Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization

  • Mizuki Tsuboi


Stochastic growth models are often solved numerically, because they are not tractable in general. However, recent several studies find the closed-form solution to the stochastic Uzawa–Lucas model in which technological progress or population dynamics follow a Brownian motion process with one or two parameter restriction(s). However, they assume that the return on the accumulation of human capital is deterministic, which is inconsistent with empirical evidence. Therefore, I develop the Uzawa–Lucas model in which the accumulation of human capital follows a mixture of a Brownian motion process and many Poisson jump processes, and obtain the closed-form solution. Moreover, I use it to examine the nexus between human capital uncertainty, technological progress, expected growth rate of human capital, and welfare.


Human capital Welfare Endogenous growth Uncertainty 

JEL Classification

C61 J24 O33 O41 



I thank Prof. Noritsugu Nakanishi, Assoc. Prof. Quoc Hung Nguyen, Prof. Hiroyuki Nishiyama, Prof. Masao Oda, Prof. Yoshifumi Okawa and seminar participants at the summer 2017 JSIE Kansai Branch Meeting for their many extensive and thoughtful comments. I would particularly like to thank Assoc. Prof. Shiro Kuwahara for his encouragement, pointing out troublesome typos, and constructive comments, “from the cradle to completion” of this paper. I am especially grateful to Prof. Yoichi Gokan, my discussant, and two anonymous referees of this journal for their detailed and exceptionally helpful comments that lead to the unthinkably substantial improvement of the earlier version of the manuscript. All remaining mistakes are my own. This paper was accepted to the J Econ under the guidance of Prof. Giacomo Corneo (Editor). Figure 2 is created with Eviews 9.5 Student Version, while the others are with MATLAB R2016b (Version 9.1, MATLAB and Simulink Student Suite). This research does not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Supplementary material

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Supplementary material 1 (m 3 KB)


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of EconomicsUniversity of HyogoNishi-KuJapan

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