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# st: Interpretation of coefficients/marginal effects in ols vs probit in a differences-in-differences context

 From "Mirnezami, Oliver" To "statalist@hsphsun2.harvard.edu" Subject st: Interpretation of coefficients/marginal effects in ols vs probit in a differences-in-differences context Date Tue, 12 Mar 2013 21:11:36 +0000

```Dear Statalist

I would be grateful for some clarification in interpreting coefficients/marginal effects in OLS and models for panel data (xtreg and xtprobit).

I'm trying to use a difference-in-differences model to look at the average treatment effect of job loss on health. Rather than the standard 2 period, 2 groups model, I have multiple time periods (1994-2010) and so include dummies for each of these time periods except 1994 which is my omitted reference point:

health(it) = constant + job loss dummy(it) + control variables(it) + year effects(t) + individual fixed effects(i) + error term(it)

My dependent variable health is discrete rather than continuous (measured on a scale of 1-5).

If I use OLS with fixed effects as below, I am using the coefficient on job loss as the average treatment effect. I understand that using OLS isn't entirely appropriate though due to some assumptions of OLS being violated. Hence, I am also considering a probit model.

If I convert my health variable to a dummy (1 = healthy, 0 = not healthy), can I estimate the model as before but now using a probit model and still interpret the job loss variable marginal effect as being the average treatment effect? I've heard that controlling for year fixed effects (time dummies) may alter the interpretation on the job loss variable here despite it being correct in OLS. I'm not interested in the actual marginal effects of the time dummies themselves, but am unsure if I can control for them and still interpret the marginal effect on job loss as the treatment effect? Or whether I should remove the year effects from the probit regression altogether? There are also no individual fixed effects in the probit model, just the main job loss variable and a series of controls.

I would appreciate any guidance on this.

Thank you

Kind regards

Oliver Mirnezami

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