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Re: st: GMM estimation program for simultaneous equations with count data

From   Darby Jack <>
Subject   Re: st: GMM estimation program for simultaneous equations with count data
Date   Fri, 5 Aug 2005 09:37:22 -0400

You might want to check out Frank Windmeijer's -ExpEnd- program for Gauss. It's at publication_id=2656.

-ExpEnd- will estimate the models described in
[Blundell et al., 2002] Blundell, R., Griffth, R., and Windmeijer, F. (2002). Individual effects and dynamics in count data models. Journal of Econometrics, 108:113–131.

[Windmeijer and Santos, 1997] Windmeijer, F. and Santos, J. (1997). Endogeneity in count data models. Journal of Applied Econometrics, 12:281–294.

[Mullahy, 1997] Mullahy, J. (1997). Instrumental variable estimation of count data models. Review of Economics and Statistics, 79(4):586–593.

These models don't coincide exactly with your problem, but it might be useful nonetheless.

Here's Windmeijer's description of the code:

"ExpEnd is a Gauss programme for non-linear generalised method of moments (GMM) estimation of exponential models with endogenous regressors for cross section and panel data. The estimators included in this package are simple Poisson pseudo ML; GMM for cross section data using moment conditions based on multiplicative or additive errors; within groups fixed effects Poisson for panel data; GMM estimation using quasi-differenced moment conditions eliminating unobserved heterogeneity and allowing for predetermined or endogenous regressors; and quasi-differenced GMM for a dynamic linear feedback model. This manual describes in detail the various estimators, the data and software requirements, and the programme commands."

On Aug 5, 2005, at 5:23 AM, chirag patel wrote:


I am trying to solve a system of simultaneous equations where the dependent
variable in both the equations is count data. I am trying to solve this problem
by modelling it as GMM type estimation so as to take into consideration the
exponential mean function.

*The simultaneous equations situation that I have is: *

y = exp (b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 + b6 x6)
z = exp (b7+ b8 x1 + b9 x2 + b10 x3 + b11 x4 + b12 x5 + b13 x6 + b14 x7 + b15 y)

y = count data (0 to 11)
z = count data (0 to 6)
x1 = 0,1,2
x2, x3,x7 = continuous variables
x4,x5,x6 = nominal (0,1)

I wanted advise on the following point:

1)What type of GMM estimation will solve the above system of equations.
Has somebody developed a STATA program for such a GMM type estimation?

I have been advised that there is a user-written program called - qvf- that will
estimate IV versions of generalised linear models, including Poisson
regressions. However, it estimates only single equations, not systems.

It would be very useful if somebody could help with appropriate STATA code.


Chirag PATEL
Lecturer, Marketing Department
ESC Rennes (Rennes International School of Business)
Ph:0033 2 99334847
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