Propensity Score Matching. Significance test for difference between ATT of OLS and ATT of PSM?

[Bill Bradford]

I have run a standard OLS model predicting the effect of treatment (D_i = 1 if treated, 0 if not), given a performance measurement, V_i , a constant, α, and a set of independent variables, X.

V_i = α + βD_i + Xδ + ε_i

Where ε_i is the error term. My interest here is β, the effect of being treated. Then I used Stata propensity score matching (PSM) using the same X control variables to estimate ATT and the standard error of ATT. I find a different β and standard error of β using these two approaches. Question: Can I test the statistical significant of the difference (ATTOLS - ATTPSM) by a t-test using their respective standard errors? Note that for my study the difference is important. Confidence intervals are not sufficient.

[kirin]

Generally i use this:
1. Run the first regression and type estimate store "giveanametotheregression"
2. Ru the PSM regression and type estimate store "giveanametotheregression"
3. run suest which the name of the 2 regression
4. Use test [name of the first regression_mean]name of the variable u need to test - [name of the second regression_mean]name of the variable u need to test =0

This is my example:
regress wellbeing year D DiD
estimates store DiD1
reg wellbeing year D DiD sex age_r yeduc region [weight=wp], vce(robust)
estimates store DiDProp
suest DiD1 DiDProp
test [DiD1_mean]DiD - [DiDProp_mean]DiD=0
This is an example with a regression ols to evaluate the ATT, and the same but with prop using weights. I hope this can help u.