... Inflation and Commitment

Transcription

1 and Commitment 1

2 : A Few Facts Average HigherinLatePartof20 th Century than efore Deflation at time of Great Depression in Weak Economy of 1970s (Consumer Price Index)

3 Issues Dynamics of Still a Hotly Debated Topic Spikes in Around War-Time Not Puzzling ut, Why did Rise in the 1970s? 4

4 Two Types of Answer: People : Mistakes Happen i. Fed Incorrectly Thought Weak Economy of 1970s Was a Cyclical Problem. This Led Them to Try and Heat Up Economy With High Money Growth (Orphanides) ii. Fed Sometimes Thinks Trade-off etween and Unemployment IsVeryFavorable,andSoTheyInflate (Sargent). iii. Seems Appealing: Surely Only a Mistake Can Cause Monetary Institutions In Democratic Societies to Produce Socially ad Outcomes. Institutions : Lack of Commitment to Target i. In Democratic Society, With Fully Informed Agents, It is Possible for Monetary Institutions to Produce ad Outcomes ii. In Absence of Commitment Private Expectations of Can Push Monetary Authority into Supplying. iii. Expectation Trap. 8

5 What s At Stake? Diagnosis Determines the Nature of the Solution Different Approaches People view - Need More and etter Research on: Identifying the Right Model of the Economy Understanding the Interface etween Monetary Authority and Economy Institutions - Redesign Institution to Have More Commitment Legal Mandate to Focus Central ank s Attention Exclusively (Subject to Carefully Designed Escape Clauses!) on Contracts for Central ankers. 12

6 Outline for Remainder of Talk What is Commitment and Why Does it Matter? An Simple Example ased on the Laffer Curve Does Lack of Commitment in Monetary Policy Help Us Understand Data? Must Incorporate It into an Economic Model First. Kydland/Prescott - arro/gordon Model (KP-G). KP-G Model Explains Rise in Average. KP-G Model Explains Observed Change in Relation etween and Unemployment. If the KP-G Model is So Good, How Come Committment Is Not At Heart of Everyone s Explanation of Dynamics? KP-G Model Has Hard Time With End of 1970s. KP-G Model Has Hard Time With End of European. Should We Dump the Commitment View ecause KP-G Model Has Shortcomings? Maybe ut first, Let s See What Modern Models Have to Say. 21

7 Commitment: What is it, and Why Might it Matter? Commitment: a. Policy Maker Declares Policy First, and No One Doubts its Intention. b. Private Economy Makes Decisions. Lack of Commitment: a. Private Economy Makes Decision ased on Guess of What Policy Maker will Do. b. Policy Maker Chooses Policy. Laffer Curve Example. a. Commitment: Get est Outcome For Sure b. Lack of Commitment: Could Get Worst Outcome, ut Could Get Worst. 24

8 Government Preferences ¼z 2 τz 2 (1-τ) Laffer Curve g ½z 2 (1-τ) 2 0 A τ 1 τ 2 1 τ Utility: c-½l 2 HH udget constraint: c=(1-τ)zl Gov t udget constraint: g=τzl 25

9 Lack of Commitment in Monetary Policy Tax Example Useful for Illustration, ut Not So Plausible Lack of Commitment in Monetary Policy Very Plausible. Kydland-Prescott, arro-gordon Used as a Vehicle to Talk About Lack of Commitment 26

10 Kydland-Prescott, arro-gordon Model Monetary Policy Situation Looks Like Situation in Laffer Curve, With No Commitment. Private Decisions Involve Some Lead Time. Monetary Authority Makes Decisions Daily, alances enefits of Surprise Against Costs. π Linearity of est Response Ensures Unique Equilibrium est Response Function KP-G Model: Volatile Only if Fundamentals Are π e 30

11 Testing the Model efore WWII, Monetary Policy Had Commitment (Gold Standard) Commitment Lost After WWII With Advent of Keynesian Stabilization Policy Predictions of Kydland-Prescott/arro-Gordon Model Should have Gone Up. Early Century: Gold Standard. Should Have Negative Relationship etween and Unemployment. Late Century: Lost Commitment. KP-G Model Predicts Positive Relationship etween and Unemployment. 33

12 Unemployment 25 Figure 1a: Unemployment and 18 Unemployment Unemployment Unemployment -4-6 Figure 1c: Component, 2-8 years Figure 1b: Unemployment versus Unemployment Unemployment Figure 1d: Component, 8-20 years Unemployment Unemployment Figure 1e: Component, years Unemployment

13 Figure 2a: Unemployment and Unemployment 11 Unemployment Unemployment Unemployment Figure 2c: Component, 2 months -1.5 years Figure 2b: Unemployment versus Unemployment Unemployment 2.0 Unemployment Figure 2d: Component, years Unemployment 1.5 Figure 2e: Component, 8-20 years 3 Unemployment 1.2 Figure 2f: Component, years Unemployment Unemployment

