Optimal Monetary Policy in a New Keynesian Forward-Looking Model

Introduction

A number of monetary policies have been developed in recent years with a view to accurately predicting economic trends and patterns. In addition, a new standard Keynesian model has emerged in the area of macroeconomics that focuses on the topic of optimal monetary policy in a simple forward-looking model. To determine an optimal monetary policy in a simple forward-looking model in the context of this New Keynesian framework, this paper reviews the relevant literature to explain the model's assumptions, its structure, the issue of "divine coincidence," and the implementation of optimal monetary policy. A summary of the research and important findings is presented in the conclusion.

Context: New Keynesian Economics

In recent years, the study of optimal monetary policy has shifted from an analysis of the welfare effects of simple parametric policy rules to the solution of optimal planning problems. Both approaches evaluate the welfare effects of monetary policy in an explicit monetary model of the economy, but they differ in scope. The first approach is more restrictive in that it finds the optimal policy within a class of prespecified policy rules for the monetary policy instrument. The second approach, by contrast, finds the optimal monetary policy among all allocations that are consistent with a competitive equilibrium in the monetary economy. Since monetary policy, in general, does not choose the economy's allocation but implements policy through a rule for the policy instruments, it is natural to ask whether the policy rule implied by the solution to the planning problem implements the optimal planning allocation. In most work on optimal planning problems, it is taken for granted that the solution of the planning problem can be implemented through some policy rule for the monetary policy instrument; however, as Dotsey and Hornstein demonstrate, this need not always be the case (113).

In the past, the real business cycle model predominated Keynesian economic thinking. More recently, a New Keynesian model has been developed. In this regard, Snowdon and Vane report that "since the mid-1980s the New Keynesian school has emerged as the main rival to the new classical approach. While most New Keynesian analysis incorporates the rational expectations and natural rate hypotheses, it does not incorporate the new classical assumption of continuous market clearing" (17). One important aspect of the New Keynesian model is the concept of sticky prices. According to Roberts, "Sticky prices are an important part of monetary models of business cycles. In recent years, a consensus has formed around the microfoundations of sticky price models, and this consensus is an important part of New Keynesian economics" (975). The primary focus of one important aspect of the emerging New Keynesian model has been to examine a wide range of factors with respect to wage and price stickiness that prohibit market clearing. Research has been directed into the causes of:

1. Nominal wage stickiness (e.g., via overlapping long-term wage contracts);
2. Nominal price stickiness (e.g., arising from menu or adjustment costs faced by monopolistically competitive firms);
3. Real rigidities in both the labor market (e.g., via efficiency wage, insider-outsider, and implicit contract models) and the product market (e.g., via customer markets); and
4. Coordination failures (Snowdon and Vane 17).

The New Keynesian model has become the tool of choice for many economists seeking to better understand optimal monetary policies. According to Blanchard and Gali, "A standard New Keynesian model has emerged. On the supply side, it consists of Calvo price and/or wage staggering. On the demand side, it is composed of an Euler equation and a Taylor rule. With more explicit microeconomic foundations than its Keynesian ancestor, and more relevance than its real business cycle predecessor, it has become the workhorse in discussions of fluctuations, policy, and welfare" (35). In Calvo's (1983) model, each firm maintains a fixed price until it receives a random signal that it can change its price; therefore, price changes are "staggered," and when setting prices, the firm takes into account the prices its competitors will charge until it has a chance to change prices again (Roberts 976).

Since competitors' prices were established in the past, the firm takes those past prices into account when establishing current ones (Roberts 976). New Keynesian models use the concepts of market failure and price inflexibility derived from conventional Keynesian economics, as well as the natural rate hypothesis and a focus on monetary policy from Monetarist economics, the concept of rational expectations from the Rational Expectations model, and a belief in the importance of developing models with microeconomic foundations from real business cycle models (Knoop 108). Researchers using New Keynesian models have sought to develop innovative and widely varied models in which market failure is generated by individuals engaging in optimizing behavior—not just through assumed or ad hoc behavioral assumptions—with the ultimate goal of better describing both the sources of imperfect competition and the role that market failure plays in business cycles (Knoop 108).

