DSGE Model-Based Forecasting of Non-Modelled Variables

Frank Schorfheide, Keith Sill, Maxym Kryshko
2008 Social Science Research Network  
This paper develops and illustrates a simple method to generate a DSGE modelbased forecast for variables that do not explicitly appear in the model (non-core variables). We use auxiliary regressions that resemble measurement equations in a dynamic factor model to link the non-core variables to the state variables of the DSGE model. Predictions for the non-core variables are obtained by applying their measurement equations to DSGE model-generated forecasts of the state variables. Using a
more » ... ale New Keynesian DSGE model, we apply our approach to generate and evaluate recursive forecasts for PCE inflation, core PCE inflation, the unemployment rate, and housing starts along with predictions for the seven variables that have been used to estimate the DSGE model. JEL CLASSIFICATION: C11, C32, C53, E27, E47 KEY WORDS: Bayesian Methods, DSGE Models, Econometric Models, Evaluating Forecasts, Macroeconomic Forecasting 1 Introduction Dynamic stochastic general equilibrium (DSGE) models estimated with Bayesian methods are increasingly used by central banks around the world as tools for projections and policy analysis. Examples of such models are the small open economy model developed by the Sveriges Riksbank (Adolfson, Laseen, Linde, and Villani, 2007 and 2008; Adolfson, Andersson, Linde, Villani, and Vredin, 2007), the New Area-Wide Model developed at the European Central Bank (Coenen, McAdam, and Straub, 2008) and the Federal Reserve Board's new Estimated, Dynamic, Optimization-based model (Edge, Kiley, and Laforte, 2009). These models extend specifications studied by Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) to open economy and multisector settings. A common feature is that decision rules of economic agents are derived from assumptions about preferences and technologies by solving intertemporal optimization problems. Compared to previous generations of macroeconometric models, the DSGE paradigm delivers empirical models with a strong degree of theoretical coherence. The costs associated with this theoretical coherence are two-fold. First, tight cross-equation restrictions potentially introduce misspecification problems that manifest themselves through inferior fit compared to less-restrictive time series models (Del Negro, Schorfheide, Smets, and Wouters, 2007, henceforth DSSW). Second, it is more cumbersome than in a traditional system-ofequations approach to incorporate variables other than a core set of macroeconomic aggregates such as real gross domestic product (GDP), consumption, investment, wages, hours, inflation, and interest rates. Nonetheless, in practical work at central banks it might be important to also generate forecasts for economic variables that do not explicitly appear in medium-scale DSGE models. Our paper focuses on the second problem. There are in principle two options for generating forecasts for additional variables. First, one could enlarge the structural model to incorporate these variables explicitly. The advantage of a larger model is its ability to deliver a coherent narrative that can accompany the forecasts. The disadvantages are that identification problems are often exacerbated in large-scale models, the numerical analysis, e.g., estimation procedures that utilize numerical optimization or posterior simulation routines, becomes more tenuous, and the maintenance of the model requires more staff resources. The second option is to develop a hybrid empirical model that augments a medium-scale core DSGE model with auxiliary equations that create a link between explicitly modelled variables and non-modelled variables. For brevity we will refer to the latter as non-core variables. One could interpret these auxiliary 3 The remainder of the paper is organized as follows. The DSGE model used for the empirical analysis is described in Section 2. We are using a variant of the Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) model, which is described in detail in DSSW. Our econometric framework is presented in Section 3. Section 4 summarizes the results of our empirical analysis. We estimate the DSGE model recursively based on U.S. quarterly data starting with a sample from 1984:I to 2000:IV and generate estimates of the latent states as well as pseudo-out-of-sample forecasts for a set of core variables, that is comprised of the growth rates of output, consumption, investment, nominal wages, the GDP deflator, as well as the levels of interest rates and hours worked. We then estimate measurement equations for four additional variables: personal consumption expenditures (PCE) inflation, core PCE inflation, the unemployment rate, and housing starts. We provide pseudo-out-of-sample forecast error statistics for both the core and non-core variables using our empirical model and compare them to simple AR(1) forecasts. Finally, we study the propagation of monetary policy shocks to auxiliary variables as well as features of the joint predictive distribution. Section 5 concludes and discusses future research. Details of the Bayesian computations are relegated to the Appendix. The DSGE Model We use a medium-scale New Keynesian model with price and wage rigidities, capital accumulation, investment adjustment costs, variable capital utilization, and habit formation. The model is based on the work of Smets and Wouters (2003) and Christiano, Eichenbaum, and Evans (2005) . The specific version is taken from DSSW. For brevity we only present the log-linearized equilibrium conditions and refer the reader to the above-referenced papers for the derivation of these conditions from assumptions on preferences and technologies. The economy is populated by a continuum of firms that combine capital and labor to produce differentiated intermediate goods. These firms have access to the same Cobb-Douglas production function with capital elasticity α and total factor productivity A t . Total factor productivity is assumed to be non-stationary. We denote its growth rate by a t = ln(A t /A t−1 ), which is assumed to have mean γ. Output, consumption, investment, capital, and the real wage can be detrended by A t . In terms of the detrended variables the model (2008), and Monti (2008) who develop state-space models that allow the analyst to use high frequency data or professional forecasts to update or improve the DSGE-model based forecasts of the core variables.
doi:10.2139/ssrn.1268319 fatcat:dpjhr7xhsjen5kmdpsrnfvjbci