《宏观经济学 Macroeconomics》课外读物：RULES, DISCRETION AND REPUTATION IN A MODEL OF MONETARY POLICY

NBER WORKING PAPER SERIES RULES, DISCRETION AND REPUTATION IN A MODEL OF MONETARY POLICY Robert J. Barro David B. Gordon Working Paper No·1079 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avent Cambridge MA 02138 1983 Prepared for the conference on "Alternative Monetary Standards," Rochester, N.Y., October 1982. We have benefitted from discussion at the conference and from seminars at Chicago, Northwestern and Iowa. We are particularly grateful for comments from Gary Fethke, Roger Myerson, Jose Scheinkman, and John Taylor. Part of this research is supported by the National Science Foundation. The research reported here is part of the NBER's research program in Economic Fluctuations. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research

NBER WORKING PAPER SERIES RULES, DISCRETION AND REPUTATION IN A MODEL OF MONETARY POLICY Robert J. Barro David B. Gordon Working Paper No. 1079 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge MA 02138 February 1983 Prepared for the conference on "Alternative Monetary Standards," Rochester, N.Y., October 1982. We have benefitted from discussion at the conference and from seminars at Chicago, Northwestern and Iowa. We are particularly grateful for comments from Gary Fethke, Roger Myerson, Jose Scheinkman, and John Taylor. Part of this research is supported by the National Science Foundation. The research reported here is part of the NEER's research program in Economic Fluctuations. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research

NBER Working Paper #1079 February 1983 Rules, Discretion and Reputation in a Model of Monetary Policy Abstract In a discretionary regime the monetary authority can print more money and create more inflation than pcople expect. But, al though these inflation surprises can have some benefits, they cannot arise systematically in equilibrium when people understand the policymaker's incentives and form their expectations accordingly. Because the policymaker has the power to create inflation shocks ex post, the equilibrium growth rates of money and prices turn out to be higher than otherwise. There fore, enforced commitments (rules) for monetary behavior can improve matters. Given: the repeated interaction between the policymaker and the private agents, it is possible that reputational forces can substitute for formal rules Here, we develop an example of a reputational equilibrium where the out comes turn out to be weighted averages of those from discretion and those from the ideal rule. In particular, the rates of inflation and monetary growth look more like those under discretion when the discount rate is h obert j. Barro Economics D University of chi 1126 E. 59th Stree Chicago, Illinois 6063 (312)962-8923 David B. Gordon Economics Department University of Rochester Rochester, N.Y. 1462 (716)275-2627

NBER Working Paper #1079 February 1983 Rules, Discretion and Reputation in a Model of Monetary Policy Abs tract In a discretionary regime the monetary authority can print more money and create more inflation than people expect. But, although these inflation surprises can have some benefits, they cannot arise systematically in equilibrium when people understand the policymakor's incentives and form their expectations accordingly. Because the policymaker has the power to create inflation shocks ex post, the equilibrium growth rates of money and prices turn out to be higher than otherwise. Therefore, enforced commitments (rules) for monetary behavior can improve matters. Given the repeated interaction between the policymaker and the private agents, it is possible that reputational forces can substitute for formal rules. Here, we develop an example of a reputational equilibrium where the out￾comes turn out to be weighted averages of those from discretion and those from the ideal rule. In particular, the rates of inflation and monetary growth look more like those under discretion when the discount rate is high. Robert J. Barro Ecdnomics Department University of Chicago 1126 E. 59th Street Chicago, Illinois 60637 (312) 962-8923 • David B. Gordon Economics Department University of Rochester Rochester, N.Y. 14627 (716) 275-2627

