سیاست پولی بهینه در مدل میکرو پایه گذاری شده با پارامتر عدم قطعیت

In this paper, we structurally model uncertainty with a micro-founded model, and investigate its implications for optimal monetary policy. Uncertainty about deep parameters of the model implies that the central bank simultaneously faces both uncertainty about the structural dynamic equations and about the social loss function. Considering both uncertainties with cross-parameter restrictions based on the micro-foundations of the model, we use Bayesian methods to determine the optimal monetary policy that minimizes the expected loss. Our analysis shows how uncertainty can lead the central bank to pursue a more aggressive monetary policy, overturning Brainard's common wisdom. As the degree of uncertainty about inflation dynamics increases, the central bank should place much more weight on price stability, and should respond to shocks more aggressively. We also show that combining a more aggressive policy response with a highly inertial interest rate policy reduces Bayesian risk.

In spite of its great popularity in recent monetary policy studies, the New Keynesian Phillips curve has been criticized for failing to match the short-run dynamics exhibited by inflation.1 Specifically, inflation seems to respond sluggishly and display significant persistence in the face of shocks, while the New Keynesian Phillips curve allows current inflation to be a jump variable that can respond immediately to any disturbance. In order to solve this empirical defect of the New Keynesian Phillips curve, several studies have proposed a hybrid Phillips curve while keeping a micro-foundation.2 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. Although increasing attention has been recently given to the estimation of the hybrid Phillips curve, the estimation results vary greatly among studies.3 That is, there has not been any empirical consensus about what fraction of firms follow a rule of thumb. This implies that the central bank faces uncertainty about the degree of inflation persistence, which the existing literature has identified as one of the most critical parameters affecting the performance of monetary policy.4 In this study, we first investigate how the central bank should conduct monetary policy under uncertainty about inflation persistence. We use Bayesian methods to determine the optimal monetary policy that minimizes the expected social welfare loss, given a prior distribution of some uncertain parameters. This approach, initially started by Brainard (1967), has recently been followed by Estrella and Mishkin (1999), Hall et al. (1999), Martin and Salmon (1999), Svensson (1999), Sack (2000), among others. These studies support Brainard's results that optimal policy should be less aggressive in the face of parameter uncertainty.5 One notable exception is Söderström (2002), who finds that uncertainty about inflation persistence leads the central bank to pursue a more aggressive monetary policy.6 His analysis is based on a backward-looking model of Svensson (1997) type with the Old Keynesian Phillips curve. Instead of a backward-looking model, we use a micro-founded forward-looking model with the hybrid Phillips curve. Because of a micro-foundation, we can structurally model parameter uncertainty. When the central bank faces uncertainty about some structural deep parameters of price-setters, this implies that the central bank is uncertain about both inflation persistence and the slope of the Phillips curve. Then, the central bank can impose cross-parameter restrictions on both uncertainties by using information based on the micro-foundation of the model. Furthermore, the micro-foundation suggests that weights of a social loss function are directly related to the structural deep parameters. Therefore, uncertainty on the deep parameters makes the central bank face uncertainty about social loss-function weights as well as uncertainty about inflation dynamics. Then, again, with the information based on the micro-foundation, the central bank can impose cross-parameter restrictions between uncertainty about loss-function weights and about inflation dynamics.7 In such a setting, we show how uncertainty can lead the central bank to pursue a more aggressive monetary policy, overturning Brainard's conservatism principle.8 Two conditions that are necessary for Brainard's conservatism principle are violated in our analysis. First, our model is forward-looking and dynamic, whereas the model of Brainard (1967) is static. This distinction is important in the presence of uncertainty about inflation persistence. As discussed by Söderström (2002), when the dynamics of inflation are uncertain, the variances of inflation and output gap increase with the distance from target. Thus, when inflation and output gap are further away from target, the uncertainty about their future development is greater. Then, it pays to make sure current inflation is very stable by reacting more aggressively to shocks. Second, and especially relevant for our analysis, the traditional applications of Brainard's conservatism principle rely on the assumption that the central bank has a fixed loss function with known weights on the variability of a specific set of target variables. However, when the central bank faces uncertainty about structural deep parameters, this assumption is highly misleading. The micro-foundation of the model suggests that the weights of social loss function are non-linear functions of the structural deep parameters, and therefore the expected weights of loss function change drastically as the degree of uncertainty about the deep parameters increases. In the case of uncertainty about inflation dynamics, the central bank should place higher weight on price stability than in the absence of uncertainty, and should respond more aggressively to shocks to stabilize inflation. We next examine the time path of optimal monetary policy. Throughout our analysis, we assume that the central bank is able to act under commitment. Previous literature suggests that under parameter certainty the central bank should adopt a highly inertial interest rate policy in order to stabilize inflation, when private agents are forward-looking. We confirm that such a principle still holds under parameter uncertainty, and show that combining a more aggressive policy response with a highly inertial interest rate policy reduces Bayesian risk. This result is completely opposite to the result suggested by previous literature. With a backward-looking model, Söderström (2002) finds that the central bank should return to a neutral stance soon after the bank initially responds to the shocks aggressively, since the strong initial move has neutralized a larger part of the shock. However, such a policy response is not desirable, when private agents are forward-looking. If the central bank commits to initially respond to shocks aggressively, but then soon returns to a neutral stance, the bank cannot stabilize the current output gap and thus inflation very much. Instead, by exploiting the expectations of the private sector and committing to an aggressive and inertial policy, the central bank can stabilize the economy more effectively under uncertainty. Finally, we apply our Bayesian approach to the case of uncertainty about the structure of aggregate demand, which is a crucial part of the transmission mechanism from monetary policy to inflation. We find that uncertainty about some structural deep parameters of consumers also leads to a more aggressive policy response. As far as we know, no previous literature supports a more aggressive policy response under uncertainty about the structure of aggregate demand. Our finding, which is completely opposite to that of the previous literature, results not only from the effect of loss-function uncertainty but also from that of the positive correlation between the policy multiplier and transmission of shocks. Both these effects are based on the micro-foundation of the model, and have been ignored in most of the existing literature that confirms Brainard's conservatism principle. The outline of the remainder of the paper is as follows. Section 2 presents the model of the economy. Section 3 poses the problem of optimal monetary policy under uncertainty about structural deep parameters of price-setters. Section 4 presents the simulation results of the model and quantitative analysis of optimal policy. Section 5 addresses the problem of optimal monetary policy under uncertainty about structural deep parameters of consumers. Section 6 offers conclusions.

