🤖 AI Summary
This study addresses the limitations of the traditional AKM wage decomposition, which relies on linear covariate adjustments and struggles to accurately disentangle the contributions of worker, firm, and match effects to wage dispersion. The authors propose a generalized AKM framework that retains the variance-component structure while incorporating unknown smooth covariate functions and group-specific nonlinear interaction effects, thereby overcoming the linearity constraint. Their approach achieves, for the first time, consistent and asymptotically normal nonparametric covariate adjustment in the presence of high-dimensional fixed effects and heteroskedastic errors, and establishes the stronger smoothness conditions required for quadratic-form estimation. Application to Portuguese employer-employee data reveals that, after controlling for worker and firm characteristics, the variance shares attributable to worker, firm, and match effects decline to 0.474, 0.121, and 0.047, respectively, with results exhibiting greater sensitivity to the choice of control variables than to functional form specifications.
📝 Abstract
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.