A cost-of-living dynamic price index, with an application to indexing retirement accounts

If a consumer wishes to protect her retirement account from the risk of price changes in order to sustain a stable standard of living, then what price index should the account be indexed to? This paper constructs a dynamic price index (DPI) that answers this question. Unlike the existing theory on price indices (which is static and certain), the DPI measures the cost of living for a consumer who lives for many periods and faces uncertainty. The first contribution of this research is to define this price index and study its theoretical properties. The DPI: is homogeneous of degree 1 with respect to all prices, is forward-looking with respect to price shocks, responds more to permanent vis-à-vis transitory price changes, includes asset prices with a potentially large weight, and distinguishes between durable and non-durable goods prices. The second contribution of the paper is to construct a DPI for the United States from 1970 to 2004. It gives an account of the cost of living in the U.S. that is strikingly different from the one provided by the CPI. The DPI is less persistent, more volatile, and a large part of its movements are driven by changes in the prices of houses and bonds.