We assess the predictors of intergenerational mobility in income and education for a sample of 137 countries, between 1960 and 2018, using the World Bank's Global Database on Intergenerational Mobility (GDIM). The Rigorous LASSO and the Random Forest and Gradient Boosting algorithms are considered, to avoid the consequences of an ad-hoc model selection in our high dimensionality context. We obtain variable importance plots and analyze the relationships between mobility and its predictors through Shapley values. Results show that intergenerational income mobility is expected to be positively predicted by the parental average education, the share of married individuals and negatively predicted by the share of children that have completed less than primary education, the growth rate of population density, and inequality. Mobility in education is expected to have a positive relationship with the adult literacy, government expenditures on primary education, and the stock of migrants. The unemployment and poverty rates matter for income mobility, although the direction of their relationship is not clear. The same occurs for education mobility and the growth rate of real GDP per capita, the degree of urbanization, the share of female population, and income mobility. Income mobility is found to be greater for the 1960s cohort. Countries belonging to the Latin America and Caribbean region present lower mobility in income and education. We find a positive relationship between predicted income mobility and observed mobility in education.