## Project CEMAPRE internal

Title | Application of self-normalization approaches for statistical testing in panel data |

Participants | Paulo M. M. Rodrigues, Nuno Sobreira (Principal Investigator) |

Summary | Panel data is a fairly prevalent type of data structure used in applied econometrics and it is becoming more important nowadays with the increased availability of data. An important assumption for panel data analysis and modeling is to ensure its structural stability throughout time. Hence, in this project we start by proposing a new statistic to test for the presence of a mean shift in a set of panel data observations. We consider a type of panel CUSUM test where a self-normalization approach is used to correct for serial correlation. Hence, instead of using one of the standard robust estimators for the long-run variances, our suggestion is to divide the statistic by a quantity that cancels the long-run variance in each panel so that the corresponding asymptotic distribution becomes free of these nuisance parameters. This alternative route has already been proposed and developed for time series by a number of authors and it has already been proven to be a relevant alternative to the traditional HAC estimator in the context of time series analysis. In particular, self-normalization avoids the always difficult choice of the kernel function and corresponding bandwidth parameter in empirical applications. Moreover, the use of HAC estimators in mean shift test statistics is associated with either severe size distortions or nonmonotonic power functions. However applications of a self-normalization approach to panel data data are nonexistent or relatively scarce. Hence we study in depth this alternative route to correct for serial correlation in panel data analysis in the context of testing for the presence of shifts in the mean of at least some of the panel units. The next step of this project is to analyse the relevance of this self-normalization approach to other statistical testing problems in the context of panel data analysis. |