Bootstrap for panel data models with an application to the evaluation of public policies

The purpose of this thesis is to develop bootstrap methods for panel data models and to prove their validity. Panel data refers to data sets where observations on individual units (such as households, firms or countries) are available over several time periods. The availability of two dimensions (cross-section and time series) allows for the identi cation of effects that could not be accounted for otherwise. In this thesis, we explore the use of the bootstrap to obtain estimates of the distribution of statistics that are more accurate than the usual asymptotic theory. The method consists in drawing many ran- dom samples that resembles the sample as much as possible and estimating the distribution of the object of interest over these random samples. It has been shown, both theoretically and in simulations, that in many instances,this approach improves on asymptotic approximations. In other words, the resulting tests have a rejection rate close to the nominal size under the null hypothesis and the resulting con dence intervals have a probability of inclu- ding the true value of the parameter that is close to the desired level. In the literature, there are many applications of the bootstrap with panel data, but these methods are carried out without rigorous theoretical justi fication. This thesis suggests a bootstrap method that is suited to panel data (which we call double resampling), analyzes its validity, and implements it in the analysis of treatment e¤ects. The aim is to provide a method that will provide reliable inference without having to make strong assumptions on the underlying data-generating process. The  rst chapter considers a model with a single parameter (the overall expectation) with the sample mean as estimator. We show that our double resampling is valid for panel data models with some cross section and/or temporal heterogeneity. The assumptions made include one-way and two- way error component models as well as factor models that have become popular with large panels. On the other hand, alternative methods such as bootstrapping cross-sections or blocks in the time dimensions are only valid under some of these models. The second chapter extends the previous one to the panel linear regression model. Three kinds of regressors are considered : individual characteristics, temporal characteristics and regressors varying across periods and cross-sectional units. We show that our double resampling is valid for inference about all the coe¢ cients in the model estimated by ordinary least squares under general types of time-series and cross-sectional dependence. Again, we show that other bootstrap methods are only valid under more restrictive conditions. Finally, the third chapter re-examines the analysis of di¤erences-in-differences estimators by Bertrand, Du o and Mullainathan (2004). Their empirical application uses panel data from the Current Population Survey on wages of women in the 50 states. Placebo laws are generated at the state level, and the authors measure their impact on wages. By construction, no impact should be found. Bertrand, Dufl o and Mullainathan (2004) show that neglected heterogeneity and temporal correlation lead to spurious  ndings of an effect of the Placebo laws. The double resampling method developed in this thesis corrects these size distortions very well and gives more reliable evaluation of public policies.

Keyphrases: Panel data models, Bootstrap, Public Policy Evaluation