ASYMPTOTIC PROPERTIES OF THE CUSUM ESTIMATOR FOR THE TIME OF CHANGE IN LINEAR PANEL DATA MODELS
研究了面板数据均值参数共同变化时点的估计问题，提出了CUSUM型估计量，建立了可用于构造一致置信区间的一阶和二阶渐近理论，并通过蒙特卡洛模拟和两个真实数据集验证了方法的有效性。
We consider the problem of estimating the common time of a change in the mean parameters of panel data when dependence is allowed between the cross-sectional units in the form of a common factor. A CUSUM type estimator is proposed, and we establish first and second order asymptotics that can be used to derive consistent confidence intervals for the time of change. Our results improve upon existing theory in two primary directions. Firstly, the conditions we impose on the model errors only pertain to the order of their long run moments, and hence our results hold for nearly all stationary time series models of interest, including nonlinear time series like the ARCH and GARCH processes. Secondly, we study how the asymptotic distribution and norming sequences of the estimator depend on the magnitude of the changes in each cross-section and the common factor loadings. The performance of our results in finite samples is demonstrated with a Monte Carlo simulation study, and we consider applications to two real data sets: the exchange rates of 23 currencies with respect to the US dollar, and the GDP per capita in 113 countries.