Good morning all,

I am using the -cmp- package developed by Roodman to estimate a three-stage Heckman selection model. I am using the following code:

Code:
cmp (stage3 = )(stage2 = ) (stage1 =), ind(stage2*$cmp_probit stage1*$cmp_probit $cmp_probit)
While the model has estimated and I am generally able to interpret it, I had a few questions.

First, standard Heckman models have a rho parameter that is the inverse Mills ratio. This controls for selection bias in the second stage of the regression. When estimating the above Heckman model, however, there are three rho parameters. Each parameter has numbers attached to it: rho_12, rho_13, and rho_23. I assume that this means there is a rho parameter being used in stage 2 that is from stage 1, stage 3 that is from stage 1, and stage 3 that is from stage 2. While this interpretation makes sense, why does rho_13 exist? Should the inverse Mills ratio of stage 1 really be put into stage 3? Would I need to constrain that parameter to zero? Some advice would be appreciated, as constraining the parameter to zero substantively changes my results.

Second, I am using probit models and want to interpret the coefficients using margins. I cannot, however, seem to write the code necessary to get marginal effects at the third stage of my model conditional on the first two stages. Here is the code from the cmp help file that is closest to what I want:

Code:
cmp (wage2 = education age) (selectvar = married children education age), ind(selectvar*$cmp_probit $cmp_probit) qui
margins, dydx(*) predict(pr eq(wage2) condition(0 ., eq(selectvar)))
This code replicates the margins, predict(pcond) code for get marginal effects in the second stage of a Heckman probit model in base Stata. It conditions margins on the first stage being equal to 1. I want to do the same with cmp, except conditioning both the first and second stage being equal to 1. How would I do this?

Thanks in advance for anyone who can help. I greatly appreciate it!

- Garrett