Estimating local average treatment effects in aggregate data

What is it about?

Often, researchers want to estimate the casual effect of some treatment or policy. Sometimes, they do so using data that is aggregated to the group level. For example, maybe there are thirty students each in two different classrooms A and B, and you want to know whether the addition of a teaching assistant to classroom B improved test scores. The researcher might compare the average test score increase in B with the introduction of the assistant to the average increase over the same time period in A. However, in many instances, not all members of the group actually received treatment. Maybe the teaching assistant never worked with some of the students in B, and also happened to be helping a few students in A on the side. If this is the case, the researcher will get a causal estimate that doesn't exactly capture the effect of being taught by the teaching assistant. This study offers a new application of a method for estimating the desired casual estimate. This new application is specific to aggregate data like our two classrooms above. The method uses the percentage of students in each class who were exposed to the assistant to correct the casual estimate. Additionally, the study suggests Google Trends data as a way to fill in the "percentage of students exposed" data in the many instances where it is not recorded in the data.

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Why is it important?

The use of aggregate data to estimate casual effects is common in economics, where the "difference-in-difference" method is in heavy use. Often, these studies are run without accounting for the fact that within groups, often some individuals receive treatment while others do not. These studies are not presenting the casual effect they think they are! This model offers a way to provide the correct casual estimate. Additionally, in standard social science data sources, treatment rates for each group are often not recorded. These treatment rates are necessary to get the correct casual estimate. In the absence of such data, I suggest the use of Google Trends to fill in the gap. This allows proper casual estimates to be provided in a much wider set of contexts than could be done previously.