I am trying to estimate a count data model (Poisson) with endogenous variables (within which there are interaction terms). I am using stata 13.
The model looks like the following:
y1 = exp( y2*b1 + y2*x1*b2 + x1*b3 + x2*b4 ) + epsilon
endogenous variable: y2 and y2*x1
instrumental variables: z1 and z1*x1
exogenous variables: x1, x2
I am trying to use a control function approach. I ran into the following problems:
I tried to estimate the 2 stages myself. I did both of the following. I am wondering which one is correct.
A: stage 1: linear regression: regress y2 on z1, z1*x1, x1 and x2. Estimate the residual r1.
stage 2: estimate the following Poisson model: poisson y1 y2 y2*x1 x1 x2 r1, vce(robust) nolog
B: stage 1: linear regression: regress y2 on z1, z1*x1, x1 and x2. Estimate the residual r1. ALSO, regress y2*x1 on z1, z1*x1, x1 and x2 and obtain residual r2.
stage 2: estimate the following Poisson model: y1 on y2, y2*x1, x1, x2, r1 AND r2.
My questions are: (1) which one between A and B is correct? (2) Is A or B the correct approach to estimate control function estimator for Poisson regression with endogenous regressors? I did try to use ivpoisson cfunction y1 x1 x2 (y2 y2*x1 = z1 z1*x1). It does not converge. it keeps saying NOT CONCAVE.
Thank you very much!
Kathy
The model looks like the following:
y1 = exp( y2*b1 + y2*x1*b2 + x1*b3 + x2*b4 ) + epsilon
endogenous variable: y2 and y2*x1
instrumental variables: z1 and z1*x1
exogenous variables: x1, x2
I am trying to use a control function approach. I ran into the following problems:
I tried to estimate the 2 stages myself. I did both of the following. I am wondering which one is correct.
A: stage 1: linear regression: regress y2 on z1, z1*x1, x1 and x2. Estimate the residual r1.
stage 2: estimate the following Poisson model: poisson y1 y2 y2*x1 x1 x2 r1, vce(robust) nolog
B: stage 1: linear regression: regress y2 on z1, z1*x1, x1 and x2. Estimate the residual r1. ALSO, regress y2*x1 on z1, z1*x1, x1 and x2 and obtain residual r2.
stage 2: estimate the following Poisson model: y1 on y2, y2*x1, x1, x2, r1 AND r2.
My questions are: (1) which one between A and B is correct? (2) Is A or B the correct approach to estimate control function estimator for Poisson regression with endogenous regressors? I did try to use ivpoisson cfunction y1 x1 x2 (y2 y2*x1 = z1 z1*x1). It does not converge. it keeps saying NOT CONCAVE.
Thank you very much!
Kathy