Conditional Rank-Rank Regression

{getToc} $title={Table of Contents}

Summary

The Conditional Rank-Rank Regression (CRRR) is introduced as an alternative to traditional rank-rank regressions with covariates (RRRX) for measuring within-group mobility and persistence. CRRR preserves the intuitive interpretation of the average conditional rank correlation between variables.

Highlights

• CRRR uses conditional ranks of variables given covariates, unlike RRRX which uses marginal ranks net of covariate effects.
• The CRRR slope has an intuitive interpretation as the average conditional rank correlation between variables.
• CRRR is suitable for subgroup analysis, maintaining a rank correlation interpretation conditional on groups.
• A distribution regression estimator is proposed for CRRR, allowing for flexible modeling of conditional distributions.
• Asymptotic theory is derived for the CRRR estimator, and an exchangeable bootstrap procedure is proposed for inference.
• CRRR is applied to study intergenerational income mobility in Switzerland, revealing a gender gap and heterogeneity across groups defined by father's education and family size.
• The results are robust to the exclusion of child's covariates and the use of logistic or Gaussian link functions.

Key Insights

• The CRRR approach provides a well-grounded measure of within-group mobility and persistence, allowing for the decomposition of overall persistence into within-group and between-group components.
• The use of conditional ranks in CRRR ensures that the slope has an intuitive interpretation as the average conditional rank correlation between variables, unlike RRRX which loses this interpretation.
• The distribution regression estimator for CRRR is flexible and can approximate the true conditional distribution function arbitrarily well, making it a practical and reliable choice for empirical applications.
• The asymptotic theory for the CRRR estimator provides a solid foundation for inference, and the exchangeable bootstrap procedure offers a convenient and reliable method for constructing confidence intervals.
• The application of CRRR to intergenerational income mobility in Switzerland highlights the importance of considering within-group mobility and persistence in understanding social and economic phenomena.
• The robustness of the results to different link functions and the exclusion of child's covariates demonstrates the reliability and flexibility of the CRRR approach in empirical applications.
• The CRRR approach has the potential to be widely applied in various fields, including economics, sociology, and education, to study mobility and persistence in different contexts.

Mindmap

If MindMap doesn't load, go to the Homepage and visit blog again or Switch to Android App (Under Development).

Citation

Chernozhukov, V., Fernández-Val, I., Meier, J., van Vuuren, A., & Vella, F. (2024). Conditional Rank-Rank Regression (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2407.06387