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Quantile Regression with Interval Data

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  • Arie Beresteanu

Abstract

This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We deï¬ ne the identification set of quantiles of random sets in a way that extends the deï¬ nition of quantiles for regular random variables. We then give sharp characterization of this set by extending concepts from random set theory. For quantile regression parameters, we show that the identification set is characterized by a system of conditional moment inequalities. This characterization extends that of parametric quantile regression for regular random variables. Estimation and inference theories are developed for continuous cases, discrete cases, nonparametric conditional quantiles, and parametric quantile regressions. A fast computational algorithm of set linear programming is proposed. Monte Carlo experiments support our theoretical properties. We apply the proposed method to analyze the effects of cleanup of hazardous waste sites on local housing values.

Suggested Citation

  • Arie Beresteanu, 2016. "Quantile Regression with Interval Data," Working Paper 5991, Department of Economics, University of Pittsburgh.
    • Handle: RePEc:pit:wpaper:5991
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    References listed on IDEAS

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    1. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    2. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
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    20. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
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