Researchers have found evidence of racial disparity in different stages of the criminal justice process for example, traffic stops, bail levels, detention decisions and incarceration. But, if the decision maker (judge, police officer, etc) observes characteristics that researchers cannot, even regression-adjusted comparisons of racial treatment do not provide an appropriate basis for distinguishing between racial disparity and discrimination. Recently, economists have proposed an alternative approach, known as outcome analysis, in the context of racial profiling by police. We intend to examine the performance of this "standard outcome analysis" (SOA) in the context of bail-setting. The key prediction of SOA in the motorist search context is that the marginal members of all searched groups must exhibit the same hit rate when police behave in a rational, unbiased fashion. But researchers cannot observe whether a given person was marginal or inframarginal at the trooper's decision time, so they must use average, rather than marginal, hit rates. Without further information, there is no reason why the average hit rate among those searched will equal the hit rate of the marginal person. This is known as the inframarginality problem. Ayres (2001) has suggested that this problem disappears in the bail-setting context, since judges are set continuous bail amounts. The main intellectual merit of this proposal comes from the fact that we can show that this conjecture does not hold in the bail case if judges take account of both the probability that defendants make bail and the probability that they commit bad acts while on release. We show how to write the first-order condition of a rational judge who takes these matters into account so that it relates the probability of FTA to a function whose average in any group depends in complicated ways on the distribution of characteristics in that group. Omitted variable bias exists whenever judges have more information than researchers. We show that SOA tests generally are not appropriate, yielding estimates that are statistically biased in an unknown direction. We offer an alternative, generalized outcome analysis (GOA), that is unbiased and straightforward to implement. We then formulate a valid test for racial discrimination when exogenous information on bail levels is available via instrumental variables. We propose to implement our GOA test on a new administrative dataset from the Washington DC Pretrial Services Agency. The dataset has rich information about arrestees, including drug test results, that is at least as detailed as the administrative datasets used in the best studies of the impact of race on the bail decision (Demuth 2003). We argue that the identity of the judge assigned to set bail can be treated as exogenous, and we will use variation in bail levels due to variation in judges' perceived costs of FTA to consistently estimate our model. The test we propose allows us not only to test for discrimination, but also to test whether the behavioral model is correctly specified. To illustrate the potential strengths and drawbacks of our approach, we propose to compare these results with those from standard regression analysis. The GOA framework can have a broader impact because it can be used in other settings to test for racial discrimination (e.g., including sentence length). Outcome testing requires a formal statement of the objectives of the actor of interest, which can be evaluated based on substantive evidence, and it makes a strong testable prediction about what rational behavior would include. This formal hypothesis testing framework should lead to more theory development in the field of criminology and criminal justice. The DC PreTrial Agency has a track record of being ``research-friendly'', and staff members have expressed a willingness to provide the Maryland Population Research Center (MPRC) with regular data transfers of their entire database of arrestees. MPRC has a strong staff of informational technology professionals who will transform the data into a secure, useable form. MPRC intends to make these data to both graduate students and other academics.
