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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
not equally substitutable for one another. If prices change in a way that highlights the assumption to the contrary, a CES index can be quite misleading. Suppose, for example, that the dollar depreciates relative to the currencies of East Asian electronic and automobile producers, so that the imported versions of these products become more expensive. This will hurt American consumers, though the damage will be offset by substitution away from Asian to European and domestic substitutes. If some such substitution is built into its construction, the CPI will rise by less than the increase in the prices of the imports, which is exactly what ought to happen. Now imagine instead that an oil shock increases the price of gasoline and home heating products. In this case, there is much less scope for substitution, and the increase in the CPI ought to be much closer to the increase in the price of fuels: BLS cannot tell consumers that the CPI has not risen by much because they should drive their cars on milk or on orange juice! A superlative index can capture the difference between the two cases because it uses information on purchases after the price change and is sensitive to the fact that the shock induces a much smaller decline in demand for fuels than for imported electronics. But a CES price index treats both identically and assumes that fuels are just as substitutable as imported electronics. In one case or the other, the CPI will be wrong and possibly quite wrong.
Of course, there is no guarantee that a Laspeyres-based CPI will do better as an approximation to a COLI. Indeed, since a Laspeyres is itself a CES with an exponent of unity, a good choice of exponent will certainly lead to an index that does at least as well as the Laspeyres. It is also conceivable that more elaborate CES indexes—such as a two-stage CES, which has the same substitution elasticity between broad groups of goods, with different substitution elasticities within each group—could do even better and remedy the equal substitution problem of a simple CES.
A CES index has an advantage over a superlative index in its timeliness, but it is otherwise inferior. For example, there would be no point in using a CES index instead of a superlative for looking at long-run trends in inflation or for other historical analyses. With some improvement in data collection, much of which is already under way, a superlative index could be produced with a delay of only 1-2 years. Given data up to that time on both a Laspeyres-based CPI and the superlative, it would be possible to make an informed estimate of what the superlative is likely to be, even in advance of its calculation. In this situation, it is not clear that a real-time CES index adds very much. Compensation, such as social security compensation, could ultimately be tied to a superlative index. Interim payments could be made from a forecast of the superlative, with forecast errors rolled into subsequent cost-of-living adjustments (see Chapter 7).
One area in which a COLI concept has already entered BLS practice is the treatment of lower-level price aggregation. This is the procedure whereby the BLS combines prices of the most finely defined goods, such as different varieties