Imperfect Credibility and Inflation Persistence

Imperfect Credibility and In(cid:223)ation Persistence Christopher J. Erceg* and Andrew T. Levin** Federal Reserve Board 20th and C Streets, N.W., Stop 42 Washington, DC 20551 USA First Version: July 2000 Current Version: June 2001 Abstract: In this paper, we formulate a dynamic general equilibrium model with staggered nominal contracts, in which households and (cid:222)rms use optimal (cid:222)ltering to disentangle persistent and transitory shifts in the monetary policy rule. The calibrated model accounts quite well for the dynamics of output and in(cid:223)ation duringtheVolcker disin(cid:223)ation, andimpliesasacri(cid:222)ceratioveryclosetotheestimated value. Our approach indicates that in(cid:223)ation persistence and substantial costs of disin(cid:223)ation can be generated in an optimizing-agent framework, without relaxing the assumption of rational expectations or relying on arbitrary modi(cid:222)cations to the aggregate supply relation. JEL classi(cid:222)cation: E31; E32; E52. Keywords: Monetary policy, disin(cid:223)ation, sacri(cid:222)ce ratio, signal extraction. * Corresponding Author: Telephone 202-452-2575, Fax 202-872-4926 Email christopher.erceg@frb.gov ** Telephone 202-452-3541, Fax 202-872-4926, Email andrew.levin@frb.gov

1 Introduction ∗ Since the pioneering work of Taylor (1980) and Calvo (1983), business cycle dynamics and the role of monetary policy have been analyzed in models with staggered nominal contracts. In recent years, such contracts have been incorporated into dynamic general equilibrium (DGE) models derived from microeconomic foundations.1 Nevertheless, models with staggered contracts have been criticized for failing to generate a sufficient degree of in(cid:223)ation persistence and for implying unrealistically low costs of disin(cid:223)ation (Ball 1994; Fuhrer and Moore 1995).2 In this paper, we formulate a DGE model with optimizing agents and staggered nominal contracts, and we show that this model can generate in(cid:223)ation persistence and substantial output costs of disin(cid:223)ation when private agents have limited information about the central bank(cid:146)s objectives.3 In particular, households and (cid:222)rms use optimal (cid:222)ltering to disentangle persistent shifts in the in(cid:223)ation target from transitory disturbances to the monetary policy rule. Under these assumptions, the speed at which private agents recognize a new in(cid:223)ation target depends on the transparency and credibility of the central bank. Thus, the signal-to-noise ratio is the key parameter determining the persistence of in(cid:223)ation forecast errors, and hence in(cid:223)uencing the persistence of actual in(cid:223)ation and output. We show that this model can account quite well for the dynamics of output and in(cid:223)ation during the Volcker disin(cid:223)ation. Using data from the Survey of Professional Forecasters, we calibrate the signal-to-noise ratio to match the observed evolution of one-year-ahead in(cid:223)ation forecasts over the period 1980:4-1985:4. With four-quarter wage and price contracts and an empirically reasonable calibration of capital adjustment costs, the model implies output costs of about 1.6 percentage points for each percentage point reduction in the in(cid:223)ation rate; this sacri(cid:222)ce ratio is remarkably close to the estimated value for the Volcker disin(cid:223)ation. Our analysis contrasts sharply with existing approaches for generating in(cid:223)ation persistence and substantial costs of disin(cid:223)ation. First, we avoid arbitrary departures We appreciate comments and suggestions from Larry Christiano, Mike Dotsey, Marty Eichen- ∗ baum, Charlie Evans, Marvin Goodfriend, Dale Henderson, Peter Ireland, Athanasios Orphanides, John Taylor, Alex Wolman, and participants in workshops at the July 2000 NBER Summer Institute, the Federal Reserve Board, the European Central Bank, and the Richmond Federal Reserve Bank. Theviewsexpressedin thispaper aresolelytheresponsibilityof theauthorsandshouldnot be interpreted asre(cid:223)ectingthe views of the Board of Governorsof theFederalReserveSystem or of any other person associated with the Federal Reserve System. 1Lucas(1986)analysedaDGEmodelwithstaggeredpricecontractsof(cid:222)xedduration,whileLevin (1989) analyzed a DGE model with staggered wage contracts of this type. For recent examples, see Rotemberg and Woodford (1997), King and Wolman (1999), and Erceg, Henderson, and Levin (2000). 2The same criticism applies to models with quadratic costs of price adjustment (cf. Rotemberg 1996;Kim2000),whichhavesimilar(cid:222)rst-orderdynamicpropertiestomodelswithstaggerednominal contracts. 3Our approach is similar in spirit to that of Ball (1995), who used a small structural model to show that imperfect credibility can raise the output costs of disin(cid:223)ation, and to that of Ireland (1995, 1997), who analyzed optimal disin(cid:223)ation paths using a highly stylized DGE framework but did not focus on the quantitative implications. 1

fromthe optimizing-agent framework, suchasadding lagged in(cid:223)ationtermsto the aggregate supply relation or imposing adaptive rather than rational expectations.4 Our assumption that agents process information efficiently is consistent with the (cid:222)ndings of Evans and Wachtel (1993), who analyzed survey data on in(cid:223)ation expectations and demonstrated that persistent ex post forecast errors during the period 1968-85 should not be viewed as (cid:147)irrational(cid:148) but rather as re(cid:223)ecting the degree of uncertainty about the underlying in(cid:223)ation regime. Second, our analysis implies that in(cid:223)ation persistence is not an inherent characteristic of the economy but rather varies with the stability and transparency of the monetarypolicyregime. Asdiscussedbelow,thisperspectiveisconsistentwithempirical evidence indicating very high U.S. in(cid:223)ation persistence (close to that of a random walk) during the period 1965-84 and much lower persistence during the remainder of the postwar period. In contrast, the empirical evidence appears to be inconsistent with models that incorporate inherent in(cid:223)ation persistence due to contract structure or adaptive expectations. Finally, in our model, the costs of disin(cid:223)ation are radically diminished if agents quickly recognize the shift in the in(cid:223)ation target, whereas the learning rate is of relatively minor importance in models with inherent in(cid:223)ation persistence.5 More generally, our approach suggests that efforts to enhance transparency and credibility can facilitate the effectiveness of monetary stablilization policy. The remainder of this paper is organized as follows. Section 2 reviews several important stylized facts, and highlights the credibility problems faced by the Federal Reserve during the Volcker disin(cid:223)ation. Section 3 presents our model, while Section 4 describes the calibration and solution methods. Section 5 investigates the model(cid:146)s simulated responses to a disin(cid:223)ation shock. Section 6 compares our approach to accounting for in(cid:223)ation persistence to the previous literature. Section 7 provides conclusions and suggests directions for future research. 2 Key Stylized Facts In this section, we brie(cid:223)y characterize the persistence properties of postwar U.S. in(cid:223)ation, and then we highlight several key aspects of the Volcker disin(cid:223)ation. We interpret large and persistent in(cid:223)ation forecast errors as largely attributable to the Federal Reserve(cid:146)s lack of credibility following the unstable policies of the 1970s and the early abandonment of the initial monetary tightening of October 1979. 4See thediscussion in Clarida, Gali, andGertler (1999). For example, Fuhrer andMoore(1995) obtained substantial costs of disin(cid:223)ation using an estimated version of the overlapping relative real wage contract speci(cid:222)cation of Buiter and Jewitt (1981), but that speci(cid:222)cation is inconsistent with standardmicro-foundedmodelsofwageandpricedetermination(cf. Roberts1997). Analternative approach is to assume that some private agents have adaptive expectations; cf. Roberts (1998, 2001), Ball (2000), and Ireland (2000). 5Inmodelswithintrinsicin(cid:223)ationpersistence,Bom(cid:222)metal. (1997)andHuhandLansing(2000) (cid:222)nd that the credibility of the central bank has relatively small effects on the costs of disin(cid:223)ation. 2

