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Causal inference with a functional outcome
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0003-1558-032X
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0003-3187-1987
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-7917-5687
2024 (English)In: The Journal of the Royal Statistical Society, Series C: Applied Statistics, ISSN 0035-9254, E-ISSN 1467-9876, Vol. 73, no 1, p. 221-240Article in journal (Refereed) Published
Abstract [en]

This article presents methods to study the causal effect of a binary treatment on a functional outcome with observational data. We define a Functional Average Treatment Effect (FATE) and develop an outcome regression estimator. We show how to obtain valid inference on the FATE using simultaneous confidence bands, which cover the FATE with a given probability over the entire domain. Simulation experiments illustrate how the simultaneous confidence bands take the multiple comparison problem into account. Finally, we use the methods to infer the effect of early adult location on subsequent income development for one Swedish birth cohort.

Place, publisher, year, edition, pages
Oxford University Press, 2024. Vol. 73, no 1, p. 221-240
Keywords [en]
early adult location, functional average treatment effect, lifetime income trajectory, simultaneous confidence bands
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-216053DOI: 10.1093/jrsssc/qlad092ISI: 001090448500001Scopus ID: 2-s2.0-85182646724OAI: oai:DiVA.org:umu-216053DiVA, id: diva2:1808740
Funder
Swedish Research Council, 2016-02851Swedish Research Council, 2008-7491Riksbankens JubileumsfondUmeå UniversityAvailable from: 2023-11-01 Created: 2023-11-01 Last updated: 2024-02-13Bibliographically approved
In thesis
1. Studying earnings trajectories as functional outcomes
Open this publication in new window or tab >>Studying earnings trajectories as functional outcomes
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Att studera inkomstbanor som funktionella utfall
Abstract [en]

In this thesis, we present methods for studying patterns of income accumulation over time using functional data analysis. This is made possible by the availability of large-scale longitudinal register data in Sweden. By modelling individuals’ cumulative earnings trajectories as continuous functions of time, we can explore temporal dynamics as well as divergences in these trajectories based on initial labour market conditions. A major contribution of this thesis consists of extending the potential outcome framework for causal inference to functional data analysis.

In Paper I, we use functional-on-scalar linear regression and an interval-wise testing procedure to study the associations between initial labour market size and income trajectories for one Swedish birth cohort. In Paper II, we present methods to draw causal conclusions in this setting. We introduce the functional average treatment effect (FATE), as well as an outcome-regression based estimator for this parameter. In addition, we show the finite sample distribution of this estimator under certain regularity conditions and demonstrate how simultaneous confidence bands can be used for inferences about the FATE. An application study in this paper estimates the causal effect of initial labour market size on income accumulation trajectories.

In Paper III, these methods are applied to study the effect of initial firm age on earnings accumulation. Paper IV presents an outcome regression based and a double robust estimator for the mean of functional outcomes when some of these outcome functions are missing at random. We derive the asymptotic distributions of these two estimators as well as their covariance structure under more general conditions. 

Place, publisher, year, edition, pages
Umeå: Umeå University, 2024. p. 26
Series
Statistical studies, ISSN 1100-8989 ; 58
Keywords
functional data analysis, causal inference, earnings trajectories, simultaneous confidence bands, missing data
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-217510 (URN)9789180702348 (ISBN)9789180702355 (ISBN)
Public defence
2024-02-09, HUM.D.220, Humanisthuset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2024-01-19 Created: 2024-01-11 Last updated: 2024-01-11Bibliographically approved

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Ecker, Kreskede Luna, XavierSchelin, Lina

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