Andrew T. Foerster

Perturbation Methods for Markov-Switching DSGE Models

This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of finding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ascertain how many of them are stable. Our methodology is applied to three models to illustrate its feasibility and practicality.

Perturbation methods for Markov‐switching dynamic stochastic general equilibrium models

Markov‐switching dynamic stochastic general equilibrium (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high‐order approximations to the solutions of MSDSGE models. Our new method—“the partition perturbation method”—partitions the Markov‐switching parameter space to keep a maximum number of time‐varying parameters from perturbation. For this method to work in practice, we show how to reduce the potentially intractable problem of solving MSDSGE models to the manageable problem of solving a system of quadratic polynomial equations. This approach allows us to first obtain all the solutions and then determine how many of them are stable. We illustrate the tractability of our methodology through two revealing examples.

Uncertainty and fiscal cliffs

Fiscal uncertainty arises in many forms. Expiring temporary stimulus measures, projections of rapid debt growth, and oscillating political concerns over general levels of taxation are examples that all contribute to fiscal uncertainty. Motivated by anecdotal evidence associated with the US Fiscal-Cliff episode near the end of 2012, we empirically investigate the impact of economic policy uncertainty on investment and employment, especially with regard to the type of investment project. Increases in policy uncertainty lower investment and employment, with some investment dropping immediately and some more gradually, depending upon the ease of installation of types of capital. Based upon this empirical evidence, we then present a DSGE model of expiring tax provisions, and show that the model generates responses to fiscal uncertainty that match key features of the data. The framework captures a few unique elements of fiscal uncertainty. First, fiscal uncertainty is over the average tax rate, rather than a mean-preserving shock to the future tax rate. Second, households obtain information that tax rates may change at a particular date in the future, though whether tax rates do ultimately change is uncertain. As a result, information indicating that a policy change may occur in the future immediately sets in motion partial adjustments toward the new policy. The degree of adjustment households undertake depends on the probability attached to the outcome that actually does result in a change in fiscal policy. Unsuccessful reforms inject noise into the economy and lower the steady state level of the capital stock and output.

Financial crises, unconventional monetary policy exit strategies, and agents' expectations

A central bank may purchase assets during a financial crisis and then exit from those purchases. Agents have rational expectations about financial crises as rare events, the probability the central bank purchases assets, and the exit strategy. Selling off assets quickly produces a double-dip recession while slowly unwinding generates a smooth recovery. Expectations about the exit strategy influence the initial effectiveness of purchases. Increasing the probability of purchases during crises distorts the pre-crisis economy and depends upon the exit strategy. The welfare benefits of unconventional policy may differ ex-ante versus ex-post, as can the preferred exit strategy.

Monetary Policy Regime Switches and Macroeconomic Dynamics

This article considers the determinacy and distributional consequences of regime switching in monetary policy. Although switching in the inflation target does not affect determinacy, switches in the inflation response can cause indeterminacy. Satisfying the Taylor principle period by period is neither necessary nor sufficient for determinacy when inflation responses switch; indeterminacy can arise if monetary policy responds too aggressively to inflation in the active regime. Inflation target switches primarily impact the level of inflation, whereas inflation response switches primarily impact the volatility. Expecting an inflation target switch has minor effects on volatility, whereas expecting an inflation response switch raises volatility more substantially.

Communicating Monetary Policy Rules

Sixty-two countries around the world use some form of inflation targeting as their monetary policy framework, though none of these countries express explicit policy rules. In contrast, models of monetary policy typically assume policy is set through a rule such as a Taylor rule or optimal monetary policy formulation. Central banks often connect theory with their practice by publishing inflation forecasts that can, in principle, implicitly convey their reaction function. We return to this central idea to show how a central bank can achieve the gains of a rule-based policy without publicly stating a specific rule. The approach requires central banks to specify an inflation target, tolerance bands, and economic projections. When inflation moves outside the band, the central bank must also specify a time frame over which inflation will return to within the band. We show how communication about time horizons and tolerance bands can uniquely pin down a policy rule, and highlight how different types of communication can be used to convey different policy rules.

Search with Wage Posting under Sticky Prices

We consider the macroeconomic implications of the interaction between nominal rigidities and labor market frictions in a framework where firms jointly make pricing and hiring decisions. In our New Keynesian model, workers randomly search for jobs and are matched with firms that post take-it-or-leave-it contracts and are subject to sticky prices. Relative to the typical model that separates search frictions and nominal frictions into wholesale and retail firms, respectively, our model implies smoother wages because firms can affect their marginal costs by adjusting prices. A consequence of smoother wages is that the vacancy-to-unemployment ratio responds much more than under the standard model. Additionally, our baseline model shows larger effects of changing the inflation target and smaller effects of changing unemployment benefits. We also show that combining search and price frictions in one firm leads to less volatility after technology shocks but more volatility after monetary policy shocks.