Calculating cost-of-living deflators without data on prices: A simple nonparametric approach

When studying large countries, having access to infranational, regional cost-of-living indicators is important to be able to make (income- or expenditure-based) welfare comparisons across regions net of differences in prices or to construct national welfare measures based on individual-level measures of welfare that reflect local variations in prices faced by households. Regional cost-of-living indices are however not always available or may not be updated as regularly as national CPI series. We propose a simple approach for calculating regional cost-of-living deflators that do not require access to data on prices and that can be implemented directly from standard surveys on income and living conditions. To calculate the regional cost-of-living index, we apply methods proposed for the similar problem of estimating equivalence scale parameters: we use subjective satisfaction data to capture indirect utility and adopt nonparametric matching methods to construct regional cost-of-living indices. As an illustration, we construct price indices for Russian regions from the Russian Longitudinal Monitoring Survey for the period 2000–2015 and compare our cost-of-living deflators with those from the Statistical Office of Russia (available from 2009 only). Over the years, covered by both series, the indices correlate highly but not perfectly. Application of regional price indices does not appear to alter inequality trends but income levels.