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Regardless of whether you use fixed effects or random effects (just replace “fe” with “re” in the commands ahead), the following might be useful additional models to estimate:

1.If the Hausman test results suggest that you should use a random effects

model, the LM test helps you decide if you should use OLS instead of random effects. The null hypothesis is that there is no variation among units (states in this example – i.e., no panel effect).

xtreg top1 demcont repcont top1lag, re

xttest0

If the number to the right of “Prob > chi2” is .05, or lower, reject the null hypothesis of no variation between entities in favor of the alternative hypothesis of variation between entities.  If the null hypothesis is rejected run OLS (e.g., “reg” command).

xttest1  (you can run this immediately after xttest0)

xttest1 is an extension of xttest0.  It offers several specification tests for

error-component models. It includes the Breusch and Pagan (1980) Lagrange multiplier test for random effects; the Baltagi-Li (1995) test for first-order serial correlation; the Baltagi-Li (1991) joint test for serial correlation and random effects; and the family of robust tests in Bera, Sosa-Escudero, and Yoon (2001). The procedure handles unbalanced panels as long as there are no "gaps" in the series; that is, individual time series may differ in their start and end period but cannot have missing values in intermediate periods. Consider the standard-error component model allowing for possible first-order serial correlation:

               y[i,t] = a + B*x[i,t] + u[i] + e[i,t]

               e[i,t] = rho e[i,t-1] + v[i,t]

Typically, researchers are interested in the hypothesis of no random

effects (Var(u[i])=0), no serial correlation (rho=0), or both. After

fitting a balanced random-effects model using xtreg, re, xttest0 produces

seven specification tests:

1) LM test for random effects, assuming no serial correlation

2) Adjusted LM test for random effects, which works even under serial

correlation

3) One-sided version of the LM test for random effects

4) One-sided version of the adjusted LM test for random effects

5) LM joint test for random effects and serial correlation

6) LM test for first-order serial correlation, assuming no random

effects

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