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Econometric Analysis of Panel Data Panel Data Analysis – Random Effects Assumptions GLS Estimator Panel-Robust Variance-Covariance Matrix ML Estimator.

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Presentation on theme: "Econometric Analysis of Panel Data Panel Data Analysis – Random Effects Assumptions GLS Estimator Panel-Robust Variance-Covariance Matrix ML Estimator."— Presentation transcript:

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 – u i is random, independent of e it and x it. – Define it = u i + e it the error components.

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

4 Random Effects Model Assumptions – Cross Section Independence

5 Random Effects Model Extensions – Weak Exogeneity – Heteroscedasticity

6 Random Effects Model Extensions – Serial Correlation – Spatial Correlation

7 Model Estimation: GLS Model Representation

8 Model Estimation: GLS GLS

9 Model Estimation: RE-OLS Partial Group Mean Deviations

10 Model Estimation: RE-OLS Model Assumptions OLS

11 Model Estimation: RE-OLS Need a consistent estimator of : – Estimate the fixed effects model to obtain – Estimate the between model to obtain – Or, estimate the pooled model to obtain – Based on the estimated large sample variances, it is safe to obtain

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

13 Model Estimation: ML Log-Likelihood Function

14 Model Estimation: ML ML Estimator

15 Hypothesis Testing To Pool or Not To Pool, Continued Test for Var(u i ) = 0, that is – If T i =T for all i, the Lagrange-multiplier test statistic (Breusch-Pagan, 1980) is:

16 Hypothesis Testing To Pool or Not To Pool, Continued – For unbalanced panels, the modified Breusch- Pagan LM test for random effects (Baltagi-Li, 1990) is: – Alternative one-side test:

17 Hypothesis Testing To Pool or Not To Pool, Continued References – Baltagi, B. H., and Q. Li, A Langrange Multiplier Test for the Error Components Model with Incomplete Panels, Econometric Review, 9, 1990, – Breusch, T. and A. Pagan, The LM Test and Its Applications to Model Specification in Econometrics, Review of Economic Studies, 47, 1980,

18 Hypothesis Testing Fixed Effects vs. Random Effects EstimatorRandom Effects E(u i |X i ) = 0 Fixed Effects E(u i |X i ) =/= 0 GLS or RE-OLS (Random Effects) Consistent and Efficient Inconsistent LSDV or FE-OLS (Fixed Effects) Consistent Inefficient Consistent Possibly Efficient

19 Hypothesis Testing Fixed Effects vs. Random Effects Fixed effects estimator is consistent under H 0 and H 1 ; Random effects estimator is efficient under H 0, but it is inconsistent under H 1. Hausman Test Statistic

20 Hypothesis Testing Fixed Effects vs. Random Effects Alternative (Asym. Eq.) Hausman Test – Estimate any of the random effects models – F Test that = 0

21 Hypothesis Testing Fixed Effects vs. Random Effects Ahn-Low Test (1996) – Based on the estimated errors (GLS residuals) of the random effects model, estimate the following regression:

22 Hypothesis Testing Fixed Effects vs. Random Effects References – Ahn, S.C., and S. Low, A Reformulation of the Hausman Test for Regression Models with Pooled Cross-Section Time-Series Data, Journal of Econometrics, 71, 1996, – Baltagi, B.H., and L. Liu, Alternative Ways of Obtaining Hausmans Test Using Artificial Regressions, Statistics and Probability Letters, 77, 2007, – Hausman, J.A., Specification Tests in Econometrics, Econometrica, 46, 1978, – Hausman, J.A. and W.E. Taylor, Panel Data and Unobservable Individual Effects, Econometrics, 49, 1981, – Mundlak, Y., On the Pooling of Time Series and Cross-Section Data, Econometrica, 46, 1978,

23 Example: Investment Demand Grunfeld and Griliches [1960] – i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years: – I it = Gross investment – F it = Market value – C it = Value of the stock of plant and equipment


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