Why is consumption more log normal than income? Gibrat's law revisited

Abstract

Significant departures from log normality are observed in income data, in violation of Gibrat’s law. We identify a new empirical regularity, which is that the distribution of consumption expenditures across households is, within cohorts, closer to log normal than the distribution of income. We explain these empirical results by showing that the logic of Gibrat’s law applies not to total income, but to permanent income and to maginal utility. These findings have important implications for welfare and inequality