Disinfiatior, with imperfect credibility

(Reccigcd !U;lrzh !YYZ; til:.d lcrsion recc~vcd AII~U~~ IYv-II

Abstract

This paper presents a theory of the real effects of disinflation. As in New Kcyncsian models, price adjustment is staggered across firms. As in New Classical models. credihil- tty is imperfect: the monetary authorrty may not complete a promised disinflation. The cwnbination of imperfect credibility and staggering yields more plausible results than 4ther of these assumptions alone. In particular. an announced disinflation reduces cx;uctcd output if credibility is sufficiently 1w.v.

kc?)* wrds: Business fluctuations; Disintllition

1. Introduction

Disinflations arc an important cause of recessions in economics like the postwar United States. In explaining the effects of disinflation, New Classical economists stress the inability of rhc monetary authority to make credible policy announcements. New KeyncGns emphasize rigidities in nominal wages and prices and especially the stag.Jcred timing of price adjustment. This paper argues that both schools arc rqht. 1 present a model that explains the effects of disinllation through the irr~o’trcvior~ ;)I- imperfect crc::ibility and staggering.

I am grateful for cxccllcnt research assisrancc from Boris Simkovich and Demosthenes Tambakis. and for suggestions from Stephen Cccchetli. N. Gregory Mankiw. Bennett McCallum. David Romcr. Laurence Summers. and seminar pnrticipar.ts at BU. Columbia. Michigan. NBER. and Princeton. Financial support was provided by an NBER Olin Fellowship and ,m Alfred P. Sloan Research Fcllouship.

0304-3Y32;YS, SOY.50 ,( 1905 Elscvicr Sc~e~cc H.V. All rights reserved SSDI 030439329401 I66 X

This p;lpcr start\ ~IOIY the results in I%;{11 I I YW) on ciisinlkltion lvith st.~ggcr- in!!. ?‘h;:t pilpcr ;1ssumc5 full crctiibi!ity: 2 disillllillic~n is ;1IlIlOUIlCCd at its 0UtSCt. and t hc ;~nnounccnicnl is bclic~~eci. l‘hc surprising linding is that quick disinh-

lions can cause /RKJUIS rather t ban rcccssio:l$. This result is empirically implaus- ~hlc. and thus SU~~CS~S th:lt si:iSgt’rlng ill(JnC d~s not explain the O~~CC~S of disinflation. The current paper 5hoM.s !hat the results arc more appealing if the assumption of full credibility is rclawd. Most important. combining imperfect credibility with staggering yields a bcttcr cxplanaticn for the effects of disinfla- tion than credibility problems alone.

To clarify the role of staggering. 1 begin in Section 2 with a model that lacks it. Firms set prices each period bcforc observing the current money stock. The monetary authority (hcrcaftcr. the ‘,Fcd’) announce’s a slowdown in money growth. Howcvcr. credibility is imperfect: with a known probability. the Fed does not keep its promise. The results in this model arc rather trivial. Firms base prices ok the cxpe,;cd path of money growth gilfen the likelihood that lhe Fed kci-ps I! promise. A recession occuvs ii morlcy growth falls more than expected. bet a !,oom occurs if money growth falls less than expected. With rational expectations. the taw~q~ oUiput response is zero regardless of the level 01 credibility. i argue that this rcsult is unrealistic. In actual economies, announce- ments of disinllation lead to recessions 29 ave~agc: output is more likely to fdll than to rise.

Sections 3 and 4 consider a continuous-time m ,&I in which price adjustment is staggered. In this case, I foc’us :,. L tilt following exrzrime:it. which IS detailed in Section 3. As in Ball (1994). mo*lcy growth is initially positive? but the Fed announces that it will decline !i;lcarly to zero. The Fed begins to carry out this promise. However, departing from t1.c r,;evious paper. there is a constant hazard at each instant that the Fed ‘rcnegcs’. If it rcnegcs, it stops disinllating and instead keeps money growl:: :lt the c~rent level forcvcr. I interpret a large hazard of reneging as a low level of credibility.

