1. Panel Data Analysis Using GAUSS 2 Kuan-Pin Lin Portland State University

2. Fixed Effects Model Within Model Representation

3. Fixed Effects Model Model Assumptions

4. Fixed Effects Model Model Estimation Within Estimator: FE-GLS

5. Fixed Effects Model Model Estimation: Transformation Approach Let [F T,T-1,1 T /  T] be the orthonormal matrix of the eigenvectors of Q T = I T -i T i ’ T /T, where F T,T-1 is the Tx(T-1) eigenvector matrix corresponding to the eigenvalues of 1. Define

6. Fixed Effects Model Model Estimation Panel-Robust Variance-Covariance Matrix Consistent statistical inference for general heteroscedasticity, time series and cross section correlation.

7. Fixed Effects Model Model Estimation: ML Normality Assumption

8. Fixed Effects Model Model Estimation: ML Log-Likelihood Function Since Q is singular and |Q|=0, we use orthonomral transformation of the eigenvectors of Q, we maximize

9. Fixed Effects Model Model Estimation: ML ML Estimator

10. Fixed Effects Model Hypothesis Testing Pool or Not Pool F-Test based on dummy variable model: constant or zero coefficients for D w.r.t F(N-1,NT-N-K) F-test based on fixed effects (unrestricted) model vs. pooled (restricted) model

11. First-Difference Model First-Difference Representation Model Assumptions

12. First-Difference Model Model Estimation First-Difference Estimator: OLS Consistent statistical inference for general heteroscedasticity, time series and cross section correlation should be based on panel-robust variance- covariance matrix.

13. First-Difference Model Model Estimation First-Difference Estimator: GLS

14. First-Difference Model Model Estimation: Transformation Approach The first-difference operator  is a (T-1)xT matrix with elements: Using the transformation matrix (   , then we have the Forward Orthogonal Deviation Model:

15. First-Difference Model Model Estimation: Transformation Approach FD-GLS Consistent statistical inference for general heteroscedasticity, time series and cross section correlation should be based on panel-robust variance- covariance matrix.

16. References B. H. Baltagi, Econometric Analysis of Panel Data, 4th ed., John Wiley, New York, 2008. W. H. Greene, Econometric Analysis, 7th ed., Chapter 11: Models for Panel Data, Prentice Hall, 2011. C. Hsiao, Analysis of Panel Data, 2nd ed., Cambridge University Press, 2003. J. M. Wooldridge, Econometric Analysis of Cross Section and Panel Data, The MIT Press, 2002.