Testing Generalized Regression Monotonicity

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 paper. Examples include the monotone instrumental variable assumption of Manski and Pepper (2000) and the monotonicity of the conditional mean function when only interval data are available for the dependent variable.? 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. ? JEL classification: C01, C12, C21 ? Keywords: Generalized regression monotonicity, hypothesis testing, monotone instrumental variable, interval outcome, uniform size control