Quantifying Threshold Manipulation in the Presence of Rounding: The Case of Lead Monitoring in U.S. Drinking Water

Many laws and economic actions depend on thresholds. As a consequence, threshold manipulation is a common concern in a variety of settings. Existing methods for detecting and quantifying threshold manipulation assume a continuous counterfactual distribution absent manipulation. This assumption is violated in the presence of rounding, which is prevalent in many applications and distinct from manipulation. This paper develops methods for testing and quantifying threshold manipulation when rounding is a prominent feature of the data. We demonstrate the usefulness of our approach in an empirical application examining threshold manipulation in lead monitoring under the U.S. Safe Drinking Water Act.