We explore the quantitative nexus among economic growth of a country, diversity and specialization of its productions, and evolution in time of its basket of exports. To this purpose we set up a dynamic model and construct economic complexity measures based on panel data concerning up to 1238 exports of 223 countries for 21 years. Key statistical features pertaining to the distribution of resources in the different exports of each country reveal essential in both cases. The parameters entering the evolution model, combined with counterfactual analyses of synthetic simulations, give novel insight into cooperative effects among different productions and prospects of growth of each economy. The complexity features emerging from the analysis of dynamics are usefully compared with gross domestic product per capita (GDPpc) and with an original measure of the efficiency of the economic systems. This measure, whose construction starts from an estimate of bare diversity in terms of Shannon's entropy function, is made fully consistent with the degree of specialization of the products. Comparisons of this measure with the model parameters allow clear distinctions, from multiple perspectives, among developed, emerging, underdeveloped and risky economies.