Partial identification of spread parameters

• 成果类型: Article
• 署名作者: Stoye, Joerg
• 署名单位: Cornell University
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE24
• 发表日期: 2010
• 页码: 323-357
• 关键词: partial identification; nonparametric bounds; Missing Data; sensitivity analysis; variance; INEQUALITY

摘要

This paper analyzes partial identification of parameters that measure a distribution's spread, for example, the variance, Gini coefficient, entropy, or interquartile range. The core results are tight, two-dimensional identification regions for the expectation and variance, the median and interquartile ratio, and many other combinations of parameters. They are developed for numerous identification settings, including but not limited to cases where one can bound either the relevant cumulative distribution function or the relevant probability measure. Applications include missing data, interval data, short versus long regressions, contaminated data, and certain forms of sensitivity analysis. The application to missing data is worked out in some detail, including closed-formworst-case bounds on some parameters as well as improved bounds that rely on nonparametric restrictions on selection effects. A brief empirical application to bounds on inequality measures is provided. The bounds are very easy to compute. The ideas underlying them are explained in detail and should be readily extended to even more settings than are explicitly discussed.