咖 The MIT Press The Optimal Degree of Commitment to an Intermediate Monetary Target Author(s): Kenneth Rogoff Source: The Quarterly Journal of Economics, Vol. 100, No. 4(Nov, 1985), pp. 1169-1189 Published by: The MIT Press StableUrl:http://www.jstor.org/stable/1885679 Accessed:14/07/200910:59 Your use of the jStOR archive indicates your acceptance of jSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jspJstOr'sTermsandConditionsofUseprovidesinpartthatunless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you ay use content in the JSTOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showpublisher?publishercode=Mitpress Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed of such transmission JStOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the holarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor. org The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly Journal of ittp://www.jstor.org
The Optimal Degree of Commitment to an Intermediate Monetary Target Author(s): Kenneth Rogoff Source: The Quarterly Journal of Economics, Vol. 100, No. 4 (Nov., 1985), pp. 1169-1189 Published by: The MIT Press Stable URL: http://www.jstor.org/stable/1885679 Accessed: 14/07/2009 10:59 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=mitpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org. The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly Journal of Economics. http://www.jstor.org
THE OPTIMAL DEGREE OF COMMITMENT TO AN INTERMEDIATE MONETARY TARGET* KENNETH ROGOFF Society can sometimes make itself better off by appointing a central banker who does not share the social objective function, but weight on inflation-rate stabilization relative to stabilization. A t head the central bank te of inflation, it suboptimally raises the variance of em t when supply hocks are large. Using an envelope theorem, we show that a large, but finite, weight on infation. The analysis also provides a new framework for choosing among alternative intermediate monetary targets I INTRODUCTION It is now widely recognized that even if a country has a per- ctly benevolent central bank (one that attempts to maximize the social welfare function), it may suffer from having an inflation rate which is systematically too high. Suppose, for example, that a distortion(such as income taxation)causes the market rate of employment to be suboptimal. Then inflation can arise because wage setters rationally fear that the central bank will try to take advantage of short-term nominal rigidities to raise employment systematically. Only by setting high rates of wage inflation can wage setters discourage the central bank from trying to reduce the real wage below their target level This paper considers some institutional responses to the time- consistency problem described above. In particular, we examine the practice of appointing "conservatives'to head the central bank, or of giving the central bank concrete incentives to achieve an intermediate monetary target. Our analysis of intermediate monetary targeting is quite different from conventional analyses in which the central bank is rigidly constrained to follow a par ticular feedback rule. Indeed, an important conclusion is that it is not generally optimal to legally constrain the central bank to hit its intermediate target(or follow its rule)exactly, or to choose Gordon egsa. Ample, Phelps 1967 Kydland and Prescott 1977, or Barro and b
THE OPTIMAL DEGREE OF COMMITMENT TO AN INTERMEDIATE MONETARY TARGET* KENNETH ROGOFF Society can sometimes make itself better off by appointing a central banker who does not share the social objective function, but instead places "too large" a weight on inflation-rate stabilization relative to employment stabilization. Although having such an agent head the central bank reduces the time-consistent rate of inflation, it suboptimally raises the variance of employment when supply shocks are large. Using an envelope theorem, we show that the ideal agent places a large, but finite, weight on inflation. The analysis also provides a new framework for choosing among alternative intermediate monetary targets. I. INTRODUCTION It is now widely recognized that even if a country has a perfectly benevolent central bank (one that attempts to maximize the social welfare function), it may suffer from having an inflation rate which is systematically too high.' Suppose, for example, that a distortion (such as income taxation) causes the market rate of employment to be suboptimal. Then inflation can arise because wage setters rationally fear that the central bank will try to take advantage of short-term nominal rigidities to raise employment systematically. Only by setting high rates of wage inflation can wage setters discourage the central bank from trying to reduce the real wage below their target level. This paper considers some institutional responses to the timeconsistency problem described above. In particular, we examine the practice of appointing "conservatives" to head the central bank, or of giving the central bank concrete incentives to achieve an intermediate monetary target. Our analysis of intermediate monetary targeting is quite different from conventional analyses in which the central bank is rigidly constrained to follow a particular feedback rule. Indeed, an important conclusion is that it is not generally optimal to legally constrain the central bank to hit its intermediate target (or follow its rule) exactly, or to choose *I am indebted to Matthew Canzoneri, David Folkerts-Landau, Maurice Obstfeld, Michael Parkin, Alessandro Penati, Franco Spinelli, Lawrence Summers, Clifford Wymer, and to three anonymous referees for helpful comments on an earlier draft. 1. See, for example, Phelps [1967], Kydland and Prescott [1977], or Barro and Gordon [1983a,b]. t? 1985 by the President and Fellows of Harvard College. Published by John Wiley & Sons, Inc. The Quarterly Journal of Economics, November 1985 CCC 0033-5533/85/041169-21$04.00
