رفتار قاعده تجربی و سیاست پولی

We investigate the implications of rule-of-thumb behaviour by consumers or price setters for optimal monetary policy and simple interest rate rules. This behaviour leads to endogenous persistence in output and inflation and alters the policymaker's welfare objective. Our main finding is that highly inertial policy is optimal regardless of what fraction of agents occasionally follow a rule of thumb. We also find that a first-difference version of Taylor's (Carnegie–Rochester Conf. Ser. Public Policy 39 (1993) 195–214) rule generally has desirable properties. By contrast, the coefficients in other optimised simple rules tend to be extremely sensitive with respect to the fraction of rule-of-thumb behaviour.

The characterisation of desirable monetary policy has been the subject of a large body of recent research. The question of what constitutes “optimal” monetary policy within structural models derived from optimising behaviour of households and firms has been a particularly lively area. A number of these studies are based on models in which the non-neutrality of monetary policy is derived from assuming frictions to price adjustment on the part of imperfectly competitive firms (e.g., Ireland, 1997; Rotemberg and Woodford, 1997; Clarida et al., 1999; Woodford, 1999b). In these models, the price decisions of firms that are optimal given the assumed frictions to price adjustment1 lead to a relation linking current inflation to a measure of the current output gap, or current marginal cost, and expected future inflation, which Roberts (1995) has called the “new-Keynesian Phillips curve”. This description of the supply side of the economy is usually complemented on the demand side by a standard Euler equation characterising households’ optimal consumption choice. A notable feature of such models is the absence of lagged variables in the structural equations. The dynamics of output and inflation depend entirely on expectations of future values of these variables as well as future monetary policy actions. From an empirical perspective, this class of models has been criticised as being unable to replicate the high serial correlation found in both output and inflation data of many industrialised economies, unless one is willing to assume a substantial degree of serial correlation in the structural disturbances of the model (Fuhrer 1997a and Fuhrer 1997b). The failure of the consumption Euler equation to capture the dynamics of aggregate nondurable consumption, let alone those of aggregate output, has been debated for a long time (Mankiw et al., 1985; Deaton, 1992; and many others). One proposed solution that maintains the assumption of optimal consumption choice is to allow for habit formation in preferences. Habit formation has been shown to improve the fit of small-scale business cycle models on U.S. time series, including aggregate consumption data (e.g., Fuhrer, 2000), as well as being able to explain various anomalies in the finance literature (e.g., see Campbell et al., 1997, Chapter 8). However, while habit formation may be useful in explaining various aspects of aggregate data, direct evidence for habit formation based on data at the household level is hard to find (e.g., Dynan, 2000). More recently, attention has focused on the question whether the new-Keynesian Phillips curve is able to explain the high serial correlation in inflation in the United States (Fuhrer and Moore, 1995a) as well as other industrialised countries (Coenen and Wieland, 2000). Fuhrer and Moore argue that the price setting problem underlying the new-Keynesian Phillips curve is misspecified, and propose a contracting specification in which price setters are concerned about their relative real contract price. However, their specification seems at odds with optimising behaviour, since profit maximisation motivates only a concern for relative nominal contract prices or wages. On the other hand, Sbordone (2002) and Gali and Gertler (1999) provide evidence that the source of inflation inertia arises from the sluggish response of firms’ real marginal cost to fluctuations in output. An alternative approach to explaining the apparent dependence of current values of output and inflation on past as well as expected future conditions is to allow the choices of some agents to deviate from optimal behaviour due to, e.g., limits on their capacity to form fully rational expectations. Roberts (1997) considers deviations from rational expectations formation on the part of price setters. Similarly, Gali and Gertler (1999) derive a structural relationship explaining current inflation as depending on lagged inflation as well as current marginal cost and expected future inflation by assuming that a fraction of firms set prices by following a rule of thumb, while the remaining firms set prices in the optimal, forward-looking manner. This article studies the implications for optimal monetary policy of rule-of-thumb behaviour. We believe there are compelling reasons for considering such behaviour, for example, the managerial costs involved in changing prices (Zbaracki et al., 2000). In fact, recently there has been general interest in the implications of optimisation costs for consumption choice (Gabaix and Laibson, 2002) and price setting (Mankiw and Reis, 2001). We take a slightly different approach than these authors by following Gali and Gertler. The rules of thumb that we consider specify that decisions by a fraction of the population (“rule-of-thumbers”) today mimic yesterday's behaviour of all agents (i.e. including “optimising” agents). We assume that optimisation costs are independent random draws.2 Those whose cost exceeds a certain threshold use instead a rule of thumb. These rules are appealing for at least three reasons. First, they involve virtually no computational burden: All that is needed is for agents to observe last period's consumption or price setting decisions. Second, they involve passive learning of the behaviour of optimising agents.3 Third, all agents behave identically in the steady state. That is, there is convergence among individual choices once the effects of all shocks are eliminated from the economy. One of the main purposes of this study is to provide a bridge between the studies assessing optimal monetary policy alluded to above – studies with purely forward-looking dynamics (i.e. with optimising agents) – and models with lagged dynamics imposed. One main advantage of our approach is that we can characterise precisely how lagged endogenous variables enter the model equations. Taking the standard dynamic new Keynesian model as our reference point, we introduce departures from optimising behaviour in exactly symmetrical fashion on both the supply and the spending side of the economy. Moreover, introducing lagged endogenous variables in a utility-based framework