Purchasing power adjusted incomes applied in cross-country comparisons are measured with bias. In this paper, we estimate the purchasing power parity (PPP) bias in Penn World Table incomes and provide corrected real incomes. The bias is substantial and systematic: the poorer is a country, the more its income tends to be overestimated. Consequently, international income inequality is substantially underestimated. Our methodological contribution is to exploit the analogies between PPP bias and the bias in consumer price index (CPI) numbers. The PPP bias, and consequently real incomes, is measured by estimating Engel curves for food, which is an established method of measuring CPI bias.