substitution s, the CES price index can be evaluated using the same information used to evaluate the usual Laspeyres index.
How might the statistical agency obtain an estimate for the substitution parameter s? Shapiro and Wilcox (1997:121-123) provide one method. They calculate superlative Törnqvist indexes for the United States for the years 1986-1995 and then the CES index for the same period using various values of s. They then chose the value of s (in this case 0.7) which caused the CES indexes to most closely approximate the corresponding Törnqvist indexes (which could be evaluated on a delayed basis).2 Assuming that the Törnqvist index is more or less free from substitution bias, it can be seen that the Shapiro and Wilcox procedure will generate a historical time series of CES index values which are largely free of substitution bias. Thus the CES price index, combined with a method for estimating the elasticity of substitution, could be used to provide a timely estimator for a superlative index, which can only be produced on a delayed basis. However, there are some risks associated with this methodology: namely, that past (average) movements in relative prices (which are used in order to obtain an estimator for the elasticity of substitution) are no guarantee for future (or present) movements in relative prices. It is also possible that the historical pattern of demand is determined by other factors not recognized in the analysis, such as changes in incomes, demographic factors, or tastes and technologies. Therefore a risk exists that the CES price index, based on a historical procedure for estimating s, could generate misleading advance estimates for a superlative index.