with a representative agent is compatible with the evaluation of the effects of monetary policy based on the maximisation of households’ welfare. As the incidence of rule-of-thumb behaviour increases, there are two changes in the model that have consequences for optimal policy. Of greatest importance, the transmission of shocks to the economy changes. Of less significance, the objective for monetary policy is also altered. The existence of rule-of-thumb price setting increases the degree of endogenous inflation persistence, and therefore makes shocks to inflation more long-lived, and inflation more variable. But rule-of-thumb behaviour also dampens the effects of shocks on inflation by reducing the sensitivity of inflation to the output gap. This latter effect dominates the increase in persistence, leading to a decline in the variability of inflation. In addition, we show that the presence of rule-of-thumb price setting implies that the monetary authority should seek to stabilise the first difference of inflation, as well as pursuing the standard goals of inflation and output gap stabilisation (see, e.g., Rotemberg and Woodford, 1997). The adaptation of monetary policy to this change in objectives helps contribute further to the reduction in the variance of inflation in equilibrium. At the same time, the output gap becomes more volatile, because monetary policy is now less effective in influencing changes in current and expect future real interest rates due to greater persistence in expected inflation resulting from the rule of thumb. Overall, it turns out that there is very little change in the desired dynamic response of interest rates to shocks with respect to changes in the fraction of rule-of-thumb price setting behaviour. Similarly, the presence of rule-of-thumb consumption behaviour increases the endogenous persistence in output (and the output gap); dampens the impact of shocks on output; and supplements the standard policy objective with a desire to smooth fluctuations in output growth. In addition, rule-of-thumb consumption affects the process governing the natural rate of interest, the summary statistic of the shocks to our model economy.4 The main effect of these changes is that the economy becomes easier to stabilise because the transmission of shocks to the output gap, and hence inflation, is reduced in magnitude. However, monetary policy now faces a trade-off between, on the one hand, inflation and output gap stabilisation, and on the other hand, output growth stabilisation. This implies that increasingly less importance is attached to stabilising inflation as the prevalence of rule-of-thumb consumption behaviour grows. In addition to investigating the effects of rules of thumb on optimal monetary policy, we explore the properties of simple interest rate rules as a means for implementing policy. Our most striking result is that a highly inertial interest rate policy is desirable, as characterised by a feedback coefficient greater than one on the lagged interest rate term in simple interest rate rules. This finding is valid even when the vast majority of price or consumption choices are made using the rule of thumb, and is robust across a wide range of parameterisations. Our finding regarding the benefits of superinertial interest-rate setting affirms the conclusions of Rotemberg and Woodford (1999) and Woodford (1999b), who were the first to argue in favour of this type of policy within the context of a completely forward-looking model. It also stands in direct contrast to the suggestion (e.g., Taylor, 1999a) that such an inertial interest rate policy ceases to be optimal, or even feasible, once backward-looking behaviour is incorporated into the structure of the model.5 Finally, our examination of various forms of rules suggests that the rule which implements the optimal plan in the situation when agents are always acting optimally continues to be nearly optimal under arbitrary degrees of rule-of-thumb behaviour. However, we show that the optimal coefficients in simpler versions of this rule change significantly in the presence of rules of thumb. Interestingly, a first-difference version of Taylor's (1993) original rule exhibits desirable welfare properties in all the cases we investigate. The remainder of the article is structured as follows. The next section lays out our model, including the introduction of rule-of-thumb consumers and price setters into an otherwise standard sticky-price optimising framework. It also provides a brief comparison of our approach to related literature. The section ends with a discussion of households’ welfare that monetary policy seeks to maximise. Section 3 describes our calibration of the model, and then analyses the implications of rule-of-thumb behaviour for optimal monetary policy and interest rate rules. Section 4 examines the robustness of our results for policy. Section 5 offers conclusions. The derivation of several results is taken up in Appendix A; some calibration issues are discussed in Appendix B; and the conditions characterising optimal policy are given in Appendix C.

In this paper, we investigate the implications for monetary policy of agents occasionally relying upon a rule of thumb when making consumption and pricing decisions. We find that this type of behaviour creates endogenous persistence in the processes for output and inflation; changes the dynamic responses of these variables to shocks; and alters the welfare function that policymakers seek to optimise. In the face of rule-of-thumb price setting, the implications for monetary policy turn out to be minimal, at least in terms of how interest rates should move in response to shocks. By contrast, the path that interest rates should take following a shock is more sensitive to the degree of rule-of-thumb consumption behaviour present in the economy. Our most striking finding, across all model specifications that we consider, is that highly inertial policy is desirable, supporting and extending the same conclusion reached by Woodford in a purely optimising model. We also find that two rules in particular are robust in terms of welfare outcomes achieved and stability of coefficients. The first is the rule that implements the optimal plan when agents are always acting optimally. This rule requires that the current interest rate be set in response to its level in the past two periods, the current inflation rate and the change in the output gap. The second is a first-difference version of Taylor's rule. Further work is required to show that the type of rules of thumb we consider are good approximations to actual decision making behaviour on the part of consumers and firms. Still, as we argued above, our model equations appear to be roughly consistent with different specifications of behaviour and preferences that have appeared in the literature so far.