Frequency Weights

[Alex Lampert]

Hello,

Has anyone ever used frequency weights for a differences-in-differences regression? I'm obtaining unexpected standard errors for all of the control variables in my models: the standard errors in the weighted model are always larger than the unweighted model, despite the two models using the exact same data (i.e. the only difference between the two models is the frequency weight) I would expect the weighted model standard errors to be lower than the unweighted model due to "multiplied" observations.

I've done summarize on the outcome variable using weights vs. no weights, and it seems no matter how I slice and dice the data, the weighted sums always have lower standard errors (as I expect), but this seems to contradict my DiD model. I was thinking that perhaps the observations being weighted were the observations that deviated the most from the mean.

Does anyone know if I'm missing a key piece of theory that would explain why my weighted SEs are larger than unweighted in the DiD framework?

Thanks!
Alex

[Maarten Buis]

This is possible. The simplest way this could happen if your weights contain lots of 0s, so the weighted sample size goes down rather than up. Alternatively, the standard errors for coefficients is a function of a couple of things, not just the sample size. For example, the standard deviation of the residual could go up in a weighted sample.

[Alex Lampert]

Thanks Maarten. My weights range between 1 and 5 (all integers), so they essentially act as multipliers or duplicators. The purpose of the weights was to avoid unnecessarily expanding my data and instead storing the duplicates in a frequency variable.

Are you surprised that the weighted means produce lower SEs than unweighted (as I expected, since I only added duplicated information), but the weighted coefficients have higher SEs?