Section 4 derives the real effects of disinflation. With fu!l credibility -. a zero hazard that the l-cd rel$cges quick disinflation5 r3isc output, as in Ball (i994). With a positive hazard. output depends on whether and when the Fed reneges. However, if the hazard is sufficiently high, the esp~c~tc~rl output effect is negative. That is, in contrast to the model with,)ut staggering. credibility problems can reduce output on a\‘?ra$c. Indeed. the ‘expected sacriticc ratio’ the expected output loss divided by the expected fall in inflation increases monotonically with the hazard of reneging. Finally, for a sufficiently large hazard there is a stronger rescllt: output falls not only on average, but for all realizations of Fed behavior. There is a small recession if the Fed reneges quickly. and a large recession if it does not.

To gain some intuition fog thc:;c results. consider first the case of full crcdibil- ity. When money growth begins to fall. only a fraction of firms can adjust prices quickly, becabsc of staggering. However. the firms that do adjust early in the

disinflation knc>?v that nlc~nzy gro\vt!~ \vill fall cc>nsi~icrahly Khilc their pril cs arc in cffcct. As ;t result. the! grc,jtly rl:ducc rhcir price increases. causing aggrcgatc inflation to fall quickly cvcn thtrugh most prices are fixed. In contr;ist. if disinflation begins but tirms fear that the Fed will soon renege. they set higher prices. lnflatlon does not fall fast cnc‘iI?ll 10 match the fa11 in money gro\vth that occurs as long as the Fed has not rc?:Ct!Ld yet. The initial tigt,tenmp plus the prospect rjf future easing causes :I IcccsGon.

Section 5 considers the robustness of the results to alternative specitications of imperfect credibility. Section 6 concludes.

2. Disinflation with synchronizaticn

This sectiorl considers a sim\Je model without staggered price adjustment. An annI-unced disinflation h,ts no effect UII avcragc output. rcgaidless of the level cf credibility.

The economy contains a continuum of imperfectly competitive firms indexed by i and distributed uniformly on [O. 11. Firm i’s profit-maximizing relative price is increasing in aggregate output:

where pi is the firm’s nominal price. p is :h c apgrc_eate price level. and ~3 is aggregale output (all variables are in logs). This equation c;‘n be dcrlvcd from isoelastic cost and demand functions (SC:: Ball, 1YY4). Ir,:ui!ively. an inc.ease in aggregate spending raises a firm’s desired price by shl,‘ing out thz deman.j curve that It faces.

Money enters the model through :: quirntity equation for money demand:

;:? -- P = j’. (3

where IPI is the money stock. Combining (‘) and (3) yields :A firm’s desireu nominal price in terms of IPI and p:

p) = rn1 + ( 1 - I’) p. (3)

For simplicity, the model is set in discrete time. A firm adjusts its price every period, but it adjusts before observing current money. The firm set:. its price for I. p,,, cquat to E, , ~2. where E,. , is the expectation conditional 0:: information

Asslim~: th;~t m~)nc\ g.r:b\\ I’! is ii:itl,tll> C.~l~\idIlt ;irlti c\pcctd to rcm;liv ionbt:~nt. At scjmc p01nt. the I-‘ccl ;IIIII~~~IIICC\; t h.!. money gro\f th \vill decline over (~nc‘ or niorc pcricd3 (t hc prccisc’ p;~th I hat it :innounc‘Cs is not important! f ,lcrc ix sonic prohahilit>. \\ hich price scttcr5 hnc)vt. Ihat the I-‘cd disinflates 113:. :h:111 promised. I intcrprtt ;I high probability 4s ;I lot!, Ic\cl of credibility.