a discretionary regime the monetary authority can print more money and create more inflation than people expect. The benefits from this sur- prise inflation may include expansions of economic activity and reductions n the real value of the government's nominal liabilities. However, because people understand the policymaker's incentives, these types of surprises--and their resulting benefits--cannot arise systematically in equilibrium People ad just their inflationary expectations in order to eliminate a con sistent pattern of surprises. In this case the potential for creating infla- tion shocks, ex post, means that, in equilibrium, the average rates of inflation and monetary growth--and the corresponding costs of inflation- will be higher than otherwise Enforced commitments on monetary behavior, as embodied in monetary or price rules, eliminate the potential for ex post surprises. Therefore, the equilibrium rates of inflation and monetary growth can be 1 tary institutions that all to ones that enforce rules ten monetary rules are in place, the policymaker has the tempt each period to cheat" in order to secure the benefits from inflation shocks B f existing distortions in the economy, these benefits can accrue enerally to private agents, rather than merely to policymaker.)How ever, this tendency to cheat threatens the viability of the rules equilibrium and tends to move the economy toward the inferior equilibrium under dis cretion. Because of the repeated interactions between the policymaker and the private agents, it is possible that reputational forces can support the rule. That is, the potential loss of reputation--or credibility--moti vates the policymaker to abide by the rule. Then, the policymaker foregoes the short-term benefits from inflation shocks in order to secure the ga

In a discretionary regime the monetary authority can print more money and create more inflation than people expect. The benefits from this sur￾prise inflation may include expansions of economic activity and reductions in the real value of the government's nominal liabilities. However, because people understand the policymaker's incentives, these types of surprises--and their resulting benefits- -cannot arise systematically in equilibrium. People adjust their inflationary expectations in order to eliminate a con￾sistent pattern of surprises. In this case the potential for creating infla￾tion shocks, ex post, means that, in equilibrium, the average rates of inflation and monetary growth--and the corresponding costs of inflation-- will be higher than otherwise. Enforced commitments on monetary behavior, as embodied in monetary or price rules, eliminate the potential for ex post surprises. Therefore, the equilibrium rates of inflation and monetary growth can be lowered by shifts from monetary institutions that allow discretion to ones that enforce rules. When monetary rules are in place, the policymaker has the temptation each period to "cheat" in order to secure the benefits from inflation shocks. (Because of existing distortions in the economy, these benefits can accrue generally to private agents, rather than merely to the policymaker.) How￾ever, this tendency to cheat threatens the viability of the rules equilibrium and tends to move the economy toward the inferior equilibrium under dis￾cretion. Because of the repeated interactions between the policymaker and the private agents, it is possible that reputational forces can support the rule. That is, the potential loss of reputation--or credibility--moti￾vates the policymaker to abide by the rule. Then, the policymaker foregoes the short-term benefits from inflation shocks in order to secure the gain

from low average inflation over the long term We extend the positive theory of monetary policy from our previous paper (Barro and Gordon, 1983)to allow for reputational forces. Some mone tary rules, but generally not the ideal one, can be enforced by the policy maker's potential loss of reputation. We find that the resulting equili- brium looks like a weighted average of that under discretion and that under the ideal rule. Specifically, the outcomes are superior to those under discretion--where no commitments are pertinent--but inferior to those under the ideal rule (which cannot be enforced in our model by the potential loss of reputation). The results look more like discretion when the policy maker 's discount rate is high, but more like the ideal rule when the discount rate is low. Otherwise, we generate predictions about the behavior of monetary growth and inflation that resemble those from our previous anal ysis of discretionary policy. Namely, any change that raises the benefits of inflation shocks--such as a supply shock or a war--leads to a higher owth rate of money and prices The Policymaker's objective As in our earlier analysis, we think of the monetary authority 's objective as reflecting the preferences of the "representative" private agent. Ultimately, we express this objective as a function of actual and expected rates of inflation. Specifically, benefits derive from positive inflation shocks (at least over some range), but costs attach to higher rates of inflation

