Sophisticated Monetary Policies. Andrew Atkeson. V.V. Chari. Patrick Kehoe

Transcription

1 Sophisicaed Moneary Policies Andrew Akeson UCLA V.V. Chari Universiy of Minnesoa Parick Kehoe Federal Reserve Bank of Minneapolis and Universiy of Minnesoa

2 Barro, Lucas-Sokey Approach o Policy Solve Ramsey problem choose a = {policies, prices, allocaions} o max Uiliy s.. a Compeiive Equilibrium Answer: Ramsey oucome a * funcion of exogenous shocks

3 Barro, Lucas-Sokey Approach o Policy Solve Ramsey problem choose a = {policies, prices, allocaions} o max Uiliy s.. a Compeiive Equilibrium Answer: Ramsey oucome a * funcion of exogenous shocks Wan o ge How o ge here uniquely Lef open: Implemenaion Designing policies so Ramsey oucome is unique equilibrium

4 Our Soluion o Implemenaion Problem Sophisicaed policies can Depend on hisories of agens acions Differ on and off equilibrium pah Equilibrium concep ha specifies oucomes for all hisories

5 Our Soluion o Implemenaion Problem Sophisicaed policies can Depend on hisories of agens acions Differ on and off equilibrium pah Example If Accepable Region, follow Ramsey policy If no, swich o alernaive policy (reversion)

6 Our Soluion o Implemenaion Problem Sophisicaed policies can Depend on hisories of agens acions Differ on and off equilibrium pah Main Resul Can uniquely implemen any desired compeiive oucome

7 Our Soluion o Implemenaion Problem Sophisicaed policies can Depend on hisories of agens acions Differ on and off equilibrium pah Main Resul Can uniquely implemen any desired compeiive oucome Noe: Differs from implemenaion via nonexisence Here coninuaion equilibria exis afer all deviaions

8 Message of Our Paper Follow Barro, Lucas-Sokey Approach o Policy

9 Message of Our Paper Follow Barro, Lucas-Sokey Approach o Policy Implemenaion Problem Now Solved

10 Implemenaion: A Nonrivial Problem in Moneary Models Sargen-Wallace resul Indeerminacy if ineres raes depend only on exogenous evens Indeerminacy risky

11 Conrass wih Lieraure Our approach: Implemenaion by discouraging deviaions Lieraure: Implemenaion via nonexisence

12 Conrass wih Lieraure Our approach: Implemenaion by discouraging deviaions Lieraure: Implemenaion via nonexisence Our Approach: Discourage Deviaions Oucome pah Equilibrium exiss Equilibrium exiss

13 Conrass wih Lieraure Our approach: Implemenaion by discouraging deviaions Lieraure: Implemenaion via nonexisence Lieraure: Nonexisence afer Deviaions Oucome pah No equilibrium No equilibrium

14 Conras Concerning Taylor Principle Lieraure: Taylor principle needed for uniqueness Taylor principle i i ( ), 1 raise ineres raes more han 1 for 1 wih inflaion Oucome pah No equilibrium (inflaion explodes) No equilibrium (inflaion explodes)

15 Main Resuls Simple Sicky Price model Implemen wih sophisicaed policies Indeerminacy wih linear feedback rules Exend o New Keynesian model Imperfec Informaion

16 Simple Sicky Price Model

17 Ouline of Secion Model Seup and 4 Equilibrium Condiions Implemen wih Sophisicaed Policies Canno implemen wih linear feedback rules

18 Seup and 4 Equilibrium Condiions

19 Seup: Technology and Preferences Final good echnology Y Y( j) dj 1 Inermediae good echnology Y( j) L ( j) Preferences E 0 0 U( C, L ) where L L( j) Cash-in-advance

20 Seup: Technology and Preferences Final good echnology Y Y( j) dj 1 Inermediae good echnology (some producers sicky p some flexible p) Y( j) L ( j) Preferences E 0 0 U( C, L ) where L L( j) Cash-in-advance

21 One-Period Sickiness Le h 1 be hisory of pas acions and shocks a sar of period h 1 h g = (h 1, x ) h y = (h g, policy, ) h Sicky price Regime Shock Flexible prices se x (j,h 1 ) δ(h g ) Consumers move where x = p s p 1 Policy i(h g ) or (h g ) Sraegies of agens and cenral bank depend on relevan hisory Sicky price producers only ineresing sraegic players

22 One-Period Sickiness Le h 1 be hisory of pas acions and shocks a sar of period h 1 h g = (h 1, x ) h y = (h g, policy, ) h Sicky price Regime Shock Flexible prices se x (j,h 1 ) δ(h g ) Consumers move where x = p s p 1 Policy i(h g ) or (h g ) Sraegies of agens and cenral bank depend on relevan hisory Sicky price producers only ineresing sraegic players Nex, 4 equaions of his New Classical sicky price model

