Consumer Price Index versus cost of living index: Substitution effects and their measurement

The Boskin Commission recommends to replace the American Consumer Price Index (CPI) (Laspeyres-type) by a cost of living index (COLI). Unfortunately, the Commission did not develop a valid concept of a COLI. Thus it is that a "price index" (an index isolating the price changes) should be preferred. In any case there exists the problem to measure the effects of substitution, if they occur. The usual method of a compromise between base period weighting and current period weighting is not satisfying for several reasons. A possibility little noticed in the literature are indices with an implicit price elasticity of demand of -1, that is to say indices arithmetic, harmonic, geometric - weighted with constant values (instead of quantities).