A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

We study identification and estimation of the average treatment effect in a correlated random coefficients model that allows for first stage heterogeneity and binary instruments. The model also allows for multiple endogenous variables and interactions between endogenous variables and covariates....

The ability to allow for flexible forms of unobserved heterogeneity is an essential ingredient in modern microeconometrics. In this paper we extend the application of instrumental variable (IV) methods to a wide class of problems in which multiple values of unobservable variables can be...

Rain affects electoral turnout both through a direct effect on the cost of voting and by changing the opportunity cost. In a panel of Norwegian municipalities I find that rain on Election Day increases turnout. As turnout affects electoral outcomes, rain provides an exogeneous source of...

In the large empirical literature that investigates the causal effects of education on outcomes such as health, wages and crime, it is customary to measure education with years of schooling, and to identify these effects using the exogenous variation provided by school reforms increasing...

The ability to allow for flexible forms of unobserved heterogeneity is an essential ingredient in modern microeconometrics. In this paper we extend the application of instrumental variable (IV) models to a wide class of problems in which multiple values of unobservable variables can be...

In this paper, we investigate what can be learned about average counterfactual outcomes when it is assumed that treatment response functions are smooth. The smoothness conditions in this paper amount to assuming that the differences in average counterfactual outcomes are bounded under different...

This chapter reviews instrumental variable models of quantile treatment effects. We focus on models that achieve identification through a monotonicity assumption in the treatment choice equation. We discuss the key conditions, the role of control variables as well as the estimands in detail and...

This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can...

We use a Regression Discontinuity Design (RDD) to evaluate the impact of cost-sharing on the use of health services. In the Italian health system, individuals reaching age 65 and earning low incomes are given total exemption from cost-sharing for health services consumption. Since the...