Factor Models, Macro Forecasts, and Macroeconometrics

本研究包含五个项目，分别涉及因素模型、宏观经济预测和宏观计量经济学。宏观计量经济学的一个令人兴奋的前沿领域是使用大量的数据--大量的序列--这些数据是在真实的时间内可用的。虽然有各种方法可用于分析大量的宏观序列，目前占主导地位的框架是建模的系列共同遵循动态因子模型，其中少数未观察到的因素占许多观察到的时间序列之间的共动。最近的计量经济学研究已经产生了大量的理论，涉及这些因素的估计及其随后用于预测和（最近）用于估计结构经济模型。这里提出的四个研究项目中的两个研究动态因素模型的适当性，第一种情况是应用于预测，第二种情况是作为宏观经济时间序列数据的更一般性描述。关于宏观经济预测的拟议研究将后退一步，审查除了前几个因素所包含的内容之外，在大量时间序列中还有多少其他预测内容。第二个相关项目涉及，除其他事项外，研究美国宏观时间序列数据中似乎有多少动态因素。这两个项目的目标是，广泛地说，提供可靠的证据的经验有效性的近似提供的动态因素模型。这些拟议的项目既有理论计量经济学的组成部分，也有经验的组成部分。第三个相关的研究项目涉及预测通货膨胀这一困难但实际上重要的问题。这种对单一系列的关注可能看起来很狭隘，但它具有更广泛的方法学意义，因为它是一个在其时间序列过程中经历了大量有据可查的变化的系列的一个主要例子（它现在不那么波动，在某些方面也不那么持久）。这些变化与以前成功的通货膨胀预测模型的崩溃有关。拟议中的研究需要开发一个简约的通货膨胀过程中的变化的特征，然后使用此特征来了解历史预测故障，并希望，以改善现有的预测模型。最后两个研究项目涉及的工作中存在的弱识别GMM和规范测试模型的低频波动的推断。虽然有大量的动态因素模型的预测与最近的工作，少得多的是知道从理论上或经验上的可能收益超越预测的基础上只有几个因素。该研究为多因子预测提供了新的理论和实证结果，放宽了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。拟议的研究弱识别和规范测试的模型与低频波动涉及开发新的测试程序，建立在以前的工作由PI和其他人，但智力和实质性的不同。更广泛的影响本提案中讨论的预测问题对政府和工业具有实际重要性。一些基于调查人员开发的方法的大型模型预测系统已经到位。 例如，芝加哥的联邦储备银行产生了一个月度指数，该指数是一个估计的真实的因素（CFNAI），由调查人员开发的模型组合技术被用于美国财政部的真实的时间系统。本提案第一部分的研究目标是，要么超越少数因素预测，要么根据多因素预测的替代方案验证这些预测。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，预测通货膨胀在理论上很有意义，但它在联邦储备银行和其他地方也具有重要的实际意义，这项研究如果成功，应该会给通货膨胀预测界带来实际回报。此外，有兴趣在实证研究界的推理方法与潜在的弱工具在时间序列GMM设置，部分拟议的研究旨在开发这样的方法。最后，拟议工作的另一个影响将是通过研究生在拟议项目上的工作进行培训。

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.