Testing Models with Multiple Equilibria by Quantile Methods

In this paper, we present methods for deriving testable implication from models with multiple equilibria. Our framework includes many economic models with a one-dimensional endogenous variable---examples are macroeconomic growth models (Solow, 1956), partial equilibrium models, and games of strategic complementarities. Unlike traditionally assumed in the literature, the multiple equilibria models considered here have no implications for the conditional mean of the endogenous variable. We show that such models typically have strong implications for the tail of the conditional distribution of the endogenous variable. We present an econometric framework for testing these implications which reposes on quantile methods and extreme-value theory. We construct a novel order-restricted test based on conditional quantiles of the endogenous variable rather than its mean, which distinguishes our approach from commonly used tests similar to that of Bartholomew (1959)