Presentation on theme: "Econometric Analysis of Panel Data"— Presentation transcript:
1 Econometric Analysis of Panel Data Panel Data AnalysisRandom EffectsAssumptionsGLS EstimatorPanel-Robust Variance-Covariance MatrixML EstimatorHypothesis TestingTest for Random EffectsFixed 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 Homoschedasticity X includes a constant term, otherwise E(ui|X)=u.HomoschedasticityConstant Auto-covariance (within panels)
4 Random Effects ModelAssumptionsCross Section Independence
5 Random Effects ModelExtensionsWeak ExogeneityHeteroscedasticity
6 Random Effects ModelExtensionsSerial CorrelationSpatial Correlation
11 Model Estimation: RE-OLS Need a consistent estimator of q:Estimate the fixed effects model to obtainEstimate the between model to obtainOr, estimate the pooled model to obtainBased on the estimated large sample variances, it is safe to obtain
12 Model Estimation: RE-OLS Panel-Robust Variance-Covariance MatrixConsistent statistical inference for general heteroscedasticity, time series and cross section correlation.
15 Hypothesis Testing To Pool or Not To Pool, Continued Test for Var(ui) = 0, that isIf Ti=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 ReferencesBaltagi, 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 EffectsE(ui|Xi) = 0Fixed EffectsE(ui|Xi) =/= 0GLS or RE-OLS(Random Effects)Consistent and EfficientInconsistentLSDV or FE-OLS(Fixed Effects)ConsistentInefficientPossibly Efficient
19 Hypothesis Testing Fixed Effects vs. Random Effects 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
20 Hypothesis Testing Fixed Effects vs. Random Effects Alternative (Asym. Eq.) Hausman TestEstimate any of the random effects modelsF Test that g = 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 ReferencesAhn, 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 Hausman’s 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 i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years:Iit = Gross investmentFit = Market valueCit = Value of the stock of plant and equipment
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