xtmlogit vs linear probability model

[David Hanson]

Hi,

I'm struggling to use a proper method to figure out what I want.

What I want: I have a long panel data (non-balanced): multiple firms over many years. I also observe the firm's different characteristics, such as size, profitability, productivity, etc. Firms also have different statuses regarding a particular economic activity, let's call it X (which has 2 possible statuses, X1, X2). So over the years, some firms engaged in X, and some firms don't engage in X. For those who engage in X, they either have the status X1 or X2.

I want to figure out which type of firm-level characteristics are more likely to result in X1 or X2 or non-X(firm do not engage in activity X at all).

My struggle: Based on my understanding, there are at least two possible ways to figure it out:

1. One is multinomial logit within a panel setting, which can be done by the code `xtmlogit'. In this case, I would choose non-X as the base outcome.
2. The other candidate is a simple linear probability model. In which I create two dummy variables, one for X1 and one for X2. Then run linear regression with a binary dependent variable.

Which method is more appropriate in this case?

I would really appreciate it if I can receive some help here. Thank you!

[Carlo Lazzaro]

David:
at a very first glance, I would say that most depends on what the goal of your research is, since:
a) -xtmlogit- considers a three-option dependent variable;
b) the LPM considers a two-level dependent variable.