We study the dynamics of corruption relying on two fundamental observations: (a) Given agents detected as corrupt are typically fired and replaced, the historical levels of corruption have an impact on current corruption through the distribution of corruption costs of old agents; (b) Institutions negatively affected by their agents' corrupt activities are likely to respond optimally to it thereby decreasing the payoff from being corrupt. We model this situation by considering an agent who is supposed to monitor a contractor's delivery of a product or service and can manipulate his reports thus allowing the contractor to deliver lower quality in exchange for a bribe. Given the two generations of agents overlapping at any particular date, the administration sets an optimal level of quality in each period. We find that (i) A unique steady state level of corruption exists; (ii) Regardless of the initial distribution, apart from an initial period, equilibrium sequences are decreasing and converge to the steady state, a result we term the "Hadleyburg effect". We use these findings to study the dynamic response of corruption to both temporary and permanent shocks to the profitability of corruption and we find that the "Hadleyburg effect" has important positive and normative implications.