Inflation expectations, adaptive learning and optimal monetary policy

Transcription

1 Inflaion expecaions, adapive learning and opimal moneary policy Vior Gaspar, Frank Smes and David Vesin Key developmens in moneary economics Frankfur am Main, 29 Ocober 2009 The opinions expressed are our own and do no necessarily reflec hose of he Banco de Porugal, ECB or Sveriges Riksbank.

2 Anchoring inflaion expecaions has become he modern manra of cenral banking: Triche (2009): I is absoluely essenial o ensure ha inflaion expecaions remain firmly anchored in line wih price sabiliy over he medium erm Bernanke (2007): The exen o which inflaion expecaions are anchored has firs-order implicaions for he performance of inflaion and he economy more generally Volcker (2006): I have one lesson indelible in my brain: don le inflaion ge ingrained. Once ha happens, here is oo much agony in sopping momenum

3 Anchoring has been successful in he euro area HICP inflaion HICP excluding unprocessed food and energy inflaion HICP inflaion expecaions (SPF) for he wo-year period ahead HICP inflaion expecaions (SPF) for he five-year period ahead Upper bound of definiion of price sabiliy Longer-erm inflaion expecaions (Consensus Economics Forecass) Sage Three of EMU Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10

4 and in many oher indusrial counries

5 and in many oher indusrial counries

6 even a shorer horizons.

7 even a shorer horizons.

8 Modelling inflaion expecaions Sandard approach is o assume raional or model-consisen expecaions: e.g. HB chaper by Mike Woodford; Imporan benchmark, bu Credibiliy (disincion beween discreion and commimen) is a binary variable: he cenral bank eiher has he credibiliy o commi o fuure policy acions or no (HB Chaper by Bob King); Some implicaions are counerfacual: e.g. cosless disinflaions; RE is an exreme assumpion given he pervasive model uncerainy economic agens are facing.

9 Modelling inflaion expecaions There are RE alernaives: Limied processing power and raional inaenion (e.g. HB chaper by Sims, Mackowiac and Wiederhol, Adam, ) Limied informaion and signal exracion (e.g. Erceg and Levin, Schorfheide, ) Bu: Even rivial models become exremely cumbersome o solve; Assumes quie knowledgeable individuals (no even rained economiss can work ou he opimal priceseing plans wihou considerable effor!)

10 Modelling inflaion expecaions A reasonable alernaive is adapive learning or consan-gain leas squares learning : Agens are endowed wih an economeric specificaion, which may be consisen wih he reduced form of he raional expecaions equilibrium; As ime goes by, hey updae heir knowledge and he associaed forecasing rule; Consan gain akes ino accoun he possibiliy of breaks and ime-varying parameers. Moreover, such specificaions work empirically: Orphanides and Williams (2004), Milani (2005), Slobodyan and Wouers (2009)

11 Objecive of his chaper Characerize opimal moneary policy responses when agens use adapive learning o form inflaion expecaions; Assess he robusness of policy rules ha are opimal under raional expecaions (RE) o small deviaions from RE. The chaper builds on he work by: Orphanides and Williams (2005, ) Gaspar, Smes and Vesin (2005) Molnar and Sanoro (2006)

12 Relaed lieraure Evans and Honkapohja (2001) and many relaed papers: Analyze how leas-squares learning affecs he sabiliy and deerminacy of macro-economic equilibria under various moneary policy ineres rae rules See Evans and Honkapohja (2008) for an excellen survey. This chaper focuses on he implicaions of argeing rules aking he non-lineariy of he expecaion formaion process ino accoun.

13 Relaed lieraure Large lieraure on moneary policy making under uncerainy (e.g. Hansen and Sargen, Taylor and Williams) A few papers analyse he ineracion wih learning by he privae secor: Orphanides and Williams (2007) sudy he ineracion of imperfec knowledge by he cenral bank and consan gain learning by privae agens. Evans and Honkapohja (2003a,b) Woodford (2005) analyses opimal policy when agens expecaions may be disored away from raional expecaions.

14 Relaed lieraure Alernaive ypes of learning: Branch and Evans (2007) and Brazier, Harrison, King and Yaes (2006) assume ha privae agens may use differen forecas models, wih he proporion changing over ime wih relaive forecas performance. Arifovic, Bullard and Kosyshyna (2007) and De Grauwe (2007) use social learning Bullard, Evans and Honkapohja (2007)

15 Ouline New Keynesian model and is soluion under raional expecaions. Adapive learning consisen wih discreionary RE equilibirum: Simple rules and opimal policy. Model calibraion and resuls. The workings of opimal policy. Sensiiviy analysis. Conclusions.

