# Measuring substitution bias in price indexes.

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, 1959-82.'

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, 1959-82.'

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Publication: | Monthly Labor Review |
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Date: | Jan 1, 1985 |

Words: | 318 |

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