Abstract

As we have seen, in order to interpret OLS or IV estimates causally, we need that E[xiui] = 0 or E[ziui] = 0; in other words, we need to be sure that some variables are orthogonal to any unobserved factors that may influence the outcome. This is a difficult requirement to meet in many settings. One of the most important things to understand is the following: Just because you have data, does not mean you can answer a causal question!!! When can we be guaranteed of orthogonality? If the “treatment ” of interest is randomly assigned, then it must be independent of any unobserved factors. For example, if we could somehow take a group of individuals and randomly assign half to go to college, and half to stop at high school (and make sure they comply with their assignment), then by construction, the distribution of pretreatment “motivation ” and “ability ” would be the same in both the college and high school groups. So a randomized experiment represents an ideal situation, where orthogonality holds by construction. This is why medical therapies must be evaluated by randomized clinical trials in the U.S., and why many economists have turned to running experiments to try