Panel Data Analysis: Hierarchical Structures, Heterogeneity and Serial Dependence

Empirical analysis based on panel data facilitates the user on the one hand to specify richer models allowing for assessing dynamics and conditional effects, it requires on the other hand explicit handling of latent heterogeneity and serial dependence among the observations. Defining panel data as repeated measurements on the same sample of objects, it provides data referenced by two indices. Considering that panel data sets can be classified according to dimension and scale of the dependent variable under consideration, this lecture will discuss the statistical approaches prevailing within the literature to handle these features for typical panel data environments covering metric, binary, ordinal, and categorical dependent variables and dimensions of data sets ranging from small cross sections (sample size) and moderate time dimension (Macro panel or time series cross section data) to large cross sections with small time dimension (micro panel data). Parameter estimation within this model frameworks will be presented in terms of likelihood based estimation with extensive cross reference to alternative estimation procedures. Empirical illustration of the panel estimation routines will be based on typical publicly available panel data sets.

Day 1 – Lecture

The contents of day 1 will pay attention to the typical characteristics of panel data and highlight why these panel data characteristics may cause a failure of standard properties of estimators routinely used in the analysis of linear regression models. Based on a review of the Least Squares estimator in matrix notation, properties of Maximum Likelihood estimation and test routines, are assessed in the context of panel data. Next to the linear regression model as a workhorse for illustrating the effects of panel data on standard estimators, the lecture will discuss binary panel probit models as a model framework often applied in empirical analysis.

Day 1 – Computer Exercise

The computer exercise aims at providing hands on experience with the behaviour of standard estimators, e.g. the least squares estimator within the linear regression framework, when applied to panel data. This includes running simulations allowing for gauging the behaviour of the estimator, when classical assumptions such as homoscedasticity and absence of serial correlation among the errors of a linear regression model are violated. Next to estimators for the linear regression model, also estimation for the standard binary panel probit model is implemented to serve for the basis of upcoming panel extensions. The participants will learn how to use available implementations in R, as well as using own code developed in the course.

Day 2 – Lecture

The second lecture will present the typical modelling and estimation procedures to cope with latent heterogeneity and serial dependence. Next to use of robust standard errors, random coefficients as an extension to a random effects specification and cluster specific or fixed effects are discussed to deal with latent heterogeneity. The discussion will highlight how each of the proposed modelling devices copes with the incidental parameter problem inherent to panel data. The consequences on estimation for each of the modelling devices will be presented for both the linear regression model and the binary panel probit framework.

Day 3 – Computer Exercise

The participants will exercise the handling of panel data structures discussed in the lecture. One focus is set on interpretation the parameter estimates in empirical analysis using available code and data sets. Further, a focus is set also on using the discussed modelling devices in the context of unbalanced panel data sets, i.e. data sets with a different number of observations per sample unit.

Day 4 – Lecture

The lecture presents modelling of correlation dependence structures in Heckman type simultaneous regression frameworks. A special focus is set on the inherent identification problem and the robustness of parameter inference under alternative model specifications incorporating further panel structures to different degrees. Given the variety of model devices to cope with latent heterogeneity the lecture will present model specification tests that allow for checking the empirical adequacy of the different model specifications.

Day 4 – Computer Exercise

Estimation routines for the considered Heckman type simultaneous regression framework are implemented. Given the implemented estimation routines, model specification and testing devices are assessed for simulated as well as empirical data sets to assess their statistical power.

Day 5 – Lecture

As panel data are often based on surveys, missing values for single measurements on individuals will inevitably occur in any non-mandatory survey. Standard panel estimation routines in case of missing values have not only to face the risk to loose single observations per individual thus reducing estimation efficiency, but complete cross sectional units, thus inducing bias as well. As one possible strategy, the lecture will discuss the use of multiple imputation adapted towards panel data requirements with a short reference to alternative approaches based on direct modelling or data augmentation.

Day 5 – Computer Exercise

Participants will be presented possibilities to adapt existing multiple imputation routines towards panel data requirements. Given the provided implementation, the participants will check the effects of ignoring missing values in the data and accounting for the missing values by multiple imputation using both simulated and empirical data sets.

Participants should have knowledge of:

• Least-Squares Estimation in the Linear Regression Model under the classical assumptions
• Properties of sample means, sample variances, and the expectation operator
• Vector and matrix notation
• Principles of maximum likelihood estimation under standard regularity conditions
• Statistical software R