Testing Regression Monotonicity in Econometric Models

TL;DR

This paper introduces a flexible nonparametric framework for testing regression monotonicity in econometrics, providing new methods for critical value simulation, adaptive testing, and demonstrating superior power through simulations and real data application.

Contribution

It develops a comprehensive nonparametric testing framework for regression monotonicity, including new simulation methods and an adaptive, rate-optimal test that adjusts to unknown smoothness.

Findings

New tests outperform prior methods in power.

Adaptive tests achieve optimal uniform consistency.

Application indicates strategic entry deterrence in pharmaceuticals.

Abstract

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 paper 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 paper 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 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). An application of the developed procedures to the dataset of Ellison and Ellison (2011) shows that there is some evidence of strategic entry deterrence in pharmaceutical industry where incumbents may use strategic investment to prevent generic entries when their patents expire.