Asymptotically exact inference in conditional moment inequality models

By T. Armstrong. 2011

65 citations recorded by the source corpus.

This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov–Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A Monte Carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods.

Subfields: Sociology and Political Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/586cf49e66d9046fe5f4d3d2fc956633908bc1d1

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Citations in the corpus

Adaptive test of conditional moment inequalities (2011, methodology): “Methods specific for conditional moment inequalities were developed in Khan and Tamer (2009), Kim (2008), Chernozhukov et al. (2009), Andrews and Shi (2010), Lee et al. (2011), Armstrong (2011a), and Armstrong (2011b).”
Inference on Causal and Structural Parameters using Many Moment Inequalities (2013, background): “…papers on testing conditional moment inequalities, which can be treated as an infinite number of unconditional moment inequalities; see Andrews and Shi (2013), Chernozhukov, Lee, and Rosen (2013), Lee, Song, and Whang (2013a,b), Armstrong (2015), Chetverikov (2017), and Armstrong and Chan (2016).”
Testing Many Moment Inequalities (2013, background): “…papers on testing conditional moment inequalities, which can be treated as an infinite number of unconditional moment inequalities; see Andrews and Shi (2013), Chernozhukov, Lee, and Rosen (2013), Lee, Song, and Whang (2013a,b), Armstrong (2011), Chetverikov (2011), and Armstrong and Chan (2012).”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, background): “…moment inequalities includes Andrews and Shi (2013), Andrews and Shi (2014), Andrews and Shi (2017), Aradillas-López, Gandhi, and Quint (2016), Armstrong (2015), Armstrong and Chan (2016), Chernozhukov, Lee, and Rosen (2013), Chetverikov (2017), Fan and Park (2014), Khan and Tamer (2009),…”
Weighted KS Statistics for Inference on Conditional Moment Inequalities (2011, background): “As shown by Armstrong (2011), KS statistics with bounded weights will converge at different rates on the boundary of the identified set depending on the shape of the conditional mean.”