1. Data organization

2. Regression Models
Time series
Cross-sectional
Panel
Multi-dimensional panel

3. Errors in Uni-dimensional Data
In standard time series or cross-sectional data sets, we must adjust for non-independent errors.
Serial correlation
Errors correlated across time
Spatial correlation
Errors correlated across cross-sections
Heteroskedasticity
Error variance changes over time or cross-sections

4. Errors in Panel Data
Heterogeneous serial correlation
Errors correlated across time and differently for different cross-sections.
Heterogeneous spatial correlation
Errors correlated across cross-sections but differently for different time periods.
Heterogeneous heteroskedasticity
Error variance changes over time, but does so differently for different cross-sections.
Serial-spatial correlation
Past errors from one cross-section are correlated with future errors from a different cross-section.

5. Generalized Least Squares
The error covariance matrix shows the covariances of error terms across different observations.

6. Ordinary Least Squares Assumptions

7. Ordinary Least Squares (Heteroskedasticity)

8. Ordinary Least Squares (Serial Correlation)

9. Two-Dimensional Panel Data: OLS Assumptions

10. Two-Dimensional Panel Data: OLS Assumptions

11. Two-Dimensional Panel Data: OLS (homogeneous serial correlation)

12. Two-Dimensional Panel Data: OLS (heterogeneous serial correlation)

13. Two-Dimensional Panel Data: OLS (serial-spatial correlation)

14. OLS vs. Panel Estimation

15. Fixed versus Random Effects
Under the random effects assumption, and are treated as stochastic.
Under the fixed effects assumption, they are treated as fixed in repeated samples.

16. Random vs. Fixed Effects
Random Effects Assumption
Pro: Estimators are more efficient
Con: Estimators are inconsistent if any of the three errors are not IIN(0,σ2) across all dimensions.
Fixed Effects Assumption
Pro: Estimators are consistent regardless of and .
Con: Estimators are less efficient.
 See Hausman test for endogeneity.

17. Random vs. Fixed Cross-Sectional Effects
Test statistic = 22

18. Alternatives to Panel Techniques
Separate Regressions
Drawbacks
Less efficient estimators due to lost information about cross-sectional error covariance.
Remove the ability to restrict parameter values across cross-sections.

19. Alternatives to Panel Techniques
Pooled Regression
Drawbacks
Less efficient estimators due to lost information about cross-sectional error covariance.
Restricts parameter values to be equal across cross-sections.

20. Alternatives to Panel Techniques
Pooled Regression with Cross-Sectional Dummies
Drawbacks
This is the fixed effects panel technique.
If the cross-sectional dummies are IIN, then parameter estimates are less efficient than under the random effects panel technique.

21. Procedures to use with panel data
Generalized least squares (GLS)
Generalized method of moments (GMM)
OLS with “automated” corrections for serial correlation, etc. is GLS.

22. Extra stuff
Panel data reveals information that is unattainable with non-panel data.

23. Three-Dimensional Structure of the ASA-NBER Data Set

24. Shock Occurrence vs. Shock Impact
These shocks all impact inflation in quarter 9 but occur in different quarters.
These shocks all occur in quarter 6 but impact inflation in different quarters.

25. Cross-sectional shocks
Shock Occurrence vs. Shock Impact
Cumulative shocks
Cross-sectional shocks
Discrete shocks

26. Shock Occurrence vs. Shock Impact