This paper provides new evidence on the convergence process toward the achievement of three important SGDs: 2 6 and 7. We collect data on water, energy, and food per capita consumption for 108 countries from 1971 to 2018. We also analyze the group of countries in the MENA region, which is a critical region as far as water and food are concerned. We establish a new notion of multivariate sigma and beta-convergence. For the first notion, we look at the time behavior of the determinant of the covariance matrix of the three variables. For the second notion we use the Arellano-Bond method to jointly estimate the interrelated system of beta convergence equations for water, food, and energy. The results reveal that there is evidence of conditional sigma- convergence and beta-convergence processes for the countries. The multivariate approach reveals that there are spillover effects with complex positive impact of each variable on the others in the analyzed countries. The speed of convergence is computed to assess when the desired levels according to the prescription of the SDG are attained for water, energy, and food per capita consumption by each country. Results have important policy implications for interventions on macro variables. Investment has a positive accelerating effect on water and energy convergence. In addition, openness to foreign trade and inflow of foreign direct investment have a positive accelerating effect on water and food convergence, respectively.