فهرستی از قوانین ساده سیاست پولی در یک مدل جدید اقتصاد کلان کینزی

We derive necessary and sufficient conditions for simple monetary policy rules that guarantee equilibrium determinacy in the New Keynesian monetary model. Our modeling framework is derived from a fully specified optimization model that is amenable to analytical characterisation. The monetary rules analyzed are variants of the basic Taylor rules ranging from simple inflation targeting (current, forward, backward) to canonical Taylor rules with and without inertial nominal interest rates. We establish that determinacy obtains for a wide range of policy parameters, especially when the monetary authority targets output and smoothes interest rates. Contrary to other results in the literature, we do not find a case for super-inertial interest rate policy.

This paper derives parameter restrictions for simple monetary policy rules which deliver a fully determinate equilibrium in an otherwise standard monetary general equilibrium model. Following the seminal contribution of Rotemberg and Woodford (1997), this model has become the workhorse in the literature on monetary policy. The main result from our analysis is that the monetary authority should implement an aggressive anti-inflationary stance irrespective of whether the interest rate rule is current-, forward- or backward-looking, or whether output gap targeting is desired or not. However, a rule with a large response coefficient on inflation does not necessarily lead to determinacy when there is no interest rate inertia or output targeting. When these are introduced, determinacy obtains for a wide range of parameter constellations, thereby ‘supporting’ the monetary authority's inflation response. Notably, and contrary to policy recommendations for super-inertial interest rate setting, an inertial coefficient lower than one is found to be necessary for determinacy. Recent research explores the characteristics of monetary dynamic general equilibrium models under both empirical and theoretical aspects. Researchers such as King and Watson (1996) or Kim (2000) analyze the properties of the New Keyenesian modeling framework with respect to its ability to replicate basic business cycle regularities. The contribution of Rotemberg and Woodford (1997) was to shift emphasis towards the performance of such models when a Taylor (1993) type policy rule is applied. The conference volume edited by Taylor (1999) presents a wide collection of papers in this vein. The issue of equilibrium determinacy, however, has come to the forefront of this literature only recently. It has been recognized in the literature that monetary policy rules can actually be destabilizing. An interest rate policy that is not aggressive enough in the face of rising inflation can lead to adverse outcomes where non-fundamental or ‘sunspot’ shocks can affect aggregate dynamics which would not be present otherwise. In such a case, agents would rationally respond to extraneous beliefs that are not tied to economic fundamentals. As an example, consumers might react to unsubstantiated newspaper accounts of worsening economic conditions by working harder, even though output growth is in line with expectations. Under indeterminacy, the monetary authority would validate these beliefs by lowering interest rates, thereby stimulating output, which requires a higher labor supply. This leaves agent worse off since they would otherwise have preferred to keep leisure at the level implied by fundamentals.2 In a determinate equilibrium, however, the central bank would tighten policy, which counters the expansionary beliefs; sunspot-driven business cycles could therefore never arise in the first place. The seemingly purely theoretical issue of equilibrium determinacy thus becomes a matter of policy design. We derive a taxonomy of determinacy for a simple forward-looking monetary model in the New Keynesian vein. We analyze monetary policy rules that include pure inflation targeting (current, forward and backward looking); rules with both inflation and output targeting (current, forward and backward looking), and rules with interest rate inertia (current and forward looking). As discussed by McCallum and Nelson (1999), the rules employed in this paper are all ‘operational’ in the sense that policy makers either react to: (i) lagged values of inflation and output deviations from their respective targets; or (ii) react to their expectations of current values of inflation deviations and the output gap. This line of analysis has been succinctly summarized by Woodford (2003) who also presents some results in a model similar to ours. Our paper contributes to the literature in that it derives determinacy properties for a wide range of policy rules in a unified framework. We develop a richly parameterized version of the standard New Keynesian framework used for the analysis of monetary policy. A key element is the formal derivation of the aggregate supply equation under a different specification for modeling nominal rigidities, namely quadratic costs of price adjustment à la Rotemberg (1982), which stands in contrast to the more commonly used Calvo-type price setting. The (linearized) Phillips-curves implied by either approach are commonly thought to be equivalent in terms of endogeneous variables. We show that the parameter describing the output elasticity of inflation is a non-trivial and highly non-linear function of the underlying structural parameters, and therefore not be considered prima facie as structural. Bullard and Mitra (2002), for instance, address determinacy in a similar New Keynesian framework. They do not, however, derive their model from first principles, which could violate the cross-equation restrictions embedded in our reduced form. On the other hand, we show how the boundaries of the determinacy region explicitly depend on the structural model parameters. Benhabib, Schmitt-Grohé, and Uribe (2001) shadow most of our results, albeit in a continuous-time setting and with non-separable utility in consumption and money balances. It has been pointed out by Carlstrom and Fuerst (2001) that a continuous-time price-setting framework implies a different timing convention when compared to discrete-time models, so that the determinacy results are not strictly comparable. Carlstrom and Fuerst (2000) are closest to this paper, but their use of a different timing convention for money holdings leads to different determinacy results. None of these papers, however, examines as wide a taxonomy of rules as that proposed in our work. In particular, we derive, to the best of our knowledge, a new result on the determinacy properties of interest rate smoothing rules. We envision this paper as providing a yardstick and reference for policymakers and academic researchers alike who are interested in assessing simple monetary policy models with respect to their determinacy properties. The paper is organized as follows. In the next section we present a simple monetary model usable for policy analysis, the reduced form of which is derived from a fully optimization-based model of consumer and firm choice. In Section 3, we derive determinacy conditions for pure inflation targeting in several variants, while Section 4 adds output targeting. Section 5 studies the role of interest rate inertia in the policy rule. Section 6 summarizes and concludes.

