centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Nonparametric instrumental variable estimation under monotonicity

Authors: Denis Chetverikov and Daniel Wilhelm
Date: 13 July 2015
Type: cemmap Working Paper, CWP39/15
DOI: 10.1920/wp.cem.2015.3915


The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that restricting the problem to models with monotone regression functions and monotone instruments significantly weakens the ill-posedness of the problem. In stark contrast to the existing literature, the presence of a monotone instrument implies boundedness of our measure of ill-posedness when restricted to the space of monotone functions. Based on this result we derive a novel non-asymptotic error bound for the constrained estimator that imposes monotonicity of the regression function. For a given sample size, the bound is independent of the degree of ill-posedness as long as the regression function is not too steep. As an implication, the bound allows us to show that the constrained estimator converges at a fast, polynomial rate, independently of the degree of ill-posedness, in a large, but slowly shrinking neighborhood of constant functions. Our simulation study demonstrates significant finite-sample performance gains from imposing monotonicity even when the regression function is rather far from being a constant. We apply the constrained estimator to the problem of estimating gasoline demand functions from U.S. data.

Download full version
New version:
Denis Chetverikov and Daniel Wilhelm September 2016, Nonparametric instrumental variable estimation under monotonicity, cemmap Working Paper, CWP48/16, The IFS

Publications feeds

Subscribe to cemmap working papers via RSS

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us