In this setting. the t‘lI’~cts ~~fdisinfloti~~n arc c~hvwus. Each pcrlnd. firms base thci:- pricl:s on espcctcd 11101wf gro\vth given the probability that the Fed keep:, its promise. If mctnq growth li~lls IAtcr than cxpcctd thrtt is. ifthc Fed provs unusually tough th:‘ll (~utpt~t I’rllls. If m~~llc‘! .fKN?Il filllS ICSs than CXpCCtCd,

Ihen output rises. With rittional cxpcct;ttl,ms. the ct~.c~rcc+’ output elkct is zero. rcgardlcss of the level of c:cdibillty. Annclullced disinlldtions GIllnOt systcmati- tally rcducc output il; this n:oJcl ’

A rlumbcr of prcvlous authors. such as Fischer (IO%! and Cukicrman and Meltzcr (19X6). argue that noncredible disinilations do rcducc output. However. these papers and the current one focus on Jiffcr~~nt questions. Prcvions papers consider cp+dcs in which ‘1 tough policym;tkcr rduccs money growth cvcn though the public dew not cxpcct it. That is. they consider particular rculi- /ations or Fed bchil\ior in \vhich money growth is less than its mean. As conlirmcd in my model. thcsc rc;lliz;\ti:>ns product racssions. In this section. my ccntr:ll point is that credibility does not affect average output if cxpcctations arc correct un avcragc. Previous nvdcls arc consistent with this result.

3. IXsinflation with sbgg:cring: ‘I‘!Ic c\pcrirnrnt

The specification of stagpcring li~llous Bali (19%) ;tnd is close in spirit to Taylor ( 1979. 19X0) and Blanchad (1983. i9M). The model is set in continul,us tind. AggzgAtc output illld firms’ desired prices arc still given hy (1 ) 42). II;ich firm adjusts its price at intcrvids of kngth 1 (a normi~lizati(~n), with ildjustmcnts by diticrwt firms Jistributd unil;)rmly over timc. I.ct x(I) dcnotc an iIlJiViJllilI

price set t time I fkr the intcw;tl [I. f -+- I I (1 drop ,hc i <ubscript hccausc all firms acting at I C~~NISC the SitmC priccL A firm SCIS \‘(I) equal 10 I;IC ilvcrilgC of

its desired prices owr [f.f + I kJ

Finally. with uniform staggering the price Iad is the averilgc of prices set ovc’r the last unit of time:

P(f) = -’ I

s(f -- s)ds. (6) . \ 0

With staggering, the cfTccts of disinflation iire sensitive to the particular path announced by the Fed and the nature of the credibility problem. I ~YXS w. one example. and condcr robustness in Section 5. In the cxumplc. money growth is initially steady: at 311 I < 0. money g;-nws iit rate I (another normalization):

m(1) = 1, cl(t) = 1. i <n. (7)

\vherc IN is the level of money and ril is money growth. At f < 0. firms expect rt. -nq growh to remain constant forcvcr. Howcvcr. at time 0 the Fed an- il(junccs a JisintL~ii::,: It promises that mow> grw th will decline linearly. reach 0 in k units ,.:I .I-X. iIIlJ then rC)n?;lIn at xro pcrmancntlg:

h’(r) = 1 - I I;. 0 < I < A.

ZZ 0. 12k. (8;

, , - - - - - - I /

\ \

\

I \ I

0 I \ ------___ I

i _ _ L.... ._. -..- .-_. L ._ __ .__ _ ,

O\, k ar,nc~mcament I

The Actual :‘alb 1: the fed Reneges at T m(r)

-- .-.--- ..-- -.- I

o!

L -..--. -~. L----l. -... _L--.--.--- -~.-_-...-.-------!

O\\ T k announc.emer~t

where CI is announced money growth. Fig. I (upper pan,4) piots this path. The parameter k measures the speed of disinflation.

