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. Unlike the existing literature, we consider a setting where the designer can choose the test variable, i.e., whether to test inputs, outputs, or a combination of the two. Although both the market and the designer care about outputs only, we find that tests based exclusively on inputs are most effective at incentivizing output production if the designer can coordinate market beliefs and agents’ behavior on her preferred equilibrium. However, such pure input tests are prone to adverse equilibria, supported by pessimistic market beliefs about the types of agents passing the test. If the designer is concerned about the worst equilibrium outcome, input tests are suboptimal. Pure output tests are not optimal either. Indeed, while robust to adverse equilibrium selection, they fail to motivate high-productivity agents adequately. The reason is that high-productivity agents can reach the output threshold with relatively low input investment, leading to “free-riding on talent.”
We derive the optimal pass/fail test designed to incentivize total output production robustlyand demonstrate its straightforward implementation through three simple components: two output thresholds (one high and 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. In an extension, we show how the main insights carry over to more general multi-threshold tests. Using tests based on inputs alone is optimal if the designer can coordinate beliefs. However, under adversarial equilibrium selection, the designer can improve by using a combination of input and output components.