14 Testing the Model efore WWII, Monetary Policy Had Commitment (Gold Standard) Commitment Lost After WWII With Advent of Keynesian Stabilization Policy Predictions of Kydland-Prescott/arro-Gordon Model Should have Gone Up Early Century: Gold Standard. Should Have Negative Relationship etween and Unemployment. Late Century: Lost Commitment. KP-G Model Predicts Positive Relationship etween and Unemployment Predictions Are orn out in US Data. These Are (Some of) the Reasons Why Commitment Attracted A Lot Of Attention. Problem: End of InUS. 36

15 Modern Approach (ased on Structural Models) Embed KP/G Ideas in Standard General Equilibrium Models. Models Have Rich Implications: Predicts Persistent Periods of Low as Well as High. Models Much More Testable than KP-G Model. π Non-Linear est Response Creates Possibility of Multiple Equilibria est Response 45 o A Possibility Ruled Out y Assumption in KP-G π e Modest Evidence in Data of Such Equilibria. Type of Equilibria That Occur: Expectation Traps (Chari, Christiano, Eichenbaum, 1999 JET). 40

16 Expectation Traps Low Private Agents Expect Low Private Actions Monetary Authority Supplies low High Private Agents Expect High Private Actions Monetary Authority Supplies High 41

17 US in the 1970s: An Expectation Trap? Arthur urns, Chairman of the US Federal Reserve in the 1970s, Spoke as Though He Were Caught in an Expectation Trap: urns, May 1970: An effort to offset, through monetary and fiscal restraints, all of the upward push that rising costs are now exerting on prices would be most unwise. Such an effort would restrict aggregate demand so severely as to increase greatly the risks of a very serious business recession. If that happened, the outcries of an enraged citizenry would probably soon force the government to move rapidly and aggressively toward fiscal and monetary ease, and our hopes for getting the inflationary problem under control would then be shattered. US in the 1990s: Another Expectation Trap? 42

18 Conclusion Dynamics of Continues to be a Hotly Debated Topic AbsenceofCommitmentInMonetaryPolicyHasLostFavorInRecentYears. This is True in Academic Research in Monetary Policy. Notion of Commitment In Monetary Policy is Also Losing its Grip Among Some Policy Makers. This May e a Mistake. 43

19 Embedding KP/G in General Equilibrium Equilibrium Reflects Interplay etween Incentives and Disincentives to Inflate. Incorporate Incentives and Disincentives into a Lucas-Stokey Cash-Credit Good Model. Incentives: Monopolistic Competition. Some Preset Prices. Disincentives: Svensson Timing (Pc M 1 ). Distortions to Relative Prices. Endogeneity of Payments Technology. Finding: Incentives and Disincentives May alance At Different Rates. 35

20 Model Households, Firms, Monetary Authority. Continuum of Goods. Infinite Horizon. 36

21 Timing in a Period Exogenous Shocks Realized Households Choose Fraction, z, of Goods to Purchase with Cash A Fraction, µ, of Firms Set Their Price, P e Monetary Authority Takes Its Action, x Goods Markets Meet and Clear

22 Description of the Model Description Proceeds ackward Through Time, Starting With Decisions Taken at End of Period. Decision by Firms and Households At the End of the Period. Decision by the Monetary Authority. Household Choice of z, and Choice of P e by Firms With Preset Prices. 38

23 Private Sector Decisions At the End of the Period Variables that are Pre-Determined At this Point: z, P e,x Description of Agents Problem: Firms Households 39

24 Firms Each good, y(ω),ω [0, 1], produced by a monopolist. Production Technology: y(ω) =θn(ω), ω [0, 1]. Firms use Usual Price Markup Rule. 1 µ Firms set Prices, ˆP,After Monetary Authority: ˆP = W θρ. (µ Sticky Price Firms set Prices, P e, efore Monetary Authority.) 40

25 Households Problem: max X β t u(c t, labor t ),c= t=0 Z 1 c(x) ρ dx 0 1 ρ C(x) Cash Goods Costly Credit Goods Free Credit Goods z z-bar x 1 41

26 Payments Technology: ( z z)1+ν labor = n + η, z given. 1+ν Cash in advance constraint: M 1 P e µzc cash,preset price + ˆP (1 µ)zc cash,flex price Usual Wealth Evolution Equation. 42

27 Monetary Authority Problem: max U(s, z, P e,r), R s ~Exogenous Shocks Necessary Conditions for Monetary Authority Maximization: U R = ψ ID (R)+ψ MD (R, z) 0 with equality if R>1. Policy Correspondence ψ ID ~ Distortion : ψ ID =(R 1) R 1 ρ 1 ψ ID (1) = (R 1) M P lim ψ ID(R) =0. R 43