A summary of this paper is simple: Inflation targeting works! A monetary authority that is worried about introducing instability in an economy can safely adhere to a policy rule that raises the real interest rate in response to inflationary pressures. In the simple inflation-targeting framework, this implies setting the nominal rate such that it moves more than proportionally than the inflation target. If the central bank's objectives include concern for output the range of stabilizing policy expands up to the point where not even an aggressive anti-inflationary stance is required. Targeting expected or lagged inflation does impose an upper bound on the responsiveness of the interest rate to inflation. However, this bound is wide enough to accommodate policy rules applied in practice, especially if output targeting is an added goal. Empirical studies also show that monetary authorities respond to lagged interest rates. We find that a policy of interest rate smoothing strongly supports the determinacy of simple rules up to a degree where any plausible combination of inflation and output coefficients guarantees a unique equilibrium. Many authors, such as Carlstrom and Fuerst (2000), express a certain degree of determinacy pessimism. We do not find this warranted. Irrespective of the central bank's targets, there is an interest rate rule that guarantees equilibrium determinacy if it is sufficiently responsive to economic conditions. In other words, monetary authorities have to be prepared to respond to a wider range of target variables than is commonly analyzed in the theoretical literature. Yet, this is what central bank practitioners already do! It is outside the scope of this paper to analyze the choice between different rules with respect to optimality criteria, such as maximizing the welfare of consumers or output and inflation stabilization. This paper takes the position that in the absence of formal welfare criteria, monetary policymakers should pay attention to the possibility of equilibrium indeterminacy. To avoid such an outcome, our recommendation is to pursue a mildly anti-inflationary policy that is supported by an output objective as well as interest rate smoothing. There is, however, a potential shortcoming of this, and other, research on the determinacy properties of policy rules: recommendations are conditional on the modeling framework- and often strikingly so. For instance, Carlstrom and Fuerst (2001) show that a subtly different timing convention for money holdings from the one used in this paper, and most monetary models, implies different determinacy properties. Along the same line, introducing investment also affects determinacy. In such a framework, the real rate of return on capital provides an additional transmission and feedback mechanism for monetary policy. Carlstrom and Fuerst (2000) and Lubik (2003) show how the standard intuition of stabilizing anti-inflationary monetary policy no longer applies. Moreover, in a seminal paper, Leeper (1991) has demonstrated that analysis of monetary policy cannot be separated from fiscal policy. The discussion in this paper implicitly assumes that fiscal policy is passive and accommodates intertemporal budget balance. A more independent fiscal policy therefore changes the determinacy properties of monetary rules. Where do we go from here? It seems obvious and redundant to suggest that economists need to develop a better understanding of the macroeconomy. However, at the very least they should be more careful and aware in using models for policy analysis that can deliver markedly different recommendations at the change of seemingly small details. Ultimately however, this is an empirical question. Our work may prove useful for guiding researchers in the empirical analysis of monetary policy models that allow for multiple equilibria. Since aggregate dynamics under determinacy and indeterminacy are potentially different, an empirical analysis needs to take this into account, such as in Lubik and Schorfheide (2004).