2SLS Panel Data for Logit/Probit regression

[Ken Yang]

Dear Statalists,

I just have a general question of how to proceed with the logit model with instrument variables and specifically how to do it for panel data, so I may not need to upload any sample dataset here.

Can I use xtivreg2 command for my dummy depvar (dependent variable) (value =1 or 0)?

Or Can anyone show me how to do it? And normally for logit model, how to obtain marginal effects, instead of odd ratios?

I will really appreciate if you can help.
Thank you so much.

xtset id year

xtivreg2 depvar (endo_var = iv1 iv2 iv3) controls i.year, fe first cluster (id) endog(endo_var)

[Jeff Wooldridge]

Is your endogenous variable roughly continuous? Binary? Something else?

You can always use the linear model estimated by FE2SLS as a starting point, as above. Otherwise, you should use probit and a control function method.

[Ken Yang]

Dear Jeff,

Thank you for your message.

May I ask if there is any difference when the endogenous variables are continuous, binary or mixed?

Since my dependent variable is binary, if using the FE2SLS, how can I interpret the result? if I run only xtlogit without the instruments, I obtain the odds ratios, but with this FE2SLS, I am not sure the interpretation.

[Jeff Wooldridge]

If you're going to use a nonlinear model for the dependent variable then you should take the nature of the endogenous variable seriously. The short answer is: yes, it matters whether y2 is continuous, binary, and so on. Not, though, if you are just going to use a linear model.

If you use FE2SLS you are estimating a linear probability model, and the coefficients have the usual interpretation of an LPM; they tell you (roughly), if you increase y2 by one unit, the probability that y1 = 1 changes by the coefficient (on average).