TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS

By D. Chetverikov. Econometric Theory, 2012

49 citations recorded by the source corpus.

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).

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e72ab795c7e580c6a00a62189405a75425c77969

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Citations in the corpus

Inference on Causal and Structural Parameters using Many Moment Inequalities (2013, background): “Indeed, by Theorem 2 in Chernozhukov, Chetverikov, and Kato (2015), the primary 16Some applications of this result can be found in Chetverikov (2017, 2012), Wasserman, Kolar and Rinaldo (2013), and Chazal, Fasy, Lecci, Rinaldo, and Wasserman (2013). factor for the bound on the Kolmogorov distance…”
Heterogeneous Peer Effects and Rank Concerns: Theory and Evidence (2017, unknown): “I formally test monotonicity of m̂(·) using the method developed in Chetverikov (2013). It would be computationally unfeasible to perform the test in all classrooms.”
Jackknife multiplier bootstrap: finite sample approximations to the U-process supremum with applications (2017, background): “sumption on the conditional distribution of ", which is maintained in [1]. Our results below also cover these alternative tests. F.2. Alternative tests for monotonicity of regression function f. [16] considers testing monotonicity of the regression function fwithout the assumption that the erro”
Using Wasserstein Generative Adversarial Networks for the design of Monte Carlo simulations (2019, unknown): “To illustrate this we use a recent test statistic for monotonicity of the regression function proposed in Chetverikov [2019], see also Chetverikov et al.”
TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, methodology): “Our test can also be used as an alternative to testing monotonicity of mean regression (e.g., Chetverikov (2012) and Ghosal, Sen, and van der Vaart (2000)) as well as testing stochastic monotonicity (e.g., Lee, Linton, and Whang (2009) and Delgado and Escanciano (2012)).”
Improved central limit theorem and bootstrap approximations in high dimensions (2019, unknown): “For example, it appears in selecting the regularization parameters for the Lasso estimator and the Dantzig selector ([12]), in carrying out reality checks for data snooping and testing superior predictive ability ([42, 25]), in constructing model confidence sets ([26]), in testing conditional and/or”