1170 QUARTERLY JOURNAL OF ECONOMICS too"conservative an agent to head the central bank. By appoint ng a conservative or by providing the central bank with incen- tives to hit an intermediate monetary target, it is possible to induce less inflationary wage bargains. But this comes at the cost of distorting the central banks responses to unanticipated dis turbances, especially supply shocks. This is a cost because al though the central bank cannot systematically raise employment (since private agents anticipate its incentives to inflate )monetary olicy can still be used to stabilize inflation and employment around their mean market-determined levels. Thus, rigid tar geting is appropriate only in certain very special cases. It is im- portant to stress that, while"flexible"monetary targeting is pref- erable to either fully discretionary monetary policy or rigid monetary targeting, it is not necessarily the first-best solution to he problem of stagflation in this model. That depends on the source of the underlying labor market distortion which causes the market-determined level of employment to be too low. If this distortion can be removed at low social cost, then it would be possible both to raise employment and to lower inflation. A sec ond-best solution, which does nothing to raise the mean level of employment, would be to legally impose a complete state-contin gent money supply rule. As is discussed in Section IIl, there are a number of problems inherent in designing such a rule. But it is only when the first- and second-best solutions are too costly or unachievable that monetary targeting(or appointing a"conserva- tive"central banker)should be used as a"third-best "solution to the problem of stagflation Section II of the text describes a stochastic rational expec tations macroeconomic model in which, because of wage contract ing, there is a well-defined role for central bank stabilization olicy. Section IlI derives the time-consistent equilibrium under fully discretionary monetary policy Section IV shows how society can make itself better off by appointing as head of the central bank an agent whose dislike for inflation relative to unemploy- ment is known to be stronger than average. Section V reinterprets the formal analysis of Section Iv as a model of inflation-rate targeting, and demonstrates how to extend the framework to en compass nominal GNP targeting, money supply targeting, and nominal interest rate targeting Section Vi discusses comparisons 2. This follows from the assumption that there are nominal wage contracts See, for example, Fischer [1977]
1170 QUARTERLY JOURNAL OF ECONOMICS "too" conservative an agent to head the central bank. By appointing a conservative or by providing the central bank with incentives to hit an intermediate monetary target, it is possible to induce less inflationary wage bargains. But this comes at the cost of distorting the central bank's responses to unanticipated disturbances, especially supply shocks. This is a cost because although the central bank cannot systematically raise employment (since private agents anticipate its incentives to inflate) monetary policy can still be used to stabilize inflation and employment around their mean market-determined levels.2 Thus, rigid targeting is appropriate only in certain very special cases. It is important to stress that, while "flexible" monetary targeting is preferable to either fully discretionary monetary policy or rigid monetary targeting, it is not necessarily the first-best solution to the problem of stagflation in this model. That depends on the source of the underlying labor market distortion which causes the market-determined level of employment to be too low. If this distortion can be removed at low social cost, then it would be possible both to raise employment and to lower inflation. A second-best solution, which does nothing to raise the mean level of employment, would be to legally impose a complete state-contingent money supply rule. As is discussed in Section III, there are a number of problems inherent in designing such a rule. But it is only when the first- and second-best solutions are too costly or unachievable that monetary targeting (or appointing a "conservative" central banker) should be used as a "third-best" solution to the problem of stagflation. Section II of the text describes a stochastic rational expectations macroeconomic model in which, because of wage contracting, there is a well-defined role for central bank stabilization policy. Section III derives the time-consistent equilibrium under fully discretionary monetary policy. Section IV shows how society can make itself better off by appointing as head of the central bank an agent whose dislike for inflation relative to unemployment is known to be stronger than average. Section V reinterprets the formal analysis of Section IV as a model of inflation-rate targeting, and demonstrates how to extend the framework to encompass nominal GNP targeting, money supply targeting, and nominal interest rate targeting. Section VI discusses comparisons 2. This follows from the assumption that there are nominal wage contracts. See, for example, Fischer [19771
THE OPTIMAL DEGREE OF COMMITMENT across regimes. Which target works best depends, of course, on che structure of the economy and the nature of the underlying disturbances. (Though we demonstrate that the interest rate is generally an unsatisfactory tool for precommitment. )In Section VIl, the Conclusions, we stress the envelope-theorem interpre- tation of the main result: society wants the central bank to place too large"a weight on inflation-rate stabilization relative to em loyment stabilization, but the weight should not be infinite II. THE MACROECONOMIC MODEL Here we develop a stochastic rational expectations IS-LM model Monetary policy can have short-term real effects in this model because nominal wage contracts are set a period in advance are not indexed fully against all possible disturbances o Contracts Due to high administrative and negotiation costs, these I Aggregate Supply Each of the large number of identical firms in the has a Cobb-Douglas production function. In the aggregate yr=Co+ ak +(1-a)nt+ zt where y is output, k is the fixed capital stock, n is labor, co is a constant term, and z is an aggregate productivity disturbance z-N(O, 02). Throughout, lowercase letters denote natural loga rithms and subscript t denotes time. All coefficients are nonnega tive. Firms hire labor until the marginal product of labor equals e rea Co log(1-a)+ak-and+a =wr-pr where w is the nominal wage p is the price level, and nd is labor demand Labor supply ns is an upward-sloping function of the real wage ni =n+ o(wr-p) To simplify algebra without loss of generality, n is set equal to k +(1/)log(1-a)+Col. As we shall later discuss, the above abor supply curve (3)is assumed to embody a distortion that The aggregate demat tion is the same as in Canzoneri, he
