The Common Break Date for Factor Models In Long and Short Panels: Estimation and Inference

Description

High-dimensional factor models are powerful tools to analyze the common driving force of a large number of variables in economics and finance. These models are usually estimated under the assumption that the parameters in the model are stable over time. This assumption is likely to be violated in practice. We are interested in the setup where the factor loading coefficients change at a certain point of time, which is the so called structural break. Once practitioners know the existence of a break in the model, the next question of interest is to find the date of the break. Some methods have been developed to estimate the break point, but most of them cannot characterize the estimation uncertainty of the estimator in finite samples. In contrast, confidence intervals provide interval estimates instead of point estimates, so they account for the estimation uncertainty in finite samples. This project is interested in how to onstruct valid confidence intervals, which contain the true break point at a pre-specified probability level.The computation of confidence intervals is usually based on the limiting distribution of the estimator. To the best of our knowledge, our previous work (Bai, Han and Shi, 2019, BHS hereafter, accepted at Journal of Econometrics) is the only study that considers the limiting distribution of the break point estimator in factor models. BHS show that the distribution depends on the data generating process of the unobserved factors. Hence, it is practically difficult to directly apply the result of BHS to construct confidence intervals. Moreover, BHS only considered factor models with long time span. Their theory cannot be applied when the time span is short. This project plans to extend the theory of BHS in several aspects. First, we will develop theoretically valid and practically feasible methods to construct confidence intervals for the estimated break point. These methods are based on the bootstrap and simulationtechniques. The distribution of the estimated break point based on the resampled data resembles the distribution of the estimator based on the original data. Preliminary simulation experiments show that these methods are promising. We will develop a theoryfor these methods. Second, we will develop a method to estimate break points in factor models with short time span to complement the BHS theory. The new method allows practitioners to detect the break soon after the break date so that forecasts and policiescan be promptly updated and adjusted.