Estimating hazard and survival functions for self-employment

[Clotilde Mahe]

Dear all,

I am using a four year panel dataset. I would like to estimate the probability to become self-employed at time t, conditional on not being self-employed in t-1 (probability to start-up a business at time t); and the probability to be self-employed at time t, conditional on being self-employed at time t-1 (probability to survive as self-employed) - replicating the empirical strategy of this JDE paper 'Aiding Violence or Peace? The impact of foreign aid on the risk of civil conflict in sub-Saharan Africa' in a way. Intuitively, and as in this paper, I would think of a hazard/survival type of analysis. However, I am not sure how to proceed in Stata... Should I run a 'standard' linear probability model with panel data (random or fixed effects)? A dynamic panel with lags? A survival analysis as such? If yes, should I use the -xtcloglog- command? I have seen that some new commands have been added to run such a type of model with panel data, but I am not even sure how to organise the data...

Thanks for your time and your help in this.

Clotilde

[Maarten Buis]

Sounds like you have a straightforward discrete time survival analysis problem. How to deal with that in Stata is well discusses by Stephen Jenkins here: https://www.iser.essex.ac.uk/resourc...sis-with-stata

[Clyde Schechter]

A survival analysis is one way to approach this, but also have a look at -xttrans-. If you are just looking for a single time-invariant panel-invariant probability of transition or stasis, -xttrans- will get you that with less effort. If you are looking at variation over time or across panels and want to model that, then -xttrans- is too simplistic.

[Clotilde Mahe]

Dear Marteen,

Thank you for your reply. I was a little confused about where to find information for panel data on this website - although I have found some Stata list threads, I was not sure...

Dear Clyde,

Thank you by your reply. by -xttrans- do you mean the generalization of tabulate to report transition probabilities? This will be indeed very useful to describe the data. I might however need some deeper analysis, by trying to estimate a model...

Thanks again for your time.

Clotilde

[Carlo Lazzaro]

Clotilde:
for those interested in panel data analysis with Stata, the best approach is to start off from the -xt- and related entries in Stata .pdf manual.

[Clyde Schechter]

by -xttrans- do you mean the generalization of tabulate to report transition probabilities?

Yes, that's what I mean.

[Clotilde Mahe]

Dear Clyde,

Thanks for this clarification.

Dear Carlo,

How, in this case, to use xtcloglog with fixed effects? Of what I read in the documentation, you could only use either random effects or population averages. Would xtcloglog with Mundlak type of regressions be of some use? Can I, with xtcloglog obtain estimates for i) probability to start-up, and ii) probability to survive?

Thanks for your time.

Best,

Clotilde

[Maarten Buis]

´Here I disagree with Carlo. Survival analysis naturally occurs within panel data, so there is no need to use xt commands. The xt commands only play a role if you also want to use frailty models. That may be possible, but it would definately not be your first step. Given Clotilde's question, I suggest she just start with the basics, and do a simple discrete time hazard model, with as little bells and whistles as possible, and extend that model as needed.

[Carlo Lazzaro]

I agree with Maarten's approach.
My suggestion referred to a potential Clotilde's interest in panel data analysis (not necessarily related to her main question).

[Clotilde Mahe]

Dear Carlo,

I am indeed interested in using the longitudinal dimension of these data. The problem that I am having is that I do not observe duration of status as such, but whether an individual is self-employed or not at time t, t=1,2,3,4, which seems to be a relatively short time span to run a survival analysis... What I have seen doing, is running an analysis on some sub-samples: for instance, excluding those individuals who were self-employed in t-1 to obtain probability estimates to start-up, and the reverse for survival; hence my questions...

Best regards,

Clotilde

[Carlo Lazzaro]

Clotilde:
I think that Maarten's approach still holds, with shared frailty as a possible option (if feasible in discrete time hazard models, a topic I'm not familiar with).

[Maarten Buis]

Clotilde: Survival analysis is exactly what you want. Survival analysis is exactly designed for your type of longitudinal data. So, as confusing as it may sound you do not want panel methods for dealing with your panel data. Panel methods are great, but they are not designed for your problem.

[Clotilde Mahe]

Dear Marteen,

Thanks again for this clarification. Will try to implement!

Best,

Clotilde