The Econometric SocietyEdited by: Marina Halac • Print ISSN: 0012-9682 • Online ISSN: 1468-0262
Econometrica: Sep, 2025, Volume 93, Issue 5
https://doi.org/10.3982/ECTA19153
p. 1885-1913
Richard H. Spady|Sami Stouli
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible maximum likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.
Richard Spady and Sami Stouli
In Section 2 of this Supplementary Material we collect auxiliary results used in the proofs of our main results, Sections 3 and 4 contain proofs for Corollary 1 and Theorems 3-5. In Section 5 we give implementation details and additional results for the empirical application. To assess the finite sample performance of our estimator, Section 6 gives results of Monte Carlo simulations. We compare our Gaussian Transform Regression (GTR) estimator to related methods for the estimation of distributional regression functions. Overall, we find that GTR performs very well in finite samples.
Richard Spady and Sami Stouli
The replication package for this paper is available at https://doi.org/10.5281/zenodo.15171317. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.July 5, 2026
