[Limdep Nlogit List] A selection qeustion--a quick follow-up

[Fred Feinberg]

William Greene wrote:

> Christer.  There is a paper by Joe Terza in the Journal of Applied
> Econometrics, 2004, I believe, that specifically discusses this
> application.  Your suggestion does not work - the IMR approach is
> only appropriate for linear models.

Prof. Greene is of course correct about Inverse Mills Ratios; you need an
actual residual to apply them, and logit/probit models don't supply those
(unless you use some form of multiple imputation or Bayesian methods to sample
over the unobserved "utility"; but then you wouldn't bother with IMLs in the
first place.)

There are two papers by Terza that deal with this:

"The Effect of Physician Advice on Alcohol Consumption: Count Regression with
an Endogenous Treatment," DS Kenkel, JV Terza - Journal of Applied
Econometrics, 2001.

"Alcohol abuse and employment: a second look," JV Terza - Journal of Applied
Econometrics, 2002.

Both use estimators based on approximations (in one case, something like the
Mills Ratio; in the other, a Taylor series). These may be expedient, but there
is no guarantee that they look like the real likelihood, particularly when the
error correlations intrinsic to the Heckman set-up are far from zero.
Generally speaking, there are three ways to go about it; putting each
casually:

1) Two-Step Estimators: quick, easy to use, but you have no idea if the answer
is correct
2) MLEs: higher-dimensonal search, provides correct answer for unimodal
likelihoods, but standard errors of coefficients based on asymptotics that may
not hold
3) Bayesian: correct everything, but you have to code it yourself, wait
forever for the sampling, and you can't be sure it's really converged (least
noxious possibility: use WinBugs; at least you don't have to calculate full
conditional densities)

Dr. Bilgic recommended two other papers:

Boyes, W. J., D.L. Hoffman, and S. A. Low. 1989. An Econometric analysis of
the bank credit scoring problem, Journal of Econometrics 40, 3-14.

Poirier D. J. 1980. Partial observability in bivariate probit models, Journal
of Econometrics 12, 210-217.

The Low paper cites Poirier, and writes the likelihood out explicitly, which
it then claims to maximize... somehow (also calculate standard errors). It
seems to be a "Heckman's Probit" model -- with a binary selection and
prediction -- and as such is directly estimable by Limdep. I don't think it
shows how to estimate the model you're after, but I could be wrong. That would
be covered by the Lee paper in my prior e-mail, as well as the other paper of
mine I linked to.

FF

=====

Fred Feinberg
Hallman Fellow and Professor of Management
Stephen M. Ross School of Business
University of Michigan
feinf at umich.edu