Solved – Adding coefficients to obtain interaction effects – can I add standard errors

I posted this question earlier and am rewriting it in hopes of getting some guidance. I am using a weighted regression (after propensity score matching) to obtain estimates of the effects of a treatment (treat) on an outcome for different income quintiles. I include interactions of the quintiles and the treatment in the equation, as shown below:

regress outcome treat quintile2 quin3 quin4 quin5 treatXquin2 treatXquin3 treatXquin4   treatXquin5 

To obtain the effect of treatment on quintile2 I add the coefficient on treat with the coefficient on treatXquin2. However, what do I do with the standard errors? Can I simply add the standard errors on the two coefficients together? Can I add the t-stats together?

Any advice would be much appreciated. I'm not a stats expert but have a basic understanding of econometrics.

Your impact of treatment depends updon quintile status. After running the 'regress' command, type, 'lincom treat + treatXquin2' to get the impact of treatment for those in quintile 2. This gives a confidence interval and standard error for this estimate. Note that, as is typical in Stata, using the names of the variables in a post-estimation step refers to the coefficients on those variables, not the variables themselves.

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