—2— from low average inflation over the long term. We extend the positive theory of monetary policy from our previous paper (Barro and Gordon, 1983) to allow for reputational forces. Some mone￾tary rules, but generally not the ideal one, can be enforced by the policy￾maker's potential loss of reputation. We find that the resulting equili￾brium looks like a weighted average of that under discretion and that under the ideal rule. Specifically, the outcomes are superior to those under discretion--where no commitments are pertinent--but inferior to those under the ideal rule (which cannot be enforced in our model by the potential loss of reputation). The results look more like discretion when the policy￾maker's discount rate is high, but more like the ideal rule when the discount rate is low. Otherwise, we generate predictions about the behavior of monetary growth and inflation that resemble those from our previous anal￾ysis of discretionary policy. Namely, any change that raises the benefits of inflation shocks--such as a supply shock or a war--leads to a higher growth rate of money and prices. The Policymaker's Objective As in our earlier analysis, we think of the monetary authority's objective as reflecting the preferences of the "representative" private agent. Ultimately, we express this objective as a function of actual and expected rates of inflation. Specifically, benefits derive from positive inflation shocks (at least over some range), but costs attach to higher rates of inflation

The Benefits from Surprise Inflation We assume that some benefits arise when the inflation rate for period t t exceeds the anticipated amount,t One source of benefits--discussed in Barro and Gordon (1981)and in an example from Kydland and prescott(1977 p 477)--derives from the expectational Phillips Curve. Here, unanticipate monetary expansions, reflected in positive values for T lead to increases in real economic activity. Equivalently, these nominal shock lower the unemployment rate below the natural rate. By the natural rate, we mean here the value that would be ground out by the private sector in the absence of monetary disturbances. This natural rate can shift over time because of supply shocks, demographic changes, shifts in governmental tax and transfer programs, and so on. The natural rate also need not be optimal In fact, the benefits from surprise inflation arise when the policymaker views the natural rate as excessive. This can occur, for example, if the distortions from income taxation, unemployment compensation, and the like make the average level of privately-chosen work and production too low. Be cause of the externalities from these distortions, the government (andthe private agents) would value stimulative policy actions that lower the unem ployment rate below its natural value Other sources of benefits from surprise inflation involve governmental revenues. Barro (1983) focuses on the proceeds from inflationary finance The expectation of inflation (formed the previous period),T determines people's holdings of real cash, M,-1/Pt-1. Surprise inflation-ic t depreciates the real value of these holdings, which allows the government to issue more new money in real terms,(M -Mt-1/P,, as a replacement. The policymaker values this inflationary finance if alternative methods of

-3- The Benefits from Surprise Inflation We assume that some benefits arise when the inflation rate for period t, exceeds the anticipated amount, n. One source of benefits--discussed in Barro and Gordon (1981) and in an example from Kydland and Prescott (1977, p.477)--derives from the expectational Phillips Curve. Here, unanticipated monetary expansions, reflected in positive values for iTt - lead to increases in real economic activity. Equivalently, these nominal shocks lower the unemployment rate below the natural rate. By the natural rate, we mean here the value that would be ground out by the private sector in the absence of monetary disturbances. This natural rate can shift over time because of supply shocks, demographic changes, shifts in governmental tax and transfer programs, and so on. The natural rate also need not be optimal. In fact, the benefits from surprise inflation arise when the policymaker views the natural rate as excessive, This can occur,' for example, if the distortions from income taxation, unemployment compensation, and the like make the average level of privately-chosen work and production too low. Be￾cause of the externalities from these distortions, the government (and the private agents) would value stimulative policy actions that lower the unem￾ployment rate below its natural value. Other sources of benefits from surprise inflation involve governmental revenues. Barro (1983) focuses on the proceeds from inflationary finance. The expectation of inflation (formed the previous period), 'rr, determines people's holdings of real cash, Mt i/Pt . Surprise inflation, depreciates the real value of these holdings, which allows the government to issue more new money in real terms, (Mt - Mt1)/Pt, as a replacement. The policymaker values this inflationary finance if alternative methods of

