An Extended Nonlinear Ordinary Differential Equation Model for Unemployment Dynamics on Ghana’s Labour Market

Abstract

Globally, unemployment constitutes a major socio-economic concern and Ghana cannot escape its threats. The absence of jobs and its creation as always hunted by individuals who legitimately fall within the labour force actively searching for jobs worsens the menace rapidly in a burgeoning economy. Therefore, this study analysed unemployment dynamics on Ghana’s labour market with three economic sectors using nonlinear ordinary differential equations model. Seven dynamic variables from the three sectors were introduced and used to develop the nonlinear ordinary differential equations model. Stability analysis of the system of differential equations was carried out to establish the characteristics of the system subject to time. The Routh-Hurwitz stability criterion was used to establish both the local and global asymptotic stability of the equilibrium point. SageMath and MatLab softwares were employed for computations, qualitative analyses, programming, simulation and graphing. Perturbation analysis of some parameters was performed to confirm their impacts on unemployment, employment and newly created vacancies at equilibrium. The analysis of the model confirmed the rates of movement of unemployed persons joining the employed in agriculture, industry and services sectors as inverse correlates of unemployment across all three sectors. The rate at which new vacancies are created in favour of the unemployed persons is an inverse determinant of the number of unemployed persons across all three economic sectors. The number of employments relates directly with the rate at which new vacancies are created in favour of the already employed persons. Sensitivity analysis was performed to measure the degree of responsiveness of unemployment and employment to variations of the model’s parameters across the three sectors. The results of the sensitivity analysis confirmed that unemployment and newly created vacancies in all the three sectors is highly sensitive to variations in the rates of transitions of individuals from the unemployment class to the employment class in agriculture, industry and services sectors. Thus, unemployment and newly created vacancies are associated with higher elasticities than employment with respect to variations in these parameters across the three sectors. The implication is that a unit change in Ghana’s economic growth rate will cause the rate of movement of unemployment to employment to increase with high positive margins. In this study, the incorporation of the three economic sectors into the model, the inclusion of the rate at which new vacancies are created in favour of the employed persons among others are relevant contributions to knowledge.