Accounting for state fixed effects in probit model

[Selver Berbic]

Hi!

I've been using World Bank Enterprise Survey data on India for 2022 to investigate the link between corruption and innovation on a firm level. The data is found here: https://www.enterprisesurveys.org/en/survey-datasets

I've been advised to control for state fixed effects, but reading here I've discovered that it isn't applicable to probit models in Stata. I have about 10 000 firm level observations, and I see suggestions that one can simply cluster and use the i.variable, but it is not clear to me how these would account for fixed effects. Does anybody have insights on how one would go about controlling for fixed effects? Could one argue that fixed effects is not necessary in a probit model using many observations?

[Selver Berbic]

I want to add that I've followed this research: https://onlinelibrary-wiley-com.ezpr...9.2012.00171.x
Where the researcher simply adds a "state fixed effects coefficient", but he does not explain how he arrives at this coefficient. Does anybody have a clue how a fixed effects coefficient was added to the model?

[Maxence Morlet]

What are all of your sources of variation? State, firm, and?

I would suggest using a two-way or one-way Mundlak approach to control for this unobserved heterogeneity. This approach is also called the Chamberlain-Mundlak device. How many time periods do you have?

You can specify states as i.state, however the probit model is prone to the incidental parameters problem. However, this problem is attenuated when you have sufficient observations to estimate each fixed effect.

[Selver Berbic]

The sources of variation would be state, sector and firm. As of now I'm using datapoints from the 2022 survey only, so one time period. It seems to me the number of observations are enough to mitigate the incidental parameters problem. I'll look up the Mundlak approach, thank you for providing help, I'm a bit out of my depth right now.

[Maxence Morlet]

So how many observations per state do you have? That is an important question.

[Jeff Wooldridge]

I can't imagine including state dummies will be a problem in this setting. There are 28 states and 8 union territories. With 10,000 firms that should be plenty of observations per state, although smaller states might not have many firms.

[Maxence Morlet]

Dear Professor Jeff Wooldridge, regarding your comment in #6 I have a question regarding standard errors: If the number of firms varies a lot across states, does this speak against the validity of the so-called "CV1" cluster-robust standard errors by state? i.e. clusters of unequal sizes? If so, what would you recommend be done with standard errors in this case?

[Selver Berbic]

Thank you all for the feedback! I noticed that a few hundred observations are omitted when running the fixed effect model. Would it be correct to say that the state dummy approach may still suffer from the incidental parameter problem? Are there any other issues I need to worry about when including state dummy variables?

[Stephen Jenkins]

The "few hundred observations" that are dropped probably correspond to obervation for which "state" is missing (my conjecture). Your question about "incidental parameters" is misplaced. "State fixed effects" is a misnomer (as pointed out above) -- you have a set of dummy (binary indicator) explanatory variables. "Incidental parameters" refers to the case if you'd included dummy variables for each /observation/.