Advanced Moneary Theory and Policy EPOS 2012/13 Policy regimes Theory Giovanni Di Barolomeo giovanni.dibarolomeo@uniroma1.i
The moneary policy regime The simple model: x = - s (i - p e ) + x e + e D p = b p e + g x + e S Three variables (x, p, i) and wo equaions!!! We need anoher equaion o close he model. How is he ineres rae se? Moneary regime 2
More in deail: 3 approaches Insrumenal rule The policy-maker commis o a (simple) feedback rule (e.g., Taylor rule or imeless perspecive). Welfare loss minimizaion Discreion: Each insan of ime, he policy-maker behaves by minimizing an approximae social loss derived from he micro-founded model. Targeing rule Each insan of ime, he policy-maker behaves by minimizing a differen loss based on arge deviaions differen from hose derived from he micro-founded model. I commis o he arges. 3
Welfare loss Under some condiions he welfare loss can be defined as 1 2 E I is derived as a second order approximaion of he consumer preferences. Then α is a funcion of he deep parameers, i.e. α = s/e, where e is he elasiciy of subsiuion in he monopolisic good marke, while s measures nominal rigidiies. Try o give he inuion!!! i 2 2 b p i x i i0
The wo-sep problem The problem can be divided ino wo sub-problems: 1. Choose {x(+i), p(+i)} o minimize he lossfuncion subjec o he Phillips curve; 2. Using he focs in he IS-curve o find he opimal ineres rae rule. 5
The Lagrangian wih respec o imply: 6 2 2 1 0 1 2 i i i i i i i i i E x E kx u b p b p p - - 0 0 (3) 0 0 (2) 0 (1) 1 - - - i k x E i E i i i i i p p i i x p,
Dynamic inconsisency From equaion (1) and (2): A ime, i is opimal o se 1. π() = -() 2. π(+1) = - ((+1) - () ); When ime +1 arrives and he CB re-opimizes i will be opimal o se 1. π(+1) = -(+1) (condiion (1) updaed a ime +1), which is differen from 2 above 7
The opimal rule Combining focs (1), (2) and (3): ( 4) x i - x i-1 - p i (5) x k - p using (4) and (5) ogeher wih he IS, we find he opimal ineres rae rule: k k iˆ 1 ( 6) 1 - Ep 1 g s s 8
Given ineres-rae rule (6), Indeerminacy The coefficien iˆ k 1 - Ep s 1 k 1-1, s 1 g s hus, he CB adjuss demand only parially in response o increase in expeced inflaion. Such a rule involves indeerminacy 9
Timeless Perspecive Commimen To avoid ime inconsisency he CB implemens condiions (2) and (3) for all periods, including he curren period. Combining he wo, he implici policy rule, ( 7) p i - i i-1 k x - x for i 0 afer some algebra, he equilibrium implies: (8) p 1- ax x -1 2 k x u 1 b 1- - a k 10 The pre-commimen policy inroduce ineria.
The disadvanage Dennis (2001): The policy rule is sub-opimal. p p i - - i - - In he fully opimal commimen (-1) = 0, alernaive value of (-1) = 0 lead o alernaive policy choices consisen wih imeless perspecive. Hence, he policy rule (7) may be dominaed by oher rules. -1 i-1 11
Discreion Wihou an explici commimen Cenral bank will choose is decision variables x(), π(), each period o minimaze he social loss funcion subjec o he aggregae supply curve (2) and he IS curve (1), and aking privae secor's expecaions as given. Operaively, he equilibrium is found by using (1) and (3) or by using he following equivalen procedure. 12
Discreion problem The discreion problem can be rewrien as: min where 1 x 2 s.. p x p 2 2 f F F E x f be p u 2 2 - i pi i1 1 13
Discreion The opimal soluion of he problem is: (9) in +1, we have x k - p -qu ( 10) kp x 1 1 while, in he case of imeless perspecive commimen, we have ( 11) kp 1 0 x - x 0 1 14
The opimal ineres rae rule Subsiuing (9) in he Phillips Curve, solving forward, and hen using he IS equaion, he opimal ineres rae rule, consisen wih he Taylor Principle, is: ˆ (13) i p Ep 1 g 1 s where k 1- p 1 1 s 15
Equilibrium inflaion Under opimal discreion, he equilibrium inflaion is given by: (14) p - k x 2 1- b k he uncondiional expeced value of inflaion is zero, here is no average inflaion bias. Bu here is a sabilizaion bias, (he response o inflaion o a cos-push shock differs from he response under commimen) u 16
Commimen (imeless) vs. discreion IRF (cos-push shock) 17
Sabilizaion bias Under imeless pre-commimen he cenral bank keeping oupu below is poenial for more han one period, lowers expecaions on fuure inflaion improving he rade-off beween inflaion and oupu gap. Under discreion here is no policy ineria. Oupu gap and inflaion quickly reurn o heir seady-sae values. 18
Definiion. Targeing regimes A argeing regime is defined by (a) he variables in he cenral bank s loss funcion (he objecives), and (b) he weighs assigned o hese objecives, wih policy implemened under discreion o minimize he expeced discouned value of he loss funcion. Operaionally as discreion. 19
Some argeing regimes Inflaion argeing (he mos famous). Price level argeing (Svensson 1997, Vesin 2002), Nominal income growh argeing (Jensen 2002), Hybrid price level/inflaion argeing (Baini and Yaes 2001). Average inflaion argeing (Nessén and Vesin 2003) Regimes based on he change in he oupu gap or is quasi-difference (Walsh 2003, Jensen and McCallum 2002). 20
Inflaion argeing in New Keynesian models A commimen o a moneary policy more aggressive wih respec o inflaion (inflaion argeing) may improve efficiency. No because i reduces he inflaion bias (here here is no inflaion bias) Being more aggressive wih respec o inflaion improves he bank performance because i sabilizes more he expecaions (improving he curren rade off), if shocks are persisen.. 21
Inflaion argeing The cenral bank minimizes 1 2 E i 2 T 2 b p i x i i0 where α T < α (flexible inflaion argeing) or α T = 0 (pure inflaion argeing. Recall ha i operaes as under discreion, so he regime is implemened by using somehing like (1) and (3)
Inflaion argeing C = discreion; D = commimen o a more aggressive inflaion policy (Inflaion argeing). Noe ha D is no ime consisen. Implemening he inflaion argeing he PC shifs down, hen he cenral bank may be emped o re-opimize going o E
Inflaion argeing: Raionale By inflaion argeing he cenral bank chooses a subopimal poin on he Phillips curve (i over-sabilizes inflaion), bu i can affec he fuure expecaions (and hus he Phillips curve), achieving a beer rade-off. If price-seing depends on expecaions of fuure economic condiions (i occurs when shocks are persisen), hen a cenral bank ha can credibly commi o a loss placing more emphasis on inflaion sabilizaion (inflaion argeing) faces an improved shor run rade-off beween oupu and inflaion. This occurs because expecaions abou fuure inflaion will be low as he privae secor expecs ani inflaionary policies also agains he fuure forecased shocks.
Price level argeing Vesin (2002) shows price level argeing can replicae he imeless pre-commimen soluion, if he cenral bank is assigned a loss funcion defined on zero price level deviaions insead of inflaion deviaions. Walsh (2003) adds lagged inflaion o he inflaion adjusmen equaion and shows ha he advanages of price level argeing over inflaion argeing decline as he weigh on lagged inflaion increases. 25