Productive Stock and Capital Services

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1 From: Measuring Capital - OECD Manual 2009 Second edition Access the complete publication at: Productive Stock and Capital Services Please cite this chapter as: OECD (2009), Productive Stock and Capital Services, in Measuring Capital - OECD Manual 2009: Second edition, OECD Publishing.

2 This document and any map included herein are without prejudice to the status of or sovereignty over any territory, to the delimitation of international frontiers and boundaries and to the name of any territory, city or area.

3 ISBN Measuring Capital OECD MANUAL 2009 OECD 2009 Chapter 7 Productive Stock and Capital Services 59

4 I.7. PRODUCTIVE STOCK AND CAPITAL SERVICES 7.1. Concept The stock of a particular type of assets surviving from past periods, and corrected for its loss in productive efficiency is the productive capital stock 1. Thus, productive stocks are directly related to the quantity and production aspect of capital. Productive stocks constitute an intermediate step towards the measurement of capital services. The assumption is made that the flow of capital services the actual capital input into production is proportional to the productive stock of an asset class. If the factor of proportionality is constant, the rate of change of capital services will equal the rate of change of the productive stock 2. The same rate of change constitutes the volume component when it comes to splitting the change in the total value of capital services at current prices into a price and a volume component. A different way of seeing the productive stock of a particular type of asset is as the embodied volume of current and future capital services. The concept of a productive stock is only meaningful at the disaggregate level of a particular type of asset. Once each asset s productive stock is combined with the corresponding capital service price (per unit of the productive stock), the resulting value represents the flow of capital services. This is the relevant variable for aggregation across different types of assets Computing productive stocks The productive capital stock for a single asset is measured through direct application of the perpetual inventory method, as the sum of past investments, weighted by an ageefficiency profile. The age-efficiency pattern (see also Chapter 3.2) describes the change in an asset s productive efficiency as the asset ages. Typically, the age-efficiency profile is expressed relative to the productive efficiency of a new asset 3. By applying the age-efficiency profile to quantities of past investment, all vintages are expressed in new-equivalent efficiency units. The computation of the productive stock via addition of efficiency-adjusted investments of past period implies complete substitutability of past vintages, once adjusted for efficiency differences. This is more stringent an assumption than strictly necessary 4 but has some practical advantages. Triplett (1997) discusses this assumption with the example of trucks: The assumption that old trucks can be represented as some smaller quantity of new trucks (that is, reduced proportionately by deterioration) implies somewhat unrealistic conditions about the way trucks and other inputs combine in the production process. One can think of the deteriorated truck as equivalent to a lower quality truck (compared to a new one). In the quality change literature, the assumption that permits expressing improved trucks as more unimproved ones is termed repackaging. The repackaging assumption and its limitations are discussed in Fisher and Shell (1972) The productive stock for a single (type of) asset may or may not coincide with the net stock of a single (type of) asset. The two stock measures are identical if the age-efficiency profile is identical with the age-price profile. Such an identity holds for geometric age-efficiency and age-price profiles and has been discussed earlier in this Manual. A more important difference between the productive stock and the net capital stock arises, however, in the process of 60 MEASURING CAPITAL: OECD MANUAL 2009 ISBN OECD 2009

5 I.7. PRODUCTIVE STOCK AND CAPITAL SERVICES aggregation. Net capital stock measures are aggregated on the basis of market prices and there is a clear meaning to the level of the net stock. Over time, an index of the net capital stock can be considered a weighted average of the index of net stocks for different types of assets, where each asset s share in the total market value of assets figures as weight. Productive stocks for each type of asset, on the other hand, are not aggregated as such. Rather, by attaching user costs to them, the transition is made to capital service flows which are then aggregated. Over time, an index of capital services is a weighted average of an index of productive stocks by type of asset, where each asset s share in total user costs figures as weight. Usually, an index of the net capital stock evolves quite differently from an index of the productive stock, i.e. from an index of capital services. In many empirical applications, the productive stock has risen faster than the net stock. This happens, for example, when there is a shift in the composition of investment towards more short-lived capital goods such as information technology equipment and when real investment in these goods grows faster than investment in other goods. Shortlived capital goods are marked by high depreciation and holding losses, i.e. elements that tend to raise these assets user costs share relative to their share in market value. The consequence is that fast-growing components of the productive stock get a higher weight than under the net stock calculation and the overall productive stock moves faster than the overall volume of the net capital stock. Table 7.1 continues the numerical example introduced earlier and shows how the productive stock Productive stocks measure the stock of assets, corrected for for a single asset can be computed under the perpetual efficiency loss and retirement. inventory method. Investment at historical prices is put They are seen as the stocks that on a comparable basis by applying the price index of new generate flows of capital services, the input of capital into capital goods so that the time series of investment is production expressed in prices of period 16. Then, use is made of the combined age-efficiency/retirement pattern introduced in Section 4.3. This profile serves to weight the vector of constant price investment, the Table 7.1. Computing the productive stock for a single (type of) asset Year (t) Investment at historical prices Price index (new) capital goods Investment in prices of year 16 Age-efficiency profile for cohort Investment in prices of year 16. Weighted with ageefficiency pattern Productive stock end of year 16 at (current) prices of year MEASURING CAPITAL: OECD MANUAL 2009 ISBN OECD

6 I.7. PRODUCTIVE STOCK AND CAPITAL SERVICES result of which is shown in the last column of the table. Summing up the column yields the productive capital stock at the end of period 16, and valued at period 16 prices. The same type of calculation, carried out for a sequence of years, provides the basis for measuring the flow of capital services provided by the asset group. As was mentioned above, aggregation across assets proceeds with user costs weights. The nature of user cost weights is discussed in the next section. Notes 1. One could also say that the productive stock equals a hypothetical stock of that consists solely of new goods and which yields in the current period the same level of services as the actual stock does. 2. Schreyer, Bignon and Dupont (2003) made explicit the distinction between the flow of capital services and the productive stock for a particular type of asset, by introducing a constant factor of proportionality that indicates the number of (unobserved) units of capital services per unit of productive stock. The distinction is not made here. Strictly speaking, the price of capital services (unit user costs) that is described later in this Manual should therefore be read as the price of capital services per unit of productive stock. 3. Nothing hinges on this practice. The productive stock could be expressed in efficiency units of any vintage and calculations for the total value of capital services and the quantity index of capital services would still yield identical results. 4. Diewert and Lawrence (2000) show how more general aggregation procedures with superlative index numbers can be used to aggregate quantities across different vintages. Thereby, perfect substitutability between vintages is not required. 62 MEASURING CAPITAL: OECD MANUAL 2009 ISBN OECD 2009

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