Dealing with a Technological Bias: The Difference-in-Difference Approach

I construct a nonlinear model for causal inference in the empirical settings where researchers observe individual-level data for few large clusters over at least two time periods. It allows for identification (sometimes partial) of the counterfactual distribution, in particular, identifying average treatment effects and quantile treatment effects. The model is exible enough to handle multiple outcome variables, multidimensional heterogeneity, and multiple clusters. It applies to the settings where the new policy is introduced in some of the clusters, and a researcher additionally has information about the pretreatment periods. I argue that in such environments we need to deal with two different sources of bias: selection and technological. In my model, I employ standard methods of causal inference to address the selection problem and use pretreatment information to eliminate the technological bias. In case of one-dimensional heterogeneity, identification is achieved under natural monotonicity assumptions. The situation is considerably more complicated in case of multidimensional heterogeneity where I propose three di erent approaches to identification using results from transportation theory.