this incentive. Therefore, the policymaker effectively chooses t. and m together, subject to the condition that T. Then, the term that involves the inflation shock. drops out of the cost function in eq(1). Given the way that we modeled the costs of inflation --namely, as (a/2)(.)"it follows immediately that the best rule prescribes zero inflation at all dates (rule) We use an asterisk to denote the results from a rule. Eq (6) amounts to a constant-growth -rate-rule, where the rate of growth happens to be zero Finally, we can calculate the costs under a rule from eq (1)as (rule) The general point is that the costs under the rule, z*, are lower than those under discretion, z. from eq(5). The lower cost reflects the value of being able to make commitments--that is, contractual agreements between the policymaker and the private agents. Without these commitments, infla tion ends up being excessive--specifically, t>0--but, no benefits from higher inflation result Cheating and Temptation As noted by others (e.g. Taylor, 1975; B. Friedman, 1979), the policy maker is tempted to renege on commitments. In particular, if people expect zero inflation--as occurs under the rule--then the policymaker would like to implement a positive inflation rate in order to secure some benefits from an inflation shock. Further, this desire does not stem from a peculiarity in the policymaker's tastes. Rather, it reflects the distortions that make inflation shocks desirable in the first place How much can the policymaker gain in period t by cheating? Assume that
-9- this incentive.) Therefore, the policymaker effectively chooses and together, subject to the condition that ir=ii. Then, the term that involves the inflation shock, drops out of the cost function in eq.(l). Given the way that we modeled the costs of inflation--namely, as (a/2)(rr)2__it follows immediately that the best rule prescribes zero inflation at all dates, (6) 7T = 0 (rule). We use an asterisk to denote the results from a rule. Eq.(6) amounts to a constant-growth-rate-rule, where the rate of growth happens to be zero. Finally, we can calculate the costs under a rule from eq.(l) as (7) z = 0 (rule) The general point is that the costs under the rule, z, are lower than those under discretion, from eq.(5). The lower cost reflects the value of being able to make commitments--that is, contractual agreements between the policymaker and the private agents. Without these commitments, inflationendsup being excessive--specifically, ilt>O__but, no benefits from higher inflation result. Cheating and Temptation As noted by others (e.g. Taylor, 1975; B. Friedman, 1979), the policymaker is tempted to renege on commitments. In particular, if people expect zero inflation--as occurs under the rule--then the policymaker would like to implement a positive inflation rate in order to secure some benefits from an inflation shock. Further, this desire does not stem from a peculiarity in the policymaker's tastes. Rather, it reflects the distortions that make inflation shocks desirable in the first place. How much can the policymaker gain in period t by cheating? Assume that
10 people have the inflationary expectation, T =0, which they formed at the start of period t. If the policymaker treats this expectation as a given the choice of T that minimizes z. is the one that we found before under discretion--namely 8)m,=b/a (cheating) We use tildes to denote values associated with cheating. The expected cost follows from eq(1)as 9 t (cheating The general point is that this expected cost is lower than that, z* from following the rule. We refer to the difference between these expect costs as the temptation to renege on the rule--or simply as the temptation In the present case we have temptation= E(zt-2t)=(1/2)(b)/a>0 At the present stage we have three types of outcomes. Ranging from low costs to high, these are 1) cheating (with people expecting the rule),Ez_=-(1/2)(b)/a, 2) rule,t 3) discretion, z.=(1/2)(b)"/a Discretion is worse than the rule because first, no inflation shocks arise n either case, but second, the commitment under the rule avoids excessive inflation. However, the rule is only a second-best solution. Cheating- when people anticipate the rule--delivers better results. Thatis because he inflation shock eliminates part of the existing distortion in the economy (which is worth the extra inflation). But, the cheating outcome is feasible only when people can be systematically deceived into maintaining low infla tionary expectations. In our subsequent analysis this cannot happen
-10- people have the inflationary expectation, ir = 0, which they formed at the start of period t. If the policyinaker treats this expectation as a given, the choice of that minimizes z is the one that we found before under discretion4--namely, (8) = 6/a (cheating). We use tildes to denote values associated with cheating. The expected cost follows from eq. (1) as (9) Ezt = -(l/2)(E)2/a (cheating). The general point is that this expected cost is lower than that, z = 0, from following the rule. We refer to the difference between these expected costs as the temptation to renege on the rule--or simply as the temptation. In the present case we have (10) temptation = E(z_z) = (l/2)(S)2/a>0. At the present stage we have three types of outcomes. Ranging from low costs to high, these are — —2 1) cheating (with people expecting the rule), Ezt=_(l/2)(b) /a, 2) rule, z = 0, —2 3) discretion, z = (1/2) (b) Ia. Discretion is worse than the rule because first, no inflation shocks arise in either case, but second, the commitment under the rule avoids excessive inflation. However, the rule is only a second-best solution. Cheating-- when people anticipate the rule--delivers better results. That's because the inflation shock eliminates part of the existing distortion in the economy (which is worth the extra inflation). But, the cheating outcome is feasible only when people can be systematically deceived into maintaining low inflationary expectations. In our subsequent analysis this cannot happen