Duration analysis of unemployment

Question

I am trying to run a discrete duration model for analyzing (monthly) unemployment using survey data. I have household-level data, and as such I would like to control for the household effects in my model. I thought to do this by either allowing for cluster effects in the estimation of the standard errors or by random effects (for households) - i.e., I think that fixed effects would not work because there are a lot of households and because of the incidental parameter problem.

My model will include both individual characteristics (e.g., age, school, occupation, since when the person has been unemployed - as they were asked retrospectively), and some other variables) as well as household characteristics (e.g. size, number of people unemployed).

Can anyone provide some comments on my proposed methodology? Are there any things I should be mindful of or are there any better ways of doing this?

Also I would highly appreciate any relevant references.

Answer 1

First, the incidental parameter problem is pretty easy to solve in a discrete duration model. As long as you are willing to assume a logistic form for your model, you can eliminate the incidental parameters via a clever conditioning argument. The usual cite in economics is Chamberlain (1980, Rev Econ Stud). If you prefer a textbook, there is Greene's Econometric Analysis (any of the recent editions) --- look up "fixed effects model binary choice" or "Chamberlain" in the index. In the seventh edition, the discussion runs from pg 721 through 725. The resulting estimator is usually called "fixed-effects logit" or "Chamberlain's estimator."

To be clear, you DO NOT just run a logistic regression with a bunch of dummy variables for households. If you are a Stata user, the xtlogit command with the fe option runs Chamberlain's fixed effects logit model. In R, I don't know how to do it. There are a couple of questions on this here at cross validated (one, two), and one over at stack overflow. The answers in those threads seem mostly to misunderstand what the Chamberlain estimator is, and I think the right conclusion from them is that Chamberlain's estimator is not currently implemented in R. (I would love to be corrected if I am wrong)

Looking over your question again, I wonder whether you really want a fixed effects estimator. As with any fixed effects estimator, you are not going to be able to directly estimate the effects of any household characteristic which does not change over time. Generally, schooling, occupation, household size are fixed or almost fixed in a short panel. If you include time dummies (and why wouldn't you?), then any characteristic which changes regularly with time within each household cannot be included. Age, for example, since, once you control for time, it is just birth date, a fixed characteristic of household head. Similarly, even the effect of the duration of the unemployment spell cannot be measured once you have time dummies and household dummies, unless some households have multiple unemployment spells.