Decomposing unemployment with a partially labeled mixture model: evidence from censored Korean data

This study decomposes Korean unemployment into frictional, structural, and cyclical components using microdata from the economically active population survey (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023)(2024).To address unobserved heterogeneity, the paper employs a finite mixture model estimated with a semi-supervised expectation-maximization (EM) algorithm.The model's identification is anchored by partial labels from self-reported job separation reasons, which ensures an economically meaningful classification and mitigates the arbitrariness of purely data-driven clustering.The framework also incorporates right-censoring to correct for top-coding biases and uses a multinomial logit model with individual covariates to classify unlabeled observations.Robustness is assessed by comparing exponential (constant hazard), log-normal (non-monotonic hazard), and Weibull (monotonic hazard) distributions.The results confirm that the cyclical share of unemployment is strongly pro-cyclical, while the duration of structural unemployment shows a persistent upward trend.Critically, the log-normal model, which provides a superior fit based on BIC, estimates mean durations more than 50% longer than the exponential specification.This finding highlights that models lacking flexible duration dependence risk systematically understating unemployment persistence.