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An urn-ball probabilistic model of the labor market is developed. Agents can be employed (voluntarily or involuntarily) unemployed, or entrepreneurs. The analytical long-run equilibrium probabilities for each state and the matching function are derived. In equilibrium, a higher reservation wage increases the number of start-ups, but has an overall negative impact on the unemployment rate. A more buoyant economy (higher average growth rate and higher average wages) is shown to be associated with a lower unemployment rate. Higher start-up costs discourage entrepreneurship and increase unemployment. More active search behavior leads first to a decrease in the unemployment rate, and then to a small increase, due to increased coordination failure induced by the higher number of applications sent by job seekers. The out-of-equilibrium dynamics are investigated through an agent-based simulation, which also provides results on firm demography. Important empirical regularities such as the Beveridge and the Okun curve are recovered. Finally, the simulation model is used to investigate departures from maximizing individual behavior and the effects of more realistic assumptions about profits and the business cycle.

The continuous increase in unemployment rates and their significant economic impact necessitate the rapid updating and modification of present models and policies implemented by governmental entities. To successfully handle the timely transmission of employment within the workforce, many contemporary models still need the incorporation of an individual’s job history. Consequently, in order to study the unemployment problem, this research presents a multi-order fractional nonlinear mathematical model that takes into account the Caputo fractional order derivative and three important variables: the number of skilled unemployed individuals, the number of employed individuals, and the number of open positions. The existence and uniqueness of the proposed model’s solution are demonstrated by using generalization of Picard fixed point theorem. The solution of the proposed model is bounded and non-negative. The reproduction number has been analyzed to determine the factors that would help create new job vacancies. The multi-order model utilizes real data to make predictions regarding the unemployed as well as the employed population for the Northern states of India (J&K, HP, Punjab, Haryana) with an average absolute error less than 21% and 3%, respectively. When compared to the actual data, the fractional order model better captures the characteristics of the unemployed population than the integer order model. The fractional-order model exhibits lower RMSE, MAE and MAPE values and higher correlation coefficient (r) value.