Francesco Del Prato, Yaroslav Korobka, Paolo Zacchia
arXiv 10 Aug 2026 · Econometrics
arXiv:2608.09686 · PDF · Extracted main text
How much wage dispersion is attributed to workers, firms, and their sorting depends on how wages are adjusted for observed characteristics. Standard AKM decompositions impose a known linear adjustment. We develop Generalized AKM, a framework that permits an unknown smooth covariate function and group-specific nonlinear interactions while preserving the original variance components. We prove consistency and asymptotic normality with heteroskedastic errors and many fixed effects, and characterize the stronger smoothness required for quadratic forms. In Portuguese employer-employee data, adding worker and firm-input controls lowers the bias-corrected worker-effect variance from $0.551$ to $0.474$ of total wage variance, firm-effect variance from $0.144$ to $0.121$, and sorting from $0.080$ to $0.047$. Across three group-specific nonlinear bases, firm-effect variance remains between $0.114$ and $0.117$ and sorting between $0.041$ and $0.042$, while worker-effect variance ranges from $0.474$to $0.491$. Which controls enter matters more for firm variance and sorting than how flexibly they enter; worker variance remains more sensitive to the basis.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kline, P. and Saggio, R. and Sølvsten, M (2020) Leave-out estimation of variance components | 1.000 | 18 | 8 | 100% |
| 2 | Card, D. and Cardoso, A. R. and Heining, J. and Kline, P (2018) Firms and labor market inequality: evidence and some theory | 0.928 | 4 | 3 | 100% |
| 3 | Cattaneo, M. D. and Jansson, M. and Newey, W. K (2018) Alternative asymptotics and the partially linear model with many regressors | 0.928 | 4 | 3 | 100% |
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| 6 | Cattaneo, M. D. and Jansson, M. and Newey, W. K (2018) Inference in linear regression models with many covariates and heteroscedasticity | 0.811 | 4 | 2 | 100% |
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| 10 | Kline, P (2024) Firm wage effects | 0.644 | 2 | 2 | 100% |
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