Deterministic and Stochastic Three‐Sector Dynamic Growth Model with Endogenous Labour Supply

Abstract

This study explores the stability of the stationary state for a dynamic growth model with wealth and human capital accumulation. Knowledge is created through research and learning‐by‐doing, while the time allocation between labour and leisure is endogenised. We analyse the model in both its deterministic and stochastic versions. First, we describe the deterministic model and analyse the stationary state. Second, using the stationary state, we define the stochastic perturbation and study the squared mean values of the system states for the linearised model. Third, we prove that for certain parameters, the stationary state in the deterministic model is asymptotically stable. Similarly, we also prove that the squared mean values of the variables in the linearised stochastic model are asymptotically stable. Finally, we perform the comparative dynamic analysis for the propensities to save and to enjoy leisure, the tax rates used to finance research and the knowledge utilisation efficiency.