raising revenue--such as an income tax--entail distortions. Hence, the benefit from surprise inflation depends again on some existing externality Calvo (1978) discusses the sity of existing distortions in this type of model The revenue incentive for surprise inflation relates to governmental liabilities that are fixed in nominal terms, rather than to money, per se Thus, the same argument applies to nominally-denominated, interest-: public debt. Suppose that people held last period the real amount of gov ernment bonds, B. /P t-1/P+1. These bonds carry the nominal yield, t-1,which is satisfactory given people's inflationary expectations over the pertinent horizon, Surprise inflation, e, depreciates part of the real value of these bonds, which lowers the government's future real expenditures for interest and repayment of principal. In effect, surprise inflation is again a source of revenue to the government. Quantitatively, this channel from public debt is likely to be more significant than the usually discussed mech- anism,which involves revenue from printing high-powered money. For example, the outstanding public debt for the U.s. in 1981 is around $l trillion. Therefore, a surprise inflation of 1 per cent lowers the real value of this debt by about $10 billion. Hence, this channel produces an effective lump amount of revenue of about $10 billion for each extra 1% of surprise inf la tion. By contrast, the entire annual flow of revenue through the Federal Reserve from the creation of high-powered money is about the same magnitude ($8 billion in 1981, $13 billion in 1980) The attractions of generating revenue from surprise inflation are clear if we view the depreciation of real cash or real bonds as an unexpected capital levy. As with a tax on existing capital, surprise inflation provides for a method of raising funds that is essentially non-distorting, ex post

-4- raising revenue--such as an income tax--entail distortions. Hence, the benefit from surprise inflation depends again on some existing externality. Calvo (1978) discusses the necessity of existing distortions in this type of model. The revenue incentive for surprise inflation relates to governmental liabilities that are fixed in nominal terms, rather than to money, E!!. • Thus, the same argument applies to nominally-denominated, interest-bearing public debt. Suppose that people held last period the real amount of gov￾ernment bonds, Bti/Pti. These bonds carry the nominal yield, Rti, which is satisfactory given people's inflationary expectations over the pertinent e e horizon, • Surprise inflation, depreciates part of the real value of these bonds, which lowers the government's future real expenditures for interest and repayment of principal. In effect, surprise inflation is again a source of revenue to the government. Quantitatively, this channel from public debt is likely to be more significant than the usually discussed mech￾anism, which involves revenue from printing high-powered money. For example, the outstanding public debt for the U.S. in 1981 is around $1 trillion.1 Therefore, a surprise inflation of 1 per cent lowers the real value of this debt by about $10 billion. Hence, this channel produces an effective lump amount of revenue of about $10 billion for each extra 1% of surprise infla￾tion. By contrast, the entire annual flow of revenue through the Federal Reserve from the creation of high-powered money is about the same magnitude ($8 billion in 1981, $13 billion in 1980). The attractions of generating revenue from surprise inflation are clear if we view the depreciation of real cash or real bonds as an unexpected capital levy. As with a tax on existing capital, surprise inflation provides for a method of raising funds that is essentially non-distorting, ex post

Once people have built up the capital or held the real cash or real bonds the government can extract revenue without disincentive effects. of course the distortions arise--for capital, money or bonds--when people anticipate ex ante, the possibility of these capital levies, ex post. That's why these forms of raising revenue will not end up being so desirable in a full equilibrium where people form expectations rationally. But, for the moment e just listing the benefits that attach, ex post, to surprise inflation The Costs of inflation The second major element in our model is the cost of inflation, Costs are assumed to rise, and at an increasing rate, with the realized infla tion rate, T. Although people generally regard inflation as very costly, economists have not presented very convincing arguments to explain these costs Further, the present type of cost refers to the actual amount of inflation for the period, rather than to the variance of inflation, which could more easily be seen as costly. Direct costs of changing prices fit reasonably well into the model, although the quantitative role of these costs is doubt ful. In any event the analysis has some interesting conclusions for the case where the actual amount of inflation for each period is not perceived as costly. Then, the model predicts a lot of inflation! The setup of our Exampl Le We focus our discussion on the simplest possible example, which illus- trates the main points about discretion, rules and reputation. Along the way, we indicate how the results generalize beyond this example The policymaker's objective involves a cost for each period, z, which

