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

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The Nobel Prizes

precise probabilities. Indeed Knight (1921) posed a direct challenge to time se-

ries econometrics:

We live in a world full of contradiction and paradox, a fact of which 

perhaps the most fundamental illustration is this: that the existence 

of a problem of knowledge depends on the future being different than 

the past, while the possibility of the solution of the problem depends 

on the future being like the past.

While Knight’s comment goes to the heart of the problem, I believe the most 

productive response is not to abandon models but to exercise caution in how we 

use them. How might we make this more formal? I think we should use model 

misspecification as a source of uncertainty. One approach that has been used 

in econometric model-building is to let approximation errors be a source for 

random disturbances to econometric relations. It is typically not apparent, how-

ever, where the explicit structure comes from when specifying such errors; nor 

is it evident that substantively interesting misspecifications are captured by this 

approach. Moreover, this approach is typically adopted for an outside modeler 

but not for economic actors inside the model. I suspect that investors or entre-

preneurs inside the models we build also struggle to forecast the future.

My co-authors and I, along with many others, are reconsidering the concept 

of uncertainty and exploring operational ways to broaden its meaning. Let me 

begin by laying out some constructs that I find to be helpful in such a discussion. 

When confronted with multiple models, I find it revealing to pose the result-

ing uncertainty as a two-stage lottery. For the purposes of my discussion, there 

is no reason to distinguish unknown models from unknown parameters of a 

given model. I will view each parameter configuration as a distinct model. Thus 

a model, inclusive of its parameter values, assigns probabilities to all events or 

outcomes within the model’s domain. The probabilities are often expressed by 

shocks with known distributions and outcomes are functions of these shocks. 

This assignment of probabilities is what I will call risk. By contrast there may be 

many such potential models. Consider a two-stage lottery where in stage one we 

select a model and in stage two we draw an outcome using the model probabili-

ties. Call stage one model ambiguity and stage two risk that is internal to a model.

To confront model ambiguity, we may assign subjective probabilities across 

models (including the unknown parameters). This gives us a way of averaging 

model implications. This approach takes a two-stage lottery and reduces it to a 

single lottery through subjective averaging. The probabilities assigned by each of 

a family of models are averaged using the subjective probabilities. In a dynamic 

setting in which information arrives over time, we update these probabilities 

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Uncertainty Outside and Inside Economic Models 429

using Bayes’ Rule. de Finetti (1937) and Savage (1954) advocate this use of sub-

jective probability. It leads to an elegant and often tractable way to proceed. 

While both de Finetti (1937) and Savage (1954) gave elegant defenses for the use 

of subjective probability, in fact they both expressed some skepticism or caution 

in applications. For example, de Finetti (as quoted by Dempster (1975) based on 

personal correspondence) wrote:

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Subjectivists should feel obligated to recognize that any opinion 

(so much more the initial one) is only vaguely acceptable . . . So 

it is important not only to know the exact answer for an exactly 

specified initial problem, but what happens changing in a reasonable 

neighborhood the assumed initial opinion.

Segal (1990) suggested an alternative approach to decision theory that avoids 

reducing a two-stage lottery into a single lottery. Preserving the two-stage struc-

ture opens the door to decision making in which the behavioral responses for 

risk (stage two) are distinct from those for what I will call ambiguity (stage one). 

The interplay between uncertainty and dynamics adds an additional degree of 

complexity into this discussion, but let me abstract from that complexity tem-

porarily. Typically there is a recursive counterpart to this construction that in-

corporates dynamics and respects the abstraction that I have just described. It 

is the first stage of this lottery that will be the focus of much of the following 

discussion.

6.1  Robust Prior analysis and ambiguity aversion

One possible source of ambiguity, in contrast to risk, is in how to assign sub-

jective probabilities across the array of models. Modern decision theory gives 

alternative ways to confront this ambiguity from the first stage in ways that are 

tractable. Given my desire to use formal mathematical models, it is important to 

have conceptually appealing and tractable ways to represent preferences in envi-

ronments with uncertainty. Such tools are provided by decision theory. Some of 

the literature features axiomatic development that explores the question of what 

is a “rational” response to uncertainty.

The de Finetti quote suggests the need for a prior sensitivity analysis. When 

there is a reference to a decision problem, an analysis with multiple priors can 

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Similarly, Savage (1954) wrote: “No matter how neat modern operational definitions of 

personal probability may look, it is usually possible to determine the personal probabili-

ties of events only very crudely.” See Berger (1984) for further discussion.

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