In the usual set up of estimating average causal effect in a randomized experiment, Freedman criticized using OLS coefficient of treatment as an estimate when regressing observed outcome on treatment and covariates. To reiterate, based on Neyman’s model, we assume there are n subjects (finite population of interest), assignment (Z) is the only source of randomness, covariates (X), potential outcomes Y(1) and Y(0) are fixed, observed outcomes (Y) are random because they depend on assignment.
Econometricians had begun to develop the concept of instrumental variables, long before statisticians, for drawing causal inferences without the assumption of random assignment. They were interested in studying the effect of economic policies on human behavior. From the very beginning, they acknowledged that the level of treatment is often actively influenced by economic agents (e.g.. households). Therefore, the units in question are not only different in terms of treatment received, but the active decision to seek out that treatment.
The purpose of this paper is to demonstrate how potentially incorrect conclusions about trends can be made from the available data in certain cases where either latent variables aren’t accounted for, or if certain assumptions of the approach are actually false. In particular, the purpose is to investigate if the claim made that UC Berkeley Graduate Schools (in the fall of 1973, with approximately 12763 applicants) were biased against admitting women is valid.
Observational studies create barriers for causal studies because of several reasons but primarily, selection bias - a lack of randomisation implies that the potential outcomes are not independent of treatment assignment, and also that units exposed to treatment could (and usually do) differ fundamentally from the control units.
The paper defines a balancing score as any function of the covariates (which are observed pretreatment or simply: covariates), such that the conditional distribution of x given this score is the same for treated and control units.