Sample Question #177 (econometrics – panel data)

Explain the Breusch-Pagan Lagrange multiplier test for the random effects model. What’s the null hypothesis? How does the test work? (Can you write out the test statistic?) What’s its major defect?

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ANSWER

The null hypothesis is that the variance of the random-effect term is 0; in other words, the null specifies a regular OLS model with a constant intercept. The test is based on OLS residuals. Under the null, the LM test statistic is distributed as chi-squared(1). The test’s major defect is if the null is rejected, we still cannot claim the model is random effects because it’s still possible a fixed effects specification is correct. The test is appropriate only when we know fixed effect is inappropriate to begin with, so our only two options were between random effects and OLS.

(Bonus question: how do you test for fixed vs. random effects?)