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]
THE OPTIMAL DEGREE OF COMMITMENT where r is the level of the nominal interest rate and Er(p,+1)-pr represents the rate of inflation expected by investors, based complete period t information. The serially uncorrelated goods market demand disturbance is ur N(O, 04; u may be viewed as a transitory shift in intertemporal consumption preferences The demand for real money balances is a decreasing function of the nominal interest rate and an increasing function of output where m is the logarithm of the nominal money supply and v is a shift in portfolio preferences between money and bonds U-N(O, 02). To simplify exposition, the disturbances, U, u, and z, are assumed to be independent and serially uncorrelated 3. The social loss function The principal differences between the present paper and I vious rational expectations cum wage contracting analyses of monetary stabilization policy derive from the specification of the social objective function. Because most models embody the nat. ural rate hypothesis, the issue of whether or not the central bank wishes it could lower the average level of employment is com monly ignored. But this potential source of tension is fundamental le conduct of stabilization policy. Indeed, if there does not exist any temptation for the monetary authorities to inflate sys tematically, then there is no reason to consider any regime other than fully discretionary monetary policy. (Note that the central bank's incentives to inflate need not be motivated by employment considerations, but can also arise due to the presence of nominal government debt or short-term rigidities in the tax system. Here we shall assume that some factor such as income taxa tion or unemployment insurance distorts the labor-leisure deci sion and causes the market-determined level of employment n and Gordon [1983a). We shall further assume that a ee barro to lie below the socially optimal level of employment nl(se constant and equal to n -n The social loss function A depends on deviations of employ ment and infation from their optimal(socially desired)levels n19rnodified tion. the main 学此比品 in Kydland and Prescott multiperiod objective fu
THE OPTIMAL DEGREE OF COMMITMENT 1173 where r is the level of the nominal interest rate and E,(p,, 1) - Pt represents the rate of inflation expected by investors, based on complete period t information. The serially uncorrelated goods market demand disturbance is ut - N(0,a2); u may be viewed as a transitory shift in intertemporal consumption preferences. The demand for real money balances is a decreasing function of the nominal interest rate and an increasing function of output: (9) mt - Pt - Xrt + 'PYt + Vt, where m is the logarithm of the nominal money supply and v is a shift in portfolio preferences between money and bonds; v N(O, U). To simplify exposition, the disturbances, v, u, and z, are assumed to be independent and serially uncorrelated. 3. The Social Loss Function The principal differences between the present paper and previous rational expectations cum wage contracting analyses of monetary stabilization policy derive from the specification of the social objective function. Because most models embody the natural rate hypothesis, the issue of whether or not the central bank wishes it could lower the average level of employment is commonly ignored. But this potential source of tension is fundamental to the conduct of stabilization policy. Indeed, if there does not exist any temptation for the monetary authorities to inflate systematically, then there is no reason to consider any regime other than fully discretionary monetary policy. (Note that the central bank's incentives to inflate need not be motivated by employment considerations, but can also arise due to the presence of nominal government debt or short-term rigidities in the tax system.) Here we shall assume that some factor such as income taxation or unemployment insurance distorts the labor-leisure decision and causes the market-determined level of employment nt to lie below the socially optimal level of employment h' (see Barro and Gordon [1983a]). We shall further assume that h' - ni is constant and equal to h - n. The social loss function A depends on deviations of employment and inflation from their optimal (socially desired) levels:5 5. A similar social objective function is employed in Kydland and Prescott [1977] and Barro and Gordon [1983a]. Although the analysis below would have to be modified substantially if the central bank had a multiperiod objective function, the main points would still obtain
1174 QUARTERLY JOURNAL OF ECONOMICS (10) A2=(n-n1)2+X(m1-亓)}, where T,=p,- Pr-1, t is the socially desired trend inflation rate. and x is the relative weight society places on inflation stabili zation versus employment stabilization It is somewhat difficult, in the context of a rational expec- tations model, to argue that the level of the inflation rate has much direct weight in the social loss function b(However, the analysis below does not depend on x being particularly large The costs of inflation include the administrative costs of posting new prices and the costs of adjusting the tax system to be fully neutral with respect to inflation. And, of course, high rates of inflation force agents to economize on their holdings of non-in- terest-bearing money-the so-called shoe leather cost of infa tion. Despite the foregoing considerations, i may be nonzero if through distortions(see Phelps [1973/ erate deadweight