Efficient Econometric Shrinkage and Forecasting

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In the course of empirical research or policy analysis, economists typically estimate sophisticated high-dimensional models. There are a set of standard estimation methods developed for these purposes, and these estimators share the property that they have approximate normal distributions. However, it is well known that normally-distributed estimators can be improved (have reduced risk) if they are shrunk towards a pre-specified point in the parameter space (a restriction or simpler model of interest). This suggests that common econometric estimators can be improved by shrinkage towards restricted estimators.This proposal suggests that this insight can be made rigorous. The PI develops general shrinkage estimators whose risk (the statistical expected loss) is smaller than conventional estimators. These new estimators are efficient, meaning that their risk is the lowest possible among all feasible estimators. This project proposes efficient methods for both parametric models (those defined by a finite set of parameters) and semiparametric models (when some features of the model are treated as nonparametric or high dimensional).Closely related to the question of efficient estimation is the technique of model selection and combination. These issues are particularly relevant for economic forecasting, where forecast combination is routinely applied, yet little theoretical guidance exists for selection of the combination weights. This proposal focuses on developing rigorous criteria for selection of combination weights in the context of multi-step forecasts. Multi-step forecasts are critical for policy analysis, yet have particular technical challenges. This project investigates methods for direct forecasts, iterated forecasts, and forecast intervals. The econometric methods developed in this proposal are expected to have broad application in applied economic analysis, policy analysis, and economic forecasting. It is expected that the theory and methods uncovered by this research will find productive use by applied economists, statisticians, and other social scientists both in academics and the public sector.