The view that empirical strategies in economics should be transparent and credible now goes almost without saying. By revealing for whom particular instrumental variables (IV) estimates are valid, the local average treatment effects (LATE) framework helped make this so. This lecture uses empirical examples, mostly involving effects of charter and exam school attendance, to illustrate the value of the LATE framework for causal inference. LATE distinguishes independence conditions satisfied by random assignment from more controversial exclusion restrictions. A surprising exclusion restriction is shown to explain why enrollment at Chicago exam schools reduces student achievement. I also make two broader points: IV exclusion restrictions formalize commitment to clear and consistent explanations of reduced‐form causal effects; the credibility revolution in applied econometrics owes at least as much to compelling empirical analyses as to methodological insights.

This study uses Social Security data on the earnings of military applicants to the all-volunteer forces to compare the earnings of Armed Forces veterans with the earnings of military applicants who did not enlist. Matching, regression, and Instrumental Variables (IV) estimates are presented. The matching and regression estimates control for most of the characteristics used by the military to select qualified applicants from the military applicant pool. The IV estimates exploit an error in the scoring of exams used by the military to screen applicants between 1976 and 1980. All the estimates suggest that soldiers who served in the early 1980s were paid considerably more than comparable civilians while in the military. Military service also appears to have led to a modest (less than 10 percent) increase in the civilian earnings of nonwhite veterans while actually reducing the civilian earnings of white veterans. Most of the positive effects of military service on civilian earnings appear to be attributable to improved employment prospects for veterans.

Parents gauge school quality in part by the level of student achievement and a school's racial and socioeconomic mix. The importance of school characteristics in the housing market can be seen in the jump in house prices at school district boundaries where peer characteristics change. The question of whether schools with more attractive peers are really better in a value-added sense remains open, however. This paper uses a fuzzy regression-discontinuity design to evaluate the causal effects of peer characteristics. Our design exploits admissions cutoffs at Boston and New York City's heavily over-subscribed exam schools. Successful applicants near admissions cutoffs for the least selective of these schools move from schools with scores near the bottom of the state SAT score distribution to schools with scores near the median. Successful applicants near admissions cutoffs for the most selective of these schools move from above-average schools to schools with students whose scores fall in the extreme upper tail. Exam school students can also expect to study with fewer nonwhite classmates than unsuccessful applicants. Our estimates suggest that the marked changes in peer characteristics at exam school admissions cutoffs have little causal effect on test scores or college quality.

The effect of government programs on the distribution of participants' earnings is important for program evaluation and welfare comparisons.This paper reports es- timates of the effects of JTPA training programs on the distribution of earnings.The estimation uses a new instrumental variable (IV) method that measures program impacts on the quantiles of outcome variables.This quantile treatment effects (QTE) estimator accommodates exogenous covariates and reduces to quantile regres- sion when selection for treatment is exogenously determined.The QTE estimator can be computed as the solution to a convex linear programming problem, although this requires first-step estimation of a nuisance function.We develop distribution theory for the case where the first step is estimated nonparametrically.For women, the empirical results show that the JTPA program had the largest proportional impact at low quantiles.Perhaps surprisingly, however, JTPA training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution.

We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Quantile regression (QR) fits a linear model for conditional quantiles just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean-squared error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR minimizes a weighted mean-squared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile regression concept, similar to the relationship between partial regression and OLS. We also present asymptotic theory for the QR process under misspecification of the conditional quantile function. The approximation properties of QR are illustrated using wage data from the U.S. census. These results point to major changes in inequality from 1990 to 2000.

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi-experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery-generated randomization integral to such designs from non-random preferences and priorities remains open. This paper develops easily-implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.