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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

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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.

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

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Random Effects Model Assumptions – Cross Section Independence

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Random Effects Model Extensions – Weak Exogeneity – Heteroscedasticity

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Random Effects Model Extensions – Serial Correlation – Spatial Correlation

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Model Estimation: GLS Model Representation

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Model Estimation: GLS GLS

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Model Estimation: RE-OLS Partial Group Mean Deviations

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Model Estimation: RE-OLS Model Assumptions OLS

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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

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

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Model Estimation: ML Log-Likelihood Function

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Model Estimation: ML ML Estimator

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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:

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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:

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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,

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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

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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

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

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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:

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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,

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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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