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Simultaneous mean-variance regression

Author

Listed:
  • Richard Spady

    (Institute for Fiscal Studies and Johns Hopkins)

  • Sami Stouli

    (Institute for Fiscal Studies and University of Bristol)

Abstract
We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression outcome across the support of conditioning variables by using weights that are jointly determined with mean regression parameters. Simultaneity generates outcome predictions that are guaranteed to improve over ordinary least-squares prediction error, with corresponding parameter standard errors that are automatically valid. Under shape misspecification of the conditional mean and variance functions, we establish existence and uniqueness of the resulting approximations and characterize their formal interpretation. We illustrate our method with numerical simulations and two empirical applications to the estimation of the relationship between economic prosperity in 1500 and today, and demand for gasoline in the United States.

Suggested Citation

  • Richard Spady & Sami Stouli, 2018. "Simultaneous mean-variance regression," CeMMAP working papers CWP25/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:25/18
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    References listed on IDEAS

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    Cited by:

    1. Chaudhuri, Saraswata & Renault, Eric, 2023. "Efficient estimation of regression models with user-specified parametric model for heteroskedasticty," The Warwick Economics Research Paper Series (TWERPS) 1473, University of Warwick, Department of Economics.
    2. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    3. Philippe Goulet Coulombe, 2022. "A Neural Phillips Curve and a Deep Output Gap," Working Papers 22-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    4. Richard Spady & Sami Stouli, 2020. "Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions," Papers 2011.06416, arXiv.org.
    5. Philippe Goulet Coulombe, 2022. "A Neural Phillips Curve and a Deep Output Gap," Papers 2202.04146, arXiv.org, revised Oct 2024.

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