Hello,
To estimate treatment effects using regression adjustment (RA) in STATA, one can use either teffects ra or margins.
The STATA guide section on "margins, contrast" explains how to use margins to implement regression adjustment (pp.1714-1718 in the STATA manual for version 18). It says "The point estimates of the ATE [using teffects ra] are identical to those we obtained using margins, though the standard errors differ slightly from those reported by margins. The standard errors from the two estimators are, however, asymptotically equivalent, meaning they would coincide with a sufficiently large dataset." I can add that in all examples and tests I ran, the standard errors from the margins implementation were slightly larger.
I would like to understand better the source of this difference in standard errors between the margins and the teffects ra implementations of RA. My understanding is that teffects ra estimates RA in one step: it writes down the RA estimator as a series of equations (GMM style) and then estimates the parameters of interest and their variance using quasimaximum likelihood (QML). I'm less clear about how standard errors are estimated in the margins implementation of RA. The STATA manual says that the "linearization method" is used to estimate the variance of the parameters when using the vce(unconditional) option, which we need to use in implementing RA with margins. But I'm not really familiar with the linearization method used, and I don't understand precisely how this differs from the QML method used by teffects ra.
I would be very grateful for any guidance in understanding (even just intuitively, as a start) the source of the difference in standard errors; whether one of the two methods has better finite-sample properties in estimating standard errors; and whether it is always true that standard errors using margins are more conservative than those using teffects ra.
Thanks
Daniele
To estimate treatment effects using regression adjustment (RA) in STATA, one can use either teffects ra or margins.
The STATA guide section on "margins, contrast" explains how to use margins to implement regression adjustment (pp.1714-1718 in the STATA manual for version 18). It says "The point estimates of the ATE [using teffects ra] are identical to those we obtained using margins, though the standard errors differ slightly from those reported by margins. The standard errors from the two estimators are, however, asymptotically equivalent, meaning they would coincide with a sufficiently large dataset." I can add that in all examples and tests I ran, the standard errors from the margins implementation were slightly larger.
I would like to understand better the source of this difference in standard errors between the margins and the teffects ra implementations of RA. My understanding is that teffects ra estimates RA in one step: it writes down the RA estimator as a series of equations (GMM style) and then estimates the parameters of interest and their variance using quasimaximum likelihood (QML). I'm less clear about how standard errors are estimated in the margins implementation of RA. The STATA manual says that the "linearization method" is used to estimate the variance of the parameters when using the vce(unconditional) option, which we need to use in implementing RA with margins. But I'm not really familiar with the linearization method used, and I don't understand precisely how this differs from the QML method used by teffects ra.
I would be very grateful for any guidance in understanding (even just intuitively, as a start) the source of the difference in standard errors; whether one of the two methods has better finite-sample properties in estimating standard errors; and whether it is always true that standard errors using margins are more conservative than those using teffects ra.
Thanks
Daniele
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