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Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs

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  • Fiorini, Mario
  • Stevens, Katrien

Abstract

Whenever treatment effects are heterogeneous, and there is sorting into treatment based on the gain, monotonicity is a condition that both Instrumental Variable and fuzzy Regression Discontinuity designs must satisfy for their estimate to be interpretable as a LATE. However, applied economic work often omits a discussion of this important assumption. A possible explanation for this missing step is the lack of a clear framework to think about monotonicity in practice. In this paper, we use an extended Roy model to provide insights into the interpretation of IV and fuzzy RD estimates under various degrees of treatment effect heterogeneity, sorting on gain and violation of monotonicity. We then extend our analysis to two applied settings to illustrate how monotonicity can be investigated using a mix of economic insights, data patterns and formal tests. For both settings, we use a Roy model to interpret the estimate even in the absence of monotonicity. We conclude with a set of recommendations for the applied researcher.

Suggested Citation

  • Fiorini, Mario & Stevens, Katrien, 2021. "Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs," Working Papers 2021-01, University of Sydney, School of Economics.
    • Handle: RePEc:syd:wpaper:2021-01
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    1. Attar, Itay & Cohen-Zada, Danny & Elder, Todd E., 2024. "Measuring and Correcting Monotonicity Bias: The Case of School Entrance Age Effects," IZA Discussion Papers 17088, Institute of Labor Economics (IZA).
    2. Julio Cáceres-Delpiano & Eugenio Giolito, 2024. "School starting age and the impact on school admission," Empirical Economics, Springer, vol. 67(1), pages 225-251, July.
    3. Seltzer, Andrew J. & Wadsworth, Jonathan, 2024. "The impact of public transportation and commuting on urban labor markets: Evidence from the New Survey of London Life and Labour, 1929–1932," Explorations in Economic History, Elsevier, vol. 91(C).
    4. Mette Goertz & Vibeke Myrup Jensen & Sarah Sander, 2023. "Daycare Enrollment Age and Child Development," CEBI working paper series 22-26, University of Copenhagen. Department of Economics. The Center for Economic Behavior and Inequality (CEBI).
    5. Diana Alessandrini & Bharat Diwakar, 2023. "The Intergenerational Effects of Recessions," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 69(4), pages 1060-1087, December.
    6. Paolo, Antonio Di & Shidiqi, Khalifany-Ash, 2025. "Education and ethnic intermarriage: evidence from higher education expansion in Indonesia," World Development, Elsevier, vol. 195(C).
    7. Karim Bekhtiar & Benjamin Bittschi & Richard Sellner, 2024. "Robots at work? Pitfalls of industry‐level data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(6), pages 1180-1189, September.

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