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Closed Form Solutions for the Generalized Extreme Value Distribution

Author

Listed:
  • Walter Beckert

    (Department of Economics, Mathematics & Statistics, Birkbeck)

  • Yuya Takahashi

    (Johns Hopkins University)

Abstract

This manuscript derives closed form solutions for conditional expectations of order statistics in models that are based on the extreme value and generalized extreme value distributions. Such conditional expectations are of interest in empirical anal-yses when the (identity of the) maximal statistic is observed, but the econometric model also relies on lower-rank order statistics which are unobserved. This is the case, for example, in some (sequential) bargaining models (e.g. Beckert, Smith and Takahashi (2015), for which this manuscript is a companion piece), or in empirical auctions models. The manuscript also provides an algorithm to derive the density of the GEV cumulative distribution function. This density is required to simulate nested logit models following the MCMC approach proposed by McFadden (1999).

Suggested Citation

  • Walter Beckert & Yuya Takahashi, 2015. "Closed Form Solutions for the Generalized Extreme Value Distribution," Birkbeck Working Papers in Economics and Finance 1512, Birkbeck, Department of Economics, Mathematics & Statistics.
    • Handle: RePEc:bbk:bbkefp:1512
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    File URL: https://eprints.bbk.ac.uk/id/eprint/15267
    File Function: First version, 2015
    Download Restriction: no
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    More about this item

    Keywords

    generalized extreme value distribution; order statistics.;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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