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st: HLM with Probit and Selection bias

From   "Stephen P. Jenkins" <[email protected]>
To   <[email protected]>
Subject   st: HLM with Probit and Selection bias
Date   Tue, 24 May 2005 10:09:35 +0100

> Date: Mon, 23 May 2005 11:28:21 -0700 (PDT)
> From: Hella Bel <[email protected]>
> Subject: st: HLM with Probit and Selection bias
> Hello,
> how does one program an HLM with a Probit to correct
> for sample selection in STATA? 
> I need to estimate a Probit to model a decision (say,
> whether to impose a new tax) then use the estimate
> (based on the inverse Mill's ratio) to correct for
> selection bias when estimating (say) separate
> expenditure regressions for jurisdictions that choose
> to impose the tax, and those that do not.

An "HLM" is, I understand, also referred to as a multi-level model by
other disciplines (you allow random slopes as well as random

In any case, it is not obvious to me that a 2-stage approach to this
problem would necessarily have the properties that you are hoping for
(cf. -heckman-).  

-gllamm- provides a modelling framework in which you could probably
estimate main equation and the selection equation jointly (cf.
presentation by Alfonso Miranda at UKSUG last week using -gllamm- to
model an ordered probit with selection).  As usual, use -findit- to
search for potentially relevant materials, and look through the -gllamm-
manual at amongst other places.

A more fundamental issue is whether you will be able to identify your
model (in the statistical sense) other than by appeal to non-linearities
in functional form.

Final thought: it's probably not a selection model you require, but an
"endogenous switching" one (probit to model which tax regime chosen;
regression for each regime). A quick search using -findit- reveals
information about the -movestay- program

SJ-5-1  st0071_1  . . . . . . . . . . . . . . . . Software update for
        (help movestay if installed)  . . . . . . . . M. Lokshin and Z.
        Q1/05   SJ 5(1):139

Professor Stephen P. Jenkins <[email protected]>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.   

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