Normative Studies of Portfolio Choice and Risk Management

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Macroeconomists in business and government operate in a data-rich environment. For example, in the United States data on thousands of economic time series are available monthly. Recently, there has been theoretical and applied interest in developing forecasting methods that exploit this wealth of information in a way that is systematic, replicable, and subject to scientific analysis. The results have been encouraging: the first few estimated factors from large dynamic factor models (hundreds of predictors) appear to have predictive content for the main economic aggregates -real activity and inflation - that is unavailable in smaller systems. Within the past year, two Central Banks (the Federal Reserve Bank of Chicago and the Bank of Italy/CEPR) have started releasing real-time many-variable activity indexes. Research to date on many-predictor macroeconomic forecasts has centered on approximate factor structures that, while useful as data reduction methods, constitute only one way to approach large data sets; moreover, the models investigated so far are essentially time-invariant. The objective of the research outlined in this proposal is to move beyond the first few estimated factors from time-invariant systems and thereby to investigate many-predictor time series forecasts in potentially time-varying systems. This proposal contains four specific projects within this broader research agenda. The objective of the first project is to develop empirical Bayes methods for linear time- invariant models that exploit information in the many predictors, beyond what is contained in their first few estimated dynamic factors. The purpose of the second project is to estimate linear prediction bounds, that is, upper bounds on the population of forecasts made using linear time-invariant equations with many predictors. There is substantial evidence that low-dimensional macroeconomic forecasting relations are unstable over time. The next two projects extend the work on many-predictor forecasting to models with time variation. The objective of the third project is to develop tests for time variation in models with many predictors and to develop and to implement estimators that exploit this time variation. The objective of the fourth project is to provide a coherent resolution of the "forecasting combining puzzle" (the result that simple means or trimmed means of panels of macroeconomic forecasts outperform individual forecasts and typically are stable even when the individual forecasts are not); it is hoped that this will lead to many-predictor forecasting methods that are robust to time variation. Finally, it is proposed to apply some of the methods developed in this research to a different problem, instrumental variables regression with many weak instruments, and to continue other ongoing work in the area of weak instruments. It is hoped that the proposed research will have broader impacts on practical forecasting. For example, the ongoing real-time projects at U.S. and European central banks builds on previous work by the Principal Investigators and others on high-dimensional systems, and it is hoped that the tools developed in the proposed research will be useful in those and related projects.