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An identity links the rate of economic growth, the speed of poverty reduction and changes in the distribution of income during some time period in a given country. A few authors used that identity to understand the causes for observed changes in poverty and to identify the exact role of economic growth in poverty reduction. Yet, many empirical cross-country studies of the relationship between growth and poverty are based on linear regression models that are ill specified because they ignore that identity. This paper provides approximations that permit doing much better than these linear models. In particular, it gives closed-form solutions under the assumption that the underlying distribution of income is Log-normal. The second part of the paper analyzes the quality of these approximations in a sample of actual growth spells in developing countries. It turns out that the discrepancy between empirical and theoretical growth elasticities of poverty amounts to much less than 50 per cent and is mostly explained by distributional changes.