2.1 The Dynamic Properties of U.S. In(cid:223)ation Figure 1 depicts the postwar evolution of the U.S. GDP price in(cid:223)ation rate (that is, the annualized one-quarter in(cid:223)ation rate of the chain-weighted GDP price de(cid:223)ator). From this (cid:222)gure, it is apparent that in(cid:223)ation exhibited relatively high persistence between the mid-1960s and mid-1980s: annual average in(cid:223)ation rose progressively from 2 percent to around 10 percent in 1980, and then fell to about 4 percent by the end of the Volcker disin(cid:223)ation. Our analysis focuses on explaining the dynamics of in(cid:223)ation during the latter period, while leaving an explanation of the 1965-79 period to future research.6 Interestingly, while U.S. in(cid:223)ation appears to have followed a random walk over roughly the 1965-84 period, the in(cid:223)ation rate exhibits much less persistence prior to 1965andafterabout1984. Theseshiftsinin(cid:223)ationpersistencehavebeendocumented using several different econometric approaches. For example, Taylor (2000) found that the largest autoregressive root of in(cid:223)ation has a 95 percent con(cid:222)dence interval of 0.94, 1.05 for the years 1960-79, compared with a con(cid:222)dence interval of 0.50, { } { 0.86 for the years 1982-99.7 Similar conclusions have been reached by Evans and } Wachtel (1993), who estimated a Markov regime-switching model of in(cid:223)ation, and by Cogley and Sargent (2001), who analyzed a vector autoregression with time-varying parameters. Thus, a high degree of in(cid:223)ation persistence does not seem to be an inherent characteristic of the U.S. economy. As we will see below, our approach is consistent with this evidence, because our model exhibits moderate persistence when monetary policy is transparent and credible, and much higher persistence when agentsmustusesignalextractiontomakeinferencesaboutthecentralbank(cid:146)sin(cid:223)ation target. 2.2 A Brief Chronology of the Volcker Disin(cid:223)ation In October 1979, newly appointed FederalReserve Chairman Paul Volcker announced amajorshiftinpolicyaimedatreducingthein(cid:223)ationrate. Volckerdesiredthispolicy change to be interpreted as a decisive break from past policies that had permitted in(cid:223)ation to rise to double-digit levels. As shown in Figure 2, the federal funds rate increased about 6 percentage points between October 1979 and April 1980, an unprecedented rise over such a short period. The contractionary effect of high real interestrateswasreinforcedbytheimplementionofextensivecreditcontrolsinMarch 1980. In response, GDP contracted at an annual rate of nearly 9 percent in 1980:2, the steepest one-quarter decline in the postwar period. Alarmed by the apparent free fall in output, the Federal Reserve quickly lowered interest rates: by mid-1980, short-term nominal and real interest rates fell slightly below their values prior to the October 1979 tightening. 6See Christiano and Gust (2000), Clarida, Gali, and Gertler (2000), and Orphanides (2000) for alternative views of why in(cid:223)ation rose during the late 1960s and 1970s. 7Even stronger evidence for this result is obtained when one allows for a post-1991 shift in the meanof thein(cid:223)ationprocess; for example, wefoundinthiscasethatthelargestautoregressiveroot of in(cid:223)ation is only 0.55 over the 1983-2000 period. 3

Inlate1980,theFederalReserveembarkedonanewroundofmonetarytightening. The federal funds rate rose to 20 percent by early 1981, implying an ex post real interest rate of about 10 percent. Real interest rates were maintained near this extraordinarily high level until mid-1982. Volcker(cid:146)s aggressive anti-in(cid:223)ation policy succeededinreducingthein(cid:223)ationratefroma10percentpeakinlate1980toaround4 percent by mid-1983, albeit atthecostof themost severecontractioninpost-warU.S. history. Figure 3 shows the evolution of the output gap as measured by the OECD. Based on this measure of the output gap, the Volcker disin(cid:223)ation was associated with a sacri(cid:222)ce ratio of 1.7 percent.8 2.3 In(cid:223)ation Forecast Errors and Credibility Figure 4 shows the four-quarter average in(cid:223)ation rate of the GDP price de(cid:223)ator and its expected value four quarters ahead (as measured by the median projection of the Survey of Professional Forecasters). The behavior of actual in(cid:223)ation and expected in(cid:223)ation seem consistent with the hypothesis that the Federal Reserve faced severe credibility problems in its efforts to reduce in(cid:223)ation. Despite the transient policy tightening that began in October 1979, both actual and expected in(cid:223)ation continued to rise over the next nine months. After renewed Federal Reserve tightening in late 1980, survey-based measures of expected in(cid:223)ation (cid:222)nally began to fall, suggesting somewhat greater con(cid:222)dence in the Fed(cid:146)s commitment to this policy stance. Nevertheless, realized in(cid:223)ation fell much more rapidly than was predicted, implying large and persistent in(cid:223)ation forecast errors (also shown in Figure 4).9 From 1981 to 1985, these forecast errors averaged over 1.5 percentage points. Figure 5 shows two measures of long-term expected in(cid:223)ation (the Barclay survey of in(cid:223)ation expectations 5-10 years ahead, and the Philadelphia Federal Reserve survey of the expected 10year average in(cid:223)ation rate). Both of these surveys indicate that long-term in(cid:223)ation expectations adjusted even more slowly.10 Inlight of these data, it appears that individuals did revise their in(cid:223)ation expectations in response to shifts in monetary policy, rather than simply adapting to current and lagged in(cid:223)ation rates. In particular, expected in(cid:223)ation began to decline in late 1980, whereas actual in(cid:223)ation did not begin to decline until early 1981. In fact, ex- 8The sacri(cid:222)ce ratio is estimated by dividing the cumulative undiscounted sum of the annualized outputgapbetween1980:H2and1984:H2bythechangeinthein(cid:223)ationrateoftheGDPde(cid:223)atorover thesameperiod. Forthiscalculation,weusetheoutputgapseriestakenfromtheOECD Economic Outlook. Ourestimateisclosetothevalueof1.8obtainedbyBall(1994b). Nevertheless,itshould be recognized that estimated sacri(cid:222)ce ratios are somewhat sensitive to the speci(cid:222)c measure of the output gap. For example, Sachs (1985), Blinder (1987), and Mankiw (1991) obtained somewhat higher estimates of the sacri(cid:222)ce ratio for the Volcker disin(cid:223)ation. 9The in(cid:223)ation forecast error in any quarter t is measured as the difference between expected in(cid:223)ation in period t and the realized in(cid:223)ation rate over the forecast period. Thus, the in(cid:223)ation forecast error shown in 1980:4 re(cid:223)ects the error in predicting the year-over-year in(cid:223)ation rate in 1981:4. 10Goodfriend (1993) draws attention to the slow convergence of long-term nominal interest rates. He interprets the temporary spike in nominal interest rates in 1983 as re(cid:223)ecting a continued lack of faithonthepartofmarketparticipantsintheFederalReserve(cid:146)swillingnesstomaintainatighthold on in(cid:223)ation. 4

pected in(cid:223)ation remained below the current in(cid:223)ation rate throughout the subsequent year. Furthermore,weinterpretthepersistentpositiveforecasterrorsre(cid:223)ectingsubstantial doubts about whether the Federal Reserve would continue to pursue a disin(cid:223)ationary policy. As Goodfriend (1993) has emphasized, such doubts were reasonably well-founded, given that the Federal Reserve had shown a high degree of tolerance for rising in(cid:223)ation in the 1970s and had aborted the monetary tightening that began in October 1979. A second capitulation became increasingly plausible as the severity of the 1982 recession became more apparent and generated mounting Congressional pressure. The forecasting problem was compounded by the fact that the Federal Reserve did not announce a target path or band for the in(cid:223)ation rate; indeed, as the disin(cid:223)ation progressed, it became increasing difficult to assess how far Volcker intended to push down the in(cid:223)ation rate. Thus, persistent forecast errors seem consistent with rational expectations subject to limited information, and do not necessarily re(cid:223)ect non-rational expectations. 2.4 Evidence from Other Countries Although our analysis is primarily devoted to matching the behavior of the U.S. economy during the Volcker disin(cid:223)ation, it is interesting to note that similar patterns appear to be characteristic of the roughly contemporaneous disin(cid:223)ation episodes in the United Kingdom and Canada. As seen in Figure 6, the United Kingdom(cid:146)s shift towards an aggressive in(cid:223)ation-reduction strategy in 1981 succeeded in reducing the in(cid:223)ation rate from a peak of 20 percent in mid-1980 to around 5 percent by mid- 1983.11 Similarly, as shown in Figure 7, Canada(cid:146)s adoption of tighter policies in 1981 contributed to a fall in its in(cid:223)ation rate from double digit levels to around 3-4 percent by late-1983.12 As in the Volcker disin(cid:223)ation, both the U.K. and Canadian disin(cid:223)ations were associated with large and highly persistent in(cid:223)ation forecast errors. Moreover, the estimated sacri(cid:222)ce ratio for each country (1.4 for the United Kingdom and 1.3 for Canada) appear very similar to the estimate of 1.7 for the Volcker disin(cid:223)ation. 3 The Model As in Erceg (1997), we assume that labor and product markets each exhibit monopolistic competition, that wages and prices are determined by staggered four-quarter nominal contracts, and that the capital stock is endogenously determined subject to 11See Sargent (1986) for discussion of the initial stages of the Thatcher disin(cid:223)ation. 12Thein(cid:223)ationratefortheUnitedKingdomisthefourquarter-changeintheGDPpricede(cid:223)ator, whilethein(cid:223)ationrateforCanadaisthefourquarter-changeintheGNPpricede(cid:223)ator. Thedataon expectedin(cid:223)ationaresemiannual,andtakenfromsuccessiveissuesoftheOECDEconomic Outlook. The in(cid:223)ation forecast reported in the (cid:222)rst half of each year is taken from the December survey of the previous year, and represents the in(cid:223)ation rate expected to prevail over the subsequent four quarters; the in(cid:223)ation forecast reported in the second half of each year is taken from the mid-year survey (typically published in June or July). 5

