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TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS

Published online by Cambridge University Press:  18 September 2018

Denis Chetverikov
Denis Chetverikov*
Affiliation:
Department of Economics, UCLA
*
*Address correspondence to Denis Chetverikov, e-mail: [email protected].
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Abstract

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Monotonicity is a key qualitative prediction of a wide array of economic models derived via robust comparative statics. It is therefore important to design effective and practical econometric methods for testing this prediction in empirical analysis. This article develops a general nonparametric framework for testing monotonicity of a regression function. Using this framework, a broad class of new tests is introduced, which gives an empirical researcher a lot of flexibility to incorporate ex ante information she might have. The article also develops new methods for simulating critical values, which are based on the combination of a bootstrap procedure and new selection algorithms. These methods yield tests that have correct asymptotic size and are asymptotically nonconservative. It is also shown how to obtain an adaptive and rate optimal test that has the best attainable rate of uniform consistency against models whose regression function has Lipschitz-continuous first-order derivatives and that automatically adapts to the unknown smoothness of the regression function. Simulations show that the power of the new tests in many cases significantly exceeds that of some prior tests, e.g., that of Ghosal, Sen, and Van der Vaart (2000).

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 4 , August 2019 , pp. 729 - 776
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

Date: First version: March 2012. This version: July 9, 2018. Email: [email protected]. I thank Victor Chernozhukov for encouragement and guidance. I am also grateful to Anna Mikusheva, Isaiah Andrews, Andres Aradillas-Lopez, Moshe Buchinsky, Glenn Ellison, Jin Hahn, Bo Honore, Rosa Matzkin, Jose Montiel Olea, Ulrich Muller, Whitney Newey, Joris Pinkse, and Jack Porter for valuable comments. The first version of the article was presented at the Econometrics lunch at MIT in April, 2012.

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