Structural Changes in High Dimensional Factor Models

该项目研究高维因子模型中的结构变化。结构性变化可能是技术进步、偏好变化或政策体制转变的结果。结构性变化意味着经济变量之间的关系不稳定。因素模型强调的是，几个共同的冲击可以解释大量经济变量的协同运动，因此高维数据集中的信息可以由少数共同因素来概括。近年来，不允许结构变化的要素模型在宏观经济和金融领域得到了广泛的应用。然而，结构变化如果被忽视，就会产生重要的后果，但如果考虑到它们的存在，就会带来相当大的好处。因此，从业者必须谨慎对待经济数据集潜在的结构性变化。这一担忧具有经验相关性，因为模型不稳定是经济数据中普遍存在的现象。这个项目考虑如何在高维因素模型中进行关于结构变化的推理。研究结果有助于评估政策变化的有效性，识别消费者偏好的制度变化，并构建更好的经济活动预测。高维因素模型中结构变化的推断是一个具有挑战性的问题，因为因素和因素负荷都是不可观测的，使得经典分析不适用。研究人员将开发计量经济学方法，同时估计因素、要素负荷和突破点。我们将研究小幅度和大幅度的破裂。这个项目旨在回答高维因素模型中结构变化引起的关键问题：在什么程度的突变下可以确定断点？研究人员如何描述估计的突破点的随机性？估计的断点是否存在极限分布？如果存在，极限分布采取什么形式？能否在不等待新制度的大量观察结果的情况下，迅速确定新制度的开始？后一个问题与横截面较大但时间段较少的数据集有关。本项目提供了回答这些问题的一般框架。

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.