Partial identification of spread parameters

By Jörg Stoye. 2010

49 citations recorded by the source corpus.

This paper analyzes partial identification of parameters that measure a distribu- tion’s spread, for example, the variance, Gini coefficient, entropy, or interquartile range. The core results are tight, two-dimensional identification regions for the ex- pectation and variance, the median and interquartile ratio, and many other com- binations of parameters. They are developed for numerous identification settings, including but not limited to cases where one can bound either the relevant cumu- lative distribution function or the relevant probability measure. Applications in- clude 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-form worst-case bounds on some pa- rameters 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. Keywords. Partial identification, nonparametric bounds, missing data, sensitiv- ity analysis, variance, inequality. JEL classification. C14, C24.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8e2904fce1a9580865d1dfe222885cfbc483aaae

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Citations in the corpus

Inference on breakdown frontiers (2017, methodology): “We use the same grid of ε’s as in our Monte Carlo simulations in Appendix F in the Online Supplemental Material.”
Identification of Treatment Effects Under Conditional Partial Independence (2017, methodology): “Nonetheless, the cdf and mean bounds we derived can be used as a direct input into theorem 2 of Stoye (2010) to derive explicit, analytical bounds on these spread parameters.”
PARTIAL IDENTIFICATION OF THE DISTRIBUTION OF TREATMENT EFFECTS AND ITS CONFIDENCE SETS (2009, methodology): “AU:2 The references (Manski, 1997; Galichon and Henry, 2006; Stoye, 2008; Beresteanu and Molinari, 2006) have not been included in the reference list.”
Communicating Uncertainty in Official Economic Statistics: An Appraisal Fifty Years after Morgenstern (2014, background): “Manski (2003, Chapters 1 and 2; 2007, Chapters 3 and 4) and Stoye (2010) characterize the identifying power of various such assumptions.”