Simulation Error and Root-n Inference in Dynamic Inequality Estimation: A Comment on Bajari, Benkard, and Levin (2007)

Abstract

Bajari, Benkard, and Levin (2007) derive a root-n distribution for a simulated minimum-distance estimator based on equilibrium inequalities. Their published growth condition permits the number of sampled inequalities to increase too slowly to remove centered forward-simulation error. A bounded one-player dynamic model satisfies S1 and every displayed part of S2. Along n = m^4, n_I = m, and n_s = m^3, its simulation score contributes an N(0,2) term while the published covariance is zero. This Comment derives a replacement limit indexed by κ = lim n/(n_I n_s). The published covariance applies at κ = 0; finite positive κ adds simulation covariance; divergent κ changes the convergence rate. Binding inequalities can also generate a root-n mean shift governed by n/n_s. The stronger rates in the paper's working-paper version cover both channels. Under the stated uniformity conditions, the correction leaves the equilibrium inequalities, forward simulator, and point target unchanged.

Technical point

The published growth condition can leave centered forward-simulation noise in the root-n limit, requiring an added simulation covariance term or stronger simulation rates.

Scope