What Rule for the Federal Reserve? Forecast Targeting V. V. Chari - - PowerPoint PPT Presentation

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What Rule for the Federal Reserve? Forecast Targeting V. V. Chari - - PowerPoint PPT Presentation

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Discussion of Svenssons What Rule for the Federal Reserve? Forecast Targeting V. V. Chari & Keyvan Eslami University of Minnesota & Federal Reserve Bank of Minneapolis October 2017 What Svenssons Paper Is About Hates Taylor

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SLIDE 1

Discussion of Svensson’s

What Rule for the Federal Reserve? Forecast Targeting

  • V. V. Chari & Keyvan Eslami

University of Minnesota & Federal Reserve Bank of Minneapolis October 2017

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What Svensson’s Paper Is About

Hates Taylor rule

Not optimal, too rigid, too mechanical

Apparently wants to implement optimal policy derived from model Likes current regime because it seems to be moving in the right direction

Chari & Eslami What Rule for the Federal Reserve?

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Svensson’s Proposal

Consider many policy paths For each path, compute equilibrium in model, assuming commitment

Chari & Eslami What Rule for the Federal Reserve?

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Svensson’s Proposal

Consider many policy paths For each path, compute equilibrium in model, assuming commitment

Hidden question: How to select equilibrium if model has multiplicity?

Chari & Eslami What Rule for the Federal Reserve?

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Svensson’s Proposal

Consider many policy paths For each path, compute equilibrium in model, assuming commitment

Hidden question: How to select equilibrium if model has multiplicity?

Seting aside hidden question, pick “best” policy path

Chari & Eslami What Rule for the Federal Reserve?

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What Is Missing in Proposal

What will policymaker do if outcome = forecasts?

Presumably implement announced policy

What will policy maker do if outcomes = forecasts? What will policy maker do if circumstances change, shocks affect economy?

Chari & Eslami What Rule for the Federal Reserve?

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What Is Needed to Complete Proposal

Implement announced path if outcomes = forecasts Commit to what policy will do if no shocks and outcomes = forecasts

Needed to solve indeterminacy problem

Commit to what policy will do if shocks affect economy

Chari & Eslami What Rule for the Federal Reserve?

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What Will We End Up with?

Let policy be rt Let history of outcomes be h0

t = (Y0, Y1, . . . , Yt−1; π0, . . . , πt−1; other endogenous variables)

Yt: output in t πt: inflation in t Let history of shocks be st History of policymakers ht = (h0

t , st)

Let rt = rt (ht) But this is exactly what all economic theory says you should do!

Policymaker should go away until there is a compelling reason to change model

Chari & Eslami What Rule for the Federal Reserve?

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My Discussion

Lay out optimal policy in New-Keynesian model Show how optimal policy looks like forecast targeting Discuss how to solve indeterminacy problem Suggest practical ways of ataining commitment

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy in a New-Keynesian Model

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Ingredients of New-Keynesian Model

Monopolistic competition as in Dixit-Stiglitz-Spence-Ethier Calvo price seting Shocks to technology: implicit in efficient output y∗

t

Shocks to intertemporal Euler equation: εt Shocks to markups: ut

Chari & Eslami What Rule for the Federal Reserve?

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Equilibrium Conditions

Log-linearize around zero inflation, efficient steady state ˜ yt = Et (˜ yt+1) − 1 σ [˜ rt − Et (πt+1)] + εt ˜ πt = βEt (˜ πt+1) + κ˜ yt + ut ˜ yt = yt − y∗

t

˜ πt = πt − 0 ˜ rt = rt − r∗

t

y∗

t : efficient output level

r∗

t : real interest rate in efficient allocation (nominal rate since π∗ t = 0)

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy

Solves min

∞

  • t=0

βt (˜ yt)2 + λ (˜ πt)2 subject to equilibrium conditions Optimal policy tries to keep ˜ yt and ˜ πt close to zero

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Technology Shocks

Suppose y∗

t iid

Can keep πt = 0, ˜ yt = 0 = yt − y∗

t by lowering rt

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Technology Shocks

Suppose y∗

t iid

Can keep πt = 0, ˜ yt = 0 = yt − y∗

t by lowering rt

˜ yt = Et (˜ yt+1) − 1 σ [˜ rt − Et (πt+1)] + εt ˜ πt = βEt (˜ πt+1) + κ˜ yt + ut ˜ yt = yt − y∗

t

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Technology Shocks

Suppose y∗

t iid

Can keep πt = 0, ˜ yt = 0 = yt − y∗

t by lowering rt

Suppose y∗

t random walk ⇒ r∗ t constant

Can keep πt = 0, ˜ yt = 0 = yt − y∗

t by leaving rt unaffected

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Markup Shocks

Say markup shock positive Cannot keep πt = 0 and y0 = y∗ Compromise is to let π0 go up, y0 fall Compromise also by leting πt+1 = 0 and ˜ yt+1 = 0 for t ≥ 0

