Measuring Precision of Statistical Inference on Partially Identified Parameters

Abstract

Planners of surveys and experiments that partially identify parameters of interest face trade offs between using limited resources to reduce sampling error or to reduce the extent of partial identification. Researchers who previously attempted evaluating these trade offs used the length of confidence intervals for the identification region to measure the precision of inference. I show that other reasonable measures of statistical precision yield qualitatively different conclusions, often implying higher value to reducing the extent of partial identification. I consider three alternative measures - maximum mean squared error, maximum mean absolute deviation, and maximum regret (applicable when the purpose of estimation is binary treatment choice). I analytically derive and compare estimation precision and tradeoffs implied by these measures in a simple statistical problem with normally distributed sample data and interval partial identification.

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