By and large, the New Keynesian economic model is targeted at identifying distinctive microeconomic foundations compared to the previous Keynesian models that have been accepted as macroeconomic conclusions (Rotheim 3). According to Rotheim, the New Keynesian model "focuses on a representative agent's reactions to changes in nominal variables observed in output, capital and labor markets as the sources of fluctuations in output and employment" (3). As Snowdon and Vane point out, however, "One problem with the new Keynesian developments is that there is no single New Keynesian model; rather, the research program has led to a multiplicity of explanations of wage and price rigidities, and their macroeconomic consequences" (17). In this regard, the New Keynesian model has both weak and strong approaches:

1. Weak New Keynesian economics maintains that fluctuations in output and employment in the aggregate are caused by market failures or coordination problems, uniquely focused on the supply side, which either result in wages and prices being relatively sticky in a downward direction or settle at sub-optimal equilibria in response to aggregate demand shocks.
2. Strong New Keynesian economics places greater emphasis on questions of interdependences, spillovers, and strategic complementarities in the context of such coordination failures of the market (Rotheim 3).

The New Keynesian model contains a number of important assumptions that can affect the outcome of the analyses it provides; these issues are discussed further below.

Assumptions of the Model

The New Keynesian model assumes that, from a welfare perspective, stabilizing inflation and the output gap is desirable. The core equation of the model assumes that these two goals are not mutually exclusive (Blanchard and Gali 35). For instance, according to Blanchard and Gali, "Stabilizing inflation also stabilizes the output gap. Thus, for example, in response to an increase in the price of oil, the best policy is to keep inflation constant; doing so implies that output remains equal to its natural level" (35). Likewise, Rotheim reports that, generally speaking, New Keynesian economists assume that over the long term, adequate wage and price flexibility will result in any random exogenous nominal shock being experienced entirely by other nominal rather than real variables. In the short term, however, small costs faced by firms may constrain them from reducing prices when confronted by nominal demand shifts—costs that New Keynesian economists assume have large external aggregate effects on welfare loss and output (3).

Structure of the Model

The structure of the standard framework is the so-called New Keynesian Phillips curve. In its most basic form, it is represented as:

π = βEπ(+1) + κ(y − y*)     (1)

where π is inflation, y is (log) output, y* is (log) natural output, and (y − y*) is the output gap. The effects of changes in factors such as the price of oil or the level of technology appear through their effects on natural output y* (Blanchard and Gali 35).

According to Giannoni, "Optimal policy rules are those that perform best in the worst-case parameter configuration, within a specified set of parameter configurations. Robust rules are designed to avoid an especially poor performance of monetary policy in the event of an unfortunate parameter configuration. They guarantee an acceptable performance of monetary policy across the specified range of models" (180). The need for a set of robust rules is highlighted in a study by Giannoni and Woodford, who cite the importance of clarifying the advantages of forward-looking rules. In this regard, Giannoni and Woodford report that "in the context of a given specification of the statistical properties of the disturbances, and the associated optimal equilibrium, we may find a forward-looking policy rule that is consistent with the equilibrium; but there will necessarily also be a rule that makes no reference to expectations (and that may instead depend on lagged endogenous variables) that is equally consistent with the optimal equilibrium, obtained by replacing the expectation terms in the policy rule by the functions of current and lagged variables that represent rational forecasts in the context of this equilibrium" (1427). This suggests that fine-tuning the model may be required in order to identify optimal approaches. As Giannoni and Woodford add, "It is only if we ask whether the same policy continues to be optimal when we vary the statistical properties of the disturbances that we can hope to find an advantage of one representation of the policy rule over the other" (1427).

