Under minimal assumptions, finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the "conditional pivotal property" of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear...

We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of very many regressors in a model with possibly non-Gaussian and heteroscedastic disturbances. We allow for the number of regressors to be larger than the sample size. To make...

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...

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...

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...

Data with a large number of variables relative to the sample size?"high-dimensional data"?are readily available and increasingly common in empirical economics. High-dimensional data arise through a combination of two phenomena. First, the data may be inherently high dimensional in that many...

Finite-sample inference methods are developed for quantile regression models. The methods are conservative in that (i) they apply to arbitrary sample sizes without the liberal assumption that sample sizes approach infinity, (ii) they apply when the quantiles are partially or set identified,...

We use instrumental quantile regression approach to examine the effects of 401(k) plans on wealth using data from the Survey of Income and Program Participation. Using 401(k) eligibility as an instrument for 401(k) participation, we estimate the quantile treatment effects of participation in a...