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Quantile Regression with Generated Regressors

Author

Listed:
  • Liqiong Chen

    (Department of Economics, University of Iowa, Iowa City, IA 52242, USA)

  • Antonio F. Galvao

    (Department of Economics, University of Arizona, Tucson, AZ 85721, USA)

  • Suyong Song

    (Department of Economics & Finance, University of Iowa, Iowa City, IA 52242, USA)

Abstract
This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

Suggested Citation

  • Liqiong Chen & Antonio F. Galvao & Suyong Song, 2021. "Quantile Regression with Generated Regressors," Econometrics, MDPI, vol. 9(2), pages 1-35, April.
    • Handle: RePEc:gam:jecnmx:v:9:y:2021:i:2:p:16-:d:534600
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    References listed on IDEAS

    as
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    2. Hartwig, Benny & Meinerding, Christoph & Schüler, Yves S., 2021. "Identifying indicators of systemic risk," Journal of International Economics, Elsevier, vol. 132(C).
    3. Khan, Yasir & Hassan, Taimoor & Guiqin, Huang & Nabi, Ghulam, 2023. "Analyzing the impact of natural resources and rule of law on sustainable environment: A proposed policy framework for BRICS economies," Resources Policy, Elsevier, vol. 86(PA).
    4. Christis Katsouris, 2023. "Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models," Papers 2311.08218, arXiv.org, revised Apr 2024.
    5. Dianliang Deng & Mashfiqul Huq Chowdhury, 2022. "Quantile Regression Approach for Analyzing Similarity of Gene Expressions under Multiple Biological Conditions," Stats, MDPI, vol. 5(3), pages 1-23, July.
    6. Jayeeta Bhattacharya, 2020. "Quantile regression with generated dependent variable and covariates," Papers 2012.13614, arXiv.org.

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