Optimal monetary policy in a simple forward-looking model

Optimal Monetary Policy in a Simple Forward-Looking Model

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 recent years in the area of macroeconomics that has a focus 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 model, this paper reviews the relevant literature to explain the assumptions, the structure of the model, the issue of "divine coincidence" and the implementation of the optimal monetary policy. A summary of the research and important findings are presented in the conclusion.

Review and Discussion

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 the scope of analysis. 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. On the other hand, the second approach 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 indeed taken for granted that the solution of the planning problem can be implemented through some policy rule for the monetary policy instrument but, as we show in this article, this need not always be the case (Dotsey and Hornstein 113).

In the past, the real business cycle model predominated Keynesian economic thinking. More recently, though, 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. For example, 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). In fact, 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 that has involved research 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 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. For example, 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 competition will charge until it has a chance to change prices again (Roberts 976).

Since the prices of competitors were established in the past, the firm takes into account such past prices in establishing current ones (Roberts 976). The 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, though, "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 as follows:

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. By contrast, 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, though, that can affect the outcome of the analyses it provides and these issues are discussed further below.

Assumptions of the model

The New Keynesian model assumes that, from a welfare perspective, that stabilizing inflation the output gap is desirable. The equation outlined in the context section above 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, it is reasonable to expect that adequate wage and price flexibility will result in any random exogenous nominal shock to be experienced entirely by other nominal instead of real variables; however, in the short-term, the potential exists for small costs that are regarded by firms that would constrain them from reducing prices when confronted by nominal demand shifts which 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 is comprised of the following representation:

[pi] = [beta]S[pi](+1) + [kappa](y - [y.sup.*]), (1)

where [pi] is inflation, y is (log) output, [y.sup.*] is (log) natural output, and (y - [y.sup.*]) 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.sup.*]

Source: Blanchard and Gali 35.

According to Giannoni, "Optimal policy rules 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 to yield an acceptable performance of monetary policy in 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 thee avantages 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. For instance, Gionnani and Woodford add that, "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).

Gionnani 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 reports that 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. 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 I-S curve and a monetary policy rule, are estimated using the full-information maximum-likelihood procedure. They are shown to have some robustness with respect to the Lucas critique. These researchers then computed optimal monetary policy rules in the class of dynamic Taylor rules. Based on their findings, Jondeau and Le Bihand report that optimal policies imply a strong degree of interest-rate smoothing. Moreover, German optimal policy was determined 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).

The issue of "divine coincidence"

The property described in the assumptions section above is termed the divine coincidence; this property differs from the popular views concerning the undesirability of policies that attempt to completely and always stabilize inflation irrespective of the costs involved in terms of output (Blanchard and Gali 35). In this regard, Blanchard and Gali notes that, "That consensus underlies the medium-term orientation adopted by most inflation targeting central banks" (Blanchard and Gali 35). The divine coincidence is closely associated with a specific aspect of the standard New Keynesian model with respect to the fact that the gap between the efficient (first-best) level of output and the natural level of output is constant and remains unchanged in response to shocks (Blanchard and Gali 35). This aspect suggests that stabilizing the output gap (e.g., the gap that exists between actual and natural output) is comparable to also stabilizing the welfare-relevant output gap (e.g., the gap that exists between actual and efficient output), and it is this equivalence that represents the basis for the so-called divine coincidence. According to Blanchard and Gali, "The New Keynesian Phillips curve implies that stabilization of inflation is consistent with stabilization of the output gap. The constancy of the gap between natural and efficient output implies in turn that stabilization of the output gap is equivalent to stabilization of the welfare-relevant output gap" (36).

This property can likewise be attributed to the lack of nontrivial real imperfections in the standard New Keynesian model, but the New Keynesian model contains one such real imperfection which is real wage rigidities (Blanchard and Gali 35). In this regard, Blanchard and Gali note that, "The existence of real wage rigidities has been pointed to by many authors as a feature needed to account for a number of labor market facts. Once the New Keynesian model is extended in this way, the divine coincidence disappears" (Blanchard and Gali 37). The reason for the disappearance of the divine coincidence in this area relates to the fact that the gap that exists between efficient output and natural output is no longer invariant and is susceptible to shocks (Blanchard and Gali 35).