The Price-Quantity Decomposition of Capital Values Revisited: Framework and Examples

The often discussed problems of aggregating tangible capital assets across vintages and of decomposing value aggregates into quantity and price aggregates are revisited. For stock values and service flow values, some new results are given, and illustrated by examples, along with reinterpretations of familiar ones. If the definitions and measurement methods for prices and quantities do not ‘match’, a third, ‘quality’, component may be needed. Should this ‘buffer’ component be included in the price or quantity components, or both, or should it be accounted for separately, and in the latter case, how does it depend on the interest rate and the capital’s age? In discussing these issues, five related quantity variables and five related price variables are introduced and discussed. For certain parametric profiles for survival and efficiency loss they are equal. Some variables are observable from market data without large efforts, some are genuinely unobservable, and some can be quantified only if certain (sometimes questionable and often nontestable) assumptions are made. Examples based on three sets of parametric profiles, including exponential decay, are given.