One of the major problems with panel data is heterogeneity across panels. If the
unobserved heterogeneity effects of the individual panels are correlated with the
variables, a fixed-effect model is estimated.
However, if the unobserved effects are uncorrelated with the variables, there will
be efficiency gains if we model the individual panel -effects as randomly distributed
components of the error using a random-effect estimator (Baltagi, 1995).24 We perform a
Hausman specification test to test compare the estimates from the consistent fixed effects
model to the estimates from the efficient random effects estimator. The null hypothesis is
that the individual effects are uncorrelated with the model. If null hypothesis is rejected
(individual effects are correlated), a random effect model produces biased estimators and
a fixed effects model is preferred. For both the models the Hausman test rejected the null
hypothesis in favor of the fixed effects model. But, when we used the Bresusch and
Pagan Lagrangian multiplier test for random effects, we rejected the null hypothesis in
favor of the random effects model.25 However, due to the inconsistencies of the Hausman
test, we decided to use the random effects model.26
24
The standard random effects estimator is that the weighted average of the fixed effect and between effect
estimator. See Baltagi (1995) chapter 7 for details.
25 We also test for random effects using the Breusch and Pagan Lagrange multiplier (LM) test. The null
hypothesis is that the variances across groups are zero. If the null hyothesis is not rejected, pooled OLS
regression is appropriate. We reject the null hypothesis in favour of random effect model in both models.
26 One of the more stronger assumptions of the Hausman test is that one of the estimators is efficient, that
is, has minimum asymptotic variance. If this is violated, results are inconsistent. In our analysis, when we
specified the random effects model as efficient (tested fixed vs random), we rejected the null hyothesis in
favour of the fixed effect model in both models I and II. However, when we specified the fixed effects
model as efficient (that is tested random vs fixed) we obtained a negative Chi-Square value in both the
models. Though a negative Chi-Square value may be interpreted as allowing us to accept that the random
effects model in favour of the fixed effects model. However, the results of the Hausman test are sensitive to
specification of the regression model and need to interpreted with caution. Please see Greene (2003) for
more details.
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