•Develops the Production Ability measure for locations and Sophistication measures for industries.•Product Sophistication reveals how specific industry requirements are, and how sensitive industries are to the absence of these requirements.•Production Ability is strongly associated with income levels and economic growth of countries and cities.•An industry’s Sophistication value is strongly linked to its skill-level.•Together, these indices predict the likelihood of birth or death of industries across locations.•These new indices perform well compared to previous economic complexity measures. Cities and countries undergo constant structural transformation. Industries need many inputs, such as regulations, infrastructure or productive knowledge, which we call capabilities. And locations are successful in hosting industries insofar as the capabilities that they can provide. We propose a capabilities-based production model and an empirical strategy to measure the Sophistication of a product and the Production Ability of a location. We apply our framework to international trade data and employment data in the United States, recovering measures of Production Ability for countries and cities, and the Sophistication of products and industries. We show that both country- and city-level measures have a strong correlation with income and economic growth at different time horizons. Product Sophistication is positively correlated with indicators of human capital and wages. Our model-based estimations predict product appearances and disappearances through the extensive margin.