Ball (1994) assumes that (8) is carried out with certainty. In this paper. bq contrast. the Fed may not fully keep its promise. Specifically. the Fed starts to carry out (8). but at each instant there is a hazard /z that it ‘reneges’. jr is ;1 constar;t known to price setters. If the Fed rrlnegcs, it .;:c~ps reducing money growth and instead kqx money growth at its r,,xren levci forever. That is. if the Fed reneges at time 7 < k. the actual path of money growth is

rit(t) = 1 -- f/I. osr<r,

= 1 - r/k. 127. (9)

This path is prcscntcd in the I~~wcr p;incl of I-‘ig. I. If ~hc t’cd dots not rcncgc hcforc time k. actual money growth follows the promised path (81.

This specification captures situations in which policymakcrs launch a disinfla- tion but may bc unable to complctc ii. For isample. in 1979 hlargarct Thatcher announced a five-year tlisinll;ltion path a~rd began to tighten policy. Howckcr. tlierc were political i>c tacles 1,~ the completion of the plan. which was opp bsed by Labor and the Social Democrats. At the outset of the program. Sargent (1953. pp. 57 58) wrote:

Mrs. Thatcher’< party now runs third in the political opinion polls. In addition, throughout her acf.ninis!ration. specula!ion has uascd and waned about whether Mrs. Thatcher herself would be driven to imp1emer.t a [J-turn in macroeconomic policy actions, and whether her stringent monc- tary poliq, actions would be rcvcrsed by the Conservative Party itself. i,y choosing a new party leader.

The risk that disinflation ends prcmaturcly with a shift to loos-r policy is captured in my model by t’lc hazard th,tL the Fed reneges. I interpret it large hazard as a low lcvcl OI’CY ii\ .lity.

4. The behavior of output

This section derives the behavior of output during disinflation. I begin by reviewing the full credibility case in Ball ( 1994). Then : derive the expected path of output with imperfect credibility and the paths for particular realizations of Fed behavior.

4. I. Full cwdihiiit~~

The mode1 reduces to the full credibility case when the hazard of reneging is zero. In this case. fairly quick disintlations cause booms: output rises above the natural rate and never falls below it. In particular. Ball (1994) shows that the linear path (8) produces a boom as long as k. the length of disinflation, exceeds 0.68. Recall that the time unit is the period between price adjustments. If prices are lixed for a year. d boom occurs if disintlation lasts at least 0.68 years.’

To understand this result, consider the early stages of disinflation. Money growth begins to faall and. with staggering, only a fraction of prices can adjust quickly. With full credibility. however. the firms that do adjust know that money growth will fall considerably while their prices are in effect. As a result, they

“A year is the median inter\al bctwcsn priw adjwmcn!s in Hlindcr’~ (IYY I) wvey of firms

When /I is positive. the path of output depends on whether and when the Fed reneges. However. Ihe following result lets one calculate the csl~~c~i output path without considering individual realizations. Let E denote an expectation at time 0. :vhen disinflati:>n has just been announced. Then:

That is. expcctcd outpu! depends only on the mean of money growth. not on its distribution. This certainty-equivalence result follows from the log-linearity 01 the model (see Appendix).

Given ‘he Lemma, the first step in finding expected output is to lind the expected path of money growth. T!?is path is determined by the announced path (8) and the hazard of switching to (9). The Appendix derives

E,i~(t) = 1 + c-;$ OIf<k,

t 2k. (10)

For k = 1. Fig. 2 shows expected money growth for various values of II. When /I is positive. expected money growth declines sharply at first but then flattens. because it becomes increasingly likely that the Fed has reneged. E~ir is constant after time k, because disinflation ends at k if not before.

Eq. (10) and the equations defining prices yield an implicit solution for the expected output path (see Appendix). Explicit paths are derived numerically. For k = 1 and I: = $. Fig. 3 presents expected output for several vslues of II. When /I = 0, there is a boom (note that k = 1 exceeds the bound of 0.68 discussed above). For positive but small values of II, such as /I = i. thi:rr: is an expected boom. However. large k’s. such as 5 qr 10. produce expected recessions.

?iec Ha!1 (1994) for a more detailed discukc,n of this result, and a comparison to other mod& wi.h Ml credibility. Taylor (198.1) and Fischer t 1986) tind that a credible dtsmtlation must be quite slow to avoid a recesston. T::p source of this result is the assumption that multi-period contracts spcci1.y different wages or priccc for different re -iods. My earlier paper argues that this case is let-\ important empirically than the one considered it::?

