Nonparametric instrumental variable estimation under monotonicity

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: cemmap working paper ; No. CWP39/15

Classification and Topics

• Classification: Wirtschaft

Contributors, Location and Time

• Event: Geistige Schöpfung
• (who): Chetverikov, Denis ; Wilhelm, Daniel
• Event: Veröffentlichung
• (who): Centre for Microdata Methods and Practice (cemmap)
• (where): London
• (when): 2015

Further information

• DOI: doi:10.1920/wp.cem.2015.3915
• Handle: http://hdl.handle.net/10419/130049
• Last update: 20.09.2024, 8:21 AM CEST