THE OPTIMAL DEGREE OF COMMITMENT 1171 across regimes. Which target works best depends, of course, on the structure of the economy and the nature of the underlying disturbances. (Though we demonstrate that the interest rate is generally an unsatisfactory tool for precommitment.) In Section VII, the Conclusions, we stress the envelope-theorem interpretation of the main result: society wants the central bank to place "too large" a weight on inflation-rate stabilization relative to employment stabilization, but the weight should not be infinite. II. THE MACROECONOMIC MODEL Here we develop a stochastic rational expectations IS-LM model. Monetary policy can have short-term real effects in this model because nominal wage contracts are set a period in advance. Due to high administrative and negotiation costs, these contracts are not indexed fully against all possible disturbances.3 1. Aggregate Supply Each of the large number of identical firms in the economy has a Cobb-Douglas production function. In the aggregate, (1) yt co + otk + (I - t) n, + zt, where y is output, k is the fixed capital stock, n is labor, co is a constant term, and z is an aggregate productivity disturbance; z - N(O,oz'). Throughout, lowercase letters denote natural logarithms and subscript t denotes time. All coefficients are nonnegative. Firms hire labor until the marginal product of labor equals the real wage: (2) co + log(1 - a) + ak - antd+z =wt-Pt. where w is the nominal wage, p is the price level, and nid is labor demand. Labor supply ns is an upward-sloping function of the real wage: (3) nt n + w(wt- pt. To simplify algebra without loss of generality, _n is set equal to k + (1/o&)[log(l - ox) + co]. As we shall later discuss, the above labor supply curve (3) is assumed to embody a distortion that 3. The aggregate demand specification is the same as in Canzoneri, Henderson, and Rogoff [1983]. The aggregate supply specification is based on Gray [1976]
QUARTERLY JOURNAL OF ECONOMICS raises the real wage required to induce a given level of labo The nominal wage rate for period t is negotiated(on a firm by-firm basis)at the end of period t-1. The nature of the em ployment contract is that laborers agree to supply whatever amount of labor is demanded by firms in period t, provided that firms pay che negotiated wage rate Wr. The level of employment in period t is thus found by substituting W, into equation(2): In choosing Wt, wage setters seek to minimize Et-1(n , -n')2 where Et-1 denotes expectations based on period t-1 informa- tion and ni is the level of employment that would arise if contracts could be negotiated after observing the productivity disturbance zt and all other period t information. n' is found using the labor supply and demand equations(2)and (3 nt= n oz /(1 From equations(4)and (5) where m =o(1 + ao). It is clear from equation (6)that Er-1(n,-ni)2 is minimized by setting W,= Et-1(p ) .4(The pos- sibility of indexing wages to the price level will be discussed later. With equations (1)and(4), together with the analytically convenient normalization that -Co =ak+(1-a)n so that Et-1(yu=0, one can write the aggregate supply equation as yi =(1-a)(p,-Wt)/a+ 2y/ It is very important to note that output and employment stabi lization are not equivalent to price prediction error minimization in the presence of a productivity shock(z) 2. Aggregate Demand Demand for the good that firms produce is a decreasing func tion of the real interest rat y=-8{r-[E(p2+1)-pl the fact that certainty equivalence holds when the loss function is quadratic. . of 4. This is the first of many times ghout the Sargent [1979]
1172 QUARTERLY JOURNAL OF ECONOMICS raises the real wage required to induce a given level of labor supply. The nominal wage rate for period t is negotiated (on a firmby-firm basis) at the end of period t - 1. The nature of the employment contract is that laborers agree to supply whatever amount of labor is demanded by firms in period t, provided that firms pay the negotiated wage rate wt. The level of employment in period t is thus found by substituting wt into equation (2): (4) nt = n + (Pt - wt)/o + ztIa. In choosing Zwt, wage setters seek to minimize Et 1(n, - nt where Et-1 denotes expectations based on period t - 1 information and nH is the level of employment that would arise if contracts could be negotiated after observing the productivity disturbance zt and all other period t information. Hn is found using the labor supply and demand equations (2) and (3): (5) nt= n + wzt/(l + aw). From equations (4) and (5), (6) nt - nt= ztrq + (Pt - wt)aot, where -q a(1 + aw). It is clear from equation (6) that Et-1(nt - nt)2 is minimized by setting wt = Et (pt)i' (The possibility of indexing wages to the price level will be discussed later.) With equations (1) and (4), together with the analytically convenient normalization that - co = otk + (1 - oa) n so that Et i(Yt) = 0, one can write the aggregate supply equation as (7) Yt = (1 - 0&(pt - -wt)/oL + Zt/a, It is very important to note that output and employment stabilization are not equivalent to price prediction error minimization in the presence of a productivity shock (z). 2. Aggregate Demand Demand for the good that firms produce is a decreasing function of the real interest rate: (8) d= - {r - [Et(pt+1) - Pt]} + Ut, 4. This is the first of many times throughout the paper where use is made of the fact that certainty equivalence holds when the loss function is quadratic; see Sargent [1979]