Analysis of Convergence and Stability of a Stochastic Matching Model with Mismatch Factors in the Labor Market
Keywords:
Stochastic Matching, Mismatch, Stochastic Differential Equations, StabilityAbstract
Abstract. The mismatch between job seekers and job openings is one of the factors that can cause unemployment to remain high even when job opportunities are available. Furthermore, labor market dynamics are also influenced by various random factors, so deterministic approaches are often insufficient to describe actual conditions. Therefore, this study aims to construct a stochastic matching model of labor distribution by explicitly incorporating the mismatch factor, as well as to analyze the asymptotic properties and stability of the system. The model is developed from the Diamond–Mortensen–Pissarides (DMP) model by modeling the mismatch factor as a stochastic disturbance following standard Brownian motion. The resulting model takes the form of a Stochastic Differential Equation (SDE). The analysis is conducted through verification of the Lipschitz and linear growth conditions, application of Itô’s Lemma, construction of Lyapunov functions, and the Meyn–Tweedie criterion. The results of the study show that the model has exactly one strong solution that is continuous and adapted to the filtration. In addition, conditions are obtained that guarantee the existence of a single stationary distribution and exponential convergence to long-run equilibrium. Stability analysis shows that the system is stable in probability and mean-square stable. The research findings also show that improving labor market efficiency can reduce the equilibrium unemployment rate while accelerating the system’s rate of convergence.
References
Down, D., Meyn, S. P., & Tweedie, R. L. (1994). Exponential and Uniform Ergodicity of Markov Processes.
Esteban-Pretel, J., Fujimoto, J., Albrecht, J., Asano, H., Braun, T., Ichimura, H., Imai, R., Kawaguchi, D., Kudoh, N., Nakajima, R., Owan, H., Saito, M., Shioji, E., Takii, K., Tanaka, R., & Vroman, S. (2011). The Second Search Theory Conference at Osaka University, the RIETI Empirical. http://www.cirje.e.u-tokyo.ac.jp/research/03research02dp.html
Garibaldi, P., Gomes, P., & Sopraseuth, T. (2025). Output costs of education and skill mismatch in OECD countries. Economics Letters, 250. https://doi.org/10.1016/j.econlet.2025.112278
Hasibuan, E., & Handayani, D. (2021). Pengaruh Qualification Mismatch terhadap Upah Tenaga Kerja Di Indonesia. Jurnal Ekonomi Dan Pembangunan, 29(1), 1–16. https://doi.org/10.14203/jep.29.1.2021.1-16
Mairesse, J., & Moyal, P. (2016). Stability of the stochastic matching model. http://arxiv.org/abs/1404.6677
Meyn, S., Tweedie, R. L., & Glynn, P. W. (2012). Geometric ergodicity. In Markov Chains and Stochastic Stability (pp. 362–391). Cambridge University Press. https://doi.org/10.1017/cbo9780511626630.018
Moscarini, G., & Postel-Vinay, F. (2010). STOCHASTIC SEARCH EQUILIBRIUM Stochastic Search Equilibrium *.
Øksendal, B. (1998). Stochastic Differential Equations. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-03620-4
Pissarides, C. A. (2000). Equilibrium Unemployment Theory.
Pusat Statistik, B. (n.d.). CERITA DATA STATISTIK UNTUK INDONESIA Mismatch Pendidikan-Perkerjaan Pemuda Indonesia: Implikasi bagi Bonus Demografi.
Şahin, A., Song, J., Topa, G., & Violante, G. L. (2014). Mismatch unemployment. American Economic Review, 104(11), 3529–3564. https://doi.org/10.1257/aer.104.11.3529
Salas-Velasco, M. (2021). Mapping the (mis)match of university degrees in the graduate labor market. Journal for Labour Market Research, 55(1). https://doi.org/10.1186/s12651-021-00297-x
Zylberberg, C. &. (2004). Labor Economics.
