Audit Silence and the Capacity Trap

Abstract

This paper studies how learning about an inspector's capacity affects compliance in a repeated relationship. A functioning inspector chooses effort, but the implementation of an audit remains uncertain. A constrained inspector audits at a persistently lower rate. The firm may be committed to compliance or may choose to violate; audit occurrence is observed, detection is imperfect, and a finding ends the relationship. When the constrained audit rate lies below every functioning effort level, each missed audit makes constrained capacity more likely. Under explicit payoff and belief conditions, a sufficiently long uninterrupted silence run leads to violation and maximum functioning effort in every sequential equilibrium. Further silence lowers expected auditing despite that effort. The result holds at every fixed discount factor below one, although its sufficient silence bound can become very large with patience. Entry is conditional on the specified history, and clean audits can take beliefs outside the sufficient region. We also compare technologies with the same initial maximum-effort mean audit rate. Raising the capacity floor sustains higher audit ceilings along specified silence paths and, under additional incentive and social-cost conditions, lowers expected loss over a common finite horizon. Finally, constrained inspectors become more prevalent among surviving strategic firms, while the strategic/constrained pair's share of all survivors can fall.