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Abstract

Applied economics research often uses Difference in Differences estimation techniques as it allows for reasonable assumptions to be made under which the effects of economic or social policies can be identified. The main result of this paper is that causal inference can be performed using Difference in Differences methodology even when pre-policy data is not observed for the outcome of interest. I introduce a novel framework in which the outcome of interest can be recovered from a post-outcome remotely sensed variable using a time- invariant linear map from the outcome of interest onto the post-outcome variable. Under this data generating process and assumptions that ensure that predictions of the outcome of interest made through this process are sufficiently accurate, I show that only the addition of standard Difference in Differences assumptions allow for the estimation of the treatment effect on treated units. Not only is the treatment effect identified, but the limiting distribution of estimates made with this methodology is normal, meaning that this method can be used for causal inference.