5. The Lucas Critique and Monetary Policy

Transcription

1 5. The Luas Criique and Monear Poli John B. Talor, Ma 6, 013

2 Eonomeri Poli Evaluaion: A Criique Highl influenial (Nobel Prize Adds o he ase for oli rules Shows diffiulies of eonomeri oli evaluaion when forward-looking exeaions are inrodued Bu i lef an imression of a mission imossible for monear eonomiss Tended o draw researhers awa from monear oli researh o real business le models Neverheless i was onsruive An alernaive aroah suggesed hrough hree examles: One foussed on monear oli inflaion-unemlomen radeoff The oher wo foused on fisal oli onsumion and invesmen Worh suding in he original

3 Firs Derive he Inflaion-Ouu Tradeoff Derive"aggregae sul"funion : Sul i P i i i e i where i P i ( is i i in marke i a ime is given b i is "ermanen"or "normal"sul is "lial"sul e i he log of he aual rie in marke i a ime is he ereived (in marke i general rie level in he eonom a ime Sul urve in marke i

4 /( where (1 ]( /( [, ( is disribued N is disribued normall wih mean 0 and variane and variane is disribued normall wih mean 1 i i i e i i i i i I E Thus z z Find ondiional exeaion of general rie level Covariane divided b he variane

5 Now, subsiue he ondiional e i ( (1 ( [ i i i ( ( i e i ino he marke sul funion o ge i i ((1 i Aggregaing and adding in normal level ] exeaion we ge Someimes alled Luas Sul Funion :

6 Consider a oli inervenion and he riique Now suose inflaion follows where has a mean and variane Then he aggregae sul equaion beomes 1 ( If esimaed b regressing he ouu ga ( on inflaion ( would aear o show ha monear oli ould bring above 1 1 and a onsan, he regression equaion ermanenl b raising inflaion. Bu ha would be a seriousl misaken onlusion beause he oeffiien would hange and herefore he onsan in he esimaed equaion would hange. Bu a onsruive riique? How? -

7 Oher examles: onsumion and he oeffiiens on inome an be esimaed. (1 (1 he onsumion funion is Thus,, deends on varianes of ( 0,for i (1 ( hen is seriall unorrelaed, random walk and is a where inome follows he sohasi roess aual if ( ( i i i i u k k w v I E v w v w a I E u k Friedman s (1957 ermanen inome model of onsumion

8 Now onsider a oli inervenion in he Luas onsumion examle Suose we u axes b x ermanenl a ime 0. Then inome will rise b x ermanenl Then E( 0+i I 0 u b x for all i 0. Permanen inome 0 will rise b x. Aording o he heor, onsumion 0 will rise b kx However, he esimaed eonomeri model imlies ha onsumion 0 inreases b k(1-βλx whih is muh less han kx. Onl over ime would rise u o kx.

9 Aliaion: Temorar Fisal Simulus in 008 billions of dollars 11,00 10,800 10,400 10,000 disosable ersonal inome \ wihou rebae 9,600 ersonal onsumion exendiures 9,00 Jan 07 Jul 07 Jan 08 Jul 08

10 Consumion Regressions Lagged PCE (.057 (.056 Rebae amens (.055 (.054 Dis. Pers. Inome (w/o rebae (.056 (.055 Oil Prie ($/bbl lagged 3 monhs (.35 R Deenden variable = PCE Oil rie = Wes Texas Inermediae. Samle eriod is Januar 000 o Oober 008. Sandard errors in arenheses.

11 General Formulaion of he Criique Using a framework 1 F(, x,, o evaluae oli (hanges in will in general lead o misakes, beause will hange when x x hanges. The alernaive framework is o seif a oli rule for he insrumen (mone growh, ineres rae x,, whih imlies ha G( 1 F(, x, (, A oli hange is hus a hange in whih affes and hereb he sohasi roess for.