The productive capital stock and the quantity index for flows of capital services by Peter Hill September 1999 Note intended for consideration by the Expert Group on Capital Measurement, the Canberra Group, at its meeting in November 1999. The purpose of this note is to argue that the concept underlying the productive capital stock is so important that it must be presented in such a way that its properties are transparent and clearly understood by users. In order to be analytically useful above the level of a single homogeneous asset, the so-called productive capital stock has to be defined in such a way that it becomes, in fact, an index of capital services and not a stock index. The quantity index of capital services is extremely important in its own right and needs to be explicitly recognised and accepted as such in national accounts as well as productivity analysis. Flows of capital services are not recorded at present in the SNA, but this is a omission which ought to be corrected at the earliest opportunity. The inclusion in the SNA of a quantity index of the flow of capital services into production would be a major improvement in the system, but such an index, by its nature, must relate to an item in the flow accounts of the system and not to a stock of assets in the balance sheets. Trying to present it as if it were some special kind of capital stock figure is not only conceptually inappropriate but likely to defeat the objectives of those who advocate it. It risks perpetuating the idea that, if only it can be properly defined, the capital stock itself, as distinct from the flow of capital services obtained from it, is the appropriate way in which to represent capital in production functions and productivity analysis. The estimation of the Capital Stock Two distinct stages are involved in the estimation of the capital stock : first, the different vintages of the stock of each individual homogeneous type of asset have to be aggregated; second, the resulting stocks have to be aggregated over different kinds of assets. Most of the theoretical literature focuses exclusively on the first stage. While the aggregation of different vintages poses the more interesting economic questions, it is often treated as if it were the only issue of any economic interest, the aggregation of stocks of different kinds of assets not even being discussed. At the level of an individual type of asset it is possible to aggregate different vintages in such a way that, over time, the proportionate change in the stock of the asset
is the same as the proportionate change in the flow of services provided by that stock. This is feasible because the ratio of the service flow to the quantity of the asset is constant for assets of the same type. This ratio is not the same, however, for different kinds of asset, so that aggregate stock and the flow measures covering different kinds of assets must diverge. A single measure cannot serve both purposes except at the level of a single homogeneous asset. The aggregation of different vintages of the same asset Quantities of a single homogeneous good are additive. Quantities of a particular type of homogeneous asset are therefore additive when new. Although they may be homogeneous at the time they are produced, most assets deteriorate to some extent as they get older. Different vintages can therefore be regarded as different qualities of the same type of asset, where quality is defined as the capacity to produce capital services. They only become additive after they have been adjusted for differences in their quality. Taking a new asset as the unit or norm, the quality adjusted quantity of an asset diminishes as it gets older in proportion to its declining capacity to produce services. The capacity to produce services as a function of the age of an asset is usually described as its efficiency profile. After adjusting the quantities of different vintages of the same type of asset for differences in their efficiency, their sum over all the different vintages (i.e., the total quantity of the asset) can appropriately be described as the "productive stock" of that asset. The total quantity of the services produced by the productive stock of a homogeneous asset is, in fact, simply equal to the total quantity that stock multiplied by a scalar, namely the quantity of services produced by a new asset. It follows therefore that the proportionate change over time in the total quantity of the asset must be identical with the change in the total quantity of the services it provides. In index number terms, this change is a quantity relative, not a quantity index, because only a single commodity is involved. It is immaterial whether the quantity relative is interpreted as the change in the stock of a single homogeneous asset or the change in the total quantity of services it produces. This is the desired object for purposes of productivity analysis. A monetary value can be placed on the productive stock of a single asset by multiplying the total quantity of the stock of the asset by the price of a new asset. Such an aggregate is perfectly meaningful as a stock measure at a point of time as it is equal to the total value of an equivalent stock of new assets that would provide the same total flow of services. (It still needs to be interpreted with care, however, because it may be consistent with a wide range of different market (net) values depending on the age structure of the stock.) Similarly, it would be possible to measure the total value of the flow of services produced by the stock by multiplying the value of the stock by the ratio of the value of the service produced by a new asset to the price of the asset. Assuming the price of the asset remains constant, the proportionate change over time in the value of 2
