speeches · September 19, 2013
Regional President Speech
Narayana Kocherlakota · President
Optimal Outlooks
Narayana Kocherlakota
September 2013
Disclaimer and Acknowledgements
Disclaimer: I am not speaking for others in the Federal Reserve System.
Acknowledgements: I thank Doug Clement, David Fettig, Terry Fitzgerald,
Ron Feldman, Ken Heinecke, Sam Schulhofer-Wohl, Thomas Tallarini, Moto-
hiro Yogo, and Kei-Mu Yi for their comments.
Need for Outlooks
A policymaker needs to make a decision today.
•
The current decision results in random future net benefits to society.
•
Hence, the policymaker’s decision depends on the outlook about those net
•
benefits.
Question
What’s the appropriate notion of an outlook for this policymaker?
Answer
The needed outlook is not a statistically motivated predictive density ...
•
But rather an asset-price-based risk-neutral probability density (RNPD).
•
Main Result
A policymaker reaches the same ex-ante decision by:
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— maximizing social welfare
— maximizing risk-neutral expected benefits
Maximizing statistical expectation of benefits is typically different.
•
Intuition
To make an ex-ante decision, the policymaker weighs social benefits in
•
different future states against each other.
To maximize social welfare: relevant weights are households’ ex-ante rela-
•
tive marginal valuations of resources in those states.
RNPDs are derived from financial market prices.
•
Those prices reflect households’ ex-ante relative marginal valuations of
•
resources in different future states.
Hence: the risk-neutral expectation also weighs benefits in different states
•
according to households’ ex-ante relative marginal values of resources.
Outline
1. General Policy Problem
2. Risk-Neutral Probabilities
3. Equivalence
4. Possible Concerns
5. Conclusions
GENERAL POLICY PROBLEM
Random Outcomes
Policymaker chooses an action today.
•
The result of the action next period depends on the realization of
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— The random variable has realizations
=1
{ }
The outcome ( ) results in a benefit of ( ).
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— The benefit ( ) may be positive or negative.
Examples of B
2
Inflation targeting: ( ) = ( + )
∗
• − −
— is accommodation
— is inflation shock
Financial instability: ( )
•
— is bank dividends
— is financial stress
Social Welfare
If realization occurs, households consume (( ) + ( ))
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Households’ ex-ante (subjective) expected utility is:
•
(( ) + ( ) )
=1
X
The households’ utility function is possibly state-dependent.
•
Also: are subjective probabilities, not "true" probabilities.
•
Optimal Choice
Chain rule: optimal choice of satisfies FOC:
•
( ) ( ) = 0
∗ ∗
=1
X
where ( ) is the marginal utility of consumption in state :
∗
( ) (( ) + ( ) )
∗ ∗
≡
Missing Information
Policymaker needs to know:
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— State-dependent marginal utility: ( )
∗
— Household subjective probabilities:
No good data on these!
•
But we will see:
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Relevant information is encoded in risk-neutral probability density.
RISK-NEUTRAL PROBABILITIES
RNPD
Suppose households trade assets before policymaker chooses
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Let represent the (implied) price of goods in state .
•
Define = ( ) to be:
∗ ∗ =1
•
=
∗
=1
P
is called the risk-neutral probability density (RNPD).
∗
•
— probability means: is positive and ’s sum to 1.
∗ ∗
RNPD in Equilibrium
Households treat as given when trading assets.
∗
•
In equilibrium, there is a constant 0 such that:
•
= ( )
∗
Hence:
•
( )
∗
=
∗
( )
=1 ∗
P
Risk-Neutral and "True" Probabilities
The RNPD is not the same as the "true" probability density of
∗
•
reflects households’ marginal utilities.
∗
•
And reflects households’ subjective probabilities.
∗
•
*
E
For any random variable define:
•
() =
∗ ∗
=1
X
Define risk-neutral expected benefits:
•
(( )) = ( )
∗ ∗
=1
X
EQUIVALENCE
Maximizing E*(Benefits)
Suppose policymaker chooses so as to maximize (Benefits).
∗
•
Then, satisfies FOC:
•
b ( ) = 0
∗
{ }
b
Result - Setup
0 = ( )
∗
{ }
b
= ( )
∗
{ }
=1
X
b
But we know that for some constant 0:
•
= ()
∗
b
Result - Conclusion
It follows that also satisfies:
•
b
0 = () ( )
=1
X
b b
This is the same FOC that characterized
∗
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Thus: maximizing (Benefits) is the same as maximizing social welfare.
