Pitfall of Precision in Noisy Signaling

Abstract: A principal decides whether to approve an agent based on a noisy signal (e.g., test scores) generated by the agent. High-quality agents can produce high signals on average at lower cost, but the realizations are subject to noise that depends on the screening technology's precision. We uncover a paradoxical "pitfall of precision": when precision is already high, further improvements reduce screening accuracy and lower the principal's welfare. This occurs because greater precision incentivizes strategic signaling from more low-quality agents, outweighing the direct benefit from improved precision. The pitfall of precision also has implications for statistical discrimination: groups with noisier technologies face lower approval rates yet may be favored ex ante -- a reversal of discrimination. We also examine how commitment power helps mitigate the pitfall.