Econometric Analysis of Panel Data Panel Data Analysis

Econometric Analysis of Panel Data • Panel Data Analysis: Extension – Generalized Random Effects Model • Seemingly Unrelated Regression – Cross Section Correlation • Parametric representation • Spatial dependence defined by cross section contiguity or distance

Panel Data Analysis: Extension • Generalized Random Effects Model

Panel Data Analysis : Extension • Seemingly Unrelated Regression

Panel Data Analysis : Extension • Cross Section Correlation – Unobserved heterogeneity: fixed effects or random effects – OLS with robust inference – GLS allowing time serial correlation

Panel Data Analysis : Extension • Cross Section Correlation – Parametric Representation

Panel Data Analysis : Extension • Spatial Lag Variables • Spatial Weights

Panel Data Analysis : Extension • Spatial Lag Model – OLS is biased and inconsistent – Unobserved heterogeneity: fixed effects or random effects – Observed heterogeneity

Panel Data Analysis : Extension • Spatial Error Model – Unobserved heterogeneity • Fixed effects • Random effects – Observed heterogeneity

Panel Data Analysis : Extension • Spatial Panel Data Analysis – Model specification could be a mixed structure of spatial lag and spatial error model. – Unobserved heterogeneity could be fixed effects or random effects. – OLS is biased and inconsistent; Consistent IV or 2 SLS should be used, with robust inference. – If normality assumption of the model is maintained, efficient ML estimation could be used but with computational complexity. – Efficient GMM estimation is recommended.

Panel Data Analysis : Extension • Panel Spatial Model Estimation – IV / 2 SLS / GMM – Instrumental variables for the spatial lag variable Wyt: [Xt, W 2 Xt, …] – W is a predetermined spatial weights matrix based on geographical contiguity or distance:

Panel Data Analysis : Extension • Space-Time Dynamic Model • Arellano-Bond estimator may be extended to include cross section correlation in the space-time dynamic models.

Example: U. S. Productivity • The Model (Munnell [1988]) – One-way panel data model – 48 U. S. lower states – 17 years from 1970 to 1986 – Variables: gsp (gross state output); cap (private capital); 3 components of public capital (hwy, water, util); emp (labor employment); unemp (unemployment rate)

Example: U. S. Productivity • Spatial Panel Data Model – Cross Section Correlation • Cross section dependence is defined by state contiguity: if state i is adjacent with state j, then wij=1; otherwise wij=0. The spatial weights matrix W is then row-standardized with diagonal 0. • Pooled, fixed effects, random effects models are all biased and inconsistent. IV or 2 SLS methods should be used with proper instruments.

Example: U. S. Productivity • Spatial Panel Data Model – Space-Time Dynamics