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Smooth varying-coefficient models in Stata

Author

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  • Fernando Rios-Avila

    (Levy Economics Institute of Bard College)

Abstract

Nonparametric regressions are powerful statistical tools that can be used to model relationships between dependent and independent variables with minimal assumptions on the underlying functional forms. Despite their poten- tial benefits, these models have two weaknesses: The added flexibility creates a curse of dimensionality, and procedures available for model selection, like cross- validation, have a high computational cost in samples with even moderate sizes. An alternative to fully nonparametric models is semiparametric models that com- bine the flexibility of nonparametric regressions with the structure of standard models. In this article, I describe the estimation of a particular type of semipara- metric model known as the smooth varying-coefficient model (Hastie and Tibshi- rani, 1993, Journal of the Royal Statistical Society, Series B 55: 757–796), based on kernel regression methods, using a new set of commands within vc pack. These commands aim to facilitate bandwidth selection and model estimation as well as create visualizations of the results.

Suggested Citation

  • Fernando Rios-Avila, 2020. "Smooth varying-coefficient models in Stata," Stata Journal, StataCorp LLC, vol. 20(3), pages 647-679, September.
  • Handle: RePEc:tsj:stataj:v:20:y:2020:i:3:p:647-679
    DOI: 10.1177/1536867X20953574
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    Cited by:

    1. David Stadelmann & Tobias Thomas & Nikita Zakharov, 2026. "Too hot to play it cool? Temperature and negative media bias," Public Choice, Springer, vol. 206(3), pages 593-608, March.
    2. Gnimassoun, Blaise & Grekou, Carl & Mignon, Valérie, 2026. "The industrial cost of fixed exchange rate regimes," Journal of Macroeconomics, Elsevier, vol. 87(C).
    3. Bao, Te & Ma, Mengzhong & Wen, Yonggang, 2023. "Herding in the non-fungible token (NFT) market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 39(C).
    4. African Department International Monetary Fund & Western Africa Region World Bank, 2024. "Enhancing Sustainable and Inclusive Growth in the Central African Economic and Monetary Community," World Bank Publications - Reports 38438, The World Bank Group.
    5. Gioia M. Mariani & Eleonora Porreca & Concetta Rondinelli, 2025. "How do households adjust house price expectations in an era of high inflation? Experimental evidence," Questioni di Economia e Finanza (Occasional Papers) 940, Bank of Italy, Economic Research and International Relations Area.
    6. Salisu, Afees A. & Isah, Kazeem & Vinh Vo, Xuan, 2025. "The “effect modifier” of US interest rate in the economic policy uncertainties and economic conditions of fifty (50) US states: A semi-parametric smooth varying-coefficient approach," The North American Journal of Economics and Finance, Elsevier, vol. 75(PA).
    7. Andersson, Fredrik N.G., 2023. "Income inequality and carbon emissions in the United States 1929–2019," Ecological Economics, Elsevier, vol. 204(PA).
    8. Assaf Botzer, 2025. "Publication Trends on the Varying Coefficients Model: Estimating the Actual (Under)Utilization of a Highly Acclaimed Method for Studying Statistical Interactions," Publications, MDPI, vol. 13(2), pages 1-19, April.

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