-5— Once people have built up the capital or held the real cash or real bonds, the government can extract revenue without disincentive effects. Of course, the distortions arise--for capital, money or bonds--when people anticipate, ex ante, the possibility of these capital levies, ex post. That's why these forms of raising revenue will not end up being so desirable in a full equilibrium where people form expectations rationally. But, for the moment, we are just listing the benefits that attach, ex post, to surprise inflation. The Costs of Inflation The second major element in our model is the cost of inflation. Costs are assumed to rise, and at an increasing rate, with the realized infla￾tion rate, ir. Although people generally regard inflation as very costly, economists have not presented very convincing arguments to explain these costs. Further, the present type of cost refers to the actual amount of inflation for the period, rather than to the variance of inflation, which could more easily be seen as costly. Direct costs of changing prices fit reasonably well into the model, although the quantitative role of these costs is doubt￾ful. In any event the analysis has some interesting conclusions for the case where the actual amount of inflation for each period is not perceived as costly. Then, the model predicts a lot of inflationl The Setup of our Example We focus our discussion on the simplest possible example, which illus￾trates the main points about discretion, rules and reputation. Along the way, we indicate how the results generalize beyond this example. The policymaker's objective involves a cost for each period, z, which

1s given by (1) =(a/2)〔T where a. b t The first term, (a/2)(m,), is the cost of inflation. Notice that our use of a quadratic form me ans that these costs rise at an increasing rate with the rate of inflation, t. The second term, b+t -+), is the benefit from inflation shocks. Here, we use a linear form for convenience.e Given that the benefit parameter, b, is positive, an increase in unexpected inflation, Tt -t, reduces costs. We can think of these benefits as reflecting reductions in unemployment or increases in governmental revenue we allow the benefit parameter,bt, to move around over time. For example, a supply shock--which raises the natural rate of unemployment--may increase the value of reducing unemployment through aggressive monetary policy. Alter- natively, a sharp rise in government spending increases the incentives to raise revenue via inflationary finance. In our example, t is distributed randomly with a fixed mean, b, and variance, o 23 (Hence, we neglect serial correlation in the natural unemployment rate, government expenditures, etc. The policymaker's objective at date t entails minimization of the expected present value of costs (2)z=E[z tt where is the discount rate that applies between periods t and t+1. We assume that r+ is generated from a stationary probability distribution (There fore, we again neglect any serial dependence. Also, the discount rate is generated independently of the benefit parameter, bt. For the first period ahead, the distribution of r. implies a distribution for the discount factor

-6- is given by 2 e (1) z = (a/2)(rrt) - bt(Tr — 7rt), where a, bt > 0. The first term, (a/2)(rT)2, is the cost of inflation. Notice that our use of a quadratic form means that these Costs rise at an increasing rate with the rate of inflation, Tr. The second term, bt(lrt - ir), is the benefit from inflation shocks. Here, we use a linear form for convenience.2 Given, that the benefit parameter, bt, is positive, an increase in unexpected inflation, - rr, reduces costs. We can think of these benefits as reflecting reductions in unemployment or increases in governmental revenue. We allow the benefit parameter, bt, to move around over time. For example, a supply shock--which raises the natural rate of unemployment--may increase the value of reducing unemployment through aggressive monetary policy. Alter￾natively, a sharp rise in government spending increases the incentives to raise revenue via inflationary finance. In our example, bt is distributed randomly with a fixed mean, , and variance, a.3 (Hence, we neglect serial correlation in the natural unemployment rate, government expenditures, etc.) The policymaker's objective at date t entails minimization of the expected present value of costs, (2) = E[z + (l+rt+l + r)(l+r+1) Z2 + where r is the discount rate that applies between periods t and t + 1. We assume that r is generated from a stationary probability distribution. (Therefore, we again neglect any serial dependence.) Also, the discount rate is generated independently of the benefit parameter, bt. For the first period ahead, the distribution of r implies a distribution for the discount factor

