The Correlated Response Technique: Estimation, Incentives, and Comparison with Randomized Response at Equal Statistical Precision

Randomized response is a widely used survey technique for measuring stigmatized populations, but it may provide limited information in small samples. This paper introduces a method of elicitation through perfectly correlated questions, showing that correlation can substantially improve statistical performance and allow a dominant-strategy mechanism when either the interviewer or respondents hold symmetric beliefs. The framework also allows the interviewer to possess private information about the distribution of questions, further relaxing incentive constraints. Building on an existing survey design game framework, the paper introduces a novel efficiency-normalized comparison that holds statistical performance constant across mechanisms, enabling a direct comparison of incentives. The analysis characterizes incentive properties and estimation under correlated questions and randomized response, and identifies when it is optimal to ask respondents directly, use randomized response, or correlate questions.