Structural Changes in High Dimensional Factor Models
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.