Tax fraud by firms and optimal auditing

Tax fraud is an issue of increasing importance in China. One particularly significant fraud involves excessive claims for the rebate of VAT on exported goods. This fraud has two interesting features. First, it requires the collusion of an intermediary to supply the false documentation that supports a rebate application. Second, the punishment schedule is convex--with capital punishment used in major fraud cases. These features ensure that the payoff function of a firm engaging in fraud is strictly concave in the level of fraud. This gives a well-defined optimization without the need to appeal to risk aversion. We show that the existence of fraud does not affect the real output decision of the firm nor the tax policy of the government. Audit resources can be used to detect firms engaged in fraud as well as the intermediaries who supply false documents. Under reasonable assumptions it is shown that resources should be focused on detecting firms and not intermediaries. Finally, if the government must take action on fraud a convex punishment scheme is shown to be optimal.