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st: Endogeneity in zero inflated Poisson model

From   Goedele Van den Broeck <>
To   "" <>
Subject   st: Endogeneity in zero inflated Poisson model
Date   Thu, 13 Feb 2014 10:19:01 +0000

Dear all,

I'm struggling with endogeneity in a zero inflated Poisson model, and it's hard to find decent solutions for it.
My model is: Y = B0 + B1W + B2X + e     
Where Y is the number of children per woman, W is the employment status of a woman, which is likely to be endogenous, and X are exogenous factors.
The dependent variable, Y, is a count variable with an excess of zero observations (more than 50% of my 997 observations have zero children).
Therefore, I choose to use a zero inflated Poisson model (zip in STATA).

Handling endogeneity in a zip model doesn't seem to be straightforward, because of the nonlinear nature of the model and the two different processes it simultaneously generates.
According to Terza et al. (2008), the usual approach of two-stage predictor substitution (2SPS) does not yield consistent estimates in nonlinear models.
Instead, they suggest two stage residual inclusion (2SRI), also known as the control function approach (Wooldridge, 2010, p 126-129).

The 2SRI estimation is specified as follows:
first stage:   W = a0 + a1X + a2Z + u  (Z is an IV for W)
second stage: Y = B0 + B1W + B2X + B3u_hat + e     

Does anybody know whether you could apply 2SRI approach in a zip model?
And if so, how do you exactly implement this in STATA?
I know that I could use the option ivpoisson cfunction in STATA, but then I don't take the zero excess observations into account, which results in biased estimates.

Thanks for your help!

Best regards,
Goedele Van den Broeck

Terza, Basu and Rathouz, 2008. Two-stage residual inclusion estimation: Addressing endogeneity in health econometric modelling. Journal of Health Economics, 27: 531-543.
Wooldridge, 2010, Econometric Analysis of Cross Section and Panel Data (Second Edition).

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