Adding coefficients to obtain interaction effects – what to do with SEs?

I have a multivariate regression, which includes interactions. For example, to get the estimate of the treatment effect for the poorest quintile I need to add the coefficients from the treatment regressor to the coefficient from the interaction variable (which interacts treatment and quintile 1). When adding two coefficients from a regression, how does one obtain standard errors? Is it possible to add the standard errors from the two coefficients? What about the t-stats? Is it possible to add these as well? I’m guessing not but I can’t find any guidance on this.

Thanks so much in advance for your help!

Answer

I think this the expression for SEbnew:

SE21+SE22+2Cov(b1,b2)

You can work with this new standard error to find your new test statistic for testing Ho:β=0

Attribution
Source : Link , Question Author : Sarah , Answer Author : suncoolsu

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