Demand Shocks, Monetary Policy, and the Optimal Use of Dispersed Information

Demand Shocks, Monetary Policy, and the Optimal Use of Dispersed Information Guido Lorenzoni (MIT) WEL-MIT-Central Banks, December 2006

Motivation Central bank observes an increase in spending Is it driven by fundamentals? Is it temporary consumer sentiment? In first case: accommodate In second case: offset the shock

Motivation Central bank observes an increase in spending Is it driven by fundamentals? Is it temporary consumer sentiment? In first case: accommodate In second case: offset the shock Questions: 1. What can the CB do if it cannot distinguish the two shocks? 2. What is the optimal thing to do?

Results: preview Answers: The CB can do quite a bit Use monetary policy rule to manage expectations The CB can, actually, achieve full stabilization of the output gap y t = y t Full stabilization of the output gap is not optimal

Ingredients Model of fundamental and sentiment shocks (Lorenzoni (2006)) Fundamental information is dispersed across the economy Agents know potential output in their own sector, but not the aggregate Demand shocks: shifts in average beliefs about aggregate potential output CB problem: induce efficient use of dispersed information Related theme: efficient use of public and private signals (Morris and Shin (2002), Angeletos and Pavan (2005))

Model Households: consumer/producer on [0, 1]. Preferences: E t=0 ( β t logc it 1 ) 1 + η N1+η it ( C it = C σ 1 σ ijt dj J it ) σ σ 1 random consumption basket: J it [0,1] Technology: Y it = A it N it

Shocks Individual productivity (private signal) is a it = loga it = a t 1 + θ it aggregate component and idiosyncratic component θ it = θ t + ε it Aggregate productivity is a t = a t 1 + θ t

Shocks (continued) Public signal about aggregate innovation s t = θ t + e t news aggregate statistics stock market θ t = fundamental shock e t = sentiment shock

Trading Agents have nominal balances B it 1 with CB (cashless economy) Before observing current shocks: state contingent contracts CB sets nominal interest rate on balances R t Producer set price P it Consumer observes prices in consumption basket P jt for j J it Consumer buys goods All shocks publicly revealed, state contingent contracts settled

Budget constraint B it = R t ( B it 1 + (1 + τ)p it Y it P it C it + Z it (h t ) T t ) q t ( ht ) Zit ( ht ) d ht. P it price index for goods in J it Z state contingent contracts subsidy τ to correct for monopolistic distortion T t lump sum tax to finance subsidy

Random consumption baskets 2 1.5 producers 1 0.5 θ t 0-0.5-0.4-0.2 0 0.2 0.4 0.6 0.8 1

Random consumption baskets 2 1.5 θ it producers 1 0.5 θ t 0-0.5-0.4-0.2 0 0.2 0.4 0.6 0.8 1

Random consumption baskets 2 1.5 1 producers 0.5 0-0.5-0.4-0.2 0 0.2 0.4 0.6 0.8 1 consumers

Random consumption baskets 2 1.5 1 producers 0.5 θ it 0-0.5-0.4-0.2 0 0.2 0.4 0.6 0.8 1 consumers

Random consumption baskets (continued) θ it = { θ jt : j J it } additional idiosyncratic shock: sampling shock v it θ it = θ t + v it

Monetary policy rule Interest rate rule r t = r + ξ ( p t 1 pt 1 ) Price target p t = µa t 1 + φ θ θ t + φ s s t only use past information p t aggregate price index note the term µa t 1 all lowercase = logs

Linear equilibrium Individual prices and consumption p it = φ 0 + µa t 1 + φ θ θ it + φ s s t c it = ψ 0 + a t 1 + ψ ε θ it + ψ v θ it + ψ s s t in equilibrium p t = p t interest rate constant Proposition Linear equilibrium exists under given policy rule, determinate if ξ > 1

Linear equilibrium (continued) Aggregate output Recall: s t = θ t + e t c t = ψ 0 + a t 1 + ψ θ θ t + ψ s s t Question 1: can monetary policy affect ψ θ and ψ s? Question 2: what are optimal ψ θ and ψ s?

Linear equilibrium (continued) Potential output c t = ψ 0 + a t 1 + θ t aggregate output under first best allocation = aggregate output under full information (with right τ) = linear equilibrium iff ψ θ = 1 ψ s = 0 Question 1(bis): can monetary policy achieve c t?

Linear equilibrium (continued) Mechanics and remark 1 full insurance + normal sampling shocks + iso-elastic preferences closed form linear equilibrium

Linear equilibrium (continued) Mechanics and remark 1 full insurance + normal sampling shocks + iso-elastic preferences closed form linear equilibrium e.g.: the price index for consumer i is P it = V p exp{p t + φ θ v i } where V p = exp{ 1 σ 2 φ 2 θ ˆσ 2 ε }

Linear equilibrium (continued) Mechanics and remark 2 consumers observe whole distribution P jt for j J it a sufficient statistic is θ it this is like having two noisy signals of θ t : θ it = θ t + ε it θ it = θ t + v it

Pricing Optimality condition ) p it = η (E I it [c t + σ (p t p it )] a it + ) + (E I it [p it + c it ] a it + η (ψ v + σφ θ )E I [ ] it vjt E I it expectation at pricing stage high demand relative to prod high price high consumption relative to prod high price

Consumption Euler equation c it = E II it a t+1 }{{} exp. income (r p t+1 + p it ) E II it expectation at consumption stage

