Multi-dimensional Test Design
This addresses a foundational issue in mechanism design for applications like interviews and regulations, though it is incremental as it builds on existing models of screening and manipulation.
The paper tackles the problem of jointly designing tests and testing procedures for screening agents with multi-dimensional types, where agents can manipulate or invest in their types. It shows that optimal arrangements differ: for manipulation, stringent tests with an easy sequential procedure are best, while for investment, non-stringent tests with a difficult simultaneous or random sequential procedure are optimal.
How should one jointly design tests and the arrangement of agencies to administer these tests (testing procedure)? To answer this question, we analyze a model where a principal must use multiple tests to screen an agent with a multi-dimensional type, knowing that the agent can change his type at a cost. We identify a new tradeoff between setting difficult tests and using a difficult testing procedure. We compare two settings: (1) the agent only misrepresents his type (manipulation) and (2) the agent improves his actual type (investment). Examples include interviews, regulations, and data classification. We show that in the manipulation setting, stringent tests combined with an easy procedure, i.e., offering tests sequentially in a fixed order, is optimal. In contrast, in the investment setting, non-stringent tests with a difficult procedure, i.e., offering tests simultaneously, is optimal; however, under mild conditions offering them sequentially in a random order may be as good. Our results suggest that whether the agent manipulates or invests in his type determines which arrangement of agencies is optimal.