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Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties

Author

Listed:
  • Daniel Wilhelm

    (Daniel Wilhelm)

  • Magne Mogstad

    (Magne Mogstad)

  • Azeem Shaikh

    (Azeem M. Shaikh)

Abstract
It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.

Suggested Citation

  • Daniel Wilhelm & Magne Mogstad & Azeem Shaikh, 2021. "Finite- and Large-Sample Inference for Ranks using Multinomial Data with an Application to Ranking Political Parties," RF Berlin - CReAM Discussion Paper Series 2132, Rockwool Foundation Berlin (RF Berlin) - Centre for Research and Analysis of Migration (CReAM).
    • Handle: RePEc:crm:wpaper:2132
    as

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    References listed on IDEAS

    as
    1. Magne Mogstad & Joseph P Romano & Azeem M Shaikh & Daniel Wilhelm, 2024. "Inference for Ranks with Applications to Mobility across Neighbourhoods and Academic Achievement across Countries," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(1), pages 476-518.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    3. Isaiah Andrews & Toru Kitagawa & Adam McCloskey, 2024. "Inference on Winners," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 139(1), pages 305-358.
    4. Martin Klein & Tommy Wright & Jerzy Wieczorek, 2020. "A joint confidence region for an overall ranking of populations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 589-606, June.
    5. Xie, Minge & Singh, Kesar & Zhang, Cun-Hui, 2009. "Confidence Intervals for Population Ranks in the Presence of Ties and Near Ties," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 775-788.
    6. Harvey Goldstein & David J. Spiegelhalter, 1996. "League Tables and Their Limitations: Statistical Issues in Comparisons of Institutional Performance," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 385-409, May.
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    Cited by:

    1. Denis Chetverikov & Magne Mogstad & Pawel Morgen & Joseph Romano & Azeem Shaikh & Daniel Wilhelm, 2024. "csranks: An R Package for Estimation and Inference Involving Ranks," Papers 2401.15205, arXiv.org.
    2. Magne Mogstad & Joseph P. Romano & Azeem M. Shaikh & Daniel Wilhelm, 2023. "A Comment on: “Invidious Comparisons: Ranking and Selection as Compound Decisions” by Jiaying Gu and Roger Koenker," Econometrica, Econometric Society, vol. 91(1), pages 53-60, January.
    3. Lihua Lei, 2024. "Causal Interpretation of Regressions With Ranks," Papers 2406.05548, arXiv.org.

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    More about this item

    Keywords

    Confidence sets; Multinomial Data; Multiple Testing; Polls; Ranks; Surveys;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I20 - Health, Education, and Welfare - - Education - - - General
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion

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