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Markup Shocks

Say markup shock positive Cannot keep πt = 0 and y0 = y∗ Compromise is to let π0 go up, y0 fall Compromise also by leting πt+1 = 0 and ˜ yt+1 = 0 for t ≥ 0 ˜ yt = Et (˜ yt+1) − 1 σ [˜ rt − Et (πt+1)] + εt ˜ πt = βEt (˜ πt+1) + κ˜ yt + ut ˜ yt = yt − y∗

t

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy and Markup Shocks

Say markup shock positive Cannot keep πt = 0 and y0 = y∗ Compromise is to let π0 go up, y0 fall Compromise also by leting πt+1 = 0 and ˜ yt+1 = 0 for t ≥ 0 Such a policy is optimal even if markup shocks are iid Next, impulse-response of optimal policy if ut persistent

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Response to Markup Shocks

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy with Markup Shocks

Substantial history dependence Very different from outcomes without commitment

Without commitment, do not need to react to history of markup shocks

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Discretionary Response to Markup Shocks

Chari & Eslami What Rule for the Federal Reserve?

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Forecast Targeting and Optimal Policy

Central banker can show pictures like previous ones Argue commitment outcomes are best Can also try to explain how markup shocks affect economy In this sense, forecast targeting conveys information about underlying shocks

Chari & Eslami What Rule for the Federal Reserve?

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Risks of Forecast Targeting

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Risks of Incompletely Spelled out Svensson’s Proposal

Suppose market believes policy path will be rigidly followed Even if outcomes = forecasts Economy has continuum of equilibria (indeterminacy) Point of Taylor principle was to avoid indeterminacy Not addressing this point makes paper seem irrelevant

Chari & Eslami What Rule for the Federal Reserve?

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Idea behind Indeterminacy

Start at some equilibrium Now suppose each price seter expects other price seters to set a higher price If monetary policy is sufficiently accommodative, wages and price seter’s costs will rise Optimal for price seter to go along and set a higher price

Chari & Eslami What Rule for the Federal Reserve?

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Cure for Indeterminacy

Atkeson-Chari-Kehoe (ACK) Taylor principle makes rt very responsive to πt ACK show Taylor principle neither necessary nor sufficient to cure indeterminacy ACK show that a hybrid rule can implement equilibrium uniquely Hybrid rule uses Taylor principle supplemented with a switch to money regime if inflation sufficiently high

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy with Markup Shocks along Equilibrium Path

Timing: markup shocks, prices set, interest rates set, output realized Along equilibrium path rt = rt

  • ut

ut: history of markup shocks Along equilibrium path rt may respond less than inflation Along equilibrium path, Taylor principle violated

Chari & Eslami What Rule for the Federal Reserve?

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Optimal Policy with Markup Shocks Off Equilibrium Path

On and off equilibrium path rt = rt

  • ut

+ φ

  • πt − πt
  • ut

, φ > 1 πt (ut): equilibrium inflation under optimal policy πt − πt (ut): deviation from desired equilibrium Avoids indeterminacy when coupled with hybrid rule

Chari & Eslami What Rule for the Federal Reserve?

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Svensson’s Proposal Modified

Describe policy paths for several scenarios Each scenario represents some sequence of changes in circumstances and shocks Explain and justify deviations from announced path in term of what new shocks have affected economy Lay out policy if shocks small but outcomes very different from forecasts

Chari & Eslami What Rule for the Federal Reserve?

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Main Challenge of Monetary Policy

Monetary policy is a signal extraction problem What shocks have occurred? Are they persistent or transitory? New-Keynesian model useful in solving signal extraction problem

Chari & Eslami What Rule for the Federal Reserve?

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Signal Extraction and New-Keynesian Models

˜ yt = Et (˜ yt+1) − 1 σ [˜ rt − Et (πt+1)] + εt ˜ πt = βEt (˜ πt+1) + κ˜ yt + ut ˜ yt = yt − y∗

t

Technology shocks rise output and leave inflation roughly unaffected Markup shocks drive output and inflation in opposite directions Can exploit differential responses to estimate shocks

Chari & Eslami What Rule for the Federal Reserve?