costs alternative taxes to seignorage also ger III TIME-CONSISTENT EQUILIBRIUM UNDER FULLY DISCRETIONARY MONETARY POLICY Here, stochastic equilibrium is derived under the assumption that the monetary authorities attempt to minimize the social loss function A, given by equation(10)above Expectations about the future path of the money supply are not exogenously given in this model, but depend endogenously on agents' expectations about the monetary authorities future short run stabilization objectives. Wage setters will not believe prom sed future paths for the money supply that are not time-con sistent. Instead, equilibrium nominal wage increases are set at a sufficiently high level so that, in the absence of disturbances, the central bank will not choose to inflate the money supply beyond the point consistent with wage setters desired real wage At this high level of inflation, the central bank finds that the marginal gain from trying to raise employment above the natural rate is fully offset by the marginal cost of still higher inflation. Note also that no individual group of wage setters has any incentive to change their wage bargain in the time-consistent equilibrium Even though individual wage setters are concerned about infla 6. Unanticipated infl rough its effect on employment. Fischer and M nomic costs of both anticipated and unanticipated inflation
1174 QUARTERLY JOURNAL OF ECONOMICS (10) A, = (n, - t')2 + X(TIrt - where Irt Pt - Pt- 1, r is the socially desired trend inflation rate, and X is the relative weight society places on inflation stabilization versus employment stabilization. It is somewhat difficult, in the context of a rational expectations model, to argue that the level of the inflation rate has much direct weight in the social loss function.6 (However, the analysis below does not depend on X being particularly large.) The costs of inflation include the administrative costs of posting new prices and the costs of adjusting the tax system to be fully neutral with respect to inflation. And, of course, high rates of inflation force agents to economize on their holdings of non-interest-bearing money-the so-called "shoe leather cost of inflation." Despite the foregoing considerations, fr may be nonzero if alternative taxes to seignorage also generate deadweight costs through distortions (see Phelps [1973]). III. TIME-CONSISTENT EQUILIBRIUM UNDER FULLY DISCRETIONARY MONETARY POLICY Here, stochastic equilibrium is derived under the assumption that the monetary authorities attempt to minimize the social loss function A, given by equation (10) above. Expectations about the future path of the money supply are not exogenously given in this model, but depend endogenously on agents' expectations about the monetary authorities' future shortrun stabilization objectives. Wage setters will not believe promised future paths for the money supply that are not time-consistent. Instead, equilibrium nominal wage increases are set at a sufficiently high level so that, in the absence of disturbances, the central bank will not choose to inflate the money supply beyond the point consistent with wage setters' desired real wage. At this high level of inflation, the central bank finds that the marginal gain from trying to raise employment above the natural rate is fully offset by the marginal cost of still higher inflation. Note also, that no individual group of wage setters has any incentive to change their wage bargain in the time-consistent equilibrium. Even though individual wage setters are concerned about infla- 6. Unanticipated inflation enters indirectly into the social loss function (10) through its effect on employment. Fischer and Modigliani [1978] catalog the economic costs of both anticipated and unanticipated inflation
THE OPTIMAL DEGREE OF COMMITMENT 1175 tion, the contract at their firm has only a small impact on the aggregate inflation rate By substituting equation(6)into equation(10), and recalling that n'-n'=n-n, the central bank's objective function under fully discretionary monetary policy may be written as D,=A=[z/n +(p- wP)/a-(n-n)]2 where superscript D stand for fully discretionary regime. "The central bank maximizes social welfare by choosing a level of the money supply consistent with pp, the period t price level that minimizes A: (12) p +X(pt-1+亓) Recall that (the logarithm of) wage setters'target real wage is zero. Thus, wage setters select wp by taking expectations across (12)and setting wP= Et-1(p?): 8 (13)?=E4-1m)=p2-1+亓+(h-n)xQ=p1-1+m By choosing w? according to(13), wage setters assure themselves that the monetary authorities will not systematically drive down the real wage. Thus, as Kydland and Prescott [1977] point out, the time-consistent rate of inflation is too high when n>n We are now prepared to evaluate social welfare under fully discretionary monetary policy. But to facilitate exposition in later sections, we shall first develop a notation for evaluating the ex- pected value of the social welfare function under any arbitrary monetary policy regime"A", AA 7. pl is found by setting aD/ ap,=0. The second-order conditions for a min (81)E1-1(m2+=(n-n)s+1)xa+(s+1)亓+p s≥0. (For simplicity, we treat the monetary authorities' objective function as con trolled it directly, ignoring the fact that the central bank directly controls onl he assumption of saddl stability. (For microec ion in monetary models
