st: Inverse Mills in clustered (multilevel) cross-sectional panel data

[Erkko Autio <erkko.autio@imperial.ac.uk>]

I am trying to use inverse Mill's ratio to control for self-selection in clustered data.

My problem is that I have multilevel data, clustered by year and 
country. The basic dataset comprises interviews with some 900 000 
individuals in nearly 60 countries over 10 years.

Specifically, I am assuming that self-selection of individuals into a 
given economic activity is influenced by both individual-level variables 
(such as age, gender, attitudes), as well as country-level variables 
(e.g., taxation). As behaviours may be conditioned by context (the same 
individual would behave differently under different taxation regimes, 
for example), the error terms will no longer be normally distributed, 
and techniques assuming normal distribution of error terms will thus 
give biased estimates.

My selection equation would thus consist of both individual and 
country-level variables, as would my regression equation.

Hence my problem. Normally, inverse Mill's ratio is computed using 
probit models. However, Stata has no multi-level probit. It does have 
xtmelogit, which can be used for multi-level data. If I use xtmelogit 
instead of, say, xtprobit to compute inverse Mill's ratio? Will 
xtmelogit result in biased estimates?

Alternatively, is there a way to do a probit in cross-sectional panel 
data (i.e., one-off interviews of randomly sampled individuals in lots 
of countries in many consequtive years, individuals not followed over time)?

Thank you for any suggestions.

Erkko Autio
-

Erkko Autio, Professor
Imperial College Business School
Tanaka Building
South Kensington Campus
London SW7 2AZ, UK
E: erkko.aut...@imperial.ac.uk


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