Symmetry and Selection in Boundary Moment Inequalities: A Comment on Pakes, Porter, Ho, and Ishii (2015)

Abstract

Pakes, Porter, Ho, and Ishii (2015) use symmetry of bank-specific cost shocks to construct boundary moment inequalities. The construction evaluates a sign-reversing order-statistic map at the realized number of positive choices. That count can depend on the same shocks, leaving the selected statistic's expectation unrestricted under marginal iid symmetry. A three-agent ordered-choice model satisfies the maintained choice, counterfactual, information, and symmetry conditions and yields a negative population moment at the true parameter. Joint reflection of shocks and the selected count restores finite-sample validity; a convergent selected share yields a separate large-market result. In the ATM application, the lower estimate remains 24,452 dollars; the upper estimates of 26,444 and 26,644 dollars require a repaired condition. The correction applies to the boundary sufficient-condition argument and specifications using it. The general moment inequality continues to hold when Assumptions 1–3 are imposed directly.

Technical point

Marginal iid symmetry of bank-specific cost shocks does not by itself sign the selected boundary moment when the realized positive-choice count depends on those shocks.

Scope