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

412 

The Nobel Prizes

which Stutzer (1995) featured this in his analysis. When θ = –1,

 

E

φ

s

Es

⎛

⎝⎜

⎞

⎠⎟

⎡

⎣⎢

⎤

⎦⎥

= −E logs + logEs

 

and use of this specification of ϕ gives rise to a bound that has been studied 

in several papers including Bansal and Lehmann (1997), Alvarez and Jermann 

(2005), Backus et al. (2011), and Backus et al. (2014). These varying convex 

functions give alternative ways to characterize properties of SDFs that work 

through bounding their stochastic behaviour.

22

 He and Modest (1995) and Lu-

ttmer (1996) further extended this work by allowing for the pricing equalities to 

be replaced by pricing inequalities. These inequalities emerge when transaction 

costs render purchasing and selling prices distinct.

23

3.3  The Changing Price of uncertainty

Empirical puzzles are only well defined within the context of a model. Hansen 

and Singleton (1982, 1983) and others documented empirical shortcomings of 

macroeconomic models with power utility versions of investor preferences. The 

one-period SDF of such a representative consumer is:

 

S

t

+1

S

t

= exp(−

δ)

C

t

+1

C

t

⎛

⎝⎜

⎞

⎠⎟

−

ρ

 (7)

where C

t

 is consumption, δ is the subjective rate of discount and 

1

ρ  is the in-

tertemporal elasticity of substitution. Hansen and Singleton and others were the 

bearers of bad news: the model didn’t match the data even after taking account 

of statistical inferential challenges.

24

22 

The continuous-time limit for the conditional counterpart results in one-half times the 

local variance for all choices of ϕ for Brownian information structures.

23 

There has been some work on formal inferential methods associated with these meth-

ods. For instance, see Burnside (1994), Hansen et al. (1995), Peñaranda and Sentana 

(2011) and Chernozhukov et al. (2013).

24 

Many scholars make reference to the “equity premium puzzle.” Singleton and I showed 

how to provide statistically rigorous characterizations of this and other empirical anoma-

lies. The puzzling implications coming from this literature are broader than the expected 

return differential between an aggregate stock portfolio and bonds and extend to dif-

ferential returns across a wide variety of securities. See, for instance, Fama and French 

(1992) for empirical evidence on expected return differences, and see Cochrane (2008) 

and the discussion by Hansen (2008) for an exchange about the equity premium and 

related puzzles.

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Uncertainty Outside and Inside Economic Models 413

This empirical work nurtured a rich literature exploring alternative prefer-

ences and markets with frictions. Microeconomic evidence was brought to bear 

that targeted financial market participants when constructing the SDFs. These 

considerations and the resulting modeling extensions led naturally to alterna-

tive specifications on SDFs and suggestions for how they might be measured.

The nonparametric methods leading to bounds also added clarity to the em-

pirical evidence. SDFs encode compensations for exposure to uncertainty be-

cause they discount alternative stochastic cash flows according to their sensitiv-

ity to underlying macroeconomic shocks. Thus, empirical evidence about SDFs 

sheds light on the “risk prices” that investors need as compensations for being 

exposed to aggregate risk. Using these nonparametric methods, the empirical 

literature has found that the risk price channel is a fertile source for explaining 

observed variations in securities prices and asset returns. SDFs are highly vari-

able (Hansen and Jagannathan (1991)). The unconditional variability in SDFs 

could come from two sources: on-average conditional variability or variation 

in conditional means. As argued by Cochrane and Hansen (1992), it is really 

the former. Conditional variability in SDFs implies that market-based compen-

sations for exposure to uncertainty are varying over time in important ways. 

Sometimes this observation about time variation gets bundled into the observa-

tion about time-varying risk premia. Risk premia, however, depend both on the 

compensation for being exposed to risk (the price of risk) and on how big that 

exposure is to risk (the quantity of risk). Price variability, exposure variability 

or a combination of the two could be the source of fluctuations in risk premia. 

Deducing the probabilistic structure of SDFs from market data thus enables us 

to isolate the price effect. In summary, this empirical and theoretical literature 

gave compelling reasons to explore sources of risk price variation not previously 

captured, and provided empirical direction to efforts to improve investor prefer-

ences and market structures within these models.

Campbell and Cochrane (1999) provided an influential specification of in-

vestor preferences motivated in part by this empirical evidence. Consistent with 

the view that time variation in uncertainty prices is vital for understanding fi-

nancial market returns, they constructed a model in which SDFs are larger in 

magnitude in bad economic times than good. This paper is prominent in the 

asset pricing literature precisely because it links the time series behavior of risk 

prices to the behavior of the macroeconomy (specifically aggregate consump-

tion), and it suggests one preference-based mechanism for achieving this varia-

tion. Under the structural interpretation provided by the model, the implied 

risk aversion is very large in bad economic times and modest in good times as 

measured by the history of consumption growth. This work successfully avoided 

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