OLS with binary dependent variable

[Yasmine Elsayed]

Hi everyone,

I read several papers where they employ an OLS method (xtreg with fixed effects) for panel data with a binary dependent variable and I was wondering if anyone knows why? Because my first thought would have been an xtlogit with fixed effects.

Many thanks

[Fei Wang]

Yasmine, linear models with binary dependent variables are usually called "linear probability model", and the coefficients may be interpreted as the effects of regressors on the probability of dependent variables being one. Many prefer the LPM as it's simple, flexible, and usually has consistent results with non-linear models (like xtlogit).

[Ulrich Wohak]

Just to add to Fei's excellent comment: one reason to dislike LPMs is that the predicted probability can be outside the [0, 1] interval, which does not happen with probit/logit.

[Maxence Morlet]

The literature is extremely conflictual, with Angrist & Pischke (2009) and Wooldridge (2010) classically defending LPM under certain circumstances, notably for its interpretability. Furthermore, Wooldrdige (2010) argues that if regressors are binary as well, the case for LPM is even stronger.

There is another strand of literature, e.g. Lewbel et al. (2012), that is very much against LPM due to the reason highlighted by Ulrich.

Horrace and Oaxaca (2006) underline that LPM is probably biased if values for X_i'ß are outside of the unit interval.

It is a very interesting debate.

[Jared Greathouse]

Unfortunately, I spent the first half of last semester's PhD methods course learning that "under most circumstances, LPM~=logit analysis", barring certain areas on the S curve.


So LPM isn't illegal, I would just use the logit for purely functional form's sake and the additional benefits it provides

[Rich Goldstein]

in med/epi the result of using an lpm is called "risk difference" and sometimes this is exactly what you want and is not easy to get to from risk ratios or odds ratios; a "debate" occurred on the Statistical Horizons web site which resulted in a program (predict_ldm) which gives "better predicted probabilities" - for a start on this, with links, look at: https://statisticalhorizons.com/bett...probabilities/

[daniel klein]

I think Maarten Buis has made this point: If you go for logit and then estimate average marginal effects, i.e., a linear approximation to your non-linear model; why not go for the (simpler) LPM in the first place? While slightly simplifying things, I believe the question is justified.

[Maxence Morlet]

Unfortunately, I spent the first half of last semester's PhD methods course learning that "under most circumstances, LPM~=logit analysis", barring certain areas on the S curve.


So LPM isn't illegal, I would just use the logit for purely functional form's sake and the additional benefits it provides

What papers did you study in the course? Just curious because I'm aiming to write a paper using LPM, just came back from a conference and people there told me you'd really have to justify your use of LPM.

[Jared Greathouse]

Maxence Morlet I'll send you the syllabus

[Vinbamba Boris Laurence]

I have a problem currently:


Please help me. If my dependent variable is, for example, 1 = currently employed and 0 = not employed, and my independent variable is mental health, which is either discrete or continuous, how should I interpret a result of 0.5 after using ivreg2h with the Lewbel method?


Is this method appropriate if my dependent variable is binary? If not, what solution would you suggest?


Thank you for your help.