quadratic adjustment costs.13 The central bank is assumed to react to the deviation of the output price in(cid:223)ation rate from its target value, and to the growth rate of real output. The key assumption in our analysis is that the central bank(cid:146)s long-run in(cid:223)ation target cannot be directly observed by private agents. 3.1 Firms and Price Setting Final Goods Production AsinChari, Kehoe, andMcGratten(2000), weassumethat households use a single (cid:222)nal output good Y either for consumption or investment. t AcontinuumofdifferentiatedintermediategoodsY (f)(f [0,1])istransformedinto t ∈ the(cid:222)naloutput goodusinga constant returns-to-scale technology oftheDixit-Stiglitz form: 1 1+θp 1 Y t = Y t (f)1+θp df (1) •Z0 ‚ where θ > 0. p Firmsthatproducethe(cid:222)naloutputgoodareperfectlycompetitiveinbothproduct and factor markets. Thus, (cid:222)nal goods producers minimize the cost of producing a given quantity of the output index Y , taking as given the price P (f) of each t t intermediate good Y (f). Moreover, the (cid:222)nal output good is sold at a price P that t t equals the marginal cost of production: 1 θp 1 − P t = P t (f)−θp df (2) •Z0 ‚ It is natural to interpret P as the aggregate price index. t Intermediate Goods Production Each intermediate good Y (f) is produced by a t single monopolistically competitive (cid:222)rm. This (cid:222)rm faces a demand function that varies inversely with its output price P (f) and directly with aggregate demand Y : t t (1+θp) P t (f) − θp Y (f) = Y (3) t t P t • ‚ EachintermediategoodsproducerutilizescapitalservicesK (f)andalaborindex t L (f) (de(cid:222)ned below) to produce its respective output good. The form of the t production function is Cobb-Douglas, with the level of total factor productivity X t identical across (cid:222)rms: Y (f) = X K (f)αL (f)1 α (4) t t t t − Firms face perfectly competitive factor markets for hiring capital and the labor index. Thus, each (cid:222)rm chooses K (f) and L (f), taking as given both the rental price of t t capital R and the aggregate wage index W (de(cid:222)ned below). Firms can costlessly Kt t adjust either factor of production. Thus, the standard static (cid:222)rst-order conditions 13Undertheseassumptions,atransitorymoneygrowthshockhaspersistenteffectsonoutputand the aggregate price level, but not on the in(cid:223)ation rate; cf. Chari, Kehoe, and McGratten (2000), Erceg (1997), and Edge (2000). 6

for cost minimization imply that all (cid:222)rms have identical marginal cost per unit of output. By implication, aggregate marginal cost MC can be expressed as a function t of the wage index W , the aggregate labor index L , the aggregate capital stock K , t t t and total factor productivity X , or equivalently, as the ratio of the wage index to t the marginal product of labor MPL : t W Lα W MC = t t = t (5) t (1 α)KαX MPL t t t − MPL = (1 α)KαL αX (6) t − t −t t We assume that the prices of the intermediate goods are determined by staggered nominal contracts of (cid:222)xed duration. For concreteness, we assume that each price contract lasts four quarters, and that one-fourth of the (cid:222)rms reset their prices in a given period. Thus, individual producers may be indexed so that every (cid:222)rm with index f [0,0.25] resets its contract price P (f) whenever the date t is evenly t ∈ divisible by 4; similarly, (cid:222)rms with index f [0.25,0.5] set prices during periods in ∈ which mod(t,4) = 1, and so forth. For a (cid:222)rm which resets its price during period t, P (f) = P (f) forj = 1,2,3. The(cid:222)rmchoosesthevalueofP (f) whichmaximizes t+j t t the (cid:222)rm(cid:146)s discounted pro(cid:222)ts over the life of the price contract, subject to its product demand curve (3): 3 Et ψ t,t+j ((1+τ p )P t (f)Y t+j (f) MC t+j Y t+j (f)) (7) − j=0 X e TheoperatorEt represents the conditional expectation based on all informationavailable to private agents at period t.14 Note that the tilde above the expectations operator is meeant to indicate that private agents do not have complete information about the central bank(cid:146)s policy rule. The (cid:222)rm(cid:146)s output is subsidized at a (cid:222)xed rate τ . The (cid:222)rm discounts pro(cid:222)ts received at date t+j by the discount factor ψ .15 p t,t+j The (cid:222)rst-order condition for a price-setting (cid:222)rm is 3 (1+τ ) p Et ψ t,t+j (1+θ ) P t (f) − MC t+j Y t+j (f) = 0. (8) p j=0 (cid:181) ¶ X e Roughly speaking, the (cid:222)rm sets its contract price so that its expected discounted nominal marginal revenue (inclusive of subsidies) is equal to its discounted nominal marginal cost. We assume that production is subsidized to eliminate the monopolistic distortion associated with a positive markup; that is, τ = θ . p p 14For simplicity, the variables in equation (7) are not explicitly indexed by the state of nature. 15The state-contingent discount factor ψ indicates the price in period t of a claim that pays t,t+j onedollar in a given stateof nature in periodt+j, divided by the probability that state will occur. 7

3.2 Households and Wage Setting We assume a continuum of monopolistically competitive households (indexed on the unit interval), each of which supplies a differentiated labor service to the production sector; that is, goods-producing (cid:222)rms regard each household(cid:146)s labor services N (h), h [0,1], as an imperfect substitute for the labor services of other households. t ∈ It is convenient to assume that a representative labor aggregator (or (cid:147)employment agency(cid:148)) combines households(cid:146) labor hours in the same proportions as (cid:222)rms would choose. Thus, the aggregator(cid:146)s demand for each household(cid:146)s labor is equal to the sum of (cid:222)rms(cid:146) demands. The labor index L has the Dixit-Stiglitz form: t 1 1+θw 1 L t = N t (h)1+θw dh (9) •Z0 ‚ where θ > 0. The aggregator minimizes the cost of producing a given amount of w the aggregate labor index, taking each household(cid:146)s wage rate W (h) as given, and t then sells units of the labor index to the production sector at their unit cost W : t 1 θw 1 − W t = W t (h)θ−w dh (10) •Z0 ‚ ItisnaturaltointerpretW astheaggregatewageindex. Theaggregator(cid:146)sdemandfor t the labor hoursof householdh (cid:151) or equivalently, the totaldemand for this household(cid:146)s labor by all goods-producing (cid:222)rms (cid:151) is given by 1+θw W t (h) − θw N (h) = L (11) t t W t • ‚ The utility functional of household h is Et ∞ βj 1 (C t (h))1 − σ + 1 (1 N t (h))1 − χ + (cid:181) 0 M t+j (h) 1 − (cid:181) (12) {1 σ 1 χ − 1 (cid:181) P } t+j j=0 − − − (cid:181) ¶ X e where the discount factor β satis(cid:222)es 0 < β < 1. The period utility function depends on consumption C (h), leisure 1 N (h), and real money balances. Mt(h) . t − t Pt Household h(cid:146)s budget constraint in period t states that its expenditure on goods and net purchases of (cid:222)nancial assets must equal its disposable income: P C (h)+P I (h) t t t t M (h) M (h)+ δ B (h) B (h) t+1 t t+1,t t+1 t − − (13) R = T (h)+(1+τ )W (h)N (h)+Γ (h)+ t w t t t R K (h) 0.5φ P K (h)(It(h) δ)2 Kt t − K t t Kt(h) − The household purchases the (cid:222)nal output good (at a price of P ), which it chooses t either to consume C (h) or invest I (h) in physical capital. Investment in physical t t 8

