Re-examining the Cost-of-Living Index and the Biases of Price Indices:
Implications for the U.S. CPI
The US CPI is based on the Laspeyres price index, an index type that has an upward "substitution bias." Thus, the CPI tends to overstate increases in the cost of living. To address this bias, the Advisory Commission to Study the Consumer Price Index recommended adopting for the CPI a "superlative" price index, e.g., the Fisher or Tornqvist indices. Under the assumption of homothetic preferences, superlative indices always have smaller substitution biases-hence, are closer to the "true" cost-of-living index (COLI)-than the Laspeyres index, but this assumption implies that: all income elasticities equal 1, the true COLI is independent of the utility level (standard of living), and expenditure shares are unaffected by changes in income. These implications are contradicted, however, by all known household budget studies. Therefore, superlative indices are not necessarily closer to the true COLI than the Laspeyres index except in the unrealistic case of homothetic preferences. Under more realistic non-homothetic preferences, expenditure shares vary with income and, thus, "income bias" is introduced into the superlative indices. This, in turn, could result in biases larger than the Laspeyres substitution bias in the CPI. The Commission did not, however, address this possibility. The Laspeyres index has a larger substitution bias but no income bias because it uses fixed expenditure shares. Under plausible conditions, by using a non-homothetic "almost ideal demand system" (AIDS) model, we carry out empirical simulations that show that the combined substitution and income biases of either the Fisher or the Tornqvist index could be either positive or negative-that is, a superlative index could differ even more from the true COLI than is the case for the present CPI. Thus, income adjustments resulting from a CPI.
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