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I look at a binary DV for 139 companies over 8 years. Thus, I have panel data. I have three IV, of which one is also a binary variable, and several control variables. As it is the first time that I look at a binary DV I have a few questions regarding pre-tests and the general approach and I am just insecure about the correct procedure. My approach so far:

  1. Classical data cleaning / preperation including transformation to panel data via xtset id year
  2. Descriptive statistics including correlation and multicollinarity check (VIF). VIF below 10 -->no multicollinarity. Two of the IV are medium correlated and I may sepearte them into two equations.
  3. Heteroscedasticity check confirming heteroscedasticity in my sample. Thus, I thought I have to include robust standard errors via adding vce (robust) at the end of my regression equation.

Now my questions for the further procedure: With panel data I need to use xtlogit as the command, I guess. I used Hausman test to evaluate if I need random or fixed effects. The first time I did it my result said to use fixed effects. Then, I added a CV and the result changed to random effects. However, in both cases I cannot include vce(robust) as I get an error notification. Do I just leave them out now or what is the explanation behind that it cannot be included? Or is there a common way of including them?

Next, I want to include industry, country and year fixed effects. Is there a certain test that I have to do to decide whether these effects need to be included or do I just include them as common sense to reduce the risk for an omitted variable bias and reducing endogeneity concerns? If there is a test, which one and how do I apply it?

Once that is all clarfied and I have my final regression equation I would use Mc Fadden to look at the model fit and the "margins, dydx(IV) atmeans" command for interpreation correct?

Can anyone help me wioth my open questions? Any feedback on my procedure? Am I missing out an important step?

Thanks in advance!

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You're started off with the fairly common approach of using a battery of econometrics tools and thinking about lack of model fit but IMHO you did not think of model fit in a fundamental way: what are the serial correlation patterns and how to account for them in the model? Instead of dealing with robust standard errors I'd spend more effort on likely-to-work model specification. Markov logistic models are promising in this context, see for example the last chapter of https://hbiostat.org/rmsc and some earlier sections. Make sure the DV is truly "all or nothing" or you will have the biggest lack of fit ever by using a binary LRM.

If using a first-order Markov process it may be the case that you need to sacrifice one "panel" in order to best model the correlation structure, i.e., use the first measurement per company only for getting the lagged value for the second period. But there are specialized methods that deal with that more efficiently.

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