Paths of the vocational training graduates: Estimation of a multi-state model using a stationary Markov chain

Located at the hinge of education and employment, vocational training is supposed to provide profiles adapted to the labour market requirements. However, Moroccan graduates of vocational training often find it difficult to fit into the labour market. Indeed, according to the Ministry of Employment and Vocational Training, only 63% of the graduates in 2006 succeeded in integrating the working environment. Yet, this rate hides several realities and is likely to overestimate integration since it does not take into account some crucial variables in the analysis of professional integration, namely the duration of employment, the precariousness of employment, etc. Studies about the paths of vocational training graduates realized periodically (every two years) since 1987 by the Ministry of Employment and Vocational Training aim, by virtue of their longitudinal aspect, to analyze the stability and the evolution of these graduates employment as well as their behaviour. In other words, these studies seek to answer some questions about the dynamics of youth employment in the labour market. This work aims to model the transitions of vocational training graduates using a retrospective calendar recalling their professional situation starting from the date of obtaining the diploma (2002) until the date of the survey (2006). Our model uses a transition process generated by a homogeneous, stationary and ergodic Markov chain for the graduates state space. We propose to explain the transitions from one state to another, via a multivariate logistic link, through variables which can influence between-state transitions. This leads that the processual variables explain these transitions. To estimate the parameters of our model, we use an iterative method of unconstrained nonlinear optimization: Conjugate Gradient "CG”. The stationarity of the Markov chain and the estimation of the transition matrix allow us to compute labour market indicators used to describe the behaviour of young graduates as well as their professional mobility.