Correction for Probit with FE (Cross-section) - Incidental parameters

[Peter Crown]

Dear all,

I am running a probit model (since my dependent variable is binary) using Fixed Effects (I need to include them in my model). My data are cross-section data (not panel data), so I am running:

probit Dependent x1 x2 x3 i.region i.industry

I have just realized that using probit with fixed firm effects gives biased/inconsistent estimates and standard errors due to the incidental parameters problem.

How can I address this problem? I have read some about solutions (probitfe or xtspj) but they are all designed for panel data. So, I would appreciate if you could tell how could I run this kind of estimation not incurring into the incidental parameters problem.

Thanks in advance.

[Andrew Musau]

There is a very nice discussion of this here.

https://www.statalist.org/forums/for...uated-at-means

[Peter Crown]

Thanks Andrew

I have read the post but I am still wondering how if I should move to an alternative model ( Linear Probability Model (LPM) or a conditional logit model) or whether there is a package/correction/solution that could be used to run my initial probit model but accounting for fixed effects.

Any clue?

Thanks again

[Joseph Coveney]

Are you thinking of i.industry as your fixed effects? If not, then what makes you believe that you have an incidental parameters problem? If so, then simulate under the sample size conditions of your observed dataset and see whether and how bad the problem with statistical consistency is. It might not be a problem in your case.

[Jeff Wooldridge]

Peter: As Joseph said, and as I said in the post linked by Andrew, it depends on the number of firms per industry and region. I suspect you have many per region. How many per industry? If it’s at least 25 then you’re probably okay, although that depends on other data features that I can’t know about.

[Peter Crown]

Thanks Joseph and Jeff.

I have about 100,000 observations and 200 industries (since I am using a very dissagregated SIC code) and 7 regions. The point is that I have been told by a reviewer to use a different model rather than probit with fixed effects (to avoid the incidental parameters problem). That's why I was wondering if a conditional logit could be an alternative.

[Jeff Wooldridge]

Your reviewer doesn’t understand the problem. Your mistake was calling it “fixed effects.” It’s not fixed effects because your unit of observation is not the industry. You should’ve said you did probit and included industry dummies. Then you explain that you have several hundred firms per industry. This is plenty of data. If you had one industry with 500 firms would the reviewer complain about small sample size? No. And, for the parameters you care about, you have effectively more observations. If you had only a handful of firms per industry then you’d have to think about conditional logit.

As another example, if I had 1,000 adults and put in a binary variable for marital status into a probit model, should we worry about the incidental parameters problem? Obviously not.

I’ve been looking for ramifications of people overusing the term “fixed effects” and this is a good one. A reviewer has vaguely heard about the incidental parameters problem with FE probit but doesn’t remember it isn’t relevant when there are many observations per group.