capital augments the household(cid:146)s (end-of-period) capital stock K (h) according to t+1 a linear transition law of the form: K (h) = (1 δ)K (h)+I (14) t+1 t t − Financial asset accumulation consists of increases in money holdings and the net acquisition of state-contingent claims. Each element of δ represents the current t+1,t priceofanassetthatwillpayoneunitofcurrencyifaparticularstateofnatureoccurs in the subsequent period, while the corresponding element of B (h) represents the t+1 quantity of such claims purchased by the household. B (h) indicates the value of t the household(cid:146)s claims given the current realization of the state of nature. Household h(cid:146)s disposable income consists of a lump-sum government transfer T (h), labor income of (1+τ )W (h)N (h), and capital income net of adjustment t w t t costs. Pre-tax labor income W (h)N (h) is subsidized at a (cid:222)xed rate τ .16 Each t t w household receives an aliquot share of the pro(cid:222)ts of all (cid:222)rms Γ (h), and gross rental t income of R K (h) from renting its capital stock to (cid:222)rms. Households incur a cost Kt t of adjusting their net stock of physical capital. Adjustment costs are assumed to depend on the square of the deviation of the investment-to-capital ratio from its steady state level level of δ (or equivalently, on the square of the net change in the capital stock). In every period t, each household maximizes the utility functional (12) with respect to its consumption, investment, (end-of-period) capital stock, money balances, and holdings of contingent claims, subject to its labor demand function (11) its budget constraint (13), and the transition equation for capital (14). The (cid:222)rst-order conditions for consumption and for holdings of state-contingent claims imply the familiar consumption Euler equation linking the marginal cost of foregoing a unit of consumption in the current period (Λ = C σ) to the expected discounted marginal t t− bene(cid:222)t: P t Et Λ t = Et [β(1+R t )Λ t+1 ] = Et β(1+I t ) Λ t+1 (15) P t+1 • ‚ where the risk-freee realeinterest rate R t is theerate of return on an asset that pays one unit of the output index under every state of nature at time t+1, and the nominal interest rate I is the rate of return on an asset that pays one unit of currency under t every state of nature at time t+1. Our assumption of complete contingent claims markets for consumption implies that consumption is identical across households in every period (C (h) = C ), and hence that all households have the same marginal t t value of a unit of the output index. This enables us to omit household-speci(cid:222)c subscripts. The household(cid:146)s Euler condition for investment implies a linear contemporaneous relation between Tobin(cid:146)s q and the investment to capital ratio of the form: I t q = 1-φ δ +φ (16) t K KK t 16The government(cid:146)s budget is balanced every period, so that total lump-sum transfers are equal to seignorage revenue less output and labor subsidies. 9

Here q is the current value to the household of a unit of capital that becomes product tiveinthefollowingperiod(measuredinunitsofthe(cid:222)naloutputgood). Substituting this relation into the Euler equation for capital yields: R t +δ = Et R P K t+ t+ 1 1 − (1+R t )φ K Et Kt+ K 1 − t Kt + ‡ · (17) e e 2 φ K Et Kt+ K 2 − t+ K 1 t+1 + 1 2 φ K Et Kt+ K 2 − t+ K 1 t+1 ‡ · ‡ · Intheabsenceofadjustmentcosts,thehouseholdwouldsimplyaccumulatecapital e e until the expected real rental return equaled the marginal cost, including foregone interest and depreciation. Adjustment costs drive a wedge between the expected rental return and marginal cost that increases in the level of net investment. Households set nominal wages in staggered contracts that are analogous to the price contracts described above. In particular, we assume that wage contracts last four periods, and that the households are divided into four cohorts of equal size. In each period, the households in one cohort renegotiate their wage contracts, while the nominal wages of all other households remain unchanged. Thus, for a household whichresetsitscontractwageW (h)duringperiodt,W (h) = W (h) forj = 1,2,3. t t+j t The household chooses the value of W (h) to maximize its utility functional (12), t yielding the following (cid:222)rst-order condition: 3 (1+τ )Λ Et βj w t+j W t (h) (1 N t (h)) − χ N t+j (h) = 0 (18) (1+θ )P − − w t+j j=0 (cid:181) ¶ X e The discount factor βjΛt+j represents the current marginal utility of an additional Pt+j dollar received j periods in the future. Roughly speaking, equation (18) says that the household chooses its contract wage to equate the present discounted value of working an additional unit of time to the discounted marginal cost. We assume that employment is subsidized to eliminate the monopolistic distortion associated with a positive markup; that is, τ = θ . If contracts last only one period, this w w condition reduces to the familiar equality between the real wage and marginal rate of substitution of consumption for leisure. 3.3 Monetary Policy TheappropriatecharacterizationofFederalReservepolicyduringtheVolkerdisin(cid:223)ation periodremainsasubjectofcontention. However,Goodfriend(1991, 1993)arguespersuasively that it is reasonable to consider the federal funds rate as the best measure of the stance of U.S. monetary policy even during this period.17 Based on this 17From 1979:4 to 1982:3, the Federal Reserve(cid:146)s stated operational target involved the stock of nonborrowedreserves. Nevertheless,asCook(1989)andGoodfriend(1991,1993)haveemphasized, thefederalfundsrateremainedthemaininstrumentofmonetarypolicy,becausetheFederalReserve made numerous discretionary adjustments to in(cid:223)uence the amount of credit extended through the 10

perspective, we assume that the central bank adjusts the short-term nominal interest rate so that the ex post real interest rate rises when in(cid:223)ation exceeds its target value of π , or output growth rises above its trend rate. In addition, as in much of the ∗t subsequent literature, we allow for some degree of nominal interest rate smoothing or policy inertia. In particular, monetary policy is described by the following interest rate reaction function: i = γ i +(1 γ r+π(4) +γ (π(4) π )+γ (ln(y /y ) gfl ) (19) t i t − 1 − i) t π t − ∗t y t t − 4 − y h i where the four-quarter average in(cid:223)ation rate π(4) = 1 3 π , r is the steady-state t 4 j=0 t j − real interest rate, and gfl is the steady-state output growth rate. Note that this y P interest rate reaction function involves the output growth rate and not the level of the output gap; as discussed below, this speci(cid:222)cation is consistent with our empirical analysis of interest rate determination from 1980 through 1985. We assume that the in(cid:223)ation target π varies over time due to a combination of ∗t transitory and highly persistent shocks. Households and (cid:222)rms are assumed to know theformofthecentralbank(cid:146)sreactionfunction, includingtheparametersdetermining the sensitivity of the nominal interest rate to the in(cid:223)ation rate, the output growth rate, andthelaggedinterest rate(thatis, theparametersγ , γ , andγ , respectively). π y i While agents can infer the current value of the in(cid:223)ation target from knowledge of the central bank(cid:146)s reaction function, they cannot directly observe the underlying components of π . Thus, agents must solve a signal extraction problem in order to ∗t forecast the future path of the in(cid:223)ation target, which in turn in(cid:223)uences the outcome of their current decisions (e.g., in setting new wage and price contracts).18 In our baseline speci(cid:222)cation, we formulate the signal extraction problem by assuming that the central bank(cid:146)s in(cid:223)ation target is the sum of a constant steady state rate of in(cid:223)ation π and two zero-mean stochastic components. Equivalently: π π = (π π)+π = Hξ (20) ∗t pt qt t − − where H = [1 1] and ξ = [(π π) π ](cid:146). The time-varying components are t pt qt − determined by the following (cid:222)rst-order vector autoregression: π π ρ 0 π π ε pt+1 − = p pt − + pt+1 π 0 ρ π ε qt+1 q qt qt+1 • ‚ • ‚• ‚ • ‚ (21) or ξ = Fξ +ε t+1 t t+1 discount window. On this basis, prominent monetarists such as Friedman (1983) and Brunner (1983) criticized the Federal Reserve(cid:146)s failure to adopt a strict monetarist approach. 18Our formulation of the information problem is formally similar to that in Brunner, Cukierman, and Meltzer (1980), and in Gertler (1982). The latter showed how imperfect observability of the underlying components of the money supply process could induce (cid:147)inertial(cid:148) behavior in the level of the nominal wage. 11

