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Econometric Analysis of Panel Data

Econometric Analysis of Panel Data. Panel Data Analysis Random Effects Assumptions GLS Estimator Panel-Robust Variance-Covariance Matrix ML Estimator Hypothesis Testing Test for Random Effects Fixed Effects vs. Random Effects. Panel Data Analysis. Random Effects Model

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Econometric Analysis of Panel Data

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  1. Econometric Analysis of Panel Data • Panel Data Analysis • Random Effects • Assumptions • GLS Estimator • Panel-Robust Variance-Covariance Matrix • ML Estimator • Hypothesis Testing • Test for Random Effects • Fixed Effects vs. Random Effects

  2. Panel Data Analysis • Random Effects Model • ui is random, independent of eit and xit. • Define eit = ui + eit the error components.

  3. Random Effects Model • Assumptions • Strict Exogeneity • X includes a constant term, otherwise E(ui|X)=u. • Homoschedasticity • Constant Auto-covariance (within panels)

  4. Random Effects Model • Assumptions • Cross Section Independence

  5. Random Effects Model • Extensions • Weak Exogeneity • Heteroscedasticity and Autocorrelation • Cross Section Correlation

  6. Model Estimation: GLS • Model Representation

  7. Model Estimation: GLS GLS

  8. Model Estimation: RE-OLS • Partial Group Mean Deviations

  9. Model Estimation: RE-OLS • Model Assumptions • OLS

  10. Model Estimation: RE-OLS • Need a consistent estimator of q: • Estimate the fixed effects model to obtain • Estimate the pooled model to obtain • Based on the estimated large sample variances, it is safe to obtain

  11. Model Estimation: RE-OLS • Panel-Robust Variance-Covariance Matrix • Consistent statistical inference for general heteroscedasticity, time series and cross section correlation.

  12. Model Estimation: ML • Log-Likelihood Function

  13. Model Estimation: ML • ML Estimator

  14. Hypothesis Testing • Test for Var(ui) = 0, that is • If Ti=T for all i, the Lagrange-multiplier test statistic (Breusch-Pagan, 1980) is:

  15. Hypothesis Testing • For unbalanced panels, the modified Breusch-Pagan LM test for random effects (Baltagi-Li, 1990) is: • Alternative one-side test:

  16. Hypothesis Testing • Fixed Effects vs. Random Effects

  17. Hypothesis Testing • Fixed effects estimator is consistent under H0 and H1; Random effects estimator is efficient under H0, but it is inconsistent under H1. • Hausman Test Statistic

  18. Hypothesis Testing • Alternative Hausman Test • Estimate the random effects model • F Test that g = 0

  19. Example: Investment Demand • Grunfeld and Griliches [1960] • i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years: 1935-1954 • Iit = Gross investment • Fit = Market value • Cit = Value of the stock of plant and equipment

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