Interpreting Logit transformation of dependent variable

[Antonio Stanco]

Hello all,
In my master thesis I am using difference and system gmm. The problem is that the dependent variable is indeed a fraction/proportion. In order to run the linear model, I took the logit transformation of the dependent variable. Once obtained the coefficient estimates, how do I interpret them?
I don't want the effect on log(y/1-y) but rather on y.

Any help will be appreciate

[Nick Cox]

I wouldn't transform the response. I would use glm, link(logit) f(binomial) vce(robust).

Then the interpretation is just what it is for logit except that your response is (approximately) continuous not binary.

Pedantic note: log(y/1 - y) is not a useful quantity. The usual rules imply log[y / (1 - y)]

[Antonio Stanco]

Thanks for your reply. The pedantic note is actually indeed correct!

Btw, I was thinking about glm, I am afraid it does not take care about the presence of the lagged dependent variable. Beside, all the economic literature on the topic goes for difference and syste, GMM

[Nick Cox]

I believe you!

[Dina Awadalla]

Hi Antonio
I have the same question! Please let me know if you have found the answer! Thank you

[Jeff Wooldridge]

Dina: Are you using panel data? Do you want to include a lagged y? In any case, I would start by using y as the dependent variable. There is nothing wrong with starting with a linear model, as it's usually a decent approximation. I can't say more until I know more.

[Dina Awadalla]

Hi Jeff,
Thank you for replying.

Yes, I'm using panel data and the lagged dependent variable is included in the regression. In fact, I want to make the logistic transformation of my dependent variable (It's a ratio) and then run Random Effects estimation. However, I don't know how to interpret the results. My independent variables include the lagged Y, and a number of macroeconomic variables in percentages.

[Jeff Wooldridge]

If you have a lagged dependent variable you should not be using random effects. You have to use a GMM approach, which can be implemented using the user-written command xtdpdqml. Unfortunately, that does not solve the problem of undoing the log-odds transformation. What you can do is estimate the mean and variance of the heterogeneity in the log[y/(1 - y)] equations. Then, you can treat it as having a normal distribution, and use this to find the average partial effects of y after you undo the transformation.