For simplicity, we assume that the highly persistent component (π π) has an pt − autoregressive root ρ arbitrarily close to unity, while the transitory component π p qt has a much smaller autoregressive root ρ . Thus, while we assume the central bank(cid:146)s q in(cid:223)ation target eventually returns to its steady state value of π, the shock ε drives pt the in(cid:223)ation target away from steady state for a very prolonged period. On the other hand, the shock ε has only a very transient effect on the target. qt Finally, we assume that the in(cid:223)ation target innovations ε and ε are mutually pt qt uncorrelated with variances v and v , respectively, and are not correlated with any 1 2 other shocks to the model economy. Thus, the Kalman (cid:222)lter can be usedto obtain an optimal solution to the signal-extraction problem. In particular, optimal estimates of the unobserved components can be obtained recursively as follows: Et ξ t = FEt − 1 ξ t − 1 +L gain (π ∗t − HFEt − 1 ξ t − 1 ) (22) where the Kalman g e ain matr e ix K gain = FL gain . The t e erm π ∗t − HFEt − 1 ξ t − 1 is the one-step-ahead forecast error in predicting π based on its previous values, while the ∗t e matrix L determines how agents respond to a given forecast error by updating gain their estimates of the underlying components of the in(cid:223)ation target. Finally, given the current estimate Et ξ t of these components, the optimal forecast of the in(cid:223)ation target J periods ahead is given by: e Et π ∗t+J = HFJ Et ξ t (23) e e 4 Solution and Calibration To analyze the behavior of this model, we log-linearize the model(cid:146)s equations around the non-stochastic steady state associated with a constant in(cid:223)ation rate of π (that is, the central bank(cid:146)s steady-state in(cid:223)ation target). Nominal variables, such as the contract price and wage, are rendered stationary by suitable transformations. The log-linearized model consists of four key behavioral equations (the Euler equations for consumption (15), the capital stock (17), price-setting (8), and wage-setting (18)), three equations determining actual monetary policy ((19), (20), and (21)), and two equations determining private sector expectations of the in(cid:223)ation target ((22) and (23)). 4.1 Parameters of Private Sector Behavioral Equations The model is calibrated at a quarterly frequency. Thus, we assume that the discount factor β = .993, consistent with a steady-state annualized real interest rate r of about 3 percent. Theutility functionisassumedtobelogarithmicinconsumption, leisure, and real balances, implying that σ = χ = (cid:181) = 1. The Cobb-Douglas capital share parameter α = 0.3, and the depreciation rate of capital δ = .025 (consistent with an annual depreciation rate of 10 percent). The price and wage markup parameters are 12

both set equal to 1/3, so θ = θ = 1/3. We set the steady state in(cid:223)ation rate π P W equal to an annual rate of four percent. We draw on the empirical q-theory literature to calibrate a baseline value of the capital adjustment cost parameter φ . Recent literature estimating a linear regres- K sion of It on q (cid:151) consistent with equation (16) in our model (cid:151) includes Eberly (1997) Kt t and Cummins, Haskett, and Oliner (1997). Eberly(cid:146)s estimates using U.S. data of the regression coefficient on q range from 0.09 (ordinary least squares) to 0.17 (int strumental variables), implying values of φ of 11.1 and 5.6, respectively. Cummins, K Haskett, and Oliner estimate regression coefficients on q ranging from .08 (ordinary t least squares) to .11 (instrumental variables), implying values of φ of 12.5 and 9, K respectively. We set our baseline value of φ = 6, near the lower bound of the K range of estimates of adjustment costs suggested by this literature. Our choice is in part motivated by the fact that difficulty in measuring Tobins(cid:146)s q is likely to lead to upward bias in estimates of adjustment costs using the standard q-theory approach (as suggested by Shapiro (1986)).19 However, we also conduct sensitivity analysis in the results presented below. 4.2 Monetary Policy Rule Parameters The parameters of the interest rate reaction function (19) are estimated over the 1980:4-1985:4 period by two-stage least squares. In estimating this equation, we assume that the Federal Reserve maintained a constant value of π throughout this pt period; that is, we identify the error term in the estimated monetary policy reaction function as arising solely from variation in π (the transitory component of the in(cid:223)aqt tion target). We use two-stage least squares (with lagged values of in(cid:223)ation, output growth, and the nominal interest rate as instruments) to correct for possible correlation between the error term and the contemporaneous four-quarter in(cid:223)ation rate and output growth rate; in practice, however, OLS and 2SLS give reasonably similar results over the estimation period. We obtain parameter estimates of γ = 0.64, γ = π y 0.25, and γ = 0.21. We also experimented with adding the level of the output gap to i the interest rate reaction function, but found that this variable was not statistically signi(cid:222)cant.20 Figure 8 compares the actual federal funds rate with the (cid:222)tted values implied by these coefficient estimates. Evidently, this simple speci(cid:222)cation performs remarkably well in describing monetary policy during the sample period: the estimated residuals are relatively small compared with the movements in the federal funds rate itself, and these residuals exhibit negligible serial correlation.21 19Our baseline choice of φ = 6 implies that the half-life of the response of the aggregate capital K stock to a one percent permanent rise in the real interest rate (under perfect foresight) is about 14 quarters, assuming that aggregate labor hours are held (cid:222)xed. 20Interestingly,OrphanidesandWieland (1998) estimatedthe interestratereactionfunction over a longer period (1980:1 to 1996:4), and found that the level of output and lag of the level of output entered with a nearly equal but opposite sign. 21The monetary policy reaction function appears quite stable even over short very subsamples of Volker(cid:146)s tenure, at least for estimation periods beginning at or around the period of renewed 13

4.3 Evolution of the In(cid:223)ation Target We set the autoregressive parameter ρ on the highly persistent component of the p in(cid:223)ation target (π π) equal to 0.999, while the autoregressive parameter ρ is set pt q − equal to zero in our baseline. The latter choice is consistent with our empirical (cid:222)nding that the historical innovations in the monetary policy reaction function over the 1980:4-1985:4 period are close to white noise. Under these assumptions, the expected future in(cid:223)ation target Et π ∗t+j (j > 0) dependsonlyonaconstant(π)andtheexpectationofthehighlypersistentcomponent ofthetargetEt (π pt+j ). Inthisspecialcaseofequation(22)withρ q = 0e,thepersistent component of the target evolves according to: e k g Et (π pt − π) = ρ p Et − 1 (π pt − 1 − π)+ ρ (π ∗t − Et − 1 π ∗t ) (24) • p‚ Thus, agentseupdate their asseessment of the persistent comeponent of the in(cid:223)ation target by the product of the forecast error innovation and a constant coefficient. This coefficient, which is proportional to the scalar Kalman gain parameter k , is an g increasing function of the signal-to-noise ratio v1 (the ratio of the variances of the v2 persistent and transitory components of the in(cid:223)ation target). In estimating the signal-to-noise ratio, we utilize the same assumptions described above, namely, that the Federal Reserve maintained a constant value of π after pt 1980:4, so that the path of the transient component π can be computed from the qt residuals in the estimated monetary policy rule. We proceed by minimizing the sum ofsquareddeviationsbetweentheobserveddataonfourquarter-aheadexpectedin(cid:223)ation over the period 1980:4 to 1985:4 (taken from Survey of Professional Forecasters) and the corresponding in(cid:223)ation expectations implied by our model. Our point estimate of v1 implies a value of the Kalman gain of 0.13. Thus, using equation (24), we v2 (cid:222)nd that nearly half of a given change in π is incorporated into agents(cid:146)expectations pt within a year. 5 Results In this section, we analyze the behavior of the calibrated model in response to a shock to the highly persistent component π of the in(cid:223)ation target. In particular, pt we assume that π falls from an initial value of 10 percent to its steady-state level pt of 4 percent (annual rates); this shock is roughly equal to the decline in the GDP price in(cid:223)ation rate during the Volcker disin(cid:223)ation. The shock is assumed to occur in 1980:4. 5.1 The Baseline Calibrated Model Full Information about the In(cid:223)ation Target. The dashed lines in Figure 9 show the impulse response functions (IRFs) of the model when private agents have full infortightening in late 1980. 14