Ehft)

I

i.-.-.--- ..- . ..L--. -1 ---.-.---- _._ J

EY::)

O.Cl

0.03

0.02

0.01

000

-001

O\\ 1 znnouncement

r _.-. -._-..--__---._--.----.. ------__--. __-.-. .-._

t

-0 02 J 0 1 2 3

t

F1g. 3. txpeclcd 0ulput (f’ = 4 k = I).

These results illustrate the central point of the paper: with staggering. the led cf credibility influences average cutput.”

The relation between credibility and sverage output is nonmonotonic. An increase in 11 can turn ;L boom into a recession, but the recession disappears as

‘For any /I. cxpctcd output rises zt time 0. Output rises bccausc the announxmen* LUSCS indatmn IO jump down, and money growth is continuous. For a large h, hnucver. the initlal boom is negligible compared to the recession that fdlows.

II -+ X Intuitively, /I + -/> means the bed rcnegcs at time 0. so money gro\vth and output remain constant.

There is. however, a m~Xnotonic relation bctwccn 11 and the ‘expected sacrifice ratio’, defined as

,. .I R= -

I Ejs(r)dr :( I - Efi~(k)). ,, -0

The numerator of R is the expected output loss summed over time. The denominator is the expected long-run change in inflation. which equals initial rnene;. growth minus expected money growth at /L R is a natural extension of the sacrifice ratio in nonstochastic models (for example. Fischer. 1986). As illustrated in Table 1. R is increasing in /I. For I: = 4 and k = I. R is - 0.10 when h = 0. 0 when h = 3.3. and 0.09 when /I = 10. As /I + :A. R approaches a positive asymptote. ’

Why does low credibility produce expected recessions’? With full crcdihility. inflation falls quickly when money growth starts to slow. because firms reduce their price increases in anticipation of further disinflation With low credibility. by contrast, firms expect money growth to level off (see Fig. 2). They set higher prices. so inflation falls slowly even though, on average, money growth falls quickly at Crst. That is. an initial monetary tightening is accompanied by the expectation of future easing. which keeps inflation high. Thus axztgc output MS.

‘I cxmol show analytically Ihill K k mwwonic in 11. but thi:, result ib c~ml~~med by cxlensivc

numerical calculations. (The rcwlt can hc prwed xmdytically in the special USC of r = I .) One can

show that R remains fink ah II ---t I . hcc,~~sc the numerator and denominator approach 0 at IW

same rate. It is diflicult 10 dcriw lhc limtting \all;e of R. because the numerical rcsuhs arc Imprc&e

when 11 is wry large.

In addition to computing cxwctcd wtp~!t. ow can dcr~\c output paths for particular realizations of r. :hc date uhcn the Fed rcnepcs. Fcjr a gilcn r. Ihc y.111 of monzv rr:\w!h is zivzn hv !9). Prices set at c:lch instant clcprnd w . c expected money growth gi\.en the L‘~d’s behavior so far, which is dcrerminzd by (8). (9). and the hazard /I. The Appendix uses thcsc expressions to derive output paths numetkally. Fig. 4 presents the paths for k = 1, r = ?. and two values of/~. It = 5 and h = 10. For each Ir. Fig. 3 prcscnts output paths for wrious rcali- zations of r. Finally. Table 2 considers additional combinations ci It :lnd r. The table summarlz:s the results with the total deviation of output from 0 [l.c.. the integral of \(I)].

Ye) h=S

, - __--.__--.-.---.-----.-.- . . . .

/

I

1 -0.02

I -0.04 I

I

-O.O* t--_--.-_-.------.----- -..-.---.-.I 0 1 2 3

y”) . ---._--.---..-_--.-----.-.---- --“?-..--.. 7 I

0 i.

!

