I'm learning econometrics and I'm stumped with a textbook problem.

Use the JTRAIN dataset (which provides information on manufacturing plants in Michigan from the years: 1987, 1988 and 1989) to determine the effect of the job training grant on hours of job training per employee.

I'm estimating the model using three methods (FE, FD, and RE)

The estimation results are the following:

How would I go about knowing which of the three methods is the best one to use (in this case)?

Any help is appreciated.

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#### Best Answer

In most of the cases, one should go for fixed effects regression, as omitted variables pose a substantial threat in making causal inferences. Panel data and fixed effects help us to deal time-invariant omitted variables. What you essentially do with fixed effects is “within transformation” as it demeans all variables within their group, in your case manufacturing plants. In random effects model, you assume that unnobserved heterogeneity, and your independent variables are uncorrelated which is a strong assumption. First differencing is another way removing unobserved heterogeneities but this time by subtracting the lagged observation rather than group mean. If your N is small, T is large, you can go for first differences. In your case, I would go for both FE and FD and do not bother with RE.

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