Essays in Estimation of Dynamic Stochastic General Equilibrium Models
dynamic factor models
Dynamic factor models (DFM) and dynamic stochastic general equilibrium (DSGE) models are widely used for empirical research in macroeconomics. The empirical factor literature argues that the co-movement of large panels of macroeconomic and financial data can be captured by relatively few common unobserved factors. Similarly, the dynamics in DSGE models are often governed by a handful of state variables and exogenous processes such as latent preference and/or technology shocks. A general topic of this dissertation is the estimation of DSGE models on a rich panel of macroeconomic and financial data by combining a DSGE with a dynamic factor model. By incorporating richer information, this combination allows to obtain DSGE model predictions and to do more reliable policy analysis with a broader range of data series of interest than before. Moreover, the combination of a DSGE and a dynamic factor model can be used as a tool for evaluating a DSGE model. This dissertation consists of three essays summarized below. Chapter 1 “Bayesian Dynamic Factor Analysis of a Simple Monetary DSGE Model”: We take a standard New Keynesian business cycle model to a richer data set. When estimating DSGE models, the number of observable economic variables is usually kept small, and for convenience it is assumed that the model variables are perfectly measured by a single – often quite arbitrarily selected – data series. We relax these two assumptions and estimate a fairly simple monetary DSGE model on a richer data set. Building upon Boivin and Giannoni (2006), the framework can be seen as a combination of a DSGE model and a dynamic factor model in which factors are economic state variables and the factor dynamics are governed by a DSGE model solution. Using post-1983 U.S. data on real output, inflation, nominal interest rates, measures of inverse money velocity, and a large panel of informational series, we compare the data-rich DSGE model with a regular – few observables, perfect measurement – DSGE model in terms of deep parameter estimates, propagation of monetary policy and technology shocks and sources of business cycle fluctuations. We document that the data-rich DSGE model generates a higher implied duration of Calvo price contracts and a lower slope of the New Keynesian Phillips curve. Because of the data set’s high panel dimension, the likelihood-based estimation of the data-rich DSGE model is computationally very challenging. To reduce the costs, we employed a novel speedup as in Jungbacker and Koopman (2008) and achieved the computational time savings of 60 percent. Chapter 2 “Data-Rich DSGE and Dynamic Factor Models”: In addition to a data-rich DSGE model with a standard New Keynesian core, we consider an unrestricted dynamic factor model and estimate both on a rich panel of U.S. macroeconomic and financial data compiled by Stock and Watson (2008). We find that the spaces spanned by the common empirical factors and by the data-rich DSGE model states are very close. First, this implies that a DSGE model indeed captures the essential sources of co-movement in the data and that the differences in fit between a data-rich DSGE model and a DFM are potentially due to restricted factor loadings in the former. Second, this also implies a greater degree of comfort about propagation of structural shocks to a wide array of macro and financial series. Third, the proximity of factor spaces facilitates economic interpretation of a dynamic factor model, as the empirical factors are now isomorphic to the DSGE model state variables with clear economic meaning. Finally, the proximity of factor spaces allows us to propagate monetary policy and technology innovations in an otherwise completely non-structural dynamic factor model to obtain predictions for many more series than just a handful of traditional macro variables including measures of real activity, price indices, labor market indicators, interest rate spreads, money and credit stocks, and exchange rates. We can therefore provide a more complete and comprehen-sive picture of the effects of monetary policy and technology shocks. Chapter 3 “DSGE Model Based Forecasting of Non-Modeled Variables” (joint work with Frank Schorfheide and Keith Sill): We develop and illustrate a simple method to generate a DSGE model-based forecast for variables that do not explicitly appear in the model (non-core variables). Estimation is performed in two steps. First, we estimate the regular DSGE model on core observables. Second, we obtain filtered DSGE model state variables and use them as regressors in auxiliary linear regressions – resembling DFM measurement equations – for the non-core variables. Predictions for the non-core variables are then obtained by applying their estimated measurement equations to DSGE model-generated forecasts of the state variables. This estimation approach can be viewed as a simplified version of a data-rich DSGE model estimation in which we essentially decouple the analysis of the non-core measurement equations and the estimation of a DSGE model on the core observables. The proposed shortcut is practically appealing: we considerably reduce the associated computational costs and we can incorporate and forecast an additional non-core variable without having to re-estimate the whole DSGE model, a feature useful in real-time applications. We apply our approach to generate and evaluate recursive forecasts for personal consumption expenditure (PCE) inflation, core PCE inflation, the unemployment rate, and housing starts.
Francis X. Diebold