Estimating local average treatment effects in aggregate data

ABSTRACT

In some contexts, the effect of a treatment can be estimated with easily accessible aggregate rather than individual data, using difference-in-difference estimation. However, under imperfect assignment within groups, this produces intent-to-treat estimates, which may not be the treatment effect of interest. This article provides a method for estimating local average treatment effects using aggregate data. I also suggest a data source that allows the method to be applied when treatment rates are not recorded.

KEYWORDS:

• Treatment effects
• instrumental variables
• difference-in-difference
• internet data

JEL CLASSIFICATION:

• C21
• C26
• C81
• D04

Acknowledgement

I thank Andrew Gill for comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ The same principles could be applied to non-difference-in-difference (DID) designs that use aggregate data.

² There may be as few as one assigned and one unassigned group.

³ I present a basic model and estimator in this article. Standard tools can adjust the model to allow for unequal group sizes, time trends in treatment rate, covariates, number treated or log treatment rate instead of treatment rate, nonparametric specifications or SEs that account for the estimated nature of the data.

⁴ Validity is satisfied by the parallel trends DID assumption, that outcomes would have changed similarly for both groups had neither been assigned to treatment.

⁵ Those changing treatment status as a result of the assignment policy either all received more treatment, or all received less treatment.