[Meng Yu]

Hi Jeff,
Is average marginal effects the same as marginal effects calculated using post-estimation method in Stata? I mean those results we calculate using "dydx" and "margins"?

If I understand it correctly, then one cannot calculate the longitudinal effect using pooled logit because it does not allow you to set the temporal order between the predictor and the outcome variables. Then what is the benefit of using panel data over cross-sectional data in our research? The only difference will be the former kind of data give you the average association between the independent and dependent variables over some time. Am I right?

[Jeff Wooldridge]

The panel data allow you to include the time averages of the explanatory variables. If you were estimating a linear model -- and I recommend that in addition -- the procedure I describe would be identical to fixed effects. And it's identical to random effects with the time averages. So, in the linear case, all methods are the same when you include the xbar variables. In the logit case they are not all the same. They have tradeoffs. The method I described allows for any serial correlation, is simply, and gives you the magnitudes of the effects.

I think I've posted the same set of commands on Statalist before, but here goes with zj being time-constant variables and year the time index:

egen x1bar = mean(x1), by(id)
egen x2bar = mean(x2), by(id)
...
egen xKbar = mean(xK), by(id)
logit y x1 x2 ... xK z1 ... zJ i.year x1bar ... xKbar, vce(cluster id)
margins, dydx(x1 ... xK)

Perhaps you want to include lags of some of the x variables? You can do that, too.

[Meng Yu]

It will take some time for me to understand everything you said. Were you saying if there is serial correlation in the dependent variable, then it is better to use correlational random effects model with the syntax you provided? I don't know why random effects model would not work.

Also, if I would like to obtain the coefficients of the predictor variable on the outcome variable, should I still use this model?

[Jeff Wooldridge]

The traditional RE model for logit rules out serial correlation in the errors that are sometimes called e(i,t). All serial correlation is assumed to come through the time-constant component, c(i) or alpha(i). That's often too restrictive. And it causes inconsistency for the joint MLE. If you use the pooled MLE and cluster the standard errors then you allow for general serial correlation.

[Meng Yu]

Let me first make sure I understand what serial correlation is. My understanding is it means the outcome variable is related to each other from one wave to another. Am I right?

All serial correlation is assumed to come through the time-constant component,

Are you saying it is something that doesn’t change within the outcome variable that leads to serial correlation?

And is the only disadvantage of traditional RE model is it needs some assumption of the distribution of the unobserved time-invariant variables? What kind of distribution is it?

[Jeff Wooldridge]

Meng: Binary response models are often written as y(i,t) = 1[x(i,t)*b + c(i) + e(i,t) > 0] where 1[.] is the indicator function. There are three sources of correlation in y(i,t): due to x(i,t), c(i), and e(i,t). The explanatory variables are almost always correlated across time, and this causes no issues. c(i) is the same across time, so it clearly causes correlation in y(i,t) across time. That's accounted for by RE approaches. The issue is in e(i,t). The RE logit model assumes these are no correlated across time. It's too restrictive. The estimators of b are inconsistent without this assumption. Plus, one should include the averages of the x(i,t) across time for each i to allow x(i,t) to be correlated with c(i). I can do that with pooled logit, which is simple, and I can compute clustered standard errors.

I think you need to study more econometrics because you seem to be using methods you don't fully understand. It's easy to find references that explain the distribution of c(i) is taken to be normal as a default in probit, logit, ordered probit, Tobit ,and so on. This is likely explained in the Stata manual.

[Meng Yu]

Thank you, Jeff, again for your explanation. I think I should take some econometrics or statistics courses when I get the opportunity. Right now, I just try to learn as much as I can by asking people questions. You can ignore me as someone else might answer. It took me three posts for someone to respond in this thread. And that is OK.

If you were estimating a linear model -- and I recommend that in addition

Why do you recommend a linear model? To use a RE model with continuous response, the assumption is that unobserved group-level or time-invariant characteristics were uncorrelated with the explanatory variables. Is that the only assumption? And is that the only reason why Fixed Effect is hailed as more superior?

To use a RE model with binary response, the assumptions are 1) the error term is not correlated across time; 2) the time-variant and time-invariant variables are not correlated; 3) time-invariant variables have a normal distribution. My understanding is c stands for time-invariant variables. I could be wrong. If I am not, why doesn't c have a coefficient?

I read in this article https://pubmed.ncbi.nlm.nih.gov/26913806/ that they use "conditional change panel model" or "lagged effect static-score panel model" for binary response outcome variable. In their results tables, no coefficient for the Xbar was presented. I wonder what kind of model they were using.

[Meng Yu]

Your post made me recall what the economist told me that economists believe everyone has some innate ability. I believe that is what c stands for. I don't think sociologists believe in that, although I am not 100% sure. Health researchers might believe there are genetic traits that make each person unique, although I could be wrong about it.

According to what you wrote, to use a RE model with binary response, the assumptions seem to be 1) the error term is not correlated across time; 2) the time-variant variables and c are not correlated; 3) c in the population is normally distributed. 2) seems to be impossible. 3) seems to be impossible to measure if c is innate.

[Meng Yu]

I pondered the concept of "innate ability" and I think although some people may have inherited higher IQ and/or EQ from their parents, "innate ability" should be time-variant.

[Meng Yu]

egen x1bar = mean(x1), by(id)
egen x2bar = mean(x2), by(id)
...
egen xKbar = mean(xK), by(id)
logit y x1 x2 ... xK z1 ... zJ i.year x1bar ... xKbar, vce(cluster id)
margins, dydx(x1 ... xK)

I wonder how you apply longitudinal weights and bootstrap weights to this command. I know how to do it when using RE xtlogit in Stata.