Demand shocks Baseline case µ = 0 (no policy inertia) Effects of e t > 0 noise in signal s t + permanent shock raise E[a t+1 ] nominal interest rate cannot respond (no superior information) real interest rate partially responds, as agents raise prices p it (stabilizing virtue of price targeting regime) this is not enough: ψ s > 0

Demand shocks (continued) Baseline case µ = 0 Effects of e t > 0 raise c t, p t and n t Effects of θ t > 0 raise c t lower p t and n t

Monetary Policy Consumption under µ 0 Euler equation c it = E II it a t+1 }{{} exp. income (r t p t+1 }{{} future price + p it )

Monetary Policy (continued) Consumption under µ 0 Euler equation c it = E II it a t 1 + θ }{{} t (r exp. income µ θ θ t }{{} future price + p it ) larger µ θ greater response to θ t

Power of policy rule Agents have different expectations about future output...but also different expectations about real interest rate 2 crucial ingredients: agents forward looking E II it [r µ θ θ t + p it ] in the future more information than now policy rule allows to manage expectations

Power of policy rule (continued) The choice of µ θ feeds back into optimal prices p it It also affects response to s t and response of relative prices An increase in µ θ increases ψ θ reduces φ θ increases φ s decreases ψ s

Achievable linear equilibria vector ψ θ,φ θ,φ s,ψ s s.t. ψ v = ψ ε δ v /δ ε φ θ (1 + ση)φ θ = η ((ψ θ + σφ θ )β θ 1) + ((ψ θ + φ θ )β θ /δ θ 1) + +η (ψ v + σφ θ )γ (1 β θ ), 0 = η (ψ θ + σφ θ )β s + (1 + η)ψ s + +(ψ θ + φ θ )(β s δ s )/δ θ η (ψ v + σφ θ )γβ s,

Another divine coincidence? Proposition There is a µ θ fs that achieves full stabilization: ψ θ = 1 ψ s = 0 here output is always equal to potential induce agents to respond more to private productivity

1 ψ θ 0 ψ s 0 μ θ μ θ fs

More on the relation between ψ θ and φ θ increase response of output to fundamental increase response of demand to local productivity reduce price adjustment (φ θ < 0)

Welfare 4 components: ] (1 + η)e [(c t ct ) 2 a t 1 (1 + η)var (n it ) + Var ( c jt + σp jt j J ) ( ) it + σ (σ 1)Var pjt j J it 1. aggregate output gap (-) 2. labor supply cross sectional dispersion (-) 3. demand cross sectional dispersion (-) 4. relative price dispersion (+)

σ 7 η 2 σθ 2 1 σε 2 1 σe 2 1/3 γ 0.5 Table: Parameters for the example

w 1 0-0.05 w 2,w 3-0.1-0.2 0 0.2 0.4 0.6 0.8 1 1.2 0-0.5-1 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 2 w 4 1.5 1-0.2 0 0.2 0.4 0.6 0.8 1 1.2 μ θ fs μ θ

0.9 0.85 w 0.8 0.75 0.7 0.65-0.2 0 0.2 0.4 0.6 0.8 1 1.2 μ * θ μ θ fs μ θ

Optimal monetary policy Proposition Full stabilization is typically not optimal Some accommodation of demand shocks is optimal It is optimal µ < µ fs It is optimal to partially accomodate ψ s > 0 Price dispersion is larger at optimal monetary policy than under full stabilization

Special case now it is optimal ψ θ = 1 η = 0 φ θ = 1 decreasing prices proportionally to productivity gives: 1. right relative prices 2. right response of consumption

Special case (continued) p it = (E I i [p it + c it ] a it ) c it = E II i [a t+1 + p t+1 ] p it unit intertemporal elasticity of substitution proportional response is optimal

Transparency Is better public information good? (Morris and Shin (2002)) Effect on output gap may be bad Total effect always good

Effect on welfare 2 1.95 1.9 w 1.85 1.8 1.75 1.7 0 10 20 30 40 50 1/σ e

Effect on output gap volatility -0.02-0.03-0.04 w -0.05-0.06-0.07-0.08 0 10 20 30 40 50 1/σ e

Compare with Hellwig (2005) Lucas style model with unobserved money supply shocks more precision about monetary shocks is good: reduce output gap reduce price variance (spurious) Here uncertainty about real shocks more precision is good: ambiguous on output gap increase price variance (good) second effect dominates

Expectations shocks and business cycles Business cycles driven by news (Beaudry and Portier (2006), Jaimovich and Rebelo (2006)) Problem 1: in neoclassical setting demand disturbances have hard time generating right response of hours/consumption/investment Euler equation c t = E t a t+1 }{{} exp. income (r t p t+1 + p t ) with flexible prices the real rate increases automatically

Expectations shocks and business cycles (continued) Nominal rigidity can help (Christiano, Motto and Rostagno (2006)) Problem 2: monetary policy accommodation of demand shocks is typically suboptimal Euler equation c t = E t a t+1 }{{} exp. income (r t p t+1 + p t ) with full information optimal to increase r

Expectations shocks and business cycles (continued) Imperfect information + nominal rigidity can help Problem 3: policy rules still able to wipe out demand shocks...but this is not optimal a theory of demand shocks that survive optimal policy

Concluding Future superior information + forward looking consumers policy can induce efficient use of dispersed information Related themes: King (1982), Svensson and Woodford (2003), Aoki (2003) Efficient use of dispersed information full stabilization output gap Still some offsetting of demand shocks is feasible and desirable Clearly this requires commitment, which may be tough (bubble example)