Wald-Difference-in-Differences Estimation without Individual-Level Treatment Data

Takumi Hattori, Kohsuke Kubota, Keiichi Ochiai

Keywords: difference-in-differences, gaussian mixture model, non-compliance

TL;DR: We propose a method to estimate causal effects of in-store ads without individual ad exposure data, using a Gaussian Mixture Model to estimate complier proportions, overcoming limitations of methods relying on public treatment data.

Abstract:

In-store advertising, such as digital signage and in-store posters, is a crucial advertising method that influences customer purchasing behavior. While their effectiveness is typically evaluated by displaying ads on a store-by-store basis and comparing the purchasing behavior of those exposed to ads with those who are not, obtaining ad exposure data for individual customers is costly, making it challenging to conduct accurate causal inference with individual-level treatment variables.
A common approach to address this issue is to perform causal inference considering non-compliance, setting visitors to stores implementing an ad campaign as the treatment group and similar customers who have visited comparable stores as the control group. In this setting, a popular estimator is the ratio of two Difference-in-Differences (DID) estimates: one for the outcome variable and another for the treatment variable. However, previous study assume that the DID estimate for the treatment variable is known from public data, which is not always the case.
To overcome this limitation, we propose a method to estimate causal effects by utilizing the fact that, for binary treatment variables, the DID estimate of the treatment variable represents the change in the proportion of compliers in the treatment group. Our method leverages a Gaussian Mixture Model to estimate the proportion. This approach allows for the estimation of the treatment effect on the compliers even in advertising strategies where ad exposure data for individual customers is unavailable.

Submission Number: 5