I am not a statistician or econometrician, so please bear with me. For a term paper, I am estimating local treatment effects using a regression discontinuity design, and I want to test whether the effect of crossing the threshold is different for men and women. For the full sample, I keep observations only within the desired bandwidth and then run the following Stata code:

reg y rv above rv_above

where y = outcome; rv = running variable; above = indicator if the running variable is above the threshold; and rv_above is an interaction term between rv and above, allowing the slope of the control function to change above and below the threshold.

I believe there should be two (equivalent?) ways to obtain the effects for the subsample of men and the subsample of women:

1. I can create a dummy variable, for example female = 1 for women and = 0 for men, then run the code reg y rv above rv_above if female == 1 to get the treatment effect for women and the code reg y rv above rv_above if female == 0 to get the treatment effect for men. Once I do this, how do I test that the coefficient on "above" is different between the two samples? Is it as simple as showing that the 95% confidence intervals do not overlap, and then you can conclude that they are statistically different at the 5% level? Or is there another formal statistical test of significance that I should be using if I choose to do this split sample analysis?

2. Instead of splitting the sample, I can include a dummy variable for gender in the regression and interact it with all of the variables previously included:

reg y rv above rv_above gender gender_rv gender_above gender_rv_above

Is this also a correct way to do things? And in this case, how do I test that the effect for men and women is statistically different?

Thanks for any guidance you can share.

I am not a statistician or econometrician, so please bear with me. For a term paper, I am estimating local treatment effects using a regression discontinuity design, and I want to test whether the effect of crossing the threshold is different for men and women. For the full sample, I keep observations only within the desired bandwidth and then run the following Stata code:

reg y rv above rv_above, r

where y = outcome; rv = running variable; above = indicator if the running variable is above the threshold; and rv_above is an interaction term between rv and above, allowing the slope of the control function to change above and below the threshold.

I believe there should be two (equivalent?) ways to obtain the effects for the subsample of men and the subsample of women:

1. I can create a dummy variable, for example female = 1 for women and = 0 for men, then run the code reg y rv above rv_above if female == 1, r to get the treatment effect for women and the code reg y rv above rv_above if female == 0, r to get the treatment effect for men. Once I do this, how do I test that the coefficient on "above" is different between the two samples? Is it as simple as showing that the 95% confidence intervals do not overlap, and then you can conclude that they are statistically different at the 5% level? Or is there another formal statistical test of significance that I should be using if I choose to do this split sample analysis?

2. Instead of splitting the sample, I can include a dummy variable for gender in the regression and interact it with all of the variables previously included:

reg y rv above rv_above gender gender_rv gender_above gender_rv_above, r

Is this also a correct way to do things? And in this case, how do I test that the effect for men and women is statistically different?

Thanks for any guidance you can share.