Panel%20Data%20Analysis%20Using%20GAUSS

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Panel Data Analysis Using GAUSS

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• Kuan-Pin LinPortland State University

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Fixed Effects Model

• Within Model Representation

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Fixed Effects Model

• Model Assumptions

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Fixed Effects Model Model Estimation

• Within Estimator FE-GLS

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Fixed Effects Model Model Estimation
Transformation Approach

• Let FT,T-1,1T/?T be the orthonormal matrix of
  the eigenvectors of QT IT-iTiT/T, where FT,T-1
  is the Tx(T-1) eigenvector matrix corresponding
  to the eigenvalues of 1. Define

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Fixed Effects Model Model Estimation

• Panel-Robust Variance-Covariance Matrix
• Consistent statistical inference for general
  heteroscedasticity, time series and cross section
  correlation.

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Fixed Effects Model Model Estimation ML

• Normality Assumption

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Fixed Effects Model Model Estimation ML

• Log-Likelihood Function
• Since Q is singular and Q0, we use orthonomral
  transformation of the eigenvectors of Q, we
  maximize

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Fixed Effects Model Model Estimation ML

• ML Estimator

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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

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First-Difference Model

• First-Difference Representation
• Model Assumptions

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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.

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First-Difference ModelModel Estimation

• First-Difference Estimator GLS

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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

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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.

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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.