Monika Avila Márquez Souchon,
Ph.D. in Econometrics

This paper investigates the identification and estimation of dynamic heterogeneous linear models for unbalanced panel data at the cluster level when the clustering structure is known, and the number of time periods is short (greater than or equal to 3).   For this purpose,  we use a linear panel data model with additive cluster fixed effects and a mixed coefficient structure composed of cluster-specific fixed effects and random cluster-individual-time specific effects.   We propose a Mean Cluster-FGLS estimator and a Mean Cluster-OLS estimator to estimate the mean coefficients.   In order to make the GLS estimation of the cluster-specific parameters feasible,  we introduce a ridge estimator of the variance-covariance matrix of the model.   The Mean Cluster estimators are consistent: i) under stratified sampling when the number of clusters is fixed,  the proportion of observed clusters is equal to 1, and the number of individuals per cluster grows to infinity, or ii) under cluster sampling when the square root of the number of clusters grows at a slower rate than the growth rate of the number of individuals per cluster.   In addition,  we present two extensions of the baseline model.   In the first one,  we allow for cluster-individual specific fixed effects instead of cluster additive fixed effects.   In this setting,  we propose a Hierarchical Bayesian estimator that considers the problem of unknown initial conditions.   In the second extension,  we allow for cross-sectional dependence by including common factors.   We propose the Mean Cluster estimator using the time-demeaned variables to estimate this model.