Interest Rates and Inflation Stability:

Transcription

1 Inteest Rates and Inflaton Stablty: GV INVEST 09 Recent Expeence and the Cochane Ctque May 2017 João Lído Bezea Bsneto¹ In the last decade, the feld of monetay economcs has undegone a knd of foced evoluton. The fnancal css has nduced the cental banks of almost all the majo developed countes to educe nteest ates to a level nea o even below zeo. Unconventonal polces, such as quanttatve easng, wee ntoduced and the nteest ates wee kept low, almost fxed, fo a long tme. Ths scenao led to new questons egadng the means and ends of monetay polcy. Eventually, such questons geneated mpotant eseach on the feld. Ths shot study ams to clafy an mpotant puzzle that emeged thoughout the past yeas and that was emphaszed by Cochane (2016): the stablty of nflaton even when nteest ates seem to be unesponsve. The Empcal Puzzle Inteest ates have been at the zeo lowe bound n the Unted States and Euope fo yeas afte the Geat Recesson. Addtonally, n Japan, nteest ates have been stuck at low values snce the 1990s. Meanwhle, nflaton has been elatvely stable n the thee monetay aeas. Thee wee some swngs n the nflaton ate such as the woldwde dsnflaton post-2008, but nflaton/deflaton has not spalled out of contol: t has come back to the same level of befoe the ecesson. Past nflaton stablty may be attbuted to the cental banks unconventonal polces. Howeve, Cochane (2016) ponts that conventonal Keynesan theoes cannot fully explan such stablty when nteest ates wee unesponsve. The cucal stablty and detemnacy condton of nflaton n conventonal Keynesan models s the Taylo pncple: cental banks should answe shocks n nflaton wth geate swngs n the nomnal nteest ate. The stubbonness of nea-zeo nteest ates n the ecent past shows that the

2 GV INVEST Shot Studes Sees 09 Taylo pncple was not appled. Nevetheless, nflaton has emaned stable. Ths study wll ty to explan concsely the Cochane s appoach of showng ths empcal puzzle. The fst pat wll explan the smple model used to eplcate the Keynesan famewok. The second pat wll focus on the esults when adaptve expectatons ae pesent. The thd pat wll focus on the moe common and sophstcated esults when atonal expectatons ae ntoduced to the model. Fnally, the fouth pat wll summaze the analyss. Benchmak model Most of the Keynesan models have the nflaton and output equlba and dynamcs defned by the followng equatons: Whee t = t + π t e t s the tme subscpt; t s the nomnal nteest ate; t s the eal nteest ate; π t s the nflaton ate; π t e s expected nflaton; x t s the output gap; v t s the eal nteest ate shock; v t s the monetay polcy shock; φ epesents the esponsveness of monetay polcy to nflaton; and σ, κ ae postve paametes. 1 Fshe Equaton π t = π t e + κx t Phllps Cuve x t = σ( t v t ) IS Cuve t = φπ t + v t Taylo Rule 1 Fo smplcty, we wll keep Cochane s notaton to help the eade that wants to dve deepe nto the eseach. These equatons ae usually deved fom agents behavou, pce and/o wage stckness and no-abtage condtons. Dffeent studes tend to deve them fom dffeent condtons. Howeve, both the qualtatve esults and the dynamcs of the system ae not so dstnct when compang mansteam models. Cochane (2016) abstans fom usng such devaton to ncease the genealty of hs ctque, whch seems to favou hs agument. Such system can be solved to detemne nflaton n elaton to the shocks and the expected nflaton. The esult, below, can be futhe used to analyse the dynamcs and equlbum of nflaton when expected nflaton s also detemned. π t = ( φ ) π t e ( 1 + φ ) (v t v t ) Adaptve expectatons Fst and foemost, let us analyse the mplcatons of ths system when adaptve expectatons ae assumed. ( π t e = π t 1 ) In othe wods, the mplcatons of dffeent values of φ fo the detemnacy and stablty of nflaton n the old- Keynesan famewok. Clealy: pncple, π t = ( φ ) π t 1 ( 1 + φ ) (v t v t ) When monetay polcy adhees to the Taylo φ > 1 and ( 1+ ) < 1. Ths causes 1+φ nflaton to slowly etun to ts steady-state equlbum wheneve thee s a tempoay shock.

