Covariates and Causal Effects: The Problem of Context
47 Pages Posted: 15 Nov 2013 Last revised: 29 Oct 2014
Date Written: August 19, 2014
The literature contrasting structural and experimental econometrics highlights that stronger assumptions are required to identify direct effects than total effects. This paper examines the additional assumptions required to predict future experience using either type of causal effect identified in past data. I show there is a tradeoff between identification and prediction driven by a fact I call the problem of context: Treatment always influences the outcome variable in combination with covariates. The response of covariates to variation in treatment impedes identification of direct effects, while changes over time to the process generating covariates impedes prediction using total effects. I show that total effects can be used for prediction only under restrictive assumptions about the evolution of the DGP: All features of the DGP must remain the same. Direct effects allow for prediction when only some features of the DGP remain the same. To highlight implications for applied work, I discuss the strong assumptions about the behavior of covariates required for prediction when using the total effects of educational attainment successfully identified in past data. While the assumptions required to both identify and predict using standard methodology may be daunting, an explicit statement of these assumptions is a first step towards developing methodology capable of weakening them.
Keywords: Identifi cation, Prediction, Direct Effect, Total Effect, Dynamics, Dynamic Covariates, Dynamic Principal Strata, Lucas Critique, Transportability across Time, Exogeneity.
JEL Classification: C31, C36, C40, C51, C53, I21
Suggested Citation: Suggested Citation