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In this paper, we evaluate the effectiveness of history-dependent monetary policy, focusing on the design of targeting regimes and simple policy rules. Our quantitative analysis is based on a small estimated forward-looking model of the Japanese economy with a hybrid Phillips curve. Our main findings are: (1) History-dependent targeting regimes, such as price level targeting and income growth targeting, outperform inflation targeting; (2) Committing to a simple history-dependent policy rule results in nearly the same social welfare as the optimal delegation of price level targeting and income growth targeting; (3) The central bank can achieve almost the same performance as the optimal commitment policy by adopting the first difference hybrid policy rule in which the change in interest rate responds to inflation, output gap, and real income growth rate. J. Japanese Int. Economies18 (3) (2004) 330–361.

Recent monetary policy studies have emphasized the importance of history dependence in the conduct of monetary policy. Giannoni, 2000 and Woodford, 2000 point out that when private agents are forward-looking, it is optimal for the central bank not only to respond to current shocks and the current state of the economy, but that it is also desirable to respond to lagged variables. Conducting monetary policy of this kind allows the central bank to appropriately affect private sector expectations. This, in turn, improves the performance of monetary policy, because the evolution of the central bank's target variables depends not only on its current actions, but also on how the private sector foresees future monetary policy. Optimal commitment policy is history dependent and most efficient. However, it is generally time-inconsistent and therefore not particularly realistic. A lot of previous literature investigated other ways in which the monetary policy decision-making process might incorporate the sort of history dependence required for the optimal commitment policy. The design of optimal delegation is one way. On the assumption that the central bank will pursue its goal in a discretionary fashion, rather than committing itself to an optimal plan, the optimal goal with which to charge the central bank need not correspond to the true social welfare function. It is desirable that the loss function assigned to the central bank depend on lagged as well as current values of the target variables. In this case, discretionary policy is history dependent because the bank's loss function is history dependent even though the true social loss function is not. Vestin (2000) shows that, within a purely forward-looking Phillips curve, discretionary optimization results in the same equilibrium as the optimal commitment policy, if the central bank is charged with stabilization of the price level rather than the inflation rate. Price level targeting is a history-dependent policy, in the sense that the central bank's loss function depends on the cumulative sum of inflation rates over past periods. Jensen, 1999 and Walsh, 2001 show that discretionary income growth targeting is also desirable, because the central bank's loss function depends on lagged output gap as well as current values of target variables. However, there are several problems with the practical implementation of optimal delegation. Optimal delegation regimes require full information with respect to demand and price shocks for implementation by the central bank. When the central bank cannot accurately observe these shocks, which seems to be a realistic assumption, optimal delegation is not so effective as previous literature suggests. Even if the central bank can completely identify these shocks, the policy reaction function implied by optimal delegation is complicated and not transparent to the public. Instead of implementing optimal delegation, adopting a simple policy rule is another way to incorporate history dependence into monetary policy. Woodford, 1999 and Woodford, 2000 and Giannoni (2000) suggest that central banks can introduce desirable history dependence into monetary policy by adopting a policy rule in which the interest rate reacts to its own lagged value, price level, or income growth (i.e. change in output gap). Giannoni (2000) then shows that such a simple history-dependent policy rule performs better than the Taylor rule and results in lower welfare loss. Because simple policy rules involve no explicit dependence on demand and price shocks, and so do not even require that the central bank know these shocks, conducting monetary policy with emphasis on simple rules seems to be a practical and transparent scheme. Still, there remain several problems with respect to history-dependent policy, which previous literature has not solved. First, the effectiveness of history-dependent policy critically depends on the forward-looking behavior of private agents. Giannoni, 2000 and Vestin, 2000 investigate history-dependent policy with a purely forward-looking New Keynesian Phillips curve. However, the New Keynesian Phillips curve has been criticized for failing to match the short-run dynamics exhibited by inflation (see, for example, Mankiw, 2001). Specifically, inflation seems to respond sluggishly and display significant persistence in the face of price shocks, while the New Keynesian Phillips curve allows current inflation to be a jump variable that can respond immediately to any disturbance. Therefore, in order to obtain the practical implication of history-dependent policy, we must use a model with empirically plausible amounts of forward-looking behavior and inflation persistence. Second, previous literature indicates that history-dependent targeting regimes, such as price level targeting and income growth targeting, outperform inflation targeting, but it is not clear which history-dependent targeting regime performs better and to what degree the performance of each targeting regime differs quantitatively. This is because the competing regimes of delegation have been examined separately over different models. Third, previous literature does not clarify which history-dependent policy regime performs better, delegation (targeting regime) or a simple policy rule. Although a policy regime based on a simple rule is transparent to the public, if it performs worse than optimal delegation, then the policy rule regime is not desirable. On the other hand, if we can show that simple policy rules which involve no explicit dependence on demand and price shocks are as effective as optimal delegation, then it is more desirable than optimal delegation, based on the realistic assumption that the central bank cannot observe these shocks accurately.1 The purpose of this paper is to investigate history-dependent policy and attempt to solve the above unresolved problems in a unified framework. Our quantitative analysis is based on a small estimated forward-looking