Giannoni points out that rather than restricting the analysis to the Taylor rules component of the New Keynesian model, an optimal model should determine a robust optimal monetary policy rule within a larger family of rules that is sufficiently flexible to implement the optimal plan in those cases where the parameters are known with certainty. A study by Leeper examines optimal monetary policy behavior in the simplest forward-looking version of the popular class of dynamic stochastic general equilibrium models with nominal rigidities. Woodford (2003) exhaustively examines many variants on this model, noting that an important variant arises when both prices and wages are sticky (Leeper 2005).

A study by Jondeau and Le Bihan estimated two small macroeconomic models with forward-looking components: one for the U.S. economy and another for the German economy. The models, which include a Phillips curve, an IS curve, and a monetary policy rule, were estimated using the full-information maximum-likelihood procedure and were shown to have some robustness with respect to the Lucas critique. These researchers then computed optimal monetary policy rules within the class of dynamic Taylor rules. Based on their findings, Jondeau and Le Bihan report that optimal policies imply a strong degree of interest-rate smoothing. Moreover, German optimal policy was found to require a more persistent and slightly stronger response to inflation and output than the U.S. optimal policy.

Finally, according to Sarno and Taylor, "Some support for significant portfolio balance effects is provided by Ghosh (1992). Ghosh's approach is to use a forward-looking monetary model of the exchange rate in order to capture signaling effects. Since the monetary model implies that the exchange rate is a function of expected future monetary fundamentals, the monetary policy signaling effects must be captured" (225). Following this step, it is possible to test for the effects of sterilized intervention through channels besides the signaling channel (Sarno and Taylor 225).

Conclusion

This paper has reviewed the relevant literature concerning optimal monetary policy in a simple forward-looking model within the New Keynesian framework. The New Keynesian model, with its emphasis on sticky prices, rational expectations, and microeconomic foundations, provides a rich environment for analyzing the welfare effects of monetary policy. The model's key assumption—that stabilizing inflation simultaneously stabilizes the output gap—gives rise to the concept of divine coincidence. However, once real wage rigidities are introduced into the model, this coincidence breaks down and the monetary authority faces a genuine trade-off between inflation stabilization and welfare-relevant output gap stabilization. Research by Dotsey and Hornstein further demonstrates that implementing optimal monetary policy through an implied policy rule is not always feasible, particularly in a global rather than local analysis. These findings underscore the complexity of translating theoretically optimal plans into implementable monetary policy rules.

Works Cited

Blanchard, Olivier and Jordi Gali. "Real Wage Rigidities and the New Keynesian Model." Journal of Money, Credit & Banking 39.1 (2007): 35–7.

Dotsey, Michael and Andreas Hornstein. "Implementation of Optimal Monetary Policy." Economic Quarterly (Spring 2006): 113–34.

Ghosh, A. R. "Is it Signaling? Exchange Intervention and the Dollar-Deutschmark Rate." Journal of International Economics 54 (1992): 439–53. Cited in Sarno and Taylor, p. 57.

Giannoni, M. P. "Robust Optimal Monetary Policy in a Forward-Looking Model with Parameter and Shock Uncertainty." Journal of Applied Econometrics 22 (February 2006): 179–213.

Jondeau, Eric and Hervé Le Bihan. "Evaluating Monetary Policy Rules in Estimated Forward-Looking Models." Annals of Statistics and Economics 67/68 (2002): 357–363.

Knoop, Todd A. Recessions and Depressions: Understanding Business Cycles. Westport, CT: Praeger, 2004.

Leeper, Eric M. "Optimal Monetary Policy in Simple Models." Indiana University and NBER, 12 May 2005.

Roberts, John M. "New Keynesian Economics and the Phillips Curve." Journal of Money, Credit & Banking 27.4 (1995): 975–77.

Rotheim, Roy J. New Keynesian Economics/Post Keynesian Alternatives. London: Routledge, 1998.

Sarno, Lucio and Mark P. Taylor. The Economics of Exchange Rates. Cambridge, England: Cambridge University Press, 2002.

Snowdon, Brian and Howard R. Vane. A Macroeconomics Reader. London: Routledge, 1997.

Woodford, M. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton, NJ: Princeton University Press, 2003.