Factor Models, Macro Forecasts, and Macroeconometrics

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The proposed research consists of five projects concerning factor models, macroeconomic forecasting, and macroeconometrics. One of the exciting frontiers of macroeconometrics is using the wealth of data - the large number of series - that are available in real time. Although a variety of methods are available for analyzing large numbers of macro series, the currently dominant framework is to model the series as jointly following a dynamic factor model, in which a small number of unobserved factors account for the comovements among the many observed time series. Recent econometric research has produced a rich body of theory concerning estimation of these factors and their subsequent use for forecasting and (more recently) for estimation of structural economic models. Two of the four research projects proposed here examine the appropriateness of dynamic factor models, in the first instance as applied to forecasting, in the second instance as a more general description of macroeconomic time series data. The proposed research on macroeconomic forecasting would step back and examine the extent to which there is additional predictive content in the large panel of time series, beyond that contained in the first few factors. The second, related project involves, among other things, examining how many dynamic factors there appear to be in U.S. macro time series data. The objective of both projects is, broadly, to provide credible evidence on the empirical validity of the approximation provided by the dynamic factor model. These proposed projects have both theoretical econometric and empirical components. A third related research project addresses the difficult but practically important problem of forecasting inflation. This focus on a single series might seem narrow, but it has broader methodological interest because it is a leading example of a series that has undergone substantial, well-documented changes in its time series process (it is now less volatile and, in some ways, less persistent). These changes are associated with breakdowns in previously successful inflation forecasting models. The proposed research entails developing a parsimonious characterization of the changes in the inflation process, then using this characterization to understand historical forecast breakdowns and, one hopes, to improve upon existing forecasting models. The final two research projects involve work on inference in the presence of weak identification in GMM and on specification testing in models of low-frequency fluctuations. Although there has been a great deal of recent work on forecasting with dynamic factor models, much less is known theoretically or empirically about the possible gains from moving beyond forecasts based on only a few factors. The proposed research would provide new theoretical and empirical results on forecasting with many predictors, relaxing the restrictions of dynamic factor models. The other aspects of the proposed research would focus on elucidating and resolving currently recognized problems with inflation forecasting models, in ways that could more generally inform forecasting with unstable systems. The proposed research on weak identification and on specification testing in models with low-frequency fluctuations involves developing new testing procedures that build on previous work by the PIs and others but are intellectually and substantively distinct. Broader Impacts The forecasting problems discussed in this proposal are of practical importance in government and industry. Some large-model forecasting systems, based on methods developed by the investigators, are in place. For example the Federal Reserve Bank of Chicago produces a monthly index that is an estimated real factor (the CFNAI) and model combination techniques developed by the investigators were used in a real time system at the U.S. Treasury. The goal of the research in the first part of this proposal is either to push beyond few-factor forecasts or to validate them against the alternative of many-factor forecasts. Although the results are yet unknown, those results should inform the evolution of these and subsequent real-time forecasting systems. Similarly, although inflation forecasting is of interest intellectually because of the instability of inflation, it is also of practical importance at the Federal Reserve Bank and elsewhere, and this research, if successful, should have practical payoffs for the inflation forecasting community. In addition, there is interest in the empirical research community in methods for inference with potentially weak instruments in time series GMM settings, and part of the proposed research aims to develop such methods. Finally, another impact of the proposed work would be graduate student training through their work on the proposed projects.