THE OPTIMAL DEGREE OF COMMITMENT 1175 tion, the contract at their firm has only a small impact on the aggregate inflation rate. By substituting equation (6) into equation (10), and recalling that h' - n' = h - n, the central bank's objective function under fully discretionary monetary policy may be written as (11) Dt = At = [zWbq + (Pt - )/o- (nf - n + X[Pt - Pt 1 -*], where superscript D stand for "fully discretionary regime." The central bank maximizes social welfare by choosing a level of the money supply consistent with pr, the period t price level that minimizes At:7 (12) pD [t h - n - zt/ -*]/[+(1 2 Recall that (the logarithm of) wage setters' target real wage is zero. Thus, wage setters select u' by taking expectations across (12) and setting e =-Et -ID):8 I (13) O = Et-1(pD) = Pt-i + * + (h - n)/Xot = Pt-i + ir1D. By choosing t according to (13), wage setters assure themselves that the monetary authorities will not systematically drive down the real wage. Thus, as Kydland and Prescott [1977] point out, the time-consistent rate of inflation is too high when h > n. We are now prepared to evaluate social welfare under fully discretionary monetary policy. But to facilitate exposition in later sections, we shall first develop a notation for evaluating the expected value of the social welfare function under any arbitrary monetary policy regime "A", AA: 7. pt is found by setting 8DtlIpt = 0. The second-order conditions for a minimum are met; given the quadratic form of D, the minimum is global. 8. Investors can apply the same algorithm repeatedly to derive a time-consistent path for all future prices: (8.1) Et-1 (pP?8) = (h - n)(s + l)/xo + (s + 1)f* + Pt+ , S _ 0. (For simplicity, we treat the monetary authorities' objective function as constant.) Note that we are treating the price level as if the monetary authorities controlled it directly, ignoring the fact that the central bank directly controls only the money supply. The anticipated future path of the money supply consistent with (8.1) may be found using the macro model of equations (7)-(9), together with the assumption of saddlepath stability. (For macroeconomic justification of the saddlepath assumption in monetary models, see Obstfeld and Rogoff [1983].)
1176 QUARTERLY JOURNAL OF ECONOMICS M=(n-n)2+xI4+P, where l4≡(4-亓)2and ⅣA≡E1-1{+(m-E-1(mA)a2+xmA-E-1(pA (we have made use of the fact that Et-1(p2)=w). The first com ponent of Af is nonstochastic and invariant across monetary re gimes. It represents the deadweight loss due to the labor market distortion. This loss cannot be reduced through monetary policy in a time-consistent rational expectations equilibrium. The sec ond term depends on the difference between the expected rate of inflation and society' s target rate This term is also nonstochastic but does depend on the choice of monetary policy regime. The final term, TA, represents the"stabilization"component of the loss function. It measures how successfully the central bank off- sets disturbances to stabilize employment and inflation around their mean market-determined values of infation under fully discretionary monetary policy m; see equation(13). To de rive r, first multiply both sides of equation(12)by (Er -Et-1). noting that wp=Er-i(p?). This yield (15)[pr-Et-1(p.P= dpp=-zmlax +(1/a)]=p", Note that u and u do not enter the expression for the price pre- diction error that the central bank allows to occur. The central bank offsets the price level effects of aggregate demand shocks to the best of its ability(here perfect, because of the complete in- formation assumption), because offsetting these shocks is con sistent with both employment stabilization and inflation-rate sta bilization. By substituting(15)into(14), and simplifying, one can (16) PD=(2/m2)x(X+(1/a)2)] It should be observed that an individual group of wage setters has little incentive to index positively to the price level under the fully discretionary regime. The monetary authorities fully offset the effects of demand shocks and because infation as well as employment enters the social objective function, they do not allow the price level to move enough to optimally offset the employment effects of aggregate supply shocks Obviously, a first-best solution to the stagflation problem de scribed above would be to remove the labor market distortion If
1176 QUARTERLY JOURNAL OF ECONOMICS (14) It =( - n)2+xHA+FA where HA (A - X)2 and fA Et_1{Lzt/r + (p:4 - Et-1(p:))kx]2 + XAp: - Et-1(pt )]21 (we have made use of the fact that Et i(Pt) = at). The first component of AA is nonstochastic and invariant across monetary regimes. It represents the deadweight loss due to the labor market distortion. This loss cannot be reduced through monetary policy in a time-consistent rational expectations equilibrium. The second term depends on the difference between the expected rate of inflation and society's target rate. This term is also nonstochastic but does depend on the choice of monetary policy regime. The final term, ['A, represents the "stabilization" component of the loss function. It measures how successfully the central bank offsets disturbances to stabilize employment and inflation around their mean market-determined values. We have already solved for the mean level of inflation under fully discretionary monetary policy iP; see equation (13). To derive FD, first multiply both sides of equation (12) by (Et - Et_ 1), noting that e = Et - (p). This yields (15) [Pt - Et-(pt)] d - Zt/,q[OX + (I/a)] pD Zt. Note that u and v do not enter the expression for the price prediction error that the central bank allows to occur. The central bank offsets the price level effects of