psmath2 and rbounds: estimating 'interaction effect' using Propensity Score Matching, and the sensitivity analysis

[Juan Xi]

Hello,
I'm using Propensity Score Matching method to estimate a treatment effect (psmatch2 used). On top of that, I want to assess the robustness in the treatment effect to potential unobserved factors. Hence I use rbounds (Roesnbaum bounds analysis) following the estimation results from psmatch2. My question is: if I'm interested in knowing not just the main effect, but also heterogeneous effect across groups of individuals, how would the implementations be done with STATA?

So, let me start with plain model (only looking at main treatment effect). Below are the codes as an example:

psmatch2 treatment gender age X, out(wage)
gen delta = wage12- _wage12 if _treatment==1 & _support==1
rbounds delta, gamma(1 (0.1) 2)

Here, treatment indicates whether an individual received treatment or not, gender, age, and X, are the demographics and other covariates associated with each individual. I'm interested in outcome variable wage, and estimate how the impact of treatment is on the wage in the 12th period (indicated with wage12).

Now, if I want to know how the treatment effect varies across gender, how the PSM and Rosenbuam bounds analysis would be? That is, if we write a regression model:

wage ~ a*treatment + b*treatment*female + c*age + d*X + e

where the baseline gender is male, and coefficient b captures the differential effect for female, relative for male. I want to estimate b, and assess its robustness to unobservables. How should I write the psmatch2 and rbounds implementation? Thank you!!

[Juan Xi]

Or is it possible that we implement a sensitivity analysis using other method (other than rbounds?) Thanks!