The Substitution Bias of the Laspeyres Price Index: An Analysis Using Estimated Cost-of-Living Indexes
研究了消费者价格指数（CPI）作为拉斯佩耶斯价格指数时，因忽略商品替代而高估生活成本的偏差大小，通过估计真实生活成本指数来量化偏差，并指出以往研究因商品数量少而低估偏差的问题。
The most commonly used measure of the cost of living, the Consumer Price Index (CPI) published by the Bureau of Labor Statistics, is essentially a Laspeyres price index. It is well-known, however, that a Laspeyres price index provides an upward biased estimate of the cost of living, because in keeping the same base period basket of goods as weights, it does not take into account substitution among commodities induced by relative price changes. The magnitude of the bias is an empirical question, which is the focus of this study. An estimate of the substitution bias may be obtained by taking the difference between the Laspeyres price index and an estimated true cost-of-living index. The true cost-of-living index (CLI) is based on the theory of consumer demand. It is the ratio of the minimum expenditures under two different price regimes necessary to maintain a constant level of utility (as opposed to the constant basket of goods in the Laspeyres index).' The size of the bias depends on two factors: 1) the size of consumption substitution elasticities (if there is no commodity substitution then the CLI and Laspeyres index coincide, regardless of changes in relative prices); and 2) the magnitude of relative price changes (if all prices move together then the CLI and Laspeyres index again coincide, regardless of the size of substitution elasticities). In order to compute a true CLI it is necessary to specify a particular utility function and estimate the parameters of the resulting system of demand equations (see, for example, Louis Phlips, p. 135). Several estimates of the magnitude of the substitution bias have appeared in the literature, but all previous studies suffer from a common weakness-they are all based on a very small number of commodities, essentially because of econometric problems involved in estimating large systems of demand equations. In one group of studies, demand models have been estimated using highly aggregated data, in which total consumption is grouped into four to nine aggregate commodites (such as housing, durables, or clothing). Arthur Goldberger and Theodore Gamaletsos, for example, estimate the linear expenditure system (LES) demand model using data on five aggregate goods for several European countries, and compare the resulting CLI for one of the countries (Greece) to the corresponding Laspeyres price index. Tran Van Hoa estimates costof-living indexes for six Australian provinces using data on nine aggregate goods. Phlips cites work by R. Sanz-Ferrer, who computed a CLI for Belgium from data on eight aggregate commodities. In such studies using highly aggregated data, the estimate of the substitution bias may be understated because the aggregation obscures substitution in consumption within categories, which is perhaps more prevalent than substitution between gross aggregates. Another shortcoming of these three aggregate studies is the fact that they use only a single demand system, and hence do not explore the sensitivity of the CLI to a priori *U.S. Bureau of Labor Statistics. The groundwork for this study was my dissertation. I would like to thank the chairman and members of my committee, R. Robert Russell, Llad Phillips, and Robert Deacon, for their support and helpful suggestions, and Jack Triplett, Robert Pollak, Richard J. McDonald, and a referee for valuable comments on an earlier version. The views expressed are my own and do not necessarily reflect the policies of the Bureau of Labor Statistics. 'For a theoretical discussion of cost-of-living indexes, see Robert Pollak (1971b), and Paul Samuelson and Subramanian Swamy.