mation about the central bank(cid:146)s in(cid:223)ation target; that is, agents correctly interpret the reduction in the in(cid:223)ation target as a persistent shock and have perfect foresight about the subsequent path of π . In(cid:223)ation falls from 10 percent to 4 percent within a ∗t year, and exhibits very little persistence beyond the length of the four-quarter nominal contracts. The short-term nominal interest rate falls slightly in the initial period (1980:4) and is close to steady state within a couple of quarters. Real output initially declines markedly, but rebounds above baseline shortly thereafter. The initial output contraction occurs because the estimated monetary policy rule implies a sharp jump in the ex ante real interest rate. However, given that in(cid:223)ation expectations are anchored by the new lower target, progress in reducing in(cid:223)ation allows nominal and real interest rates to fall quickly and thereby causes output to rebound. These results are qualitatively similar to those obtained by Ball (1994) and Fuhrer and Moore (1995). Although those authors utilized models with staggered price contracts and (cid:223)exible wages, it is clear that the inclusion of staggered wage contracts in our model does not generate much additional in(cid:223)ation persistence. Furthermore, while the output costs of disin(cid:223)ation depend on the sensitivity of real marginal cost to output and on the form of the monetary policy reaction function, these factors have minimal effect on the duration of a disin(cid:223)ation episode when agents have full information about the shift in the in(cid:223)ation target. Imperfect Observability of the In(cid:223)ation Target. The solid lines in Figure 9 show the IRFs of the baseline version of the calibrated model; that is, the signal-to-noise ratio is set to its estimated value (implying a Kalman gain of 0.13), and hence private agents gradually learn about the persistent shock to the in(cid:223)ation target. It is evident from Figure 9 that the signal extraction problem plays a critical role in accounting for the broad features of the Volcker disin(cid:223)ation episode, namely, sluggish in(cid:223)ation adjustment, a persistently negative output gap, and an initial rise in the nominal interest rate. In(cid:223)ation exhibits much greater persistence in this case: only about half the decline in in(cid:223)ation occurs within a year, and in(cid:223)ation is still only 3/4 of the way toward steady state after two years. Our model(cid:146)s predicted path for in(cid:223)ation in the six quarters following the shock is in fact very close to what was observed in the Volcker disin(cid:223)ation. The slow in(cid:223)ation decline in our model re(cid:223)ects that current in(cid:223)ation is partly anchored by expectations about the future in(cid:223)ation target. In this case, the output gap exhibits a substantial and persistent decline, which contrasts strongly with the results for the case in which private agents have complete informationabout the in(cid:223)ationtarget. In particular, since current in(cid:223)ation decreases slowly, the policy rule requires high ex ante real interest rates over a sustained period. Output is about four percent below potential during the (cid:222)rst year after the disin(cid:223)ation shock, and only recovers gradually as the central bank reduces interest rates in response to falling in(cid:223)ation. Thus, our calibrated model yields a sacri(cid:222)ce ratio of about 1.6 during the (cid:222)ve years after the disin(cid:223)ation shock, a result which is remarkably close to the empirical estimate of 1.7, and broadly in line with the estimates for Canada and the United Kingdom discussed in Section 2.4. Furthermore, the nominal interest rate rises initially by about 300 basis points, an implication that contrasts sharply with the results obtained under full information (for which the nominal interest rate starts falling immediately at the start of the 15

disin(cid:223)ation). Thisdifferenceinnominalinterestratebehaviorresultsfromthegreater sluggishness of in(cid:223)ationandbecause output exhibits asmaller initialcontractionthan under complete information. Finally, while the signal-to-noise parameter is calibrated to (cid:222)t the four quarterahead expected in(cid:223)ation rate, it is interesting to note that our simple speci(cid:222)cation generates comovement of actual and expected in(cid:223)ation that is quite similar to that observed in the Volcker disin(cid:223)ation and in the roughly contemporaneous disin(cid:223)ation in the United Kingdom (cf. Figures 4 and 6, respectively). Expected in(cid:223)ation falls sharply below current in(cid:223)ation at the announcement of the disin(cid:223)ation, but then declines somewhat more slowly thereafter. As emphasized in Section 2, this pattern clearly departs from what one would expect if private agents(cid:146) expectations evolved in a simple adaptive fashion. In the medium term, in(cid:223)ation expectations move quite closely with actual in(cid:223)ation, demonstrating that persistent positive forecast errors are not inconsistent with rational expectations subject to limited information about the central bank(cid:146)s objectives. 5.2 Sensitivity Analysis We now consider sensitivity analysis to assess the features of our model that help it to account for an empirically plausible sacri(cid:222)ce ratio. One crucial feature is endogenous capital accumulation. Figure 10a shows the responses of output, consumption, and investment to the disin(cid:223)ation shock in the baseline calibrated model. Although the baseline investment share of output is only slightly over 20 percent, a sharp drop in investment accounts for nearly half of the output decline at the recession trough in the (cid:222)rst half of 1981. As shown in Figure 10b, the magnitude of the output decline in our model (and hence the sacri(cid:222)ce ratio) is somewhat sensitive to the calibration of the adjustment cost parameterφ . Thesolid line depicts the response under our baseline calibration K (φ = 6). The dotted line depicts the case of extremely high adjustment costs K (φ = 100); in this case, investment does not respond at all, and the output response K is sufficiently damped that the sacri(cid:222)ce ratio is only 0.7 (less than half its baseline value). The dashed line depicts a reasonable upper bound on the magnitude of adjustment costs estimated in the q-theory literature (namely, φ = 12), implying K a half-life of over 5 years for the adjustment of the capital stock to a permanent rise in the real interest rate.22 With these relatively high adjustment costs, the output response is somewhat lower than under the baseline calibration, yielding a sacri(cid:222)ce ratio of only 1.1. Finally, to take account of possible upward bias in the empirical q-theory literature, the dot-dashed line depicts relatively low adjustment costs (φ = 2); in this case, the sacri(cid:222)ce ratio rises to 2.2. K Nominal wage rigidity also raises the magnitude of the output response to the disin(cid:223)ation shock. The dashed line in Figure 10c indicates the output response with four-quarterpricecontractsand(cid:223)exiblewages,whilethesolidlineindicatestheresults 22Giventheprobableupwardbiasofadjustmentcostestimatesintheempiricalq-theoryliterature, it seems very unlikely that the true adjustment cost parameter would be any larger than ϕ=12. 16

