Efficient Econometric Shrinkage and Forecasting

在实证研究或政策分析过程中，经济学家通常会估计复杂的高维模型。有一套标准的估计方法，为这些目的而开发，这些估计量共享的属性，他们有近似的正态分布。然而，众所周知，正态分布估计量可以得到改善（具有降低的风险），如果它们朝着参数空间中的预先指定的点收缩（限制或更简单的模型）。这表明，一般的计量经济学估计量可以通过收缩到限制估计量来改进。PI开发了一般收缩估计，其风险（统计预期损失）小于传统的估计。这些新的估计量是有效的，这意味着它们的风险是所有可行估计量中最低的。该项目提出了参数模型（由有限参数集定义的模型）和半参数模型（当模型的某些特征被视为非参数或高维时）的有效方法。与有效估计问题密切相关的是模型选择和组合技术。这些问题与经济预测特别相关，在经济预测中，预测组合是常规应用的，但对于组合权重的选择几乎没有理论指导。这项建议的重点是制定严格的标准，在多步预测的背景下选择组合权重。多步预测对于政策分析至关重要，但也有特殊的技术挑战。本计画研究直接预测、重复预测及预测区间的方法。本建议中提出的计量经济学方法有望在应用经济分析、政策分析和经济预测中得到广泛应用。预计这项研究所揭示的理论和方法将被学术界和公共部门的应用经济学家、统计学家和其他社会科学家所利用。

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.