Testing rank similarity in the local average treatment effects model

Abstract This paper develops a test for the rank similarity condition of the nonseparable instrumental variable quantile regression model using the local average treatment effect model. When the instrument takes more than two values or multiple binary instruments are available, there exist multiple complier groups for which the marginal distributions of potential outcomes are identified. A testable implication is obtained by comparing the distributions of ranks across complier groups. We propose a test procedure in a semiparametric quantile regression specification. We establish the weak convergence of the test statistic and the validity of the bootstrap critical value. We illustrate the test with an empirical example of the effects of fertility on women’s labor supply.