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137

"None of these results depend on the use of specific functional forms. With general functional forms, the equilibrium is for expected and actual inflation to rise to the point where the marginal cost of inflation just balances its marginal benefit through higher output. Thus output equals its natural rate and inflation is above the optimal level. The equilibrium if the policymaker can make a binding commitment is still for inflation to equal its optimal level and output to equal its natural rate.

"In fact, the policymaker can do even better by announcing that inflation will equal

- (y* ~ y)/b and then setting = *; this yields = y* and = *.

A corollary of this observation is that low-inflation policy can be dynamically inconsistent not because of an output-inflation tradeoff, but because of government debt. Since government debt is denominated in nominal terms, unanticipated inflation is a lump-sum tax on debt holders. As a result, even if monetary shocks do not have real affects, a policy of setting 77 = 77* is not dynamically consistent as long as the government has nominally denominated debt (Calvo, 1978b).

all that the policymakers discretion does is to increase inflation without affecting output. °

Discussion

The reason that the abihty to choose inflation after expected inflation is determined makes the policymaker worse off is that the policy of announcing that inflation will be *, and then producing that inflation rate after expected inflation is determined, is not dynamically consistent (equivalently, it is not subgame-perfect). If the policymaker announces that mflation will equal * and the public forms its expectations accordingly, the pohcymaker will deviate from the policy once expectations are formed. The publics knowledge that the policymaker would do this causes it to expect inflation greater than *; this expected inflation worsens the menu of choices that the policymaker faces.

To see that it is the knowledge that the policymaker has discretion, rather than just the discretion itself, that is the source of the problem, consider what happens if the public believes the policymaker can commit but he or she in fact has discretion. In this case, the policymaker can announce that inflation will equal *, and thereby cause expected inflation to equal *. But the policymaker can then set inflation according to (9.12). Since (9.12) is the solution to the problem of minimizing the social loss function given expected inflation, this "reneging" on the commitment raises social welfare.

Dynamic inconsistency arises in many other situations. Policymakers choosing how to tax capital may want to encourage capital accumulation by adopting a low tax rate. Once the capital has been accumulated, however, taxing it is nondistortionary; thus it is optimal for policymakers to tax it at high rates. As a result, the low tax rate is not dynamically consistent.To give another example, pohcymakers who want individuals to obey a law may



want to promise tiiat violators will be punished harshly. Once individuals have decided whether to comply, however, there is no benefit to punishing violators. Thus again the optimal pohcy is not dynamically consistent.

9.5 Addressing the Dynamic-Inconsistency Problem

Kydland and Prescotts analysis shows that under fairly mild conditions, discretionary monetary policy gives rise to inefficiently high inflation. This naturaUy raises the question of what can be done to avoid, or at least mitigate, this possibility.

One approach, of course, is to have monetary policy determined by rules rather than discretion. It is important to emphasize, however, that the rules must be binding. Suppose the pohcymaker just announces that he or she is going to determine monetary policy according to some procedure, such as pegging the exchange rate or making the money stock grow at a constant rate. If the pubhc believes this announcement and therefore expects low inflation, the policymaker can raise social welfare by departing from the announced policy and choosing a higher rate of money growth. Thus the pubhc wiU not beheve the announcement. Only if the monetary authority relinquishes the ability to determine the money supply does a rule solve the problem.

There are two problems, however, with using binding rules to overcome the dynamic-mconsistency problem. One is normative, the other positive. The normative problem is that rules cannot account for completely unexpected circumstances. There is no difficulty in constructing a rule that makes money growth respond to normal economic developments (such as changes in unemployment and movements in indexes of leading indicators). But sometimes there are events that could not plausibly have been expected. In the 1980s, for example, the United States experienced a major stock market crash that caused a severe liquidity crisis, a "capital crunch" that may have significantly affected banks lending, and a collapse of the relationships between economic activity and many standard measures of the money stock. It is almost inconceivable that a binding rule would have anticipated all of these possibilities.

The positive problem with binding rules as Ihe solution to the dynamic-inconsistency problem is that we observe low rates of inflation in many situations (such as the United States in the 1950s and in recent years, and Germany over most of the postwar period) where policy is not made according to fixed rules. Thus there must be ways of alleviating the dynamic-inconsistency problem that do not involve bmdmg commitments.

Because of considerations like these, there has been considerable interest in other ways of dealing with dynamic inconsistency. The two



A Model of Reputation

Reputation can be used to address the dynamic-inconsistency problem if policymakers are in olhce for more than one period and the public is unsure of their characteristics. For example, the public may not know pohcymakers preferences between output and inflation or their beliefs about the output-inflation tradeoff, or whether their announcements about future policy are binding. In such situations, policymakers behavior conveys information about their characteristics, and thus affects the publics expectations of inflation in subsequent periods. Since policymakers face a more favorable menu of output-inflation choices when expected inflation is lower, this gives them an incentive to pursue low-inflation policies.

To see this formally, consider the following model, which is based on Backus and DriffiU (1985) and Barro (1986). Policymakers are in office for two periods, and the output-inflation relationship is given by (9.8) each period; thus = - irf). It simplifies the algebra to assume that social welfare is linear rather than quadratic in output, and that * is zero. Thus social welfare in period f is

- 1 7

Wf = ( -y)--a<

(9.14)

= - Trf)- -QTrf.

There are two possible types of policymaker; the public does not know in advance which type it is dealing with. A Type-1 policymaker, which occurs with probability p, shares the pubhcs preferences concerning output and inflation. He or she therefore maximizes

W wi+ I3W2, 0 < jS < 1, (9.15)

Two other possibiUtics are punishment equilibria and incentive contracts. Punishment equilibria (which are often described as models of reputation, but which differ fundamentally from the models considered below) arise in infinite-horizon models. These models typically have multiple equilibria, including ones where inflation stays below the one-time discretionary level (that is, below % Low inflation is sustained by beUefs that if the policymaker were to choose high inflation, the public would "punish" him or her by expecting high inflation in subsequent periods; the punishments are structured so that the expectations of high inflation would in fact be rational if that situation ever arose. See, for example, Barro and Gordon (1983b); Rogoff (1987); and Problems 9.8-9.10. Incentive contracts are arrangements in which the central banker is penalized (either financially or through loss of prestige) for inflation. In simple models, the appropriate choice of penalties produces the optimal policy (Persson and Tabellini, 1993; Walsh, 1995). The empirical relevance of such contracts is not clear, however.

approaches that have received the most attention are reputation and delegation.



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