respectively The policymaker controls a monetary instrument, which enables him to select the rate of inflation, t, in each period. The main points of our analysis do not change materially if we introduce random discrepancies between inflation and changes in the monetary instrument. For example,we could have shifts in velocity or control errors for the money supply. Also, the policymaker has no incentive to randomize choices of inflation in the model e begin with a symmetric case where no one knows the benefit parameter b,, or the discount factor for the next period, q, when they act for period t Hence, the policymaker chooses the inflation rate · without observing either b. or similarly, people form their expectations <t policymaker's choice without knowing these parameters. Later on we modify this informational structure incretionary policy Our previous paper(Barro and Gordon, 1983)discusses discretionary policy in the present context as a non-cooperative game between the policymaker and the private agents. In particular, the po licymaker treats the current inflationary

—7- = l/(].+r). We denote the mean and variance for by and respectively. The policymaker controls a monetary instrument, which enables him to select the rate of inflation, in each period. The main points of our analysis do not change materially if we introduce random discrepancies between inflation and changes in the monetary instrument. For example, we could have shifts in velocity or control errors for the money supply. Also, the policymaker has no incentive to randomize choices of inflation in the model. We begin with a symmetric case where no one knows the benefit parameter, bt, or the discount factor for the next period, when they act for period t. Hence, the policymaker chooses the inflation rate, without observing either b or Similarly, people form their expectations, ir, of the policymaker's choice without knowing these parameters. Later on we modify this informational structure. Discretionary Policy Our previous paper (Barro and Gordon, 1983) discusses discretionary policy in the present context as a non-cooperative game between the policymaker and the private agents. In particular, the policymaker treats the current inflationary

expectation and all future expectations for i>0 as givens when choosing the current inflation rate The ere tore is chosen to minimize the expected cost for the current period, Ez,, while treating me and all future costs as fixed. Since future costs and expectations are independent of the policymaker's current actions, the discount factor does not enter into the results. The solution from minimizin.r here z is given in eq.(), is a (discretion We use carets to denote the solution under discretion ith other cost Inctions, T+ would depend also on T.) Given rational expectations, people predict inflation by solving out the ker 's opt zation problem and forecasting the solution for t as well as possible. In the present case they can calculate exactly the choice of inflation from eq(3)--hence, the expectations are Since inflation shocks are zero in equilibrium--that is,T the cost from eq(1)ends up depending only on T. In particular, the cost 1 =(1/2)(b)/a (discretion) Policy under a Rule Suppose now that the policymaker can commit himself in advance to a rule for determining inflation. This rule can relate to variables that the policymaker knows at date t. In the present case no one knows the parameters, b. and t date t. But, everyone knows all previ of these parameters. There fore, the policymaker can condition the infla- tion rate, t+, only on variables that are known also to the private agent (The policymaker could randomize his choices, but he turns out not to have

-8— expectation, Tr, and all future expectations, ir. for i > 0, as givens when choosing the current inflation rate, Therefore, is chosen to minimize the expected cost for the current period, Ezt, while treating 1T and all future costs as fixed. Since future costs and expectations are independent of the policymaker's current actions, the discount factor does not enter into the results. The solution from minimizing Ez, where z is given in eq. (1), is (3) = /a (discretion) We use carets to denote the solution under discretion. (With other cost functions, ii would depend also on Tr.) Given rational expectations, people predict inflation by solving out the policymaker's optimization problem and forecasting the solution for Trt as well as possible. In the present case they can calculate exactly the choice of inflation from eq.(3)--hence,the expectations are (4) = = Since inflation shocks are zero in equilibrium-that is, the cost from eq. (1) ends up depending only on iT In particular, the cost is A —2 (5) z = (1/2) (b) /a (discretion). Policy under a Rule Suppose now that the policyinaker can conunit himself in advance to a rule for determining inflation. This rule can relate to variables that the policymaker knows at date t. In the present case no one knows the parameters, b and at date t. But, everyone knows all previous values of these parameters. Therefore, the policymaker can condition the infla￾tion rate, only on variables that are known also to the private agents. (The policymaker could randomize his choices, but he turns out not to have