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

414 

The Nobel Prizes

the need for large risk aversion in all states of the world, but it did not avoid the 

need for large risk aversion in some states. The statistician in me is intrigued by 

the possibility that observed incidents of large risk aversion might be proxying 

for investor doubts regarding the correctness of models. I will have more to say 

about that later.

4  eCoNoMiC ShoCkS aNd PRiCiNG iMPliCaTioNS

While the empirical methods in asset pricing that I described do not require that 

an econometrician identify the fundamental macroeconomic shocks pertinent 

to investors, this shortcut limits the range of questions that can be addressed. 

Without accounting for shocks, we can make only an incomplete assessment of 

the consequences for valuation of macroeconomic uncertainty. To understand 

fully the pricing channel, we need to know how the  SDF process itself depends 

on fundamental shocks. This dependence determines the equilibrium compen-

sations to investors that are exposed to shocks. We may think of this as valuation 

accounting at the juncture between the Frisch (1933) vision of using shock and 

impulses in stochastic equilibrium models and the Bachelier (1900) vision of 

asset values that respond to the normal increments of a Brownian motion pro-

cess. Why? Because the asset holders exposed to the random impulses affecting 

the macroeconomy require compensation, and the equilibrating forces affecting 

borrowers and lenders interacting in financial markets determine those com-

pensatory premia.

In what follows, I illustrate two advantages to a more complete specification 

of the information available to investors that are reflected in my work.

4.1  Pricing Shock exposure over alternative horizons

First, I explore more fully how a SDF encodes risk compensation over alterna-

tive investment horizons. I suggest a way to answer this question by describ-

ing valuation counterparts to the impulse characterizations advocated by Frisch 

(1933) and used extensively in quantitative macroeconomics since Sims (1980) 

proposed a multivariate and empirical counterpart for these characterizations. 

Recall that an impulse response function shows how alternative shocks tomor-

row influence future values of macroeconomic variables. These shocks also rep-

resent alternative exposures to macroeconomic risk. The market-based com-

pensations for these exposures may differ depending on the horizon over which 

a cash flow is realized. Many fully specified macroeconomic models proliferate 

shocks, including random changes in volatility, as a device for matching time 

series. While the additional shocks play a central role in fitting time series, even-

tually we must seek better answers to what lies within the black box of candidate 

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Uncertainty Outside and Inside Economic Models 415

impulses. Understanding their role within the models is central to opening this 

black box in search of the answers. Empirical macroeconomists’ challenges for 

identifying shocks for the macroeconomy also have important consequences for 

financial markets and the role they play in the transmission of these shocks. Not 

all types of candidate shocks are important for valuation.

I now discuss how we may distinguish which shock exposures command the 

largest market compensation and the impact of these exposures over alternative 

payoff horizons. I decompose the risk premia into risk prices and risk exposures 

using sensitivity analyses on underlying asset returns. To be specific, let X be an 

underlying Markov process and W a vector of shocks that are random impulses 

to the economic model. The state vector X

t

 depends on current and past shocks. 

I take as given a solved stochastic equilibrium model and reveal its implications 

for valuation. Suppose that there is an implied stochastic factor process S that 

evolves as:

 log 

S

t+1

 – log S

t

 = ψ

s

 (X

t

, W

t+1

). (8)

Typically economic models imply that this process will tend to decay over 

time because of the role that S plays as a discount factor. For instance, for the 

yield on a long-term discount bond to be positive,

  

lim

t

→∞

1

t

log E

S

t

S

o

X

o

= x

⎡

⎣

⎢

⎤

⎦

⎥ < 0.

Specific models provide more structure to the function ψ

s

 relating the sto-

chastic decay rate of S to the current state and next period shock. In this sense, 

(8) is a reduced form-relation. Similarly, consider a one-period, positive cash-

flow G that satisfies:

 log 

G

t+1

 – log G

t

 = ψ

g

 (X

t

, W

t+1

). (9)

The process G could be aggregate consumption, or it could be a measure 

of aggregate corporate earnings or some other process. The logarithm of the 

expected one-period return of a security with this payoff is:

 

υ

t

= log E

G

t

+1

G

t

⎪F

t

⎡

⎣

⎢

⎤

⎦

⎥ − log E

S

t

+1

G

t

+1

S

t

G

t

⎪F

t

⎡

⎣

⎢

⎤

⎦

⎥.  (10)

So-called risk return tradeoffs emerge as we change the exposure of the cash 

flow to different components of the shock vector W

t+1

.

Since cash flow growth 

G

t

+1

G

t

 depends on the components of W

t+1

 as a 

source of risk, exposure is altered by changing how the cash flow depends on 

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