16 The New Keynesian model Monopolisic compeiion Sicky prices wih parial indexaion π γπ = βε ( π γπ ) Loss funcion + κx + u L = ( π γπ ) 2 + λx 2 1 Use oupu gap (x()) as policy insrumen

17 The New Keynesian model: RE Under RE, here is a disincion beween opimal policy under discreion and commimen: Under discreion: x κ = - u 2 π = γπ -1 + u κ + λ κ 2 + λ λ Under commimen: z x λ κ ( x x ) = 1 κ = δx 1 - u λ wih z = π -γπ 1 ( 1 δ ) λ π = γπ -1 + x 1 + δu κ

18 Impulse response o a cos-push shock 1 x 10-3 Oupu gap 0 Commimen Discreion

19 Impulse response o a cos-push shock 5 x 10-3 Inflaion Commimen Discreion

20 Adapive learning Agens esimae AR(1) for inflaion: π + = cπ 1 ε Consisen wih reduced-form of RE equilibrium under discreion Recursive updaing: c 1 = c 1 + φr π 1 1 ( π π c 1) 2 1 R R + = R + φ( π )

21 Adapive learning Which info is available o agens when? Simulaneiy problem in forward-looking models. One soluion: lagged informaion Here: agens use curren inflaion in he forecas bu no in he updaing of he parameers: Ε π = + 1 c 1π Implies: 1 π = 1+ β 1 1 ( ) ( γπ + κx + u γ c )

22 Opimal argeing Formulae value funcion ( π γπ ) 2, 1 + λx V ( u π 1, c 1, R ) = max + βεv ( u+ 1, π, R + 1, c x 2, Maximize subjec o Phillips curve, learning equaions and forecasing equaion 2 ),

23 Calibraion Sd. of shocks σ Degree of indexaion γ Weigh on oupu gap λ Elas. of subs. θ Discoun rae β Key parameers Slope of Phillips curve Consan gain Fracion of nonopimal prices κ φ α 2 2 ) 1 ( ) 1 ( 1 x L u x λ γπ π κ γπ π β γπ π + = Ε =

24 Resuls: losses RE Adapive Learning Com. Disc. Opimal Com. Disc (!!) 1.37 Opimal policy abou 20% improvemen RE commimen rule comes close o opimal policy oucome

25 Resuls: Variances and auocorrelaions RE Learning Com. Disc. Opimal C-rule D-rule Var(Oupu) Var(Inflaion) Cor(Oupu) Cor(Inflaion) Lower persisence of inflaion under C-rule helps reducing inflaion volailiy a low cos in erms of oupu volailiy C-rule and opimal yield similar oucomes bu differen mechanism a play

26 Oucomes Disribuion of inflaion persisence 3.5 Opimal 3 Commimen rule 2.5 Simple rule

27 Characerising opimal policy x 1 κ κγ ( χ 1) + βκχ φr EVc = u + π κ + λχ κ + λχ + β κ + λχ κχ E V π If hen: π 1 = 0 κ x = 2 2 κ + λχ u where χ = 1+ β ( γ c 1) If γ = c 1 hen equal o discreionary rule: inraemporal rade-off.

28 Characerising opimal policy x 1 κ κγ ( χ 1) + βκχ φr EVc = u + π κ + λχ κ + λχ + β κ + λχ κχ E V π However, in general opimal policy under learning will also respond o lagged inflaion resembles hisory dependence; If γ = c 1 hen: βκφe V x c = + π κ + λ Capures ineremporal rade-off beween sabilising oupu gap and seering he perceived degree of inflaion persisence by responding more agressively o inflaion...

29 Mean dynamic response of oupu gap Oupu gap Inflaion c = 0.32 c = 0.52 c = c = 0.32 c = 0.52 c =

30 Mean dynamic response of persisence c = 0.32 c = 0.52 c =

31 Reacion funcion: no shock

32 Sensiiviy analysis Average esimaed persisence as a funcion of he gain mean(c) φ

33 Sensiiviy analysis and as a funcion of degree of price sickiness Alpha= Alpha= φ

34 Sensiiviy analysis Esimaed persisence as funcion of weigh on oupu gap λ=0.002 λ=

35 Tenaive conclusions Managemen of inflaion expecaions remains imporan under adapive learning; In addiion o he usual inraemporal rade-off, cenral banks face an ineremporal rade-off beween curren oupu sabilisaion and managemen of fuure inflaion expecaions; The mechanism is differen: In case of RE i works hrough expecaions of fuure policy; in he case of AL, i works hrough perceived inflaion persisence as funcion of pas and curren policy. Boh policy responses are hisory dependen; bu AL opimal policy response is ime-varying depending on he perceived persisence of inflaion. Neverheless, commimen rule under RE comes very close o opimal policy under learning.

36 To do lis Encompass he commimen equilibrium in he learning specificaion: Simplify model o forward-looking specificaion and analyse learning abou price level persisence; Inroduce oupu gap in learning model; use sochasic gradien learning o limi sae space. Invesigae he ransiion from a discreion rule o he opimal regime under adapive learning; Embed he analysis in he learning lieraure.

37 Oucomes 140 Opimal Simple rule commimen rule

38 Oucomes 12 Opimal Simple rule 10 commimen rule

39 Oucomes 18 x 104 Opimal 16 commimen rule Simple rule x 10-5

40 Symmery: response of inflaion 8 x u >0,π -1 <0 u <0,π -1 >

41 Symmery: response of oupu u >0,π -1 <0 u <0,π -1 >

42 Reacion funcion: response o shock