model of the Japanese economy with a hybrid Phillips curve. This Phillips curve is a modified inflation adjustment equation which incorporates endogenous persistence by including the lagged inflation rate in the New Keynesian Phillips curve. That is, it nests the purely forward-looking Phillips curve as a particular case, and allows for a fraction of firms that use a backward-looking rule to set prices. Using this model, we calculate social welfare losses under the alternative policy regimes, and then compare their performance with that under the optimal commitment policy. Although we do not consider the optimal commitment policy particularly realistic, it will serve as a useful benchmark against which policy under the alternative regimes can be evaluated. Our main findings are summarized as follows. (1) According to the estimation results of the hybrid Phillips curve based on Japan's data, about 60% of firms exhibit forward-looking price setting behavior (i.e. the remaining 40% of firms exhibit backward-looking behavior). Although the purely forward-looking Phillips curve is rejected by the data, such a degree of forward-looking behavior seems to be sufficient to make history-dependent policy effective. (2) Indeed, history-dependent targeting regimes, such as income growth targeting and price level targeting, outperform inflation targeting and result in lower social welfare losses. In addition, the optimal commitment policy can be roughly replicated by delegating either income growth targeting or price level targeting to a conservative central bank, which values price stability more than society does. Price level targeting and income growth targeting perform at almost the same level. (3) Simple history-dependent policy rules, such as a price level targeting rule and income growth targeting rule, perform much better than the Taylor rule in which history dependence is not introduced. Moreover, committing to such a history-dependent rule results in nearly the same social welfare as the optimal delegation of price level targeting and income growth targeting. (4) Among simple history-dependent rules, the most efficient is the first difference hybrid rule in which the change in interest rate responds to inflation, output gap, and real income growth rate. By adopting this rule, the central bank can achieve almost the same performance as the optimal commitment policy. (5) The good performance of the first difference hybrid rule results from partial trend-reverting behavior of the price level. Through the forward-looking expectations of private agents, the trend-reversion of the price level has the immediate effect of stabilizing inflation against price shocks. However, in the hybrid Phillips curve, it is not socially optimal for the central bank to completely bring the price level back to its initial trend path. This is because the central bank must pay the high cost of greater output gap variability to achieve full trend-reversion of the price level when a fraction of firms use a backward-looking rule to set prices. Therefore, partial trend-reversion of the price level with some degree of drift is desirable in the hybrid Phillips curve. Such partial trend-reverting behavior of the price level can be replicated by the hybrid rule, but not by other history-dependent rules. The outline of the remainder of the paper is as follows. Section 2 presents the model of the economy and poses the problem of optimal commitment and discretion policies. Section 3 presents the estimation results of the model. Then, using the estimated model, we show how endogenous variables respond to shocks and calculate welfare losses under optimal policy. 4 and 5 present quantitative analysis of optimal delegation and simple policy rules, respectively. Finally, Section 6 provides concluding remarks.

This paper has investigated the effectiveness of history-dependent policy in a unified framework based on a hybrid Phillips curve. Overall, our analysis suggests that history dependence deserves serious attention in discussions of practical policy conduct. Our main findings are summarized as follows: (1) History-dependent targeting regimes, such as price level targeting and income growth targeting, outperform inflation targeting and roughly replicate the optimal commitment policy. (2) Committing to a simple history-dependent policy rule results in nearly the same social welfare as the optimal delegation of price level targeting and income growth targeting. (3) The central bank can achieve almost the same performance as the optimal commitment policy by adopting the first difference hybrid policy rule. The result that simple policy rules perform as well as (or even outperform) optimal delegation regimes provides important implications for policy design. On the realistic assumption that the central bank cannot accurately observe demand and price shocks, this result implies that simple policy rules which involve no explicit dependence on these shocks are more desirable than optimal delegation which requires full information concerning shocks. The result that the first difference hybrid rule nearly achieves the welfare-optimal allocation is also of particular importance. When inflation exhibits endogenous persistence, as suggested by the estimation result of the hybrid Phillips curve, the central bank must pay the high cost of greater output gap variability to completely stabilize the price level against price shocks. Therefore, partial trend-reverting behavior of the price level is socially optimal. Partial trend-reversion of the price level can be replicated by the hybrid rule, but not by optimal delegation, such as price level targeting and nominal income growth targeting. Accordingly, this result can also be regarded as an endorsement of simple policy rules. Finally, we would like to remark on future research. Although the partial trend-reversion of the price can be replicated by the hybrid rule, the degree to which the central bank should bring the price level back to its initial trend path depends on the degree of forward-looking behavior in the inflation dynamics. In practice, however, central banks are uncertain about the weight of forward-looking firms. By analyzing various specifications of the hybrid Phillips curve, a central bank may reduce the uncertainty about inflation dynamics, but cannot eliminate it completely. When there is uncertainty about the persistence of inflation, how should the central bank conduct monetary policy? Should it respond more aggressively to shocks than under certainty equivalence, or more cautiously? Should the bank decrease the degree of trend-reversion of the price, or not? Although some studies have analyzed the uncertainty about the persistence of inflation, their analyses are based on the backward-looking Phillips curve, but not the hybrid Phillips curve.32 Analysis of the uncertainty about the hybrid Phillips curve remains to be solved in future.