Econometric Analysis of Panel Data

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Econometric Analysis of Panel Data Powered By Docstoc
					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




  – ui is random, independent of eit and xit.
  – Define eit = ui + eit the error components.
         Random Effects Model
• Assumptions
  – Strict Exogeneity

     • X includes a constant term, otherwise E(ui|X)=u.
  – Homoschedasticity



  – Constant Auto-covariance (within panels)
        Random Effects Model
• Assumptions
  – Cross Section Independence
        Random Effects Model
• Extensions
  – Weak Exogeneity




  – Heteroscedasticity
         Random Effects Model
• Extensions
  – Serial Correlation



  – Spatial Correlation
       Model Estimation: GLS
• Model Representation
        Model Estimation: GLS
• GLS
      Model Estimation: RE-OLS
• Partial Group Mean Deviations
        Model Estimation: RE-OLS
• Model Assumptions




• OLS
      Model Estimation: RE-OLS
• Need a consistent estimator of q:


  – 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
      Model Estimation: RE-OLS
• Panel-Robust Variance-Covariance Matrix
  – Consistent statistical inference for general
    heteroscedasticity, time series and cross section
    correlation.
        Model Estimation: ML
• Log-Likelihood Function
        Model Estimation: ML
• ML Estimator
              Hypothesis Testing
         To Pool or Not To Pool, Continued
• Test for Var(ui) = 0, that is


   – If Ti=T for all i, the Lagrange-multiplier test
     statistic (Breusch-Pagan, 1980) is:
          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:
               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, 103-107.
  – Breusch, T. and A. Pagan, “The LM Test and Its Applications to Model
    Specification in Econometrics,” Review of Economic Studies, 47, 1980,
    239-254.
            Hypothesis Testing
        Fixed Effects vs. Random Effects



Estimator          Random Effects   Fixed Effects
                   E(ui|Xi) = 0     E(ui|Xi) =/= 0
GLS or RE-OLS      Consistent and   Inconsistent
(Random Effects)   Efficient

LSDV or FE-OLS     Consistent       Consistent
(Fixed Effects)    Inefficient      Possibly Efficient
           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
            Hypothesis Testing
        Fixed Effects vs. Random Effects
• Alternative (Asym. Eq.) Hausman Test
  – Estimate any of the random effects models




  – F Test that g = 0
           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:
                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, 309-319.
  – Baltagi, B.H., and L. Liu, Alternative Ways of Obtaining Hausman’s Test
    Using Artificial Regressions, Statistics and Probability Letters, 77, 2007,
    1413-1417.
  – Hausman, J.A., Specification Tests in Econometrics, Econometrica, 46,
    1978, 1251-1271.
  – Hausman, J.A. and W.E. Taylor, Panel Data and Unobservable
    Individual Effects, Econometrics, 49, 1981, 1377-1398.
  – Mundlak, Y., On the Pooling of Time Series and Cross-Section Data,
    Econometrica, 46, 1978, 69-85.
   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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