We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on IRd and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge-Kantorovich depth, specializes...

We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks, and signs, based on canonical transportation maps between a distribution of interest on Rd and a reference distribution on the d-dimensional unit ball. The new depth concept, called...

This paper derives conditions under which preferences and technology are nonparametrically identified in hedonic equilibrium models, where products are differentiated along more than one dimension and agents are characterized by several dimensions of unobserved heterogeneity. With products...

We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances where the number of controls may be much larger than the...

We develop results for the use of LASSO and Post-LASSO methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n. We rigorously develop asymptotic...

This paper gives identification and estimation results for quantile and average effects in nonseparable panel models, when the distribution of period specific disturbances does not vary over time. Bounds are given for interesting effects with discrete regressors that are strictly exogenous or...

Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings,...

We consider estimation of policy relevant treatment effects in a data-rich environ ment where there may be many more control variables available than there are observations. In addition to allowing many control variables, the setting we consider allows heterogeneous treatment effects, endogenous...

The goal of many empirical papers in economics is to provide an estimate of the causal or structural effect of a change in a treatment or policy variable, such as a government intervention or a price, on another economically interesting variable, such as unemployment or amount of a product...

In the first part of the paper, we consider estimation and inference on policy relevant treatment effects, such as local average and local quantile treatment effects, in a data-rich environment where there may be many more control variables available than there are observations. In addition to...