23 Derive 4 equaions of New Classical Sysem Sicky price producer s bes response price se as markup over expeced marginal cos P s ( j) 1 E Q P W y 1 1 E 1 Q P y when log linearize and use W / p u / u ge leing s 1 l c 1 p ( j) E p y s x j p j p and p p 1 (1) x j E y 1

24 Derive 4 equaions of New Classical Sysem New Classical Phillips Curve use flexible price producers problem and aggregae price index o ge y x (2) Log Linearized Euler equaion ( is fligh-o-qualiy shock) (3) y E y 1( i E 1) Log Linearized quaniy equaion (cash-in-advance) (4) ( y y 1)

25 New Classical Sysem wih Sraegies and Ineres Rae Regime 1. Sicky producers bes response x( j, h, x ) E y h h h, x 1 y y 1 2. New Classical Phillips curve 3. Euler equaion hy y hy x h 1 1 y h E y h h i h x h y y y g 4. Quaniy heory hy hy y hy y 1

26 Oucome Pah versus Sraegies Oucome Pah Sraegies say wha o do a all possible hisories Oucome pah describes wha acually happens:

27 Oucome Pah versus Sraegies Oucome Pah Sraegies say wha o do a all possible hisories Oucome pah describes wha acually happens: x i y a 1, 1,,

28 How Sraegies Induce Fuure Hisories Fix sraegies for all players x,, i,, y, Sraegies recursively define fuure hisories Given h 1, hisory h generaed from sraegies and realizaion of 1 1 h x x h h h x h i i h g g g 1,, h h,, i, y h, h y g y y and so on

29 Oucome Pah a is a Compeiive Equilibrium 1. Sicky producers equilibrium response 2. New Classical Phillips curve 3. Euler equaion x E y y x y E y i x 4. Quaniy heory 1 y y 1

30 Implemenaion wih Sophisicaed Policies

31 Implemenaion wih Sophisicaed Policies Policies can differ on and off he equilibrium pah

32 Implemenaion Theorem Suppose some given oucome pah a * is a compeiive equilibrium. There are sophisicaed policies wih a unique equilibrium which generae given oucome pah.

33 Skech of Proof To implemen specific oucome pah * 1 * 1 * *,,, x i y If If * x say wih original policy i * x x x swich o money for one period and * choose money o generae original inflaion *

34 Skech of Proof Bes response of sicky producer x ( j) E [ y ] 1 Wan o discourage deviaions, ha is make x ( j) x

35 Skech of Proof Can make E [ ] 1 y o be whaever we wan Because money regime and y deermined by Flexible producers decisions y x Cash-in-advance in firs differences ( ) y y 1 So for any sicky producer choice x (wih y 1 given) and y uniquely deermined by E [ ] 1 y is monoone in

36 Skech of Proof Proof explois conrollabiliy wih money i.e. Cenral bank can induce any bes response by individual sicky price producer following aggregae deviaion x

37 Recap Unique Implemenaion wih Sophisicaed Policies Nex, show why regime swiching is necessary

38 Necessiy of Regime Swiching

39 Sandard Specificaion of Policy Linear feedback rule i i x y xs s ys s s s s0 s1 s1 Necessarily yields indeerminacy Under his rule coninuum of compeiive equilibria x 1 i c, x (1 c), y (1 c) indexed by c and x. 0

40 Sandard Specificaion Includes King Rule King rule (from King 2000 and Svensson and Woodford 2005) i i ( x x ) * * where i *, x * are desired oucomes. Our approach: King rule yields indeerminacy

41 Recap Simple sicky price model Unique implemenaion wih sophisicaed policies Necessiy of regime swiching Nex, exend o sandard New Keynesian model wih Sicky price producers use Calvo-pricing No flexible producers

42 Sandard New Keynesian Model Model Seup

43 Sandard New Keynesian Model Timing (w/o shocks) h 1 h g h y Fracion 1 Regime Consumers rese prices o δ(h g ) p s (j,h -1 ) Policy i (h g ) or (h g ) Only 1 equaion changes from simple sicky price model Sicky price producers bes response

44 Implemenaion in Sandard New Keynesian Models Works wih reversion o money Works wih reversion o ineres raes Along equilibrium pah * 1 i h i g Any deviaion a ime swich o new regime g i h i a wih i 0 and for ˆ wih unique coninuaion equilibrium se ˆ all 1 i h x s s gs s

45 Can we ge Implemenaion wih Linear Feedback Rules?

46 King Rule Works Here bu Differenly from Lieraure King rule i i ( ), 1 * * Our approach Implemens bounded oucomes Afer deviaion, reurns o desired oucomes Lieraure Afer deviaion, leads o nonexisence ( explodes)

47 Sandard New Keynesian Model Robus o Imperfec Informaion

48 Imperfec Informaion Imperfec monioring See agens acions every period wih probabiliy q Ge exac implemenaion Measuremen error See agens acions wih measuremen error Ge approximae implemenaion

49 Conclusion Follow Barro, Lucas-Sokey Check conrollabiliy of bes responses If conrollable, move on o nex paper If no?... Exend o financial crises, fiscal policy, and so on