This proposal aims to develop new tools for the computation and estimation of dynamic models in macroeconomics and for the application of those tools to relevant policy questions.
Dynamic models have become a standard instrument in modern macroeconomics. Because they are built to analyze how the economy evolves over time, they are used to study growth and business cycles, to design monetary and fiscal policy, or to investigate the aggregate aspects of financial and labor markets, among many other tasks. However, many instruments are still missing in the toolbox of the applied macroeconomic researcher. For instance, economists do not have a good understanding of the effects of changes in policy regimes ?that is, variations in the way in which economic policy is systematically conducted in opposition to changes within one regime- or how the beliefs about future policies affect current behavior by households and firms.
The goal of this proposal is to provide some of the required tools for these tasks and show how they can be used to address important questions in the design and evaluation of public policy. Consequently, much of this new research may have positive externalities for other economists within macro and, more generally, for researchers in other fields where dynamic models are also employed.
In particular, this proposal focuses on how to use perturbation methods to solve Markov switching rational expectations (MSRE) models starting from first principles, that is, from the set of non-linearized optimality conditions that describe the behavior of the economic agents, rather than from the set of linearized ones, as the literature has previously done. Perturbation methods, commonly used in natural sciences and economics, built approximated solution to models that are analytically intractable. MSRE models allow for different possible policy regimes (for instance, a hawkish central banker and a dovish central banker) that evolve and switch over time (hawkish central bankers are followed, with some probability, by dovish central bankers and so on).
The proposal derives the set of algebraic equations to be solved to find the first-order Taylor expansion to the policy functions using a perturbation. Next, it shows how the traditional approach, based on singular value decomposition (SVD) algorithms and used in the constant parameter case, does not work in the case of MSRE models. Instead, the proposal uses a Gröbner basis method. Then, it studies how to check for determinacy and, as an example, it solves a business cycle model with nominal rigidities. Finally, the proposal points out how the perturbation approach also allows us to find higher-order approximations to the solution of MSRE models.
Policy-making institutions in the U.S. and abroad can apply the methods presented in this proposal. For instance, the Federal Reserve Board and several regional Federal Reserve Banks, the International Monetary Fund, the European Central Bank, the Bank of England, and the central banks of Austria, Canada, Germany, Italy, Japan, Spain, and Sweden (just to name a few) are actively formulating and estimating dynamic macroeconomic models for policy analysis and forecasting that can benefit from the type of extensions presented in the proposal. Moreover, the economics profession is accumulating evidence of the good forecasting performance of this class of models, even when compared with judgmental predictions from staff economists. The newer and better tools that this proposal outlines are designed explicitly for the purpose of helping the Federal Reserve Board and other policy-making institutions to develop more flexible models that will contribute to the implementation of an effective public policy in the U.S.
Finally, the development of new computation techniques has potential applications in other fields of economics (such as international economics, industrial organization, or labor economics), and other social sciences where researchers want to solve and estimate dynamic models using flexible, yet powerful tools.
