Economic Theory - Christoph Carnehl - Bocconi University

Title: Inputs or Outputs: What to Test and How to Test (joint with Matteo Camboni)
Abstract: We study the optimal design of tests in environments where agents can invest in inputs (e.g., effort) to enhance their individual outputs (e.g., human capital), which are then sold in a competitive market (e.g., labor market).  Recognizing agents' heterogeneity in converting inputs into outputs, the designer devises a test to maximize the expected total output. Our findings indicate that tests focusing solely on inputs are most effective for achieving this goal, provided the designer can coordinate market beliefs and agents' behavior on her preferred equilibrium. However, such input tests are prone to adverse equilibria, supported by pessimistic market beliefs about passing agents. If the designer is concerned about the worst equilibrium outcome, input tests are suboptimal. Conversely, tests that are based solely on outputs are robust to adversarial equilibrium selection but fail to motivate high-productivity agents adequately, who may ``free-ride on their talent.'' We derive the optimal test designed to incentivize total output production robustly, and show its straightforward implementation through three simple components: two output thresholds (one high, one low) and one input threshold. Agents achieve a passing grade exclusively when their input-output combination exceeds at least two of these three thresholds.