"There are a large number of cases where corruption has been discovered investigating levels of consumption that appear to be hard to justify. Yet, in the standard moral hazard model withholding of effort by the agent is not observable to the principal. We argue that this assumption has to be revised in applications that study corruption. The informativeness of an agent's level of consumption depends on his legal income and initial level of wealth, as conspicuous consumption by wealthy agents leads to little updating of the principal's belief about their honesty. This introduces a tendency to prefer poor agents as they are easier to monitor. More generally, we describe the basic problem of choosing agents and monitoring consumption with the aim of reducing corruption, and discuss features of the practical applications. We show that when there is consumption monitoring and wealth is observed, the effect of higher wealth on equilibrium bribes is ambiguous (and that the political class will exhibit lower variance in consumption than the general population). In settings where formal contracts matter, we show that monitoring consumption introduces a tendency towards low powered incentives (and more generally low wages). We also discuss the role of ability, the tax system, and the way to derive a measure of the value of illegal funds for the agent."--abstract.