# Fixed Effects Logit Model with a Endogenous Binary Regressor

for a research project I am looking at a model to estimate a fixed effects logit model of the type

$$y_{it} = \Lambda(x_{it}'\beta +w_{it}'\theta +a_i) .$$

Now I know that I would usually do that in a conditional logit model using MLE. However I now have an binary instrument $z_{it}$ for the endogenous and also binary regressor $w_{it}$. I suspect I have to use GMM and a version of the moment condition $E[z'(\Delta(x_{it}'\beta +w_{it}'\theta +a_i))]$, but I am not sure how to transform the logistic function into a conditional logit one. I hope the problem is clear. Can anybody help me out?

• Should that delta be a lambda? – Dimitriy V. Masterov Jan 30 '18 at 1:44
• Yes, edited.... – Leon F. Jan 30 '18 at 20:45
• What about the one in the moment condition? – Dimitriy V. Masterov Jan 30 '18 at 22:25