This paper has examined the implication of optimal monetary policy under parameter uncertainty in a micro-founded forward-looking model. The results of our analysis are completely opposite to Brainard's common wisdom, which seemed to capture the way actual policy makers viewed their decisions (Blinder 1998). Our analysis suggests that uncertainty about the structure of both aggregate supply and aggregate demand leads the central bank to pursue a more aggressive monetary policy. The difference between our results and those of previous literature which confirms Brainard's conservatism principle results mainly from our consideration about cross-parameter restrictions between different types of uncertainties. That is, the cross-parameter restrictions between uncertainty about loss function and about the structural equations, and those between the policy multiplier and transmission of shocks. These cross-parameter restrictions, which are based on the micro-foundation of the models, have been largely ignored in most previous literature. Our results suggest that accounting for them is critical for investigating the effect of uncertainty on optimal monetary policy. We also confirmed that when the central bank faces parameter uncertainty, it is desirable for the bank to combine an aggressive policy response with a highly inertial policy. As first shown in Rotemberg and Woodford (1999) and Woodford (1999), a highly inertial interest rate policy allows the central bank to affect the private sector's expectations appropriately. We showed that such an inertial policy is desirable under parameter uncertainty. Finally, we would like to remark on future research. While our analysis focuses on parameter uncertainty in the model of Calvo (1983) with random-duration contracts, it might be interesting to analyze the same issue using the model of Taylor (1980) with fixed-duration contracts. Although a number of recent literature has tried to show that Calvo- or Taylor-style contracting structures are consistent with the empirical evidence on inflation persistence, the results vary among studies.24 That is, some studies find support for Calvo-style contracts, while others find support for Taylor-style ones.25 This implies that the central bank is uncertain about whether inflation dynamics is consistent with random- or fixed-duration contracts. The difference between random- and fixed-duration contracts has important implications for the welfare cost of inflation variability. As Erceg and Levin (2002) show, the welfare cost of inflation variability in fixed-duration contracts is much smaller than that in random-duration ones.26 Therefore, if the central bank is uncertain about which contracting structure fits the actual data, it also faces uncertainty about the social loss function. We should not use a fixed loss function with known weights on the variability of target variables in order to evaluate the performance of monetary policy across models with different contracting structures. Model uncertainty about different contracting structure with an endogenous loss function is an interesting avenue for future research