Structural Changes in High Dimensional Factor Models

本项目研究高维因子模型的结构变化。结构变化可能是技术进步、偏好变化或政策体制转变的结果。结构变化意味着经济变量之间的关系不稳定。因子模型强调的是，一些共同的冲击可以解释大量经济变量的共同运动，因此高维数据集中的信息可以由少数共同因素总结。近年来，不允许结构变化的因子模型在宏观经济和金融领域得到了广泛的应用。然而，结构性变化如果被忽视，就会产生重要的后果，但如果适当地加以考虑，就会带来相当大的好处。因此，从业者必须对经济数据集中潜在的结构性变化保持谨慎。由于模型不稳定性是经济数据中普遍存在的现象，因此这种担忧具有经验相关性。本课题研究如何在高维因子模型中对结构变化进行推理。研究结果对于评估政策变化的有效性、识别消费者偏好的制度变化以及构建更好的经济活动预测都是有用的。高维因子模型中结构变化的推断是一个具有挑战性的问题，因为因子和因子载荷都是不可观测的，使得经典分析不适用。研究者将开发计量经济学方法，同时估计因素、因素负荷和断点。将研究小幅度和大幅度的断裂。该项目旨在回答高维因子模型中结构变化引起的关键问题：在多大程度的断裂下可以确定断点？研究人员如何描述估计断点的随机性？是否存在估计断点的极限分布，如果存在，极限分布的形式是什么？在不等待新体制的许多观察结果的情况下，能否迅速确定新体制的开始？后一个问题与具有较大横截面但时间段较少的数据集相关。本项目为回答这些问题提供了一个总体框架。

This project studies structural changes in high dimensional factor models. Structural changes can be the consequence of technical progress, changes in preference, or policy regime shifts. Structural changes imply unstable relationships among economic variables. What underlines factor models is that a few common shocks can explain the co-movement of a large number of economic variables, so that information in a high dimensional data set can be summarized by a small number of common factors. Recently, factor models without permitting structural changes have been widely used in macroeconomics and finance. However, structural changes have important consequences when ignored but provide considerable benefits when appropriately accounted for given their presence. Therefore, practitioners have to be cautious about the potential structural changes in economic datasets. This concern is empirically relevant because model instability is a pervasive phenomenon for economic data. This project considers how to conduct inference about structural changes in high dimensional factor models. The research results are useful in evaluating the effectiveness of a policy change, in identifying regime shifts in consumer preferences, and in constructing better forecasts of economic activity. Inference for structural changes in high dimensional factor models is a challenging problem because both factors and factor loadings are unobservable, making classical analysis not applicable. The investigator will develop econometric methods that simultaneously estimate the factors, factor loadings, and the break points. Both small and large magnitudes of breaks will be studied. This project aims to answer critical questions arising from structural changes in high dimensional factor models: Under what magnitude of breaks can the break points be identified? How can researchers characterize the randomness of the estimated break points? Does there exist a limiting distribution for the estimated break points, and if so, what form does the limiting distribution take? Can the onset of a new regime be quickly identified without waiting for many observations from the new regime? The latter question is relevant for datasets with a large cross section but a small number of time periods. This project provides a general framework to answer these questions.