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A Convenient Omitted Variable Bias Formula for Treatment Effect Models

Clarke, Damian (2018): A Convenient Omitted Variable Bias Formula for Treatment Effect Models.

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Abstract

Generally, determining the size and magnitude of the omitted variable bias (OVB) in regression models is challenging when multiple included and omitted variables are present. Here, I describe a convenient OVB formula for treatment effect models with potentially many included and omitted variables. I show that in these circumstances it is simple to infer the direction, and potentially the magnitude, of the bias. In a simple setting, this OVB is based on mutually exclusive binary variables, however I provide an extension which loosens the need for mutual exclusivity of variables, and derives the bias in difference-in-differences style models with an arbitrary number of included and excluded “treatment” indicators.

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