Factor Models, Macro Forecasts, and Macroeconometrics

本研究包括因子模型、宏观经济预测和宏观计量经济学五个项目。宏观计量经济学令人兴奋的前沿之一是利用大量实时可用的数据——大量的序列。虽然分析大量宏观序列的方法多种多样，但目前占主导地位的框架是将序列建模为共同遵循动态因子模型，其中少数未观察到的因素解释了许多观察到的时间序列之间的运动。最近的计量经济学研究已经产生了丰富的理论体系，涉及这些因素的估计及其随后用于预测和（最近的）结构经济模型的估计。在这里提出的四个研究项目中，有两个研究了动态因素模型的适当性，首先是用于预测，其次是作为宏观经济时间序列数据的更一般描述。关于宏观经济预测的拟议研究将退后一步，审查除了前几个因素所包含的预测内容外，在大的时间序列面板中还有多少其他预测内容。第二个相关的项目，除其他事项外，包括检查美国宏观时间序列数据中似乎有多少动态因素。从广义上讲，这两个项目的目标是为动态因子模型提供的近似的经验有效性提供可信的证据。这些拟议的项目既有理论计量经济成分，也有实证成分。第三个相关研究项目解决了预测通胀这一困难但实际上很重要的问题。这种对单个序列的关注可能看起来很狭隘，但它具有更广泛的方法论兴趣，因为它是在其时间序列过程中经历了实质性的、记录良好的变化的序列的主要示例（它现在不那么不稳定，并且在某些方面不那么持久）。这些变化与之前成功的通胀预测模型的失效有关。拟议的研究需要对通货膨胀过程中的变化进行简洁的描述，然后利用这种描述来理解历史预测的细分，并希望改进现有的预测模型。最后两个研究项目涉及GMM中存在弱识别的推理和低频波动模型的规范测试。尽管最近有大量关于动态因素模型预测的工作，但从理论上或经验上对超越仅基于少数因素的预测可能获得的收益知之甚少。本文的研究将为多预测因子预测提供新的理论和实证结果，放宽动态因子模型的限制。拟议研究的其他方面将侧重于阐明和解决目前公认的通货膨胀预测模型问题，其方式可以更普遍地为不稳定系统的预测提供信息。拟议的关于弱识别和低频波动模型的规格测试的研究涉及开发新的测试程序，这些程序以pi和其他人以前的工作为基础，但在智力上和实质上是不同的。本文所讨论的预测问题在政府和工业界都具有重要的实际意义。一些基于研究人员开发的方法的大型模型预测系统已经就位。例如，芝加哥联邦储备银行（Federal Reserve Bank of Chicago）每月编制一个估算真实因素的指数（CFNAI），调查人员开发的模型组合技术被用于美国财政部的一个实时系统。本提案第一部分的研究目标是要么超越少因素预测，要么验证它们与多因素预测的替代方案。虽然结果尚不清楚，但这些结果应该为这些和随后的实时预报系统的发展提供信息。同样，尽管由于通货膨胀的不稳定性，通货膨胀预测在智力上引起了人们的兴趣，但它在联邦储备银行和其他地方也具有实际重要性，而且这项研究如果成功，应该会对通货膨胀预测界产生实际的回报。此外，实证研究界对在时间序列GMM设置中使用潜在弱工具进行推理的方法很感兴趣，部分拟议的研究旨在开发此类方法。最后，拟议工作的另一个影响是通过对拟议项目的工作对研究生进行培训。

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.