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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