Pooled OLS functional form

[Helen Subbotina]

Hello,
could you please comment shortly: if I need to compare the results between pooled OLS, fixed effects (FE) and random effects (RE) for unbalanced panel data, should I use simple "reg" function for pooled OLS model or I need to stick to the functional form I use for RE and FE (logit), as in my case I have binary dependent and binary independent variables and use "xtlogit" for FE and RE?

Thank you very much in advance!

[Clyde Schechter]

You're confusing some terminology. Fixed effects and random effects (in this context) refer to different models of the data. OLS is not a model: it is an method of estimating the parameters of certain models.

In the case of a pooled-data model, OLS is the method used to estimate coefficients in linear regression. But OLS is not used to estimate coefficients in logistic models. So if your FE and RE models use logistic regression, then your pooled data model should also use logistic regression, i.e. the -logit- or -logistic- command. Estimation for that regression will be by maximum likelihood, not OLS.

By the way, given that there is the question of whether pooling is acceptable here, the study design must have led to clustered data. So when you do the pooled data analysis, you probably should use the vce(cluster ...) option in your -logit- or -logistic- command.

[Helen Subbotina]

Thank you very much, Clyde! Sorry for this confusion.

Yes, that's exactly what I'm doing, I put vce(cluster pid) in the end of the pooled regression.
Then I will use pooled logit function for comparison with FE and RE, since it will be more comparable.

[Carlo Lazzaro]

Helen:
I'm not clear with what you mean by

more comparable

.

[Helen Subbotina]

Carlo, I mean comparing the coefficients between the results on logit and xtlogit fe(re), rather than on reg and xtlogit fe(re)

[Helen Subbotina]

Am I correct in this conclusion?

[Carlo Lazzaro]

Helen:
yes, you're.
As Clyde pointed out, there's no scope for linear regression with binary dependent variable.

[Clyde Schechter]

Sorry to add to confusion, but, Carlo, that's not true. It is sometimes reasonable to estimate a linear probability model for a binary dependent variable.

The original post asked whether it made sense to compare an OLS regression model to FE and RE xtlogit models. The answer to that is no, because it would not be sensible to compare a pooled data linear probability model to multi-level FE and RE logistic models on that data. The more sensible comparison is pooled-data logistic to multi-level logistic.

I then meant to make the additional point that "OLS" should not be used as a synonym for "pooled data model." In the linear regression context, OLS is the usual method of estimating the pooled data regression--so people have gotten into the habit of using "OLS" as a synonym for "pooled data." But outside the context of linear regression that's bad usage, because OLS is not used to estimate pooled-data logistic regressions.

[Carlo Lazzaro]

Clyde and Helen:
I was too fast in reading the thread.
Thanks Clyde for correcting me.

[Helen Subbotina]

Thank you very much, Clyde and Carlo for the useful insights!