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Econometric Analysis of Panel Data

Econometric Analysis of Panel Data. Panel Data Analysis Fixed Effects Dummy Variable Estimator Between and Within Estimator First-Difference Estimator Panel-Robust Variance-Covariance Matrix Heteroscedasticity and Autocorrelation Cross Section Correlation Hypothesis Testing

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Econometric Analysis of Panel Data

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  1. Econometric Analysis of Panel Data • Panel Data Analysis • Fixed Effects • Dummy Variable Estimator • Between and Within Estimator • First-Difference Estimator • Panel-Robust Variance-Covariance Matrix • Heteroscedasticity and Autocorrelation • Cross Section Correlation • Hypothesis Testing • To pool or Not to pool

  2. Panel Data Analysis • Fixed Effects Model • ui is fixed, independent of eit, and may be correlated with xit.

  3. Fixed Effects Model • Classical Assumptions • Strict Exogeneity • Homoschedasticity • No cross section and time series correlation

  4. Fixed Effects Model • Extensions • Weak Exogeneity

  5. Fixed Effects Model • Extensions • Heteroschedasticity

  6. Fixed Effects Model • Extensions • Time Series Correlation (with cross section independence for short panels)

  7. Fixed Effects Model • Extensions • Cross Section Correlation (with time series independence for long panels)

  8. Dummy Variable Model • Dummy Variable Representation • Note: X does not include constant term, otherwise one less number of dummy variables should be used.

  9. Dummy Variable Model • Dummy Variable Estimator (LSDV) • Heteroscedasticity and Autocorrelation

  10. Dummy Variable Model Panel-Robust Variance-Covariance Matrix

  11. Within Model Within Model Representation

  12. Within Model Model Assumptions

  13. Within Model • Within Estimator: FE-OLS

  14. Within Model • Within Estimator: GLS • GLS = FE-OLS • Note:

  15. Within Model • Normality Assumption

  16. Within Model Log-Likelihood Function ML Estimator

  17. Within Model ML Estimator of e2 is downward biased even for large N: For balanced panel (T=Ti: ), e2 should be estimated as:

  18. Within Model • Estimated Fixed Effects • For , is consistent but is inconsistentunless .

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

  20. First-Difference Model • First-Difference Representation • Model Assumptions

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

  22. First-Difference Model • First-Difference Estimator: GLS

  23. Hypothesis Testing • To Pool or Not to 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

  24. Hypothesis Testing • Heteroscedasticity • Serial Correlation • Spatial Correlation

  25. 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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