Predicting convergence of per capita income in Spain : a Markov and cluster approach

In this work we analyze the evolution of productivity, in terms of the convergence of per capita income, of all the Spanish provinces, based on data from the previous decade. On the one hand, a cluster analysis allows us to group the Spanish provinces according to four income levels (low, medium-low, medium-high and high), which can be determined from the quartiles of the distribution, and, on the other hand, Markov chains make it possible to study the long-term evolution of productivity and convergence between the provinces, as well as the speed of convergence towards the equilibrium situation. Moreover, we can obtain the average time to return to an income level in which a province was previously. With the above, predictions of future income levels are made for the provinces, both in the current situation, and if the pandemic caused by COVID-19 had not existed, which leads us to evaluate the impact of the health emergency.