters, then the parameter estimation can be included as part of the 

minimization problem. Parameter estimation takes on a rather different role in 

this framework than in GMM estimation. The large sample limits of the result-

ing parameter estimators will depend on the choice of θ unless (as assumed in 

much of existing econometrics literature) there are no distortions in beliefs.

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Instead of featuring these methods as a way to get parameter estimators, they 

have potential value in helping applied econometricians infer how large prob-

ability distortions in investor beliefs would have to be from the vantage point 

of statistical measures of discrepancy. Such calculations would be interesting 

precursors or complements to a more structured analysis of asset pricing with 

distorted beliefs.

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 They could be an initial part of an empirical investigation and 

not the ending point as in other work using bounds in econometrics.

Martingales are present in SDF processes, even without resort to belief dis-

tortions. Alvarez and Jermann (2005), Hansen and Scheinkman (2009), Hansen 

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Extensions of a GMM approach have been suggested based on an empirical likelihood 

approach following Qin and Lawless (1994) and Owen (2001) (θ = –1), a relative-entropy 

approach of Kitamura and Stutzer (1997) (θ = 0), a quadratic discrepancy approach of 

Antoine et al. (2007) (θ = 1) and other related methods. Interestingly, the quadratic (θ = 

1) version of these methods coincides with a “continuously updating” GMM estimator of 

Hansen et al. (1996). Empirical likelihood methods and their generalizations estimate a 

discrete data distribution given the moment conditions such as pricing restrictions. From 

the perspective of parametric efficiency, Newey and Smith (2004) show these methods 

provide second-order asymptotic refinements to what is often a “second-best” efficiency 

problem. Recall that the statistical efficiency problem studied in Hansen (1982b) took the 

unconditional moment conditions as given and did not seek to exploit the flexibility in 

their construction giving rise to a second-best problem. Perhaps more importantly, these 

methods sometimes have improvements in finite sample performance but also can be 

more costly to implement. The rationales for such methods typically abstract from belief 

distortions of the type featured here and typically focus on the case of iid data generation.

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Although Gosh et al. (2012) do not feature belief distortions, with minor modification 

and reinterpretation their approach fits into this framework with θ = 0.

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Uncertainty Outside and Inside Economic Models 427

(2011) and Bakshi and Chabi-Yo (2012) all characterize the role of martingale 

components to SDF’s and their impact on asset pricing over long investment ho-

rizons. Alvarez and Jermann (2005), Bakshi and Chabi-Yo (2012) and Borovička 

et al. (2014a) suggest empirical methods that bound this martingale component 

using a very similar approach to that described here. Since there are multiple 

sources for martingale components to SDF’s, adding more structure to what de-

termines other sources of long-term pricing can play an essential role in quanti-

fying the martingale component attributable to belief distortions. 

In summary, factorization (13) gives an abstract characterization of the chal-

lenge faced by an econometrician outside the model trying to disentangle the ef-

fects of altered beliefs from the effects of risk aversion on the part of investors in-

side the model. There are a variety of ways in which beliefs could be perturbed. 

Many papers invoke “animal spirits” to explain lots of empirical phenomenon in 

isolation. However, these appeals alone do not yield the formal modeling inputs 

needed to build usable and testable stochastic models. Adding more structure 

is critical to scientific advancement if we are to develop models that are rich 

enough to engage in the type of policy analysis envisioned by Marschak (1953), 

Hurwicz (1962) and Lucas (1976). What follows uses decision theory to moti-

vate some particular constructions of the martingale M.

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Next I explore one strategy for adding structure to the martingale alterations 

to beliefs that I introduced in this section.

6  uNCeRTaiNTY aNd deCiSioN TheoRY

Uncertainty often takes a “back seat” in economic analyses using rational expec-

tations models with risk averse agents. While researchers have used large and 

sometimes state dependent risk aversion to make the consequences of exposure 

to risk more pronounced, I find it appealing to explore uncertainty in a con-

ceptually broader context. I will draw on insights from decision theory to sug-

gest ways to enhance the scope of uncertainty in dynamic economic modeling. 

Decision theorists, economists and statisticians have wrestled with uncertainty 

for a very long time. For instance, prominent economists such as Keynes (1921) 

and Knight (1921) questioned our ability to formulate uncertainty in terms of 

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An alternative way to relax rational expectations is to presume that agents solve their 

optimization problems using the expectations measured from survey data. See Piazzesi 

and Schneider (2013) for a recent example of this approach in which they fit expectations 

to time series data to produce the needed model inputs.

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