Panel data is a data type increasingly used in research in economics, social sciences, and medicine. Its primary characteristic is that the data variation goes jointly over space (across individuals, firms, countries, etc.) and time (over years, months, etc.). Panel data allow examination of problems that cannot be handled by cross-section data or time-series data. Panel data analysis is a core field in modern econometrics and multivariate statistics, and studies based on such data occupy a growing part of the field in many other disciplines.
The book is intended as a text for master and advanced undergraduate courses. It may also be useful for PhD-students writing theses in empirical and applied economics and readers conducting empirical work on their own. The book attempts to take the reader gradually from simple models and methods in scalar (simple vector) notation to more complex models in matrix notation. A distinctive feature is that more attention is given to unbalanced panel data, the measurement error problem, random coefficient approaches, the interface between panel data and aggregation, and the interface between unbalanced panels and truncated and censored data sets. The 12 chapters are intended to be largely self-contained, although there is also natural progression.
Most of the chapters contain commented examples based on genuine data, mainly taken from panel data applications to economics. Although the book, inter alia, through its use of examples, is aimed primarily at students of economics and econometrics, it may also be useful for readers in social sciences, psychology, and medicine, provided they have a sufficient background in statistics, notably basic regression analysis and elementary linear algebra.
1: Introduction
2: Regression Analysis: Fixed Effects Models
Appendix 2A. Properties of GLS
Appendix 2B. Kronecker-product Operations: Examples
3: Regression Analysis: Random Effects Models
Appendix 3A. Two Theorems related to GLS Estimation
4: Regression Analysis with Heterogeneous Coefficients
Appendix 4A. Matrix Inversion and Matrix Products: Useful Results
Appendix 4B. A Reinterpretation of the GLS Estimator
5: Regression Analysis with Uni-Dimensional Variables
6: Latent Heterogeneity Correlated with Regressors
Appendix 6A. Reinterpretation: Block-Recursive System
Appendix 6B. Proof of Consistency of the Two-Step Estimators
7: Measurement Errors
Appendix 7A. Asymptotics for Aggregate Estimators
8: Dynamics Models
Appendix 8A. Within Estimation of the AR Coefficient: Asymptotics
Appendix 8B. Autocovariances and Correlograms ?it and ?it
9: Analysis of Discrete Response
Appendix 9A. The General Binomial Model: ML Estimation
Appendix 9B. The Multinomial Logit Model: Conditional ML Estimation
10: Unbalanced Panel Data
Appendix 10A. Between-Estimation: Proofs
Appendix 10B. GLS Estimation: Proofs
Appendix 10C. Estimation of Variance Components: Details
11: Panel Data with Systematic Unbalance
Appendix 11A. On truncated normal distributions
Appendix 11B. Partial Effects in Censoring Models
12: Multi-Equation Models
Appendix 12A. Estimating the Error Components Covariance Matrices
Appendix 12B. Matrix Differentiation: Useful Results
Appendix 12C. Estimator Covariance Matrices in Interdependent Model
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