Measuring Precision of Statistical Inference on Partially Identified Parameters

Planners of surveys and experiments that partially identify parameters of interest face trade offs between using limited resources to reduce sampling error and using them to reduce the extent of partial identification. I evaluate these trade offs in a simple statistical problem with normally distributed sample data and interval partial identification using different frequentist measures of inference precision (length of confidence intervals, minimax mean sqaured error and mean absolute deviation, minimax regret for treatment choice) and analogous Bayes measures with a flat prior. The relative value of collecting data with better identification properties (e.g., increasing response rates in surveys) depends crucially on the choice of the measure of precision. When the extent of partial identification is significant in comparison to sampling error, the length of confidence intervals, which has been used most often, assigns the lowest value to improving identification among the measures considered.