Measuring substitution bias in price indexes
During the recent inflationary period, issues surrounding
construction of the Consumer Price Index (CPI) attracted considerable
attention. One source of concern continues to be substitution bias,
which arises from the use of a fixedweight Laspeyres index formula
rather than a true cost-of-living index.
In a recent BLS working paper, we analyzed the substitution bias in
Laspeyres-type indexes such as the CPI, using 1959-82 consumption data
for 111 commodities from the National Income and Product Accounts. We
employed two methodological approaches to construction of the
cost-of-living index (COL) and calculation of the substitution bias.
First, we constructed the best theoretical bounds on the index by
applying nonparametric methods, using algorithms developed by Hal
Varian. Second, following W. Erwin Diewert, we constructed superlative
price index formulas–that is, those consistent with maximization of a
flexible utility function subject to a budget constraint. We used two
widely known index formulas shown by Diewert to be superlative. namely,
the Tornqvist and Fisher’s Ideal indexes, under a chain as well as
a fixed-base specification.
The nonparametric tests indicate that there is a homothetic
aggregate utility function consistent with the data. If the hypothesis
of homothetic utility is maintained, the COL bias has upper and lower
limits of 0.23 and 0.16 percent per year, respectively. The
substitution bias in the Laspeyres index, using the superlative indexes
as the measure of the COL, is about 0.16 percent per year for the period
1959-82. Although quite small, this estimate is somewhat larger than
those from earlier studies. Our use of more disaggregated data is
responsible for part of the difference. We also find that the
substitution bias is higher, in percentage as well as in absolute terms,
for 1972-82 than for earlier, less inflationary periods analyzed.
The study and its results are described in full in our paper,
entitled “An Analysis of Substitution Bias in Measuring Inflation,