-0CL i- I I

I -0.fJ.j :. I

I

I r=l (FeJ,,ever reneges) I

-0.06 / I

/

I -0.08 '-

i... -- -_-.-~---. __-- ---. J 0 1 2 3

O.OO!

OS;07 !;.O i 3 0.03’ 0.056 Wh 0.05 I 0.041

O.thJo

O.(H)i 0.002 o.no4 O.‘Y)b Wo2 0.008

-- O.C? 1

Not surprisingly. Table 3 show0 ihat total output is decreasing in 11 for a given T. That is, holding constant the Fed’s actual behavior. output falls with lower credibility. A more striking result is that large values of /I produce output losse; for (111 values of T. For a large II, disinflat ;aJll reduces output not only on average (as shown above), but for every realization of Fed behavior. Fig. 4 illustrates this result. For /I = 5 or h = 10. disin!iA:tion causes a large recession when T is large (:.g., T = 1) and a small recession when 5 is small (e.g.. r = 0.05).*

For a large /I, it makes sense that there is a deep recession when 7 is large: in this case, money growth falls more than expected. It is more surprising that output falls even if T is small. so tha: money growth falls less than expected. In this case, the unrealized expectation of disinflation has little effect on prices, because few firms adjust between time 0 and time r. And prices set before time 0 are too high, because the fall in money growth was pot anticipated before the announcement. Thus there is a recession (albeit a small cne, because the fall in money growth is small).

5. Robustness

So far 1 have focused on a specific example of a credibility protlem. This section asks whether the results are rcbust. I focus on the effects of imperfect credibility on expected output.

The essential feature of the example is that expected money giowth falls steeply at first, and then flattens as it becomes liltely that the Fed has reneged. In

“For small values of h, output rises for all realizations of T. For intermediate h's, output rlscs for small T’S and falls for large 1’s.

other words. it is essential that imperfect credibility makes expected money growth convex. Modilications of the model do not. change the qualitative results unless they eliminate this convexity. I now illustrate this point with several additional examples.

As a first example. ict the: hazard I: of reneging vary over time. (In particular. II migh: decrease over time, because the Fee! gains credibility if’it has not reneged so far.) This generalization cf the model does not affect the qualitative results. Expected money growth is still :onvex as long as h(t) > 0 over [O. k]. 0.;~ can show that 3 larger hazard at an,’ point in time raises the expected sacrifice ratio.

As 3 second example. assume th2.t /I is constant but modify the Fed’s behavior when it ‘reneges’. Reneging now means that th: Fed returns money growth to its initial level of 1. not that money growth stays constant. That is, if the Fed reneges L: r, then

Cl(l) = 1 - r.:k, OS/<?.

= 1. 1 2 T. (11)

Money growth still follows the announced path (8) if the Fed does not renege before time k. The path (1 I ). in which Initial gains against inflation are given up, is one interpretation of the ‘U-turn’ that Sdrgent predicted for Thatcher.

This modification of the model strertgt/rens the results. The possibilit:, that money growth jumps up makes expected money growth more convex for 3 given 11. (The path flattens morz quickly and, for large h, eventually rises.) As a result, disinflation is more likely to reduce output. Fig. 5 shows expected output paths when k = 1 and 1: = A. In this cxpcrimcrlt. the expected sacrifice ratio is negative for all It > !.I. In the basic model. R is negative only if /I > 3.3.

WV 0.04 --- --- -.-

I

i.53 -.

c 02

0.01

0.00 -

4.01

4702 J Fig. 5. Expctcd oulp. AlternaIive specification (r = !. k = 1)

F‘itlilil>. I pWWIlt ; I! :xuamplc in \\hich li)Mc’r crcdlbllity dues i10f reduce the expected sacrifice t-atio. Suppose that the Fed announces the path (81. in which money growth &clitics at rate I ,L o\cr [O L J. In fact. the I-cd switches bctwccn . reducing money grolvth at i;rc plon~i~cd rata ard keeping money growth constant. S\s;~clle~ arc ;I Markov process v,.;th the initial r,tatc chosen randomi\ based on uncondirional probabilities. In this cast’. the expected path of money growth is

EGl(t) = 1 - cir,k, 0 I f < k.