for the baseline model (with four-quarter wage and price contracts). With (cid:223)exible wages, the model yields a sacri(cid:222)ce ratio of only 1.0, compared with a sacri(cid:222)ce ratio of 1.6 for the baseline model. Intuitively, nominal wage inertia reduces the sensitivity of real marginal cost to the output gap. Because price in(cid:223)ation depends on current and expected future real marginal costs, price in(cid:223)ation falls less in response to a given output gap as wages become less (cid:223)exible. Thus, inthe context of a disin(cid:223)ation shock, nominal wage inertia implies that the real interest rate rises by a larger amount under the monetary policy rule (because price in(cid:223)ation remains further above target), and hence output declines more sharply relative to the case of completely(cid:223)exible wages. Finally, the output response is somewhat sensitive to the in(cid:223)ation coefficient (γ ) in the interest rate reaction function. To illustrate this sensitivity, we con- π sider variants in which this coefficient is two standard deviations above or below its estimated value. The solid line indicates the response for the baseline calibrated model (γ = 0.64), while the dashed line indicates a more aggressive response to the π in(cid:223)ation rate (γ = 1.05), and the dot-dashed line indicates a less aggressive policy π response (γ = 0.23). The output gap trough occurs at roughly the same date in π all three cases, but the magnitude of the output contraction obviously increases with the aggressiveness of the policy response to deviations of in(cid:223)ation from target. 5.3 In(cid:223)ation Forecast Errors Our model(cid:146)s ability to generate in(cid:223)ation persistence clearly depends on highly autocorrelated expectational errors in forecasting the central bank(cid:146)s in(cid:223)ation target, and correspondingly in forecasting in(cid:223)ation itself. For our interpretation to be empirically plausible, it is essential that the magnitude of the forecast errors implied by our model should not markedly exceed the observed pattern during the Volcker disin(cid:223)ation. In fact, Figure 11 shows that the in(cid:223)ation forecast errors implied by our model tend to be considerably smaller than those implied by the data. The dotted line indicates the forecast errors implied by our model in response to a fall in the persistent component of the in(cid:223)ation target alone, while the dash-dotted line indicates the pattern of forecast errors if the historical monetary policy innovations are also included. In either case, the forecast errors implied by the model are bounded by the historical forecast errors throughout the Volcker disin(cid:223)ation (except in 1980:4, the initial period of the shock). Thus, our model does not require implausibly large forecast errors in order to explain a high degree of in(cid:223)ation persistence. Interestingly, the historical data exhibit a considerably higher degree of persistence in in(cid:223)ation forecast errors compared with those implied by our model. In particular, while our simple speci(cid:222)cation of the in(cid:223)ation target process implies a geometric pattern of convergence in the in(cid:223)ation forecast errors, the observed forecast errors show little tendency to decline, even several years after the initiation of the disin(cid:223)ation. For example, short-run in(cid:223)ation expectations in early 1984 remained in the range of 5 percent, nearly 2 percentage points higher than the realized in(cid:223)ation rate. Moreover, survey data on long-term expected in(cid:223)ation show a considerably more sluggish decline than is implied by our calibrated model. 17

5.4 Output Persistence We have shown that our model can account for a highly persistent downturn in the level of output in response to a disin(cid:223)ation, implying an empirically plausible sacri(cid:222)ce ratio. However, even under imperfect observability, a disin(cid:223)ation has a highly frontloaded effect on the level of output, with the output trough occuring only two to three quarters after the shock. The path of output implied by our model in response to a disin(cid:223)ation shock is shown by the dotted line in Figure 12 (with the dash-dot line showing the model output path when the historical monetary policy innovation is also included). It is clear that the model implies a much more rapid downturn than actually occurred in the Volcker disin(cid:223)ation; in the historicalepisode, output reached atroughonlyinmid-1982,morethanayear-and-a-halflaterthanthemonetarypolicy tightening. The rapid output response re(cid:223)ects that the expenditure components of output in our model show very little persistence in growth rate terms. As we have seen in Figure 10b, increasing the cost of adjusting the capital stock does not delay the timing of the investment trough, but simply dampens the response of investment expenditures. Accounting for persistent effects of shocks on the growth rate of output is a challenge to a broad class of models with optimizing agents, and in our model, greater output persistence would certainly enhance its ability to account for the behavior of other endogenous variables. For example, with a sharp initial downturn in output, the nominal interest rate in our model does not peak as sharply as in the data. Although not shown here, we have found that output persistence is not substantially affected by incorporating habit persistence in consumption into the baseline model. In future research, it will be useful to consider these issues in models with timing lags in investment decisions (cf. Edge (2000b)), which may be somewhat more successful in accounting for the delayed output downturns that seem to have characterized historical disin(cid:223)ation episodes. 6 Comparison with Existing Literature As shown above, our formulation of staggered four-quarter wage and price contracts is useful in accounting for empirically reasonable costs of disin(cid:223)ation. In contrasting ourapproachwiththeexistingliterature,however,itisusefultoconsiderthefollowing stylized representation of the aggregate supply relation: π = βπ(cid:136) +λx (25) t t+1 t where π is the one-quarter annualized in(cid:223)ation rate, x is the deviation of output t t from its (cid:223)exible-price level, and π(cid:136) is the one-step-ahead in(cid:223)ation forecast; in this t+1 speci(cid:222)cation, the parameters satisfy 0 < β 1 and λ > 0. ≤ Equation(25)isimmediatelyrecognizableastheworkhorseNewKeynesianPhillips Curve under the assumption that agents make rational in(cid:223)ation forecasts using all information at time t; that is, π(cid:136) t+1 = Et π t+1 , where we use the operator Et (without 18

a tilde) to indicate that private agents have full information about monetary policy (including the central bank(cid:146)s in(cid:223)ation target). In particular, as shown by Yun (1996) and others, this equation can be derived from microeconomic foundations when prices are determined by Calvo-style contracts and wages are completely (cid:223)exible. This formulation exhibits no intrinsic in(cid:223)ation persistence and implies that disin(cid:223)ations can be conducted without any output costs. One approach to accounting for in(cid:223)ation persistence has been to incorporate lagged in(cid:223)ation terms into equation (25) while maintaining the assumption that agents make rational forecasts (cf. Clarida et al. 1999): π t = θπ t 1 +(1 θ)β Et π t+1 +λx t (26) − − When θ = 1/2 and β = 1, equation (26) can be viewed as representing overlapping e two-period relative real wage contracts (cf. Buiter and Jewitt 1981). As shown by Fuhrer and Moore (1995), this approach can account for very high in(cid:223)ation persistence and substantial costs of disin(cid:223)ation. Nevertheless, rigorous microeconomic foundations for this speci(cid:222)cation have not been provided; furthermore, as pointed out by Roberts (1997), the relative real wage contract speci(cid:222)cation has unpalatable implications for the level of real wages. An alternative approach has been to assume that some agents do not have rational expectations. For example, Roberts (1998) considers a speci(cid:222)cation in which a fraction θ of private agents make one-step-ahead in(cid:223)ation forecasts based on past in(cid:223)ation, while the remaining agents have rational expectations; evidently, this speci- (cid:222)cation can be represented exactly as in equation (26), but with a different structural interpretation than that of Fuhrer and Moore (1995).23 Of course, this approach departsfromtheoptimizing-agentframework,inwhichagentsuseinformationefficiently in making their forecasts. Furthermore, as noted above, survey data on in(cid:223)ation expectations clearly incorporate additional information beyond that containedin lagged in(cid:223)ation data. In contrast, our approach assumes that private agents have rational expectations but must use signal extraction to make inferences about the central bank(cid:146)s in(cid:223)ation target; that is, we assume that π(cid:136) t+1 = Et π t+1 , where Et indicates the rational forecast given all information available to private agents at time t. By de(cid:222)ning u = t β Et π t+1 Et π t+1 , we obtain the folloewing aggregateesupply relation: − ‡ · e π t = βEt π t+1 +λx t +u t (27) Evidently, u 0 in the New Keynesian model described above, whereas u will t t ≡ contribute to in(cid:223)ation persistence in the case where private agents do not have full information about the central bank(cid:146)s in(cid:223)ation target. We can obtain an analytic expression for the behavior of u when aggregate det mand is determined by the New Keynesian IS curve, the central bank follows a simpli(cid:222)ed interest rate reaction function (involving only the current one quarter in(cid:223)ation 23Alternativespeci(cid:222)cationsofadaptiveexpectationshaverecentlybeenanalyzedbyIreland(2000) and Ball (2000). 19

