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A large debate has risen about the hypothesis that “COVID-19 is a disease for the rich ones” suggesting that both its diffusion and mortality rates are somehow linked with economic wealth. In this study we observe a sample of 138 countries during the first wave contagion period, namely the 5 weeks between 24 March and 21 April 2020. Using different data sources, our estimates show that both the early infection and the mortality rates of COVID-19 are higher in wealthier countries, more precisely in countries with a higher GDP per capita. As an explanation of this finding, we also find that both mortality and infection rates increase with a higher share of elderly population and with the international flows of imported goods or tourists. However, the death rate decreases in countries with higher endowments of health facilities. We also demonstrate that these results are robust to simultaneity, unobserved heterogeneity, the possible poor quality of the data on COVID-19 deaths, and the extension of the time frame.