Multi-dimensional Test Design

TL;DR

This paper explores how to optimally design multi-dimensional tests and testing procedures, revealing different strategies depending on whether agents manipulate or invest in their types, with implications for interviews, regulations, and data classification.

Contribution

It introduces a new tradeoff between test difficulty and testing procedure complexity, providing optimal design strategies for manipulation and investment scenarios.

Findings

Stringent tests with easy procedures are optimal in manipulation scenarios.

Non-stringent tests with difficult procedures are optimal in investment scenarios.

Sequential testing can be as effective as simultaneous testing under mild conditions.

Abstract

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.