Regional President Speech

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, Motohiro 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: • — 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  •  — The random variable  has realizations    =1 { } The outcome ( ) results in a benefit of ( ). • — 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 (( ) + (  ))    • 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: • — State-dependent marginal utility:  ( )  ∗ — Household subjective probabilities:    No good data on these! • But we will see: • Relevant information is encoded in risk-neutral probability density.

RISK-NEUTRAL PROBABILITIES

RNPD Suppose households trade assets before policymaker chooses  • 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   ∗ • 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. •

CONCERNS

Lack of Predictive Power Concern: RNPDs predict poorly. Response: This is true but irrelevant. Policymakers’ decisions should be based on households’ relative valuations • 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 • 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 ... • Investors have no incentive to get information about its future payoffs. • Consequence: policy choice does not adequately reflect available informa- • tion. See Bernanke-Woodford (1997) for elegant exposition. •

Response This concern is mitigated by existence of options with varying strikes. • 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 ( ) • 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. • That decision suggests that their relative marginal valuations of resources • 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. • Right response: appropriate attention to robustness. • Wrong response: abandon RNPDs completely. •

CONCLUSIONS

Policy decisions often impact the economy a lag. • Hence, policymakers need some way to gauge the relative likelihoods of • future events. Monetary: How likely is deflation? How likely is high inflation? • Financial regulation: How likely is significant financial instability? •

Typical approach: attempt to figure out "true" probability of future events. • Point of this talk: For policymakers that care about social welfare, the • 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. •

Thus, the risk-neutral probability of deflation could rise because: • — 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 • influence the likelihood of deflation.

Implementation Challenges Decision-making using RNPDs is not necessarily easy. • — 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. • They report the results on the public website for a wide range of assets. • — Gold, silver, wheat, S&P 500, exchange rates, etc. They report and archive the results on a biweekly basis. • See http://www.minneapolisfed.org/banking/rnpd. •