Measuring substitution bias in price indexes During the recent inflationary period, issues surroundingconstruction of the Consumer Price Index (CPI) attracted considerableattention. One source of concern continues to be substitution bias,which arises from the use of a fixedweight Laspeyres index formularather than a true cost-of-living index.
In a recent BLS working paper, we analyzed the substitution bias inLaspeyres-type indexes such as the CPI, using 1959-82 consumption datafor 111 commodities from the National Income and Product Accounts. Weemployed two methodological approaches to construction of thecost-of-living index (COL) and calculation of the substitution bias.First, we constructed the best theoretical bounds on the index byapplying nonparametric methods, using algorithms developed by HalVarian. Second, following W. Erwin Diewert, we constructed superlativeprice index formulas–that is, those consistent with maximization of aflexible utility function subject to a budget constraint. We used twowidely known index formulas shown by Diewert to be superlative. namely,the Tornqvist and Fisher’s Ideal indexes, under a chain as well asa fixed-base specification.
The nonparametric tests indicate that there is a homotheticaggregate utility function consistent with the data. If the hypothesisof homothetic utility is maintained, the COL bias has upper and lowerlimits of 0.23 and 0.16 percent per year, respectively. Thesubstitution bias in the Laspeyres index, using the superlative indexesas the measure of the COL, is about 0.
16 percent per year for the period1959-82. Although quite small, this estimate is somewhat larger thanthose from earlier studies. Our use of more disaggregated data isresponsible for part of the difference. We also find that thesubstitution 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,1959-82.’