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

416 

The Nobel Prizes

the underlying shocks. When I refer to risk prices, formally I mean the sen-

sitivity of the logarithm of the expected return given on the left-hand side of 

(10) to change in cash-flow risk. I compute risk prices from measuring how υ

t

 

changes as we alter the cash flow, and compute risk exposures from examining 

the corresponding changes in the logarithm of the expected cash-flow growth: 

logE

G

t

+1

G

t

⎪F

t

⎡

⎣

⎢

⎤

⎦

⎥  (the first-term on the right-hand side of (10)).

These calculations are made operational by formally introducing changes in 

the cash-flows and computing their consequences for expected returns. When 

the changes are scaled appropriately, the outcomes of both the price and expo-

sure calculations are elasticities familiar from price theory. To operationalize the 

term changes, I must impose some additional structure that allows a researcher 

to compute a derivative of some type. Thus I must be formal about changes 

in 

G

t

+1

G

t

 as a function of W

t+1

. One way to achieve this formality is to take a 

continuous-time limit when the underlying information structure is that im-

plied by an underlying Brownian motion as in the models of financial markets 

as originally envisioned by Bachelier (1900). This reproduces a common notion 

of a risk price used in financial economics. Another possibility is to introduce a 

perturbation parameter that alters locally the shock exposure, but maintains the 

discrete-time formulation.

These one-period or local measures have multi-period counterparts ob-

tained by modeling the impact of small changes in the components of W

t+1

 on 

cash flows in future time periods, say 

G

t

+

τ

G

t

,

 for τ ≥ 1. Proceeding in this way, we 

obtain a valuation counterpart to impulse response functions featured by Frisch 

(1933) and by much of the quantitative macroeconomics literature. They inform 

us which exposures require the largest compensations and how these compen-

sations change with the investment horizon. I have elaborated on this topic in 

my Fisher-Schultz Lecture paper (Hansen (2011)), and I will defer to that and 

related papers for more specificity and justification.

25

 My economic interpreta-

tion of these calculations presumes a full specification of investor information as 

is commonly the case when analyzing impulse response functions.

4.2  a Recursive utility Model of investor Preferences

Next I consider investor preferences that are particularly sensitive to the as-

sumed available information. These preferences are constructed recursively 

25 

See Hansen et al. (2008), Hansen and Scheinkman (2009), Borovička et al. (2011), 

Hansen and Scheinkman (2012) and Borovička and Hansen (2014).

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Uncertainty Outside and Inside Economic Models 417

using continuation values for prospective consumption processes, and they are  

featured prominently in the macro-asset pricing literature. With these prefer-

ences the investor cares about intertemporal composition of risk as in Kreps and 

Porteus (1978) with these preferences. As a consequence, general revisions of 

the recursive utility model make investor preferences potentially sensitive to the 

details of the information available in the future. As I will explain, this feature 

of investor preferences makes it harder to implement a “do something without 

doing everything” approach to econometric estimation and testing.

The more general recursive utility specification nests the power utility model 

commonly used in macroeconomics as a special case. Interest in a more general 

specification was motivated in part by some of the statistical evidence that I 

described previously. Stochastic equilibrium models appealing to recursive util-

ity featured in the asset pricing literature were initially advocated by Epstein 

and Zin (1989) and Weil (1990). They provide researchers with a parameter to 

alter risk preferences in addition to the usual power utility parameter known 

to determine the intertemporal elasticity of substitution. The one-period SDF 

measured using the intertemporal marginal rate of substitution is:

 

S

t

+1

S

t

= exp(−

δ)

C

t

+1

C

t

⎛

⎝⎜

⎞

⎠⎟

−

ρ

V

t

+1

R

t

(V

t

+1

)

⎡

⎣

⎢

⎤

⎦

⎥

ρ−γ

 (11)

where C

t

 is equilibrium consumption, δ is the subjective rate of discount, 

1

ρ

 is 

the elasticity of intertemporal substitution familiar from power utility models, 

V

t

 is the forward-looking continuation value of the prospective consumption 

process, and R

t

(V

t+1

) is the risk adjusted continuation value:

 

R

t

(V

t

+1

)

= E V

t

+1

( )

1

−

γ

⎪F

t

⎡

⎣

⎤

⎦

(

)

1

1

−

γ

.

 

The parameter γ governs the magnitude of the risk adjustment. The pres-

ence of the forward-looking continuation values in the stochastic discount fac-

tor process adds to the empirical challenge in using these preferences in an eco-

nomic model. When ρ = γ, the forward-looking component drops out from the 

SDFs and the preferences become the commonly used power utility model as is 

evident by comparing (7) and (11). Multi-period SDFs are the corresponding 

products of single period discount factors.

The empirical literature has focused on what seems to be large values for 

the parameter γ that adjusts for the continuation value risk. Since continuation 

values reflect all current prospective future consumption, increasing γ enhances 

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