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Moving Beyond Linear Regression: Implementing and Interpreting Quantile Regression Models With Fixed Effects

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  • Fernando Rios-Avila
  • Michelle Lee Maroto

Abstract

Quantile regression (QR) provides an alternative to linear regression (LR) that allows for the estimation of relationships across the distribution of an outcome. However, as highlighted in recent research on the motherhood penalty across the wage distribution, different procedures for conditional and unconditional quantile regression (CQR, UQR) often result in divergent findings that are not always well understood. In light of such discrepancies, this paper reviews how to implement and interpret a range of LR, CQR, and UQR models with fixed effects. It also discusses the use of Quantile Treatment Effect (QTE) models as an alternative to overcome some of the limitations of CQR and UQR models. We then review how to interpret results in the presence of fixed effects based on a replication of Budig and Hodges’s work on the motherhood penalty using NLSY79 data.

Suggested Citation

  • Fernando Rios-Avila & Michelle Lee Maroto, 2024. "Moving Beyond Linear Regression: Implementing and Interpreting Quantile Regression Models With Fixed Effects," Sociological Methods & Research, , vol. 53(2), pages 639-682, May.
    • Handle: RePEc:sae:somere:v:53:y:2024:i:2:p:639-682
    DOI: 10.1177/00491241211036165
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    References listed on IDEAS

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    1. Sergio Firpo & Cristine Pinto, 2016. "Identification and Estimation of Distributional Impacts of Interventions Using Changes in Inequality Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 457-486, April.
    2. Markus Gangl & Andrea Ziefle, 2009. "Motherhood, labor force behavior, and women’s careers: An empirical assessment of the wage penalty for motherhood in britain, germany, and the united states," Demography, Springer;Population Association of America (PAA), vol. 46(2), pages 341-369, May.
    3. Bijan J. Borah & Anirban Basu, 2013. "Highlighting Differences Between Conditional And Unconditional Quantile Regression Approaches Through An Application To Assess Medication Adherence," Health Economics, John Wiley & Sons, Ltd., vol. 22(9), pages 1052-1070, September.
    4. Sergio P. Firpo & Nicole M. Fortin & Thomas Lemieux, 2018. "Decomposing Wage Distributions Using Recentered Influence Function Regressions," Econometrics, MDPI, vol. 6(2), pages 1-40, May.
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