1. 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

2. Panel Data Analysis: Extension Generalized Random Effects Model

3. Panel Data Analysis : Extension Seemingly Unrelated Regression

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

5. Panel Data Analysis : Extension Cross Section Correlation –Parametric Representation

6. Panel Data Analysis : Extension Spatial Lag Variables Spatial Weights

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

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

9. 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 2SLS 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.

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

11. 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.

12. 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)

13. 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 w ij =1; otherwise w ij =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 2SLS methods should be used with proper instruments.

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