aggregate demand shocks to the best of its ability (here perfect, because of the complete information assumption), because offsetting these shocks is consistent with both employment stabilization and inflation-rate stabilization. By substituting (15) into (14), and simplifying, one can obtain (16) rD = (or1/12)[x/(x + (1/(x)2)]. It should be observed that an individual group of wage setters has little incentive to index positively to the price level under the fully discretionary regime. The monetary authorities fully offset the effects of demand shocks, and because inflation as well as employment enters the social objective function, they do not allow the price level to move enough to optimally offset the employment effects of aggregate supply shocks. Obviously, a first-best solution to the stagflation problem described above would be to remove the labor market distortion. If
THE OPTIMAL DEGREE OF COMMITMENT this cannot be achieved at low social cost, a second-best solution would be to design a permanent constitutional reform that ab- olutely ruled out systematic inflation, and yet left the central bank scope to respond to disturbances. However, there are some practical drawbacks with constitutionally instituting a state-con tangent money supply rule. To be fully effective, a rule must be set in place in such a way that it is very difficult to change This, in turn, raises the danger that the rule will be difficult to alter after it becomes outmoded. Such problems might well arise be- cause it is very difficult to predict the qualitative nature of the shocks buffeting the economy decades in advance. In the sixties for example, it might have been difficult to anticipate the supply shocks of the seventies. Other factors such as innovations in trans- actions technology, regulatory changes, and the evolution of fi- nancial intermediaries all complicate the problem of designing a permanent monetary rule. (We are not suggesting that these prob- lems are necessarily insurmountable. IV SOCIAL WELFARE UNDER A"CONSERVATIVE CENTRAL BANKER Here we consider an alternative, less drastic, response to the stagflation problem posed above. We demonstrate that society can make itself better off by selecting an agent to head the indepen- dent central bank who is known to place a greater weight or inflation stabilization (relative to unemployment stabilization) than is embodied in the social loss function A. The term of the agent need last only one period, though in a multiperiod setting, reputational considerations will further help ameliorate the cen tral bank's time-consistency problems. However, in choosing among potential candidates, it is never optimal to choose an individual who is known to care"too little"about unemployment, in a sense that will be made precise below Suppose for example, that in period t- 1 society selects an agent to head the central bank in period t. The reputation of this individual is such that it is known that if he is appointed to head he central bank, he will maximize the following objective func tion(henceforth, time t subscripts are omitted where the meaning is obvious) (17)I=(n-n)2+(x+cm-亓)2,x+e>0 9 See Barro and gordon [1983b), for example
THE OPTIMAL DEGREE OF COMMITMENT 1177 this cannot be achieved at low social cost, a second-best solution would be to design a permanent constitutional reform that absolutely ruled out systematic inflation, and yet left the central bank scope to respond to disturbances. However, there are some practical drawbacks with constitutionally instituting a state-contingent money supply rule. To be fully effective, a rule must be set in place in such a way that it is very difficult to change. This, in turn, raises the danger that the rule will be difficult to alter after it becomes outmoded. Such problems might well arise because it is very difficult to predict the qualitative nature of the shocks buffeting the economy decades in advance. In the sixties, for example, it might have been difficult to anticipate the supply shocks of the seventies. Other factors such as innovations in transactions technology, regulatory changes, and the evolution of financial intermediaries all complicate the problem of designing a permanent monetary rule. (We are not suggesting that these problems are necessarily insurmountable.) IV. SOCIAL WELFARE UNDER A "CONSERVATIVE" CENTRAL BANKER Here we consider an alternative, less drastic, response to the stagflation problem posed above. We demonstrate that society can make itself better off by selecting an agent to head the independent central bank who is known to place a greater weight on inflation stabilization (relative to unemployment stabilization) than is embodied in the social loss function A. The term of the agent need last only one period, though in a multiperiod setting, reputational considerations will further help ameliorate the central bank's time-consistency problems.9 However, in choosing among potential candidates, it is never optimal to choose an individual who is known to care "too little" about unemployment, in a sense that will be made precise below. Suppose, for example, that in period t - 1 society selects an agent to head the central bank in period t. The reputation of this individual is such that it is known that if he is appointed to head the central bank, he will maximize the following objective function (henceforth, time t subscripts are omitted where the meaning is obvious): (17) I= (n - h')2 + (X + E) Or _*)2, X + E>. 9. See Barro and Gordon [1983b], for example