Minimum distance estimators for nonparametric models with grouped dependent

This paper develops minimum distance estimators for nonparametric models where the dependent variable is known only to fall in a specified group with observable thresholds, while its true value remains unobserved and possibly censored. Such data arise commonly in major U.S and U.K data sets where, e.g., the thresholds between which earnings fall are observed, but not its level. Under minor regularity conditions identification of such a model is shown to depend on there being at least two thresholds when the model disturbance's distribution is smooth and invertible. Estimators are motivated by conversion of the model into a set of binary choice models, each corresponding to one finite-valued threshold. This conversion illustrates that the difference of any two thresholds from a function that depends on identified components is identically zero; the function of interest is an additive component of this identity. Minimum distance estimators for possibly nonlinear functionals of the model are proposed, and shown to be consistent with a limiting distribution that is Gaussian. Estimators of the covariance matrix are provided. The estimators are applied to estimation of a problem in labor economics.