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 square error linear approximation to the conditional expectation function even...

The view that empirical strategies in economics should be transparent and credible now goes almost without saying. The local average treatment effects (LATE) framework for causal inference helped make this so. The LATE theorem tells us for whom particular instrumental variables (IV) and...

Quantitative criminology focuses on straightforward causal questions that are ideally addressed with randomized experiments. In practice, however, traditional randomized trials are difficult to implement in the untidy world of criminal justice. Even when randomized trials are implemented, not...

Individual outcomes are highly correlated with group average outcomes, a fact often interpreted as a causal peer effect. Without covariates, however, outcome-on-outcome peer effects are vacuous, either unity or, if the average is defined as leave-out, determined by a generic intraclass...

Many personal and policy decisions turn on perceptions of school effectiveness, defined here as the causal effect of attendance at a particular school or set of schools on student test scores and other outcomes. Widely-disseminated school ratings frameworks compare average student achievement...

The method of instrumental variables was first used in the 1920s to estimate supply and demand elasticities, and later used to correct for measurement error in single-equation models. Recently, instrumental variables have been widely used to reduce bias from omitted variables in estimates of...

Colombia's PACES program provided over 125,000 pupils from poor neighborhoods with vouchers that covered approximately half the cost of private secondary school. Since many vouchers were allocated by lottery, we use differences in outcomes between lottery winners and losers to assess program...

Average schooling in US states is highly correlated with state wage levels, even after controlling for the direct effect of schooling on individual wages. We use an instrumental variables strategy to determine whether this relationship is driven by social returns to education. The instrumentals...

The question of how technology affects learning has been at the center of recent debates over educational inputs. In 1994, the Israeli State Lottery sponsored the installation of computers in many elementary and middle schools. This program provides an opportunity to estimate the impact of...