We find that cross-sectional moments of countries’ consumption growth are useful factors to explain variation in expected returns across international stock market indices. The skewness alone explains 17% of that variation. The first four consumption moments explain a proportion of variation that is similar to the three global Fama-French factors. We also address the weak-identification issue common in linear macro-factor models. Some consumption-based factors happen to be weakly identified and that might constitute a threat to statistical inference for the risk prices in multi-factor models. We find in particular that having one weakly-identified factor in a multi-factor model yields unbounded confidence intervals for all prices of risk.