3 When φ < 1, howeve, ( 1+ 1+φ ) > 1. So, even when nflaton stats at the steady-state value, evey shock wll lead to nflaton spallng to nfnte nflaton o deflaton. Thus, the model s unstable. If someone had ths model n mnd when nteest ates wee appoachng the zeo-lowe bound, the only possble pedcton he/she could make would be a spallng deflaton f the zeo-lowe bound became bndng. The staghtfowad eason s that at the zeo-lowe bound, nteest ates could not be educed moe than nflaton: φ < 1. Theefoe, consdeng the ecent past, the stable nflaton s clealy a puzzle when the old-keynesan famewok s used. Ratonal expectatons Usng adaptve expectatons s outdated and does not eflect the ecent advances n economcs. A moe conventonal and obust appoach would be to ntoduce atonal expectatons. Equvalently, agents atonalze the expectatons n accodance wth the behavou of the economy (π t e = E t π t+1 ): we get: π t = ( φ ) E tπ t+1 ( 1 + φ ) (v t v t ) Usng the same esult to substtute out π t+1, GV INVEST Shot Studes Sees φ ) (v t v t ) ( 1 + φ ) ( φ ) (v t+1 + ( φ ) 2 E t π t+2 v t+1 ) Then, we can epoduce ths pocess ndefntely, fndng a patten: 1 + φ ) ( 1 + j 1 + φ ) j=0 E t (v t+j + lm ( 1 + T T 1 + φ ) E t π t+t v t+j ) When φ > 1, ( 1+ ) < 1 and nflaton s non- 1+φ explodng ( lm T ( 1+ 1+φ )T E t π t+t = 0) only f: 1 + φ ) ( 1 + j 1 + φ ) j=0 E t (v t+j v t+j ) Theefoe, the Taylo pncple nduces stablty and detemnacy by focng explodng paths out of the equlbum. Such method s dffeent fom the old-keynesan undestandng of hgh nteest ates educng aggegate demand and, then, focng nflaton down. Now, the oveeacton of the cental bank to nflaton leaves the economy two optons: explodng nflaton o stable nflaton detemned by the equaton above. Spallng nflaton s assumed as undesable and the model becomes detemnate and stable. When φ < 1, that s not the case. Inflaton could take any value and stll be consstent wth the

4 GV INVEST Shot Studes Sees 09 model. 2 Anyway, the model s only stable and detemnate on expectatons, as solatng E t π t+1 shows: E t π t+1 = ( 1 + φ 1 + ) π t ( 1 + ) (v t v t ) Thus, we cannot detemne the nflaton ate, just ts expectaton. The most we can do s to call δ t+1 = π t+1 E t π t+1 the foecast eo and defne: nflaton and nteest ates s dffeent than the nom n the case whee thee ae no foecast eos. An nteest ate se wll lead to hghe nflaton both n the shot-un and the long-un. Ths s anothe nteestng pont made by the pape: when the Taylo pncple cannot be appled, shot-un comovement between nteest ates and nflaton s nveted. π t+1 = ( 1 + φ 1 + ) π t ( 1 + ) (v t v t ) + δ t+1 In sum, the new-keynesan model wth atonal expectatons and φ < 1 s a stable model, but an ndetemnate one, whch means somethng dffeent n the economy should also be affectng nflaton. Thee ae multple equlba n the model. Cochane (2016) shows the poblem of such ndetemnacy by plottng the gaph of possble paths fo nflaton when thee s an expected nteest ate shock. Fo smplcty, we epoduce ths gaph. The sold lnes show the behavou of nflaton when thee ae no foecast eos n two dffeent stuatons: one wth hghe pce flexblty (less stcky) and one wth less. The mpotant pat ae the dashed lnes. They epesent all possble paths fo nflaton when φ < 1, showng the poblems of an ndetemnate model. The moe obsevant eade should also have notced that the shot-un elatonshp between 2 ( 1+ ) > 1 and lm ( 1+ 1+φ T 1+φ )T E t π t+t can explode fo E t π t+t > 0, but the othe tem s also an nfnte sum that wll tend to explode, makng nflaton ndetemnate. Although ths exta pont s mpotant fo the Cochane s defence of the fscal theoy of the pce level, a teatment of the subject s out of the scope of ths shot study. The man objectve s to expose what we beleve to be the most mpotant agument of Cochane (2016): that conventonal monetay theoy cannot explan the coexstence of stable nflaton and monetay polcy that s all but an nteest ate peg. Concludng Remaks The aftemath of the Geat Recesson has left us wth an almost natual expement. We could obseve nflaton stablty despte unesponsve nteest ates. Cochane (2016) tes to use ths

5 GV INVEST Shot Studes Sees 09 expement to test wdely-undestood conventonal Keynesan theoes. The concluson s that nethe the Old-Keynesan no the new-keynesan theoes can explan ths empcal combnaton of stable nflaton and nealy constant nteest ates. The dect mplcaton s the emegence of a puzzle, whch leaves a gap n the lteatue ecent eseach s tyng to close. Some possble explanatons and competng exsts, ncludng the fscal theoy of the pce level, advocated by Cochane (2016). By concsely exposng the poblem, we hope to facltate the dscusson of the possble solutons n futue studes. ¹ João Lído Bezea Bsneto, Reseache fo the GV Invest, São Paulo School of Economcs FGV. Refeences Cochane, J. H. (2016). Mchelson-Moley, Occam and Fshe: The Radcal Implcatons of Stable Inflaton at Nea-Zeo Inteest Rate. Avalable at: ch/papes/mm_occam_fshe.pdf