Partial Identification of Discrete Instrumental Variable Models using Shape Restrictions

This study examines the nonparametric instrumental variable model with discrete instruments and explores the partial identification and estimation of the target parameter, which is a linear functional of the structural function. We include numerous target parameters, such as the difference between the values of the structural function at two different points and the average effect of a hypothetical policy change. Informative bounds on the target parameter are derived using the control function approach and shape restrictions. Illustrative examples demonstrate that shape restrictions have identification power. The lower and upper bounds are estimated using the sieve method and we show that our estimator is computationally convenient and consistent. An empirical application illustrates the usefulness of our method.