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 government 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 mechanism, 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 inflation. 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 inflation 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 doubtful. 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 illustrates 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. Alternatively, 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 inflation 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