Non‐parametric inference on the number of equilibria

Summary This paper proposes an estimator and develops an inference procedure for the number of roots of functions that are non‐parametrically identified by conditional moment restrictions. It is shown that a smoothed plug‐in estimator of the number of roots is superconsistent under i.i.d. asymptotics, but asymptotically normal under non‐standard asymptotics. The smoothed estimator is furthermore asymptotically efficient relative to a simple plug‐in estimator. The procedure proposed is used to construct confidence sets for the number of equilibria of static games of incomplete information and of stochastic difference equations. In an application to panel data on neighbourhood composition in the United States, no evidence of multiple equilibria is found.