### Abstract

This paper presents a method for estimating the model A(Y) = β′X + U, where Y is a scalar, A is an unknown increasing function X is a vector of explanatory variables, β is a vector of unknown parameters, and U has unknown cumulative distribution function F. It is not assumed that A and F belong to known parametric families; they are estimated nonparametrically. This model generalizes a large number of widely used models that make stronger a priori assumptions about A and/or F. The paper develops n^{1/2}-consistent, asymptotically normal estimators of A, F, and quantiles of the conditional distribution of Y. Estimators of β that are n^{1/2}-consistent and asymptotically normal already exist. The results of Monte Carlo experiments indicate that the new estimators work reasonably well in samples of size 100.

Original language | English (US) |
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Pages (from-to) | 103-137 |

Number of pages | 35 |

Journal | Econometrica |

Volume | 64 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

### Keywords

- Empirical process
- Semiparametric estimation
- Transformation model
- Unobserved heterogeneity

### ASJC Scopus subject areas

- Economics and Econometrics