rate and the current output gap), and the in(cid:223)ation target π is the sum of a random ∗t walk component π and a white noise component π .24 In this case, we (cid:222)nd that u pt qt t follows the process u = (1 κ )u +(1 κ )φε (28) t g t 1 g pt − − − where φ < 0, κ g is the Kalman gain coefficient in the updating equation (24) for Et π pt that applies when ρ = 1, and recalling that ε is the innovation in the persistent p pt component of the in(cid:223)ation target. In the case of full information about the in(cid:223)aetion target, the Kalman gain κ = 1, and hence u = 0 as in the New Keynesian model; g t in this case, in(cid:223)ation exhibits no persistence, and disin(cid:223)ation does not involve any output costs. In contrast, a lower signal-to-noise ratio regarding the in(cid:223)ation target (and hence lower κ ) is associated with higher volatility and persistence of u , and g t this persistence passes through into the actual in(cid:223)ation process. 7 Conclusions In this paper, we have formulated a DGEmodelwith optimizing agents andstaggered nominal contracts, in which private agents use optimal (cid:222)ltering to make inferences about the central bank(cid:146)s in(cid:223)ation target. We have shown that this model accounts quite well for several important features of the Volcker disin(cid:223)ation episode: a pronounced initial rise in the nominal interest rate, a sluggish decline in the in(cid:223)ation rate, a persistently negative output gap, and persistent in(cid:223)ation forecast errors. In this framework, in(cid:223)ation persistence is not an inherent characteristic of the model economy, but rather arises whenever agents must learn about shifts in the monetary policy regime. To avoid a non-linear signal extraction problem, we have assumed that private agents have complete information about the speci(cid:222)cation and coefficients of the monetary policy rule, and that the in(cid:223)ation target itself is the only aspect of monetary policy that is not fully observed. As noted above, however, the appropriate characterization of Federal Reserve policy during the Volcker disin(cid:223)ation period continues to be somewhat contentious even after two decades, and hence was almost certainly not as transparent to market participants at the time. In future research, it would be interesting to allow for time variation in the policy rule coefficients and for a discrete probability of policy reversals.25 More generally, our analysis emphasizes the bene(cid:222)ts of explicitly considering informational constraints faced by private agents as well as by the central bank, and we believe that such an approach may be fruitful in explaining in(cid:223)ation and output persistence in other periods.26 24That is, x t = Et x t+1 − σ 1 i t − Et π t+1 − r t∗ and i t = rfl+π t +γ π (π t − π ∗t )+γ x x t , where x t denotes the output gap. ‡ · 25Fuhrer and Hoeoker (1993) analyezed a structural macroeconometric model in which agents face uncertainty about the coefficients of the monetary policy rule, but not about the in(cid:223)ation target. 26Regarding informational constraints faced by the central bank, Orphanides (2000) has recently emphasized the extent to which large and persistent output gap mismeasurements may account for FederalReservebehaviorduringthe1970s. Foranalysisofoptimaldisin(cid:223)ationarypaths,seeIreland 20

Finally, we have proceeded under the assumption that private agents behave optimally, but have not directly considered the optimization problem of the central bank itself. In future research, it will be useful to give explicit consideration to the incentives and commitment mechanisms of the central bank, and to investigate various approaches for enhancing the credibility and transparency of the monetary policy regime.27 8 References Ball, Laurence. 1994. Credible Disin(cid:223)ation with Staggered Price-Setting. American Economic Review 84, 282-289. Ball, Laurence. 1994b. What Determines the Sacri(cid:222)ce Ratio? In: N.G. Mankiw (ed.), Monetary Policy. University of Chicago Press, Chicago, 155-182. Ball, Laurence. 1995. Disin(cid:223)ation and Imperfect Credibility. Journal of Monetary Economics 35, 5-24. Ball, Laurence. 1995b. Time-Consistent Policy and Persistent Changes in In(cid:223)ation. Journal of Monetary Economics 36, 329-350. Ball, Laurence. 2000. Near-Rationality and In(cid:223)ation in Two Monetary Regimes. National Bureau of Economic Research Working Paper 7988. Bernanke, Ben, Thomas Laubach, Frederic Mishkin, and Adam Posen. 1999. In- (cid:223)ation Targeting: Lessons from the International Experience. Princeton University Press, Princeton, NJ. Blanchard, Olivier andCharlesKahn. 1980.TheSolutionofLinearDifferenceModels under Rational Expectations. Econometrica 48, 1305-1311. Blinder, Alan. 1987. Hard Heads, Soft Hearts: Tough-Minded Economics for a Just Society. Addison Welsey, New York. Bom(cid:222)m, Antulio, Robert Tetlow, Peter von zur Muehlen, and John Williams. 1997. Expectations,Learning,andtheCostsofDisin(cid:223)ation: ExperimentsusingtheFRB/US Model. Finance and Economics Discussion Series no. 1997-42. Washington, D.C.: Board of Governors of the Federal Reserve System. Brunner, Karl. 1987. Has Monetarism Failed? In: Dorn, James and Anna Schwartz (eds.), The Search for Stable Money: Essays on Monetary Reform. University of Chicago Press, Chicago and London, 163-199. Brunner, Karl, Alex Cukierman and Allan Meltzer. 1980. Stag(cid:223)ation, Persistent Unemployment and the Permanence of Economic Shocks. Journal of Monetary Economics 6, 467-92. (1997), Orphanides and Wilcox (1997), and Orphanides et al. (1998). 27For analysis of the time-consistency issue as well as incentive and commitment mechanisms for monetary policy, see Ball (1995b) and Svensson and Woodford (1999). For discussion of practical issues related to credibility and transparency of in(cid:223)ation targeting regimes, see Taylor (1982), McCallum (1995), and Bernanke et al. (1999). 21

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Figure 1. U.S. GDP Price Deflator Inflation Rate 12 10 8 6 4 2 0 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Key U.S. Macroeconomic Indicators under Volker: 1979-1985 Figure 2. Federal Funds Rate Figure 3. Output Gap (OECD) 20 Nominal 4 18 Real (ex post) 16 2 14 12 0 10 -2 8 6 -4 4 -6 2 0 -8 1979 1980 1981 1982 1983 1984 1985 1979 1980 1981 1982 1983 1984 1985 Figure 4: Short-term Expected Inflation Figure 5. Long-term Expected Inflation 12 12 Current Inflation (yr/yr) Current Inflation (yr/yr) Expected Inflation (4 qtr) Barclay 5-10 Yr Ahead 10 10 Forecast Error Ph. Fed 10 Yr Ahead 8 8 6 6 4 4 2 2 0 0 -2 -2 1979 1980 1981 1982 1983 1984 1985 1980 1981 1982 1983 1984 1985

Disinflation Episodes in the United Kingdom and Canada Figure 6. United Kingdom, 1979-85 Figure 7. Canada, 1979-1985 20 20 Current Inflation (yr/yr) Current Inflation (yr/yr) Expected Inflation (4 qtr) Expected Inflation (4 qtr) 15 Forecast Error 15 Forecast Error 10 10 5 5 0 0 -5 -5 1979 1980 1981 1982 1983 1984 1985 1979 1980 1981 1982 1983 1984 1985

Figure 8. Actual and Fitted Federal Funds Rate 20 Actual Fitted Residual 15 10 5 0 -5 1981 1981.5 1982 1982.5 1983 1983.5 1984 1984.5 1985 1985.5

Figure 9. Full Information vs. Imperfect Observability of the Inflation Target Year/Year Inflation Output Gap 12 4 Imperfect Observability Imperfect Observability Full Information Full Information 2 10 0 8 -2 6 -4 4 -6 2 -8 0 -10 1981 1982 1983 1984 1985 1981 1982 1983 1984 1985 Inflation and Expected Inflation Nominal Interest Rate (Imperfect Observability Only) 20 12 Imperfect Observability Current Inflation (yr/yr) 18 Full Information Expected Inflation (4 qtr) 10 16 14 8 12 10 6 8 4 6 4 2 2 0 0 1981 1982 1983 1984 1985 1981 1982 1983 1984 1985

Figure 10. Sensitivity Analysis a. Expenditure Components (Baseline) b. Output: Different Capital Adjustment Costs 4 2 1 2 0 0 -1 -2 -2 -4 Output -3 Consumption Baseline Investment -4 Very High Adj. Costs -6 High Adj. Costs -5 Low Adj. Costs -8 -6 -10 -7 -12 -8 1981 1982 1983 1984 1985 1981 1982 1983 1984 1985 c. Output: Sticky vs. Flex. Wages d. Output: Different Monetary Rule Parameters 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 Baseline -4 -4 Flexible Wages Baseline More Aggressive vs. Inflation -5 -5 Less Aggressive vs. Inflation -6 -6 -7 -7 -8 -8 1981 1982 1983 1984 1985 1981 1982 1983 1984 1985

Comparisons of Model Simulations with Data Figure 11. Inflation Forecast Errors Figure 12. Output Gap 3 2 1 2 0 -1 1 -2 0 -3 Data -4 -1 Model (w/o MP innov) Model (w/MP innov) -5 -6 -2 Data -7 Model (w/o MP innov) Model (w/MP innov) -3 -8 1980.5 1981 1981.5 1982 1982.5 1983 1983.5 1984 1984.5 1980.5 1981 1981.5 1982 1982.5 1983 1983.5 1984 1984.5