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Subject: st: How to derive Wooldridge and Orme approaches in xtprobit module ?

From   "Stephen P. Jenkins" <>
Subject   Subject: st: How to derive Wooldridge and Orme approaches in xtprobit module ?
Date   Sun, 21 Mar 2010 18:31:51 -0000


Date: Fri, 19 Mar 2010 13:46:12 +0100
From: "Karabulut, Yigitcan" <>
Subject: st: How to derive Wooldridge and Orme approaches in xtprobit module ?

Dear Statlist,

I am trying to estimate a dynamic random effects probit model that has the
following reduced form:

Y_it = beta*x_it + gamma*y_t-1+alpha_i +u_it (

where y_it  is a binary variable, alpha_i represents the individual specific
unobserved heterogeneity, u_it is the unobserved error, x_it is a vector of

In order to account for unobserved heterogeneity and initial conditions
problems, I have employed the Heckman approach (Heckman, 1981) using the
program module redprob by Prof. Mark Stewart. However, also as stressed in the
literature (e.g. Arulampan and Steward, 2009 or Capellari and Jenkins, 2008),
the computation of Heckman estimator takes so long (for instance,  Capellari
and Jenkins ( 2008) notes that their estimation took about 15 hours).

Since the other two approaches; Orme (1996) and Wooldridge (2002) do also
provide similar results as the Heckman estimator (Arulampan and Steward,
2009), I am willing to employ these approaches since the estimation is less
"expensive" (also as a robustness check).

I read that I can derive the Orme and Wooldridge approaches from the program
module xtprobit, however, I could not figure out how.  I was wondering if
anyone knows how to derive these approaches in xtprobit module in Stata?




(1) As the Statalist FAQ states: you are enjoined to provide full bibliographic
references to research that you cite. This is a multidisciplinary list.
[Unfortunately the work of mine you cite is not yet known worldwide! :)) ]

(2) You will also get better assistance if you show the Stata commands that you
have tried in order to implement these estimators.  We are not here to do your
research for you.

In both cases, you need your data in long form.

For the Orme estimator, fit the initial condition probit, and then generate the
generalized residual variable using the formula in his paper. Then you enter that
variable as an additional regressor in the -xtprobit- specification.

For the Wooldridge estimator, you need to first compute the longitudinally-averaged
variables for each person (think e.g. -bys personid: egen-), then enter these and
the initial binary outcome values as additional regressors in your -xtprobit-

References (which contain references to the papers by Stewart, and Arulampalam and

Cappellari, L and Jenkins, SP (2008) ?The dynamics of social assistance receipt:
measurement and modelling issues, with an application to Britain?, prepared under
contract JA0004519, ELS/SPD Division, Organisation for Economic Cooperation and
Development, September 2008, 70 pp.  Report released as OECD Social, Employment and
Migration Working Paper 67,

Cappellari, L and Jenkins, SP (2009) ?The dynamics of social assistance benefit
receipt in Britain?, ISER Working Paper 2009-29, In: D. Besharov and K.
Couch (eds.), Measuring Poverty, Income Inequality, and Social Exclusion. Lessons
from Europe. Oxford University Press, 2010, forthcoming.

Orme, Christopher D. (1997). ?The initial conditions problem and two-step
estimation in discrete panel data models?, Discussion Paper No. 9633, School of
Social Sciences, University of Manchester. Revised version, June 2001, retitled as:
?Two-Step inference in dynamic non-linear panel data models?,

Wooldridge, Jeffery M. (2005), ?Simple solutions to the initial conditions problem
in dynamic, nonlinear panel data models with unobserved heterogeneity?, Journal of
Applied Econometrics, 20: 39?54.

Professor Stephen P. Jenkins <>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
Survival Analysis using Stata:
Downloadable papers and software:

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