the flow of services would be the same as that in the value of the productive stock. Unfortunately, this property no longer holds when the stocks of different kinds of assets are aggregated because the ratio of the value of the service to the price of a new asset is not constant for different kinds of assets. On the contrary, this ratio tends decrease systematically with the length of the service life. The aggregation of the productive stocks of different kinds of assets It is possible to sum the values of the productive stocks of different kinds of assets and interpret the result in the same way as above, namely as being equal to the value of an equivalent stock of new assets that would produce the same total flows of services as the actual stock of new and used assets. Similarly, the values of the flows of services produced by the stocks of the different assets can also be summed. However, even when calculated at constant prices, the proportionate changes in the aggregate flow of services are not equal to those in the aggregate productive stock if the composition of the stock changes over time. For example, if the proportion of assets with long lives, such as structures, increases (decreases) relatively to those with short lives, such as computers, the ratio of the aggregate flow of services will tend to decrease (increase) relatively to the aggregate productive stock. This can be seen in another way. Just as the quantity relatives for individual types of assets may be interpreted either as productive stock relatives or service flow relatives, they may also be weighted in two different ways when calculating an aggregate quantity index. They may be weighted by the values of the productive stocks in the selected base year or by the values of the service flows. The two sets of value weights differ because the ratios of the prices of new assets to the values of the flows of services they provide are not the same for different types of assets when they have different efficiency profiles and service lives. There are two separate aggregate indexes to be derived from the same set of quantity relatives and the two indexes diverge if the weights are different. It is worth noting that both indexes are meaningful, but they obviously measure different things even though they may happen to be close to each other numerically. The one using asset values as weights is the quantity index pertaining to the productive stock, qua stock. It measures the change, at constant prices, in the (hypothetical) quantity of new assets that would produce the same flow of services as the actual capital stock. The second index using service values as weights is a conventional quantity index of the flow of capital services into production provided by the actual capital stock. Users choose the one in which they are interested. The second index is not only of great theoretical interest and analytical importance for productivity analysts 1 but also should be of equal interest to national accountants. On the other hand, the first index does not appear to be particularly interesting or useful, either theoretically or analytically. 1 Economists often refer explicitly to a quantity index of capital input relating to a flow of capital services in this context: see, for example, p. 4 of D. W. Jorgensen Capital as a Factor of Production, in Technology and Capital Formation, D. W. Jorgensen and R. Landau, (Eds.) Cambridge, MIT Press 1989. 3
Furthermore, the monetary value of the productive capital stock at a point of time does not appear to be useful for balance sheet purposes within the SNA. There would appear to be some consensus, at least in economics literature, about the substance of what is written above. The puzzle that arises is why some economists would wish to describe the service flow index as the productive capital stock. This seems almost calculated to create confusion in what is already a conceptually difficult area. The issue is more than just one of terminology. Conceptually, it is incorrect to classify a flow as a stock. The fact that the stock and the flow index may coincide at the level of an individual asset in no way diminishes the fundamental distinction between a flow and a stock. The situation is further confused by the fact that, in this particular instance, the aggregate service index can actually be calculated by multiplying asset quantities by service prices, a procedure which is conceptually inappropriate when stocks and flows are not commensurate dimensionally. Exceptionally, however, it can be made to yield the right answer in this case because, as already noted, at the level of a single homogeneous asset quantities of productive assets are, by definition, proportional to the quantities of services. A more serious and practical objection to describing the aggregate service index as the productive capital stock is that it perpetuates the idea that the capital stock itself, as distinct from the flow of capital services obtained from it, is the appropriate way in which to represent capital in production functions and productivity analysis. Describing the service flow index as the productive capital stock would appear to be defeating the real objectives of those advocating it. In a national accounts context, it may create the impression that if only the national accounts could come up with the right concept and definition of the capital stock, analysts could continue to use it production functions. It creates the impression that yet another type of capital stock measure is needed when in fact what are needed are new measures of flows of capital services, at current as well as constant prices, in the production account of the SNA. The analytical usefulness of the production account of the SNA would be greatly enhanced if the values of inputs of capital services into production were to be estimated and included in the production accounts alongside inputs of labour services. If this were done, the quantity index of capital services could be obtained by deflating the inputs of capital services at current prices by a price index which could be derived from an index of asset prices weighted by service values. This would place the service quantity index in its proper context, namely the flow accounts of the SNA, and show that it is essentially quite a different animal from any kind of capital stock figure that might be recorded in the balance sheets of the SNA. The Capital Stock Manual Because the productive capital stock has figured prominently in the literature on productivity measurement it must be discussed in the Manual. However, it would be better to describe it in a self contained section (possibly a box or annex) and not to build 4
it into the main text of the Manual. The conclusion of this note is that the main purpose of such a section should be to make clear that, above the level of a single homogeneous asset, the so-called productive capital stock is actually a quantity index of capital services which should occupy an important place in the flow accounts of the SNA but which has no place in the balance sheets of an enterprise or industry. It is not a convenient halfway house between the gross and net capital stocks, except perhaps in the case of an individual asset, a special case of limited interest in practice when even single enterprises typically own many different kinds of assets. It is of even less interest in a system of macro economic accounts. 5