∗
•
— But: maximizing only requires knowledge of RNPD.
∗
Verbal Summary
Standard: Policymaker’s optimal choice sets the outlook for marginal net
•
benefits equal to zero.
Novel: The appropriate notion of the outlook is given by
∗
•
Policymaker should balance benefits across states of the world using house-
•
holds’ relative marginal valuations of resources in different states.
The relative marginal valuations are given by RNPD, not statistical density.
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CONCERNS
Lack of Predictive Power
Concern: RNPDs predict poorly.
Response: This is true but irrelevant.
Policymakers’ decisions should be based on households’ relative valuations
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of resources in different states.
These aren’t predictive: they incorporate subjective probabilities and mar-
•
ginal utilities.
Heterogeneity
Concern: Households aren’t the same.
Response: The basic equivalence result extends as long as ...
Redistributions of resources generated by choice of can be offset using
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transfers.
Similar to: "expanding the pie" argument for free trade.
•
Costly Information Acquisition
Concern: Possible loss of private incentives to acquire information.
If policy is set so as to keep an asset’s current price constant ...
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Investors have no incentive to get information about its future payoffs.
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Consequence: policy choice does not adequately reflect available informa-
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tion.
See Bernanke-Woodford (1997) for elegant exposition.
•
Response
This concern is mitigated by existence of options with varying strikes.
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With options, investors value information about each outcome of even
•
if the policymaker ensures that ( ( )) always equals zero.
∗ ∗
Note: In constructing RNPDs, we need data on prices from many options
•
with distinct strikes.
Incompleteness of Observed Assets
Concern: Given observed assets, there may be multiple RNPDs.
Response: The basic equivalence result extends as long as ...
For any action the benefit ( ) is spanned by the payoffs of observed
•
assets.
Even without spanning: we can find upper and lower bounds to ( )
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consistent with absence of arbitrage
Limited Participation
Concern: Few households trade in option mkts used to construct RNPDs.
Response: This is a problem if they’re barred from participating.
However, I find it more plausible that they are choosing not to participate.
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That decision suggests that their relative marginal valuations of resources
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in various states are similar to that implied by option markets.
Illiquidity
Concern: Asset prices could differ because of liquidity, not risk, differences.
Response: This is a potential issue.
Specifically: options with similar strikes might have very different prices.
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Right response: appropriate attention to robustness.
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Wrong response: abandon RNPDs completely.
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CONCLUSIONS
Policy decisions often impact the economy a lag.
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Hence, policymakers need some way to gauge the relative likelihoods of
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future events.
Monetary: How likely is deflation? How likely is high inflation?
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Financial regulation: How likely is significant financial instability?
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Typical approach: attempt to figure out "true" probability of future events.
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Point of this talk: For policymakers that care about social welfare, the
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relevant probability is a risk-neutral probability.
RNPDs encode households’ ex-ante marginal valuations of resources in
•
different states.
Good policymaking should be based on these relative valuations.
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Thus, the risk-neutral probability of deflation could rise because:
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— Households view that outcome as more likely
— Households’ marginal utility of resources in that outcome has risen.
Both of these changes should matter for a monetary policymaker who can
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influence the likelihood of deflation.
Implementation Challenges
Decision-making using RNPDs is not necessarily easy.
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— Need to determine appropriate financial proxy for relevant event.
— Even then: Available options may not cover longer horizons or extreme
tail events.
Nothing new: Good decisions are always based on a mix of good judgment,
•
good data, and good modeling choices.
BUT:
The right goal is to model/estimate RNPDs, not statistical forecasts.
Ninth District Activities
Minneapolis Fed’s Banking Group uses options data to compute RNPDs.
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They report the results on the public website for a wide range of assets.
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— Gold, silver, wheat, S&P 500, exchange rates, etc.
They report and archive the results on a biweekly basis.
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See http://www.minneapolisfed.org/banking/rnpd.
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Cite this document
APA
Narayana Kocherlakota (2013, September 19). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20130920_narayana_kocherlakota
BibTeX
@misc{wtfs_regional_speeche_20130920_narayana_kocherlakota,
author = {Narayana Kocherlakota},
title = {Regional President Speech},
year = {2013},
month = {Sep},
howpublished = {Speeches, Federal Reserve},
url = {https://whenthefedspeaks.com/doc/regional_speeche_20130920_narayana_kocherlakota},
note = {Retrieved via When the Fed Speaks corpus}
}