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TESTING GENERALIZED REGRESSION MONOTONICITY

Published online by Cambridge University Press:  18 December 2018

Yu-Chin Hsu ,
Chu-An Liu  and
Xiaoxia Shi
Yu-Chin Hsu
Affiliation:
Academia Sinica National Central University National Chengchi University
Chu-An Liu
Affiliation:
Academia Sinica
Xiaoxia Shi*
Affiliation:
University of Wisconsin at Madison
*
*Address correspondence to Xiaoxia Shi, Department of Economics, University of Wisconsin at Madison, 1180 Observatory Dr, Social Sciences Building #6428, Madison, WI 53706-1320, USA; e-mail: xshi@ssc.wisc.edu.
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Abstract

We propose a test for a generalized regression monotonicity (GRM) hypothesis. The GRM hypothesis is the sharp testable implication of the monotonicity of certain latent structures, as we show in this article. Examples include the monotonicity of the conditional mean function when only interval data are available for the dependent variable and the monotone instrumental variable assumption of Manski and Pepper (2000). These instances of latent monotonicity can be tested using our test. Moreover, the GRM hypothesis includes regression monotonicity and stochastic monotonicity as special cases. Thus, our test also serves as an alternative to existing tests for those hypotheses. We show that our test controls the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives, and has nontrivial power against some ${n^{ - 1/2}}$ local alternatives.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 6 , December 2019 , pp. 1146 - 1200
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

Yu-Chin Hsu gratefully acknowledges the research support from Ministry of Science and Technology of Taiwan (MOST103-2628-H-001-001-MY4 and MOST107-2410-H-001 -034 -MY3) and Career Development Award of Academia Sinica, Taiwan. All errors and omissions are our own responsibility.

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