= I -- q. 1 I k. (12)

where y is the unconditional probability r?f the disinflation state. A lower (1 means less credibility: tirms cxpcct less of the promised disinflation to occur. Nonetheless. one can show that the cxpccted sacrifice ratio is independent of 4. The explanation is that (12) is always linear over [O.L]. Reducing q affects the slope of (12). but does not inirvduce ;hc convexity that lowers expected olltpat.

This example shows that the robustness of my results is limited. However, th:: example is not especially appealing. The crucial convexity in my model appears plausible: in actual disinflations, it is likely that policy is mitial!y tight bui then loosens (recall Sargent‘s discussion of Thatcher).

6. Conclusion

This paper presents a theory of the real efficts of disinllation. I assume that price adjustment is staggered. and that credibility is imperfect: the Fed ma] not complete a promised disinflation. The central result is that low credibility worsens the output inflation tradeon‘: the expected sacrifcc ratio ;iseh with the hazard that the Fed :enegcs. In addition, when the hazard is large. output falls for all rca!izations of Fed behavior. These results fit the experience of the postwar United States, whcr; disinflations systematically reduce output.

Both the New Kzynctsian assumption of staggered adjustment and the New Classical assumption of LTperfect credibility are essential for the rrsults. With staggering but full credibility. quick disinflations raise output. \‘.i:L imperfect credibility but synchronization. disintlations are neutral 07 average. Neither ol these ( ases appears realistic.

To be clear. imperfect credibility a101:c can explain output losses in c.:tain episodes. such as thr: Volcker and Thatcher disinflations. These can be inter- preted as cases when policymakers proved laugher than expected. However. the model with synchronization implies that such episodes are balanced by booms when tough-talking policymakers disintlate less than expec:ed. In practice. policymakers often make promises of disinflation that they fail to keep. but this behavior does not appear to raise output significan!ly. Voicker

L;~.Js~.LI a recession b! dirinflatin:. 1-tut N’illiam Jlillcr did not product 3 boom by Fiilrng lo disintlntc.”

I Loncludc ivith d suggestion for future rcscarch. In this paper. the behavior of the monetary authority is esogenous. It ~.ould be dcsirahlc to maker this behavior ends genous to explain K/IJT disinflatiops sometimes end ~:rcrr.+.t~~rcly. In the spirit of Alcsina (1988), imagine a model with two political pariics. C .?nservatives who favor disinflation and Liberals who do not. The parties Litcinate in po&zr stochastically. with a higher probability of a switch when the econo.11) is pcrform- ing poorI!. In this framework, a disinflation launched by Conservatives is not fully credible. because the Liberals might gain power z-,d reverse it.

I conjecture that such a model has multiplr equilibria. If the Conscr\.ativcs announce a disinflation and credibility is high. :hcn output rises. With rising output. the Conscrv?’ 1vcs are unlikely IO lose ,?ff~ce; thus they succeed ;;1 disinflating, justifying the public’s confidence. On the other hand. if crcdibili:) is low. then disinflation reduces output. In this c;*se the Liberals are likely to gain power and end the disinllation: thus low credibility is hlso self-fultilhng. Sargent (1983. p. 57) argues l;i;it di+fIation should be accompanied by a ‘once-and-for- all. widely understoo., ::nd widely agreed upon, change in the monetary and fiscal policy regime’. ‘: hi- ~zgirne change can perhaps be interpreted as a shift from a low-credibility equilibrium to a high-credibility equilibrium.“’

Appendix

Here 1 derive the general behavior of the price level ;Ind prove the Lemma in Section 4. At I < 0. steady inflation is expected to continue. so E,,n(f -t- t-) = E,p(r + r) = I + I’. Substituting these results into (5) yields s(t) = t + 1 for f < 0. s(1) is given by (5) for I 2 0. Subs!ituting the expressions for .u(r) into (6) yields an equation for the price level:

P, I’ I *I pll) =- E,.. ,p:(t - .s -t- ,)drd.v +

.I,.:, (! - 5 + :ld.s.

