A Test for Monotone Comparative Statics

In this paper we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditional quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the paper is to derive a likelihood-ratio test, which to the best of our knowledge, is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) it does not require estimating the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) it makes few assumptions on the cardinality, location or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.