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Alternative Asymptotics and the Partially Linear Model with Many Regressors

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  • Matias D. Cattaneo
  • Michael Jansson
  • Whitney K. Newey

Abstract

Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the seemingly unrelated "many instruments asymptotics" and "small bandwidth asymptotics" share a common structure, where the object determining the limiting distribution is a V-statistic with a remainder that is an asymptotically normal degenerate U-statistic. We illustrate how this general structure can be used to derive new results by obtaining a new asymptotic distribution of a series estimator of the partially linear model when the number of terms in the series approximation possibly grows as fast as the sample size, which we call "many terms asymptotics".

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  • Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Alternative Asymptotics and the Partially Linear Model with Many Regressors," Papers 1505.08120, arXiv.org.
    • Handle: RePEc:arx:papers:1505.08120
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    Citations

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    Cited by:

    1. Matias D. Cattaneo & Max H. Farrell & Michael Jansson & Ricardo Masini, 2022. "Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators," Papers 2301.00277, arXiv.org, revised Feb 2024.
    2. Matias D Cattaneo & Michael Jansson & Xinwei Ma, 2019. "Two-Step Estimation and Inference with Possibly Many Included Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1095-1122.
    3. Wang, Wenjie, 2021. "Bootstrap Inference for Partially Linear Model with Many Regressors," MPRA Paper 106391, University Library of Munich, Germany.
    4. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    5. Kuanhao Jiang & Rajarshi Mukherjee & Subhabrata Sen & Pragya Sur, 2022. "A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond," Papers 2205.10198, arXiv.org, revised Oct 2022.
    6. Smith, Simon C. & Timmermann, Allan & Zhu, Yinchu, 2019. "Variable selection in panel models with breaks," Journal of Econometrics, Elsevier, vol. 212(1), pages 323-344.
    7. Yanqin Fan & Fang Han & Wei Li & Xiao-Hua Zhou, 2019. "On rank estimators in increasing dimensions," Papers 1908.05255, arXiv.org.
    8. Galbraith, John W. & Zinde-Walsh, Victoria, 2020. "Simple and reliable estimators of coefficients of interest in a model with high-dimensional confounding effects," Journal of Econometrics, Elsevier, vol. 218(2), pages 609-632.
    9. Bruce E. Hansen, 2016. "The Risk of James--Stein and Lasso Shrinkage," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1456-1470, December.
    10. Mittag, Nikolas, 2019. "A simple method to estimate large fixed effects models applied to wage determinants," Labour Economics, Elsevier, vol. 61(C).
    11. Anatolyev, Stanislav, 2021. "Mallows criterion for heteroskedastic linear regressions with many regressors," Economics Letters, Elsevier, vol. 203(C).
    12. Duncan Sheppard Gilchrist & Emily Glassberg Sands, 2016. "Something to Talk About: Social Spillovers in Movie Consumption," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1339-1382.
    13. Riccardo D'Adamo, 2018. "Cluster-Robust Standard Errors for Linear Regression Models with Many Controls," Papers 1806.07314, arXiv.org, revised Apr 2019.
    14. Harold D Chiang & Yuya Sasaki, 2023. "On Using The Two-Way Cluster-Robust Standard Errors," Papers 2301.13775, arXiv.org.
    15. Fan, Yanqin & Han, Fang & Li, Wei & Zhou, Xiao-Hua, 2020. "On rank estimators in increasing dimensions," Journal of Econometrics, Elsevier, vol. 214(2), pages 379-412.
    16. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    17. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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