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 non-testable) assumptions are made. Examples based on three sets of parametric proﬁles, including exponential decay, are given.