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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.

onestop
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Sarah
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    Please explain why you're not satisfied with suncoolsu's answer to your previous version of the same question http://stats.stackexchange.com/q/3653/449. Also please indicate what software the code in your question is for, and add an appropriate tag. That way, someone with experience in that software package might be able to suggest explicit code. – onestop Oct 18 '10 at 14:52
  • Sorry for posting a second question. For some reason I can't figure out how to edit my question. I'm new to the site so please bear with me. And thanks again to those who have provided answers so far! – Sarah Oct 18 '10 at 15:15
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    You can edit the question by clicking 'edit' which appears below the tags for your question. If some aspect of suncoolsu's answer is not clear you should ask for clarification via commenting to the answer. There is a 'add comment' link below every answer. –  Oct 18 '10 at 15:49

2 Answers2

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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.

Charlie
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  • Thanks so much Charlie. This is very useful. I didn't know about the lincom command so this will save me lots of time. However, if I want to get the impact of treatment on the outcome for quintile 2 should i not add treat + treatXquin2 (rather than adding quintile2 + treatXquin2)? – Sarah Oct 18 '10 at 15:53
  • Charlie - I'm not sure I understand why you multiply treatXquin2 by 1 for yes. If that is the case then how do I obtain the estimate for the untreated (i.e. treat==0)? It doesn't seem to make sense that I would multiply treatXquin2 by 0. Any help would be much appreciated! – Sarah Oct 18 '10 at 16:17
  • Sorry, I misread your question. Add treat + treatXquin2 for the treatment impact for those in quintile 2. I have updated my answer. – Charlie Oct 18 '10 at 22:05
  • Thanks Charlie - Is it possible to get the estimates separately for treated and untreated? The lincom command only gives me the difference between treated and untreated. – Sarah Oct 20 '10 at 13:52
  • Estimates of what? Using a version of the lincom statement above, you get the treatment effect for each quintile (the estimate of the treatment effect for the first quintile is just the coefficient on treatment). – Charlie Oct 20 '10 at 22:08
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I am quite sure it's fine to just add the standard errors on the two coefficients together. I can then obtain the t-stats by dividing the sum of the coefficients by the sum of the standard errors. If anyone disagrees please let me know.

Sarah
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    I did not downvote but you should see the other thread as to why this is not ok. –  Oct 18 '10 at 15:47
  • Sorry, I downvoted this answer to indicate I disagreed, but that was an inapproriate and lazy way of doing so, for which I apologise. I'm afraid it's now too late to undo my vote, however - the software won't allow it, for reasons I don't entirely understand. I've just upvoted your question in an attempt to balance things out, though I realise two wrongs don't make a right. – onestop Oct 18 '10 at 22:21
  • If you want to add the standard errors together you need to square them then sum them then sqrt them. i.e. s.e(X+Y)= sqrt(s.e(x)^2 + s.e(Y)^2) – josh Apr 01 '15 at 13:53