Unbiased estimation of central moments in unbalanced two- and three-level models

Dan Ben-Moshe; David Genesove

doi:10.1016/j.econlet.2026.113013

Unbiased estimation of central moments in unbalanced two- and three-level models

Dan Ben-Moshe^*
, David Genesove

^*Corresponding author for this work

Department of Economics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper derives closed-form unbiased estimators of central moments in multilevel random-effects models with unbalanced group sizes. In a two-level model, we provide unbiased estimators for the second, third, and fourth central moments under both group-level and observation-level averaging. In a three-level model, we provide unbiased estimators for the second and third central moments.

Original language	English
Article number	113013
Journal	Economics Letters
Volume	265
DOIs	https://doi.org/10.1016/j.econlet.2026.113013
State	Published - Jun 2026

Bibliographical note

Publisher Copyright:
© 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Keywords

C13
C23
Central moments
Group-level averaging
Multilevel (hierarchical) models
Observation-level averaging
Unbalanced panels

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10.1016/j.econlet.2026.113013

Cite this

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abstract = "This paper derives closed-form unbiased estimators of central moments in multilevel random-effects models with unbalanced group sizes. In a two-level model, we provide unbiased estimators for the second, third, and fourth central moments under both group-level and observation-level averaging. In a three-level model, we provide unbiased estimators for the second and third central moments.",

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N2 - This paper derives closed-form unbiased estimators of central moments in multilevel random-effects models with unbalanced group sizes. In a two-level model, we provide unbiased estimators for the second, third, and fourth central moments under both group-level and observation-level averaging. In a three-level model, we provide unbiased estimators for the second and third central moments.

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KW - C13

KW - C23

KW - Central moments

KW - Group-level averaging

KW - Multilevel (hierarchical) models

KW - Observation-level averaging

KW - Unbalanced panels

UR - https://www.scopus.com/pages/publications/105037917823

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Unbiased estimation of central moments in unbalanced two- and three-level models

Abstract

Bibliographical note

Keywords

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