Tax audits detect and correct noncompliance on the spot, but can also change compliance in future filing behavior. In contrast to the immediate impact on tax revenues, the audit effects on future filing behavior are not directly observable and must be estimated within a counterfactual framework. This paper uses data from an experiment with random assignment to estimate the effects of audits on future self-reported deductions among wage earners. Modern tax administrations use machine learning methods to guide selection of individual taxpayers in risk-based audits. We study how the future filing response to an audit varies with the risk score of the taxpayer. This estimate speaks directly to the design of optimal risk based audits that typically sets a risk threshold and audit all taxpayers with a risk score above that value. When we account for effects on future filing behaviour, we show that the risk score audit threshold applied by the Norwegian tax administration is set far above the threshold that maximizes net public revenue.