Dynamic Heterogeneous Linear Models for Three-level Panel Data with Short Time Dimension and Stratification

Most national survey data are obtained through a sampling scheme that is stratified at multiple levels such as regions, socioeconomic groups, gender, etc., to ensure adequate representativeness of the underlying population. In such a design, the strata as well as the membership of individuals into a stratum are known. This chapter considers a three-level dynamic panel data model, the levels being group (stratum), individual (household, firm etc.) and time. It specifies a model with additive stratum fixed effects and a mixed coefficients structure composed of stratum-specific fixed effects and random stratum-individual-time specific effects. We examine the identification and estimation of this dynamic heterogeneous three-level linear panel data model under stratification when the time dimension is as short as 3. We propose a Mean Stratum-FGLS estimator and a Mean Stratum-OLS estimator to estimate the mean coefficients. To make the GLS estimation of the Stratum-specific parameters feasible, we introduce a ridge estimator of the variance-covariance matrix of the model. We show consistency and asymptotic normality of the Mean Stratum estimators for short panels, under the assumptions that apply to stratified sampling such as the number of strata (groups) is fixed, all strata are observed, and the number of individuals per stratum is large (growing to infinity).We also show the consistency of the variance parameter estimators. We discuss similarities and differences between our specification and a dynamic two-level panel data model with random coefficients. Finally, we discuss the setup of long time span.