This paper analyzes the convergence of Gross Domestic Product per capita (GDP pc) during the period 1990-2013 in Colombia. Results show a convergence process for the 1999-2006 period and statistical evidence for the existence of spatial error dependence. For these years, random shocks determine the movement of the economies and their interaction are not defined by administrative boundaries. A growth process for the Andean and Caribbean region is observed, contrary to what happens in Orinoquia and Amazon region. That convergence process occurred due to a process of unobservable spatial factors which gave a transition to the growth of the Caribbean and the Andean region. Besides, over time departments with high and low GDP pc remain constant. The main contribution of this work is the analysis on convergence that includes space and time factors simultaneously, as well as validation of the existence of convergence.