st: simplified implementation of heckman estimator with gllamm

["marc frechet (statalist)" <frechet.marc@gmail.com>]

Hi all,

I am currently trying to implement an Heckman
estimator for a dynamic probit model.

I have panel data in the long form over three periods. I especially
focus on the existence of state dependence.

To study this inertia, I have used the -redprob- program with stata 10.
This program is great but possibilities are limited.

That is why I now build on the article of Arulampalam and Stewart, which
suggest that gllamm also allows to obtain the heckman estimator.

http://www.google.fr/url?sa=t&source=web&cd=3&ved=0CDAQFjAC&url=http%3A%
2F%2Fftp.iza.org%2Fdp3039.pdf&rct=j&q=simplified%20version%20of%
20heckman&ei=zVv-Tef8Nsi98gOLg5WqCQ&usg=AFQjCNFnZK1QqnwDqM2ERuz1yJ1y1mljhQ&cad=rja

The equation (fifth equation in the paper cited above) to estimate with
gllamm seems rather simple :

Prob [ y_it = 1] = PHI [γ (1 − D_it ) y_(it −1) + (1 − D_it )X_it ' β +
D_it Z_i1' λ + {1 + (θ − 1)D_it }α_i ]

Where :

D: dummy variable for the first period.
X_it : vector of explanatory variables
Z_it : vector of variables for the first period, including instruments
alpha : unobserved heterogeity

The authors comment: "This can be viewed as a standard random effects
specification, but with a heteroskedastic factor loading for the random
effect in period 1. Software that allows this form of
heteroskedasticity, such as the gllamm program in Stata, can be used to
estimate (it)"

Unfortunately, I am not really an econometrician. Furthermore, I lack of
skill with gllamm and i do not know how to translate this formula in
gllamm code.

Does anyone know a tread to code this with gllamm ?

Any help would be greatly appreciated.

Best,

Marc Frechet
University of Toulouse



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