# Finding Exogenous Variation in Data

## TL;DR

This paper introduces a novel method for recovering exogenous variation in data by using mixture models, enabling the identification of exogenous observations without traditional instrumental variables, demonstrated through simulations and grocery data analysis.

## Contribution

It proposes a nonparametric mixture model approach to identify exogenous observations, offering an alternative to two-stage least squares without requiring instrumental variables.

## Key findings

- Successfully recovers exogenous observations in simulations
- Identifies hidden pricing experiments in grocery scanner data
- Provides an effective alternative to traditional IV methods

## Abstract

We reconsider the classic problem of recovering exogenous variation from an endogenous regressor. Two-stage least squares recovers exogenous variation through presuming the existence of an instrumental variable. We rely instead on the assumption that the regressor is a mixture of exogenous and endogenous observations--say as the result of temporary natural experiments. With this assumption, we propose an alternative two-stage method based on nonparametrically estimating a mixture model to recover a subset of the exogenous observations. We demonstrate that our method recovers exogenous observations in simulation and can be used to find pricing experiments hidden in grocery store scanner data.