Hello,
Does anyone know how to implement Heckman's (1981) solution to the initial
conditions problem (see citation below)?
What I am trying to estimate is a dynamic random effects probit model and I
need to follow Heckman's approach in order to:
"approximate the reduced form marginal probablility of the initial state by
a probit function using all pre-sample (eg period 0 in my data set)
information on the exogenous variables".
I have already implemented Wooldridge's (2005) approach and I want to
compare the results with those obtained after the implementation of
Heckman's solution.
I have tried etsimating a probit model for the first ( eg year zero) year
of my data set only and then obtain a matrix of the estimated probit
coefficients eg e(b) to include in the next step but then, when I go to the
second stage to estimate a dynamic random effects probit (inclusive of a
full set of time times) the size of the matrix e(b) is smaller than the
number of parameters to be estimated in stage two by the dynamic RE probit
model( 'cos the one period probit in stage is exclusive of the full set of
time dummies) and thus, I cannot proceed.
Would be most grateful if someone could help.
Georgios
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1.Heckman, James J. , "The Incidental Parameters Problem and the Problem of
Initial Conditions in Estimating a Discrete Time-Discrete
Data Stochastic Process"
in C. Manski and D. McFadden, eds., Structural Analysis of Discrete Data
with Econometric Applications, MIT Press (1981)
2. Wooldridge, Jeffrey M. , "Simple Solutions to the Initial Conditions
Problem in Dynamic, Non-Linear Panel Data Models with Unobserved
Heterogeneity", Journal of Applied Econometrics, 20, 2005.
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