Evgeniya Duzhak

Chair the Fed is an award-winning online educational game developed by the Federal Reserve Bank of San Francisco to help players learn about monetary policy. Players assume the role of Fed Chair and adjust the federal funds rate to try to achieve low inflation and low unemployment. If successful, they are reappointed to another term. By investigating anonymous user data from a three-month period in 2019, we find that about 20 percent of games completed result in reappointment. Chances of reappointment improve with game experience; however, players exhibit more skill in addressing some situations than others. Given the widespread interest in the game, reflected by over 80,000 games initiated per month, the implications of the game for improving economic literacy are important.

Chair the Fed is an award-winning online simulation developed by the Federal Reserve Bank of San Francisco to teach about the role of the Fed in achieving its dual mandate goals of stable prices and maximum employment. It is widely used, with an average of close to 85,000 games started each month in 2019. This article describes Chair the Fed and the results of a controlled experiment to determine its effects on learning in high school economics classes in the Fed’s 12th district. We find that students who played Chair the Fed score significantly higher on a 10-question posttest compared with students who learned about the Fed and monetary policy in more traditional ways. In evaluating our results, we compare difference-in-difference regression modeling with the traditional economic education model where the posttest score is regressed on the pretest score, and find that our results are robust across both specifications.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

The Marshallian Macroeconomic Model in Zellner and Israilevich (2005) provides a novel way to examine sectoral dynamics through the introduction of a dynamic entry/exit equation in addition to the usual demand and supply functions found in models of this class. In this paper we examine the possibility of cyclical behavior in the Marshallian Macroeconomic Model and investigate the existence of a Hopf bifurcation with respect to the parameter in the entry/exit equation.

As is well known in systems theory, the parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without knowledge of the location of such boundaries, there is no way to know whether the confidence region about the parameters’ point estimates might be crossed by one or more such boundaries. If there are intersections between bifurcation boundaries and a confidence region, the resulting stratification of the confidence region damages inference robustness about dynamics, when such dynamical inferences are produced by the usual simulations at the point estimates only. Recently, interest in policy in some circles has moved to New Keynesian models, which have become common in monetary policy formulations. As a result, we explore bifurcations within the class of New Keynesian models. We study different specifications of monetary policy rules within the New Keynesian functional structure. In initial research in this area, Barnett and Duzhak (Physica A 387(15):3817–3825, 2008) found a New Keynesian Hopf bifurcation boundary, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. Hopf bifurcation is the most commonly encountered type of bifurcation boundary found among economic models, since the existence of a Hopf bifurcation boundary is accompanied by regular oscillations within a neighborhood of the bifurcation boundary. Now, following a more extensive and systematic search of the parameter space, we also find the existence of Period Doubling (flip) bifurcation boundaries in the class of models. Central results in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the considered cases. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries and their dependence upon policy-rule parameter settings.

Grandmont (1985) found that the parameter space of the most classical dynamic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New Keynesian models. As a result, in this paper we explore bifurcation within the class of New Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

This work studies the class of new Keynesian models. We are looking at stability properties and conducting a bifurcation analysis. Bifurcation analysis is often overlooked while examining the properties of the model. Bifurcation is a qualitative change in the nature of a solution that occurs due to change of the parameter value. For example stable system can become unstable. The parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without it there is no way to know whether the confidence region about the parameters? point estimates might be crossed by such a boundary, thereby stratifying the confidence region itself and damaging inferences about dynamics. Central results in this work are the theorems on the existence and location of Hopf bifurcation boundaries. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries and their dependency upon policy-rule parameters.