Economic Forecasting Models with Many Predictors

企业和政府的宏观经济学家在数据丰富的环境中工作。例如，在美国，每月可获得数千个经济时间序列的数据。最近，有理论和应用的兴趣，开发预测方法，利用这种丰富的信息的方式是系统的，可复制的，并进行科学分析。结果令人鼓舞：大型动态因素模型（数百个预测因子）的最初几个估计因子似乎对主要经济总量-真实的活动和通货膨胀-具有预测内容，而这在较小的系统中是无法实现的。在过去一年中，两家中央银行（芝加哥联邦储备银行和意大利银行/CEPR）已开始发布实时多变量活动指数。迄今为止，对多预测因子宏观经济预测的研究主要集中在近似因子结构上，这种近似因子结构虽然作为数据简化方法很有用，但仅构成接近大型数据集的一种方法;此外，迄今为止研究的模型基本上是时不变的。在这个建议中概述的研究的目标是超越前几个估计因素的时不变系统，从而调查潜在的时变系统中的多预测器的时间序列预测。该提案在这一更广泛的研究议程内包含四个具体项目。第一个项目的目标是为线性时不变模型开发经验贝叶斯方法，该方法利用许多预测因子中的信息，超出其最初几个估计动态因子中所包含的信息。第二个项目的目的是估计线性预测界，即使用具有许多预测因子的线性时不变方程进行预测的总体上界。大量证据表明，低维宏观经济预测关系随着时间的推移是不稳定的。接下来的两个项目将多预测因子预测的工作扩展到具有时间变化的模型。第三个项目的目标是对具有许多预测因子的模型的时间变化进行测试，并开发和实施利用这种时间变化的估计器。第四个项目的目标是为“预测组合难题”提供一个连贯的解决办法（结果是宏观经济预测面板的简单方法或修剪方法优于个别预测，即使个别预测不稳定，通常也是稳定的）;希望这将导致对时间变化具有鲁棒性的多预测器预测方法。最后，建议将本研究中开发的一些方法应用于不同的问题，具有许多弱工具的工具变量回归，并继续在弱工具领域进行其他正在进行的工作。希望拟议的研究将对实际预测产生更广泛的影响。例如，美国和欧洲中央银行正在进行的实时项目建立在首席研究员和其他人以前对高维系统的工作基础上，希望在拟议的研究中开发的工具将在这些和相关项目中有用。

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.