,* 1 l-1 =

I I Ep:(r - .\ t- r)drds. 1 2 1. (A.3)

-, \ , , .’ , -.- (1

where E i< the cxpcct;iti,,n al ,imc 0. and I LIQ the law (11 I:cr,ltcd cupcctations. Fq. (A.?) simplifies to

Ep(iJ = [’ sEP:(sbds -‘- i! l-1 1

rEp: (>)ds +- I

(! + r - s) Ep:(s)ds Js-0 . 3 -, .‘\-: I

+ 4 (I -- f2 I. 0 5; I < I,

.* I ,- 1

= I

(1 - s)EpY(t - :.)ds + I

( 1 - s) Ep:(r t SldS. ;A 3) . \=‘, ,\=o

t ’ 1.

This equaiion implicitly defines the exp:.:ted path of prices in terms of the expected path of money. The eq~iation alw defines expected output !n terms of expected money since E!*(r) = E;!i(t) - Ep(t). This establishes the Lemma in Section 3.

Hcrc I derive the expected path of output for the basic example in Section 4. The first step is to fin-1 the cxpectcd path of money. At tirra t < k. the probability that the Fed has not yet reneged is e -“I. i l has rcncged at !imc .$ < I with density he-““. Usin: :i‘) and (9). cxpccted money growth is

This zqu;ltion simplifies to (101 in the text. Fln;tll~~. intcgratrnp (IO) jiclds the expected path of the /v:.cJ/ OI money:

To find r(r) numericall!. I discretire the path with step size .I 1.1 = O.(H).~ ir; the reported results). I asumc that S(I) :: j,‘,~(r + .s)ds for I > 717‘ = lo); this i4 ecjuivalent to assuming that j’(r) = 0 lor t > 7‘ - I. I then use scparatc ap- proaches to derive s(r) for t E [O. r] and for r c [ r. 7‘1. tlf t’lc I-ed neler rcncpch. I is set to I.)

To tind .\-(!bfor I E [(I. r]. I dcrivc \-((I). .s(.l). . x(r) sequcntinlty. To fini .~(r) for ;I gilen 1. I first IISC (XL 19). ;rnd the hazard it to ieri\c the p*Jth or m:;n .x, cxpcctcd at t:

For q t [t. T]. I guess a path for E, i(q). .;t:bstitLtc it into (4.8) to produce a new path. and iterate to convergzncc. l’his p:ocedurc yields the expcctcd s’s III the final term of (A.6).

For t E [T. T]. there is perkct foresight. Thus the cspectdtions operator can be dropped from (A 6). Using (8) and (9). rhc path \)f woney is

m\i) = 1 -- I7 -t 7’ ‘2. t 2 7. (A.‘))

I subs!itute this result inio the perfect foresight torsion o: (A.$). Then 1 deter- mine the path of .=-(I) over [r, T] ~-IL :;uhstituting an initi;;l gw’ss intti !A.fi’! and iicra;ir.g.

Once th; path of S(L) is detcrlrlined. I ust‘ (6) to find p(r). Sub!r;\cling p( r) from the actual path of money yields .I*(!).

Finally. I consider the a!tern.itive disintlatisn experimwi dcfiwd by ill). ‘Asing (8) and (11). one can show that expected monq growth is

Etit(f) = 1 - t e -h’. 3<r<li.

= 1 - c--h’, t 2 k.

1 he expected path for the let?; ol‘ money is

(A 10)

(A.111

As in the basic experiment, Ep( 1) and E!(t) arc deri\:d numerically after substituting EM(~) into (A.3).

References

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282.28Y. Blanchard, 0.. 1983. Price asynchronization and price level inertia. in: R. Dornhusch and M.

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