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

400 

The Nobel Prizes

This essay proceeds as follows. In Section 2, I review the development of 

time series econometric modeling, including the initiation of rational expecta-

tions econometrics. In Section 3, I review my contributions to the economet-

ric study of partially specified models, adapting to the study asset pricing and 

macroeconomic uncertainty. I describe methods and approaches to the study of 

fully specified models based on asset pricing considerations in Section 4. In Sec-

tion 5, I explore the consequences for asset pricing models when investor beliefs 

are not in full accord with an underlying model, which can result in investor be-

havior that resembles extreme risk aversion. In Section 6, I review perspectives 

on model ambiguity which draw on work by decision theorists and statisticians 

to revisit the framework that I sketch in Section 5. I draw some conclusions in 

Section 7.

2  RaTioNal exPeCTaTioNS eCoNoMeTRiCS

Rational expectations econometrics explores structural stochastic models of 

macroeconomic time series with the ambition to be a usable tool for policy 

analysis. It emerged in response to a rich history of modeling and statistical 

advances. Yule (1927) and Slutsky (1927, 1937) provided early characterizations 

of how time series models can generate interesting cyclical behavior by propa-

gating shocks. Yule (1927) showed that a second-order autoregression could 

reproduce intriguing patterns in the time series. He fit this model to sunspot 

data, known to be approximately but not exactly periodic. The model was built 

using independent and identically distributed (iid) shocks as building blocks. 

The model produced a damped periodic response to random impulses. Simi-

larly, Slutsky (1927, 1937) constructed models that were moving-averages of iid 

shocks and showed how such processes could be arbitrarily close to exact peri-

odic sequences.

2

 He also demonstrated how moving-average type models could 

account for British business cycle data.

Frisch (1933), who shared the first Sveriges Riksbank Prize in Economics 

with Tinbergen, pushed this agenda further by exploring how to capture dy-

namic economic phenomenon through probability models with explicit eco-

nomic underpinnings. Frisch discussed propagation from initial conditions 

and described an important role for random impulses building in part on the 

work of Yule (1927) and Slutsky (1927, 1937). In effect, Frisch (1933) introduced 

2 

I cite two versions of Slutsky’s paper. The first one was published in Russian. The second 

one was published in English a decade later with a more comprehensive set of results. 

English translations of the first paper were circulated well in advance of 1937.

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Uncertainty Outside and Inside Economic Models 401

impulse response functions to economics as a device to understand the inter-

temporal impact of shocks on economic variables. Haavelmo (1944) took an 

additional step by providing foundations for the use of statistical methods to 

assess formally the stochastic models. This literature set the foundation for a 

modern time series econometrics that uses economics to interpret evidence in a 

mathematically formal way. It featured important interactions among econom-

ics, mathematics and statistics and placed a premium on formal model build-

ing.

3

 Haavelmo (1944) confronts uncertainty as an econometrician outside the 

model that is to be estimated and tested.

Investment and other decisions are in part based on people’s views of the 

future. Once economic decision makers are included into formal dynamic eco-

nomic models, their expectations come into play and become an important in-

gredient to the model. This challenge was well appreciated by economists such 

as Pigou, Keynes and Hicks, and their suggestions have had durable impact on 

model building. Thus, the time series econometrics research agenda had to take 

a stand on how people inside the model made forecasts. Alternative approaches 

were suggested including static expectations, adaptive expectations or appeals 

to data on beliefs; but these approaches left open how to proceed when using 

dynamic economic models to assess hypothetical policy interventions.

A productive approach to this modeling challenge has been to add the hy-

pothesis of rational expectations. This hypothesis appeals to long histories of 

data to motivate the modeling expectations. The Law of Large Numbers gives an 

approximation whereby parameters that are invariant over time are revealed by 

data, and this revelation gives a model builder a way to formalize the expecta-

tions of economic investors inside our models.

4

 This approach to completing the 

specification of a stochastic equilibrium model was initiated within macroeco-

3 

Frisch, in particular, nurtured this ambitious research agenda by his central role in the 

foundational years of the Econometric Society. His ambition is reflected in the 1933 mis-

sion statement he wrote for the journal Econometrica: “. . . Experience has shown that 

each of these three viewpoints, that of statistics, economic theory, and mathematics, is a 

necessary, but not by itself a sufficient, condition for a real understanding of the quantita-

tive relations in modern economic life. It is the unification of all three that is powerful. 

And it is this unification that constitutes econometrics.” Frisch (1933b).

4 

More than three hundred years ago, Jacob Bernoulli proved a result that implied a Law 

of Large Numbers. He was motivated in part by social problems for which probabilities 

had to be estimated empirically, in contrast to typical gambling problems. Bernoulli’s 

result initiated an enduring discussion of both the relevance of his simple model speci-

fication and of the approximation he established. See Stigler (2014) for an interesting 

retrospective on Bernoulli’s contribution.

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