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A Permutation-Based Estimator For Monotone Index Models

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  • Bhattacharya, Debopam

Abstract

This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data. The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized (over all possible permutations) when the observations are sorted by their values. The resulting estimator is a generalization of Cavanagh and Sherman's monotone rank estimator (MRE) (Cavanagh and Sherman, 1998, Journal of Econometrics 84, 351–381) and does not require a bandwidth choice. The estimator is $\sqrt{n}$ -consistent and asymptotically normal with a consistently estimable covariance matrix. This least-squares estimator can also be used to estimate monotone-index panel data models. A Monte Carlo study is presented where the proposed estimator is seen to dominate the MRE in terms of mean-squared error and mean absolute deviation.

Suggested Citation

  • Bhattacharya, Debopam, 2008. "A Permutation-Based Estimator For Monotone Index Models," Econometric Theory, Cambridge University Press, vol. 24(3), pages 795-807, June.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:795-807_08
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    Cited by:

    1. Debopam Bhattacharya, 2021. "The Empirical Content of Binary Choice Models," Econometrica, Econometric Society, vol. 89(1), pages 457-474, January.
    2. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2024. "Demand and Welfare Analysis in Discrete Choice Models with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(2), pages 748-784.
    3. Bhattacharya, D. & Dupas, P. & Kanaya, S., 2018. "Demand and Welfare Analysis in Discrete Choice Models under Social Interactions," Cambridge Working Papers in Economics 1885, Faculty of Economics, University of Cambridge.
    4. Bo E. Honoré & Luojia Hu, 2018. "Simpler bootstrap estimation of the asymptotic variance of U‐statistic‐based estimators," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-10, February.

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