I am running a two-stage (Heckman) selection model (xtprobit in stage-1 and xtgee in stage-2) for a panel dataset - 17-year for 626 firms, for two different dependent variables (DVs). Using stage-1 results, inverse mills ratio (IMR) is being calculated and used in the stage-2 as control for selection bias.

The values of both DVs lie between 0 & 1.

The stage-2 regressions are being run with same predictor and almost same set of control variables (except for two - one industry-level control and second inverse mills ratio). My hypothesis requires the statistical comparison of two coefficients of the same predictor coming from two regressions (with two different DVs).
STATA code in simplified format for stage-2:

For y1 as DV: xtgee y1 x1 control1 control2 control3 IMR1, vce(r) family(binomial) link(logit) corr(indep) t(year_id) force -----(i)

For y2 as DV: xtgee y2 x1 control1 control2 control3 IMR2, vce(r) family(binomial) link(logit) corr(indep) t(year_id) force ------ (ii)

I wish to find out coefficient of x1 of which one of the above two regressions is stronger?

I am stuck form long so decided to post it in this forum.

Thanks in advance for any solutions!