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Alternative asymptotics and the partially linear model with many regressors

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  • Matias Cattaneo

    (Institute for Fiscal Studies and University of Michigan)

  • Michael Jansson

    (Institute for Fiscal Studies and Berkeley)

  • Whitney K. Newey

    (Institute for Fiscal Studies and MIT)

Abstract

Many empirical studies estimate the structural effect of some variable on an outcome of interest while allowing for many covariates. We present inference methods that account for many covariates. The methods are based on asymptotics where the number of covariates grows as fast as the sample size. We find a limiting normal distribution with variance that is larger than the standard one. We also find that with homoskedasticity this larger variance can be accounted for by using degrees of freedom adjusted standard errors. We link this asymptotic theory to previous results for many instruments and for small bandwidths distributional approximations.

Suggested Citation

  • Matias Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Alternative asymptotics and the partially linear model with many regressors," CeMMAP working papers CWP36/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:36/15
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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. Wang, Wenjie, 2021. "Bootstrap Inference for Partially Linear Model with Many Regressors," MPRA Paper 106391, University Library of Munich, Germany.
    3. 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.
    4. Yanqin Fan & Fang Han & Wei Li & Xiao-Hua Zhou, 2019. "On rank estimators in increasing dimensions," Papers 1908.05255, arXiv.org.
    5. 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.
    6. 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.
    7. Anatolyev, Stanislav, 2021. "Mallows criterion for heteroskedastic linear regressions with many regressors," Economics Letters, Elsevier, vol. 203(C).
    8. 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.
    9. 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.
    10. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    11. 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.
    12. Mittag, Nikolas, 2019. "A simple method to estimate large fixed effects models applied to wage determinants," Labour Economics, Elsevier, vol. 61(C).
    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. Holland, Ashley D., 2017. "Penalized spline estimation in the partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 211-235.
    15. 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.
    16. Harold D Chiang & Yuya Sasaki, 2023. "On Using The Two-Way Cluster-Robust Standard Errors," Papers 2301.13775, arXiv.org.
    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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    More about this item

    Keywords

    Non-standard asymptotics; partially linear model; many terms; adjusted variance;
    All these keywords.

    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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