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Panel Data Analysis Using GAUSS

Panel Data Analysis Using GAUSS. 2 Kuan-Pin Lin Portland State University. Fixed Effects Model. Within Model Representation. Fixed Effects Model. Model Assumptions. Fixed Effects Model Model Estimation. Within Estimator: FE-GLS.

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Panel Data Analysis Using GAUSS

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  1. Panel Data AnalysisUsing GAUSS 2 Kuan-Pin LinPortland 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 [FT,T-1,1T/T] be the orthonormal matrix of the eigenvectors of QT = IT-iTi’T/T, where FT,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 ModelHypothesis 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 ModelModel 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 ModelModel Estimation • First-Difference Estimator: GLS

  14. First-Difference ModelModel Estimation: Transformation Approach • The first-difference operator D is a (T-1)xT matrix with elements: • Using the transformation matrix (DD)-1/2D, then we have the Forward Orthogonal Deviation Model:

  15. First-Difference ModelModel 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.

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