Hi everyone,

To my understanding the first stage of a IV Poisson model includes all the exogenous predictors in the second stage Poisson model. The offset is included in the second stage Poisson model as a linear predictor, with coefficient constrained to one. To me, it seems like this means the offset variable should also be included in the first stage (without any constraint on the coefficient); but this is not the behavior in Stata, as the following (entirely made up) code shows (the first stage result doesn't include a coefficient for mpg).

Code:
sysuse auto, clear
ivpoisson cfunction headroom (weight=length), offset(mpg)
In this case, should mpg be also included in the first stage, or have I misunderstood something?

Thanks for your help.
Bing Yang