Deflation by Expenditure Components: A Harmless Adjustment?

We investigate the effect that seemingly minor features of the implementation of cost-of-living adjustments have on the distribution of household expenditures, by developing an analytical framework that is consistent with standard consumer theory, and mindful of data limitations faced by practitioners. The main result is at odds with common sense: even when multiple price indices are available (e.g., a food Consumer Price Index and a non-food one), it turns out that using a single price index (e.g., the total Consumer Price Index), to adjust the consumption aggregate is recommended. The practice of adjusting subcomponents of consumption separately (food with a food index and nonfood with a nonfood index) can lead to a systematic bias in the welfare measure, and consequently in poverty and inequality measures. Using Iran's 2019 Household Expenditures and Income Survey, we find that the bias manifests as a systematic underestimation of urban poverty and overestimation of rural poverty.