28 ψ MD ~ Monopoly Distortion : ψ MD (R, z) = (1 ρ)r 1 ρ 1 R 1 ρ ρ 1 + ψr + 1+ψ 1 ρ + ψ ρ ρ 1 + µ 1 µ ³ µ un + θ u c2 ψ ρ z 1 z R ρ ³R ρ ρ z z ρ 1 +1 Efficiency Dictates the Term in Square Should e Zero. With Monopoly Power, it is Positive. Properties of ψ MD : n R ψ MD (1) Q 0, lim R ψ MD (R) > 0. Proposition: Given z, If Monetary Authority FONC Satisfied at All, it Must e Satisfied At Least Twice. 44

29 enefits and Costs... Numerical example: µ=0.1, ρ=0.45, ψ=1,ν=2, z=0.15, η= Here are the Ψ ID and Ψ MD curves for a low value of z,z =.13 and high value of z, z = Figure 1: Marginal enefits and Marginal Costs for Monetary Authority 0.3 Distortion Monopoly Distortion, low z Monopoly Distortion, high z R In each case, the necessary conditions for an equilibrium are satisfied twice. 45

30 Details About the Candidate Equilibria: Low Equilibrium High Equilibrium Panel A: z =0.13 P e R c c n Panel : z =0.15 P e R c c n

31 utility... Necessary Conditions for Monetary Authority Optimization May Not e Sufficient. Must Verify Numerically. Necessary Conditions Do In Fact Identify Optima. z = 0.15 Figure 2a: Utility For Deviations From Low Equilibrium R 47

32 utility... Note: The High Candidate Equilibrium Almost Was Not a Global Optimum, with R=1 Coming in a Close Second. This Illustrates Importance of Verifying That Candidate Equilibria Identified by FONC s Do, In Fact, Satisfy Monetary Authority Optimization. z = 0.15 Figure 2b: Utility For Deviations From High Equilibrium R 48

33 R... y Varying z, Can Trace Out Set of R That Satisfy Necessary Conditions for Monetary Authority Optimization: 3.5 Figure 3: Interest Rate Policy Correspondence z 49

34 Household Choice of z Household Euler Equation for Choosing z Yields Another Relationship etween R and z: ( 1 ρ 1)(1 R ρ ρ 1 ) ρη( z z)ν i = z h(r 1 ρ 1 1) + ψ ρ (R ρ ρ 1 1) +(1+ ψ ρ ) 1 ( z z)1+ν η 1+ν g θ Household Payment Technology Function. Note that This is a Function of the Shocks. Can Show: Downward Sloping - If Households Expect High R, Choose Low z. 50

35 R... Markov Equilibria Figure 4a shows what happens for θ large (θ =1.9) andsmall(θ =0.1). Note how the response in the interest rate is of opposite sign across the high inflation and low inflation equilibria. Figure 4a: Markov Equilibrium With Production Technology Shocks Policy Correspondence Payment Function, Low θ Payment Function, High θ z Technology Shock, θ: Output is Increasing in Technology Shock in oth Equilibria = ρ(r, Y ) > 0 in Low Equilibrium. ρ(r, Y ) < 0 in High Equilibrium. 51

36 R... Figure 4b shows how the equilibrium responds to shocks in η. Results are displayed for high η ( ) and for η low ( ) Figure 4b: Markov Equilibrium With Payment Technology Shocks Policy Correspondence Payment Function, High η Payment Function, Low η z Payment Shock, η : Output is Increasing in Payment Technology Shock In Low Equilibrium, and Decreasing in High Equilibrium= ρ(r, Y ) < 0 in Low Equilibrium. ρ(r, Y ) < 0 in High Equilibrium. 52

37 Note Sign Switch: For Either Shock, Response of R Opposite Sign in High and Low Equilibria. With oth Shocks: ρ(r, Y ) < 0 in High Equilibrium, and Closer to Zero in Low Equilibrium. Note that R is Less Volatile in Low Equilibrium. 53

38 Empirical Analysis of ρ(r, Y ) Obtained Data From IFS On Y,R High Country : R>100 PercentinatLeastOneYear Episode of High inhigh Country : R>50 Percent. Low Country : Western Europe, the United States, Canada, Japan, Australia and New Zealand. 54

39 Evidence From High Countries There are seven high inflation countries. Five Had Episodes of High and Low. With one exception, ρ(r, Y ) Higher in Low Episodes than High Episodes. Standard Deviation of R Higher in High. 55

40 Evidence Across Countries High Countries Tend to Have ρ(r, Y ) < 0 Low Countries Tend to Have Higher ρ(r, Y ). 56

41 Conclusion Expectation Traps Equilibria Occur in Simple Monetary Models. Expecting, Agents Take Defensive Actions, Which Lead Monetary Authority to Optimally Provide High. Similarly, when Agents Expect Low. Prolonged Periods of High and Low Consistent With the Model. Some Empirical Support Found. The Expectation Trap Hypothesis About Variation and Persistence in Deserves Further Consideration. 57