Audit Silence and the Capacity Trap

Abstract

An audit that does not happen admits two readings: the authority chose not to act, or it could not act. We study a repeated inspection game where a regulated firm may be committed to compliance and an inspector may be persistently unable to implement its policy. Audits are public but stochastic, detection is imperfect, and a detected violation ends the relationship. Audit silence means no audit is carried out; a no-finding audit is a separate public outcome. Under capacity separation and explicit payoff and prior conditions, a finite run of silence carries every sequential equilibrium into a region in which the strategic firm violates and the functioning inspector exerts maximum effort. Realized enforcement then deteriorates, harmful relationships survive longer, and surviving relationships are adversely sorted toward strategic firms matched with constrained inspectors. The distribution of enforcement capacity, not only its mean, is therefore a policy object. Holding the current maximum-effort audit rate fixed, raising the capacity floor delays both the deterioration path and a uniform every-equilibrium entry bound, and lowers expected loss during a silence spell. The entry theorem allows arbitrary private-history strategies before the threshold and separates implementation capacity from enforcement effort and detection failure.