Is aggregate income enough to summarize well-being? We address this long-standing question by exploiting a quantitative approach that studies the relationship between gross domestic product (GDP) and a set of economic, social and environmental indicators for nine developed economies. We introduce a mathematical approach to the analysis of economic indicators. By employing dimensionality reduction and time series reconstruction techniques, we quantify the share of variability stemming from a large set of different indicators that can be compressed into a univariate index. We also evaluate how well this variability can be explained if the univariate index is assumed to be respectively the gross domestic product, national income, household income, or household spending. Our results indicate that all the four univariate measures are doomed to fail in accounting for the variability of all the domains. Even if GDP emerges as the best option among the four economic variables, its quality in synthesizing the variability of indicators belonging to other domains is poor (about 35%). Our approach provides additional support for policy makers interested in measuring the trade offs between income and other relevant social, health and ecological dimensions. Finally, our work adds new quantitative evidence to the vast literature criticizing the usage of GDP as a measure of well-being.