Consumption of Fixed Capital

Introducing Consumption of Fixed Capital

We have seen how operating surplus and mixed income serve as balancing items of the generation of income account, and that consumption of fixed capital is used to derive gross values from net values of balancing items (such as value added, operating surplus / mixed income and primary income). In general, the estimate of the consumption of fixed capital is not relevant to GDP or GNI, since these concepts are gross, i.e. production or income aggregates before the deduction of the fixed capital consumed.

There is, however, one very important exception to this main rule, namely non-market activity, where by convention the output value is calculated from the costs point of view, and where the consumption of fixed capital is one of the components of costs. Non-market activity occurs in Sector S.13, general government and Sector S.15, non-profit institutions serving households. The latter is private non-market output. The vast majority of non-market output comes from government.

We have not yet seen how consumption of fixed capital arises. This happens in the capital account. Before we arrive at this account the secondary distribution of income account follows the conversion of primary income into disposable income, which is the income available for final consumption. These two types of income are not the same because of the occurrence of redistribution of income. This takes place in the form of the following transactions:

• Current taxes on income, wealth

• Net social contributions

• Social benefits other than social transfers in kind; social transfers in kind are individual goods and services provided as transfers in kind to individual households by government

• Other current transfers; these consist of the following:

  • Net premiums and claims for non-life insurance

  • Current transfers between different kinds of government units

  • Current transfers such as those between different households

The transactions for the expenditure approach to GDP – household, government and NPISH final consumption expenditures – belong to the Use of disposable income account. Both of these accounts are current accounts, in which the flow of value added to disposable income (out of which final consumption is paid) is followed for one accounting period. The last current account – the use of disposable income account – closes with savings as balancing item. Following the monetary perspective, this represents surplus money in the economy that can be used for accumulating (building up) assets.

An asset, tangible or intangible, is a store of value that is capable of being owned or controlled. Assets can be financial and non-financial. Non-financial assets can be produced or non-produced. Produced assets include fixed assets, used in production repeatedly over an extended period of time, inventories and valuables. Non-produced assets include natural resources, licenses and marketing assets (including goodwill).

Transactions in non-financial assets are recorded the capital account, the first accumulation account. The following table gives an example.

The left-hand side of the capital account records the various types of investment in non-financial assets. The main use transaction is gross capital formation, which consists of the following three components:

• Gross fixed capital formation

• Changes in inventories

• Acquisitions less disposals of valuables

Apart from consumption of fixed capital the other transaction on the left-hand side of the capital account is acquisitions less disposals of non-produced non-financial assets. This transaction also involves assets, in this case:

• Natural resources; e.g. land, mineral and energy reserves

• Contracts, leases and licenses

• Goodwill and marketing assets

The right-hand side includes net saving and capital transfers receivable and capital transfers payable (with a minus sign) in order to arrive at that part of changes in net worth due to saving and capital transfers.

Capital transfers are transactions, either in cash or in kind, in which the ownership of an asset (other than cash and inventories) is transferred from one institutional unit to another, or in which cash is transferred to enable the recipient to acquire another asset, or in which the funds realized by the disposal of another asset are transferred (SNA 10.200).

As we have already seen, the transaction consumption of fixed capital represents the decline, between the beginning and the end of the accounting period, in the value of the fixed assets owned by an enterprise, as a result of their physical deterioration and normal rates of obsolescence and accidental damage (SNA 10.156). Because consumption of fixed capital is a negative change in fixed assets, it is recorded, with a negative sign, on the left-hand side of the capital account as well. We will now turn to the question how consumption of fixed capital can be calculated.

Calculating Consumption of Fixed Capital

Consumption of fixed capital is a flow concept, causing stocks in non-financial assets – the capital stock – to change. Applying the gross and net terminology introduced earlier, we have the gross capital stock and the net capital stock, with consumption of fixed capital being the difference between the two. The build-up of non-financial assets takes place by gross fixed capital formation (GFCF). Included are all fixed assets, including both tangible and intangible fixed assets. Intangibles include mineral exploration costs, software, major improvements to non-produced assets and cost of ownership transfer associated with non-produced assets.

Since non-financial assets have a lifetime of more than one year (otherwise they would not be assets) they will be part of the gross capital stock after the year in which they were introduced into the capital stock. The number of years depends on the lifetime (also known as the average service life) of the asset. The following table gives some typical values for the average service life of some asset classes.

The way in which the asset is removed from the capital stock, once it reaches the end of its lifetime is modeled by a mortality function. Different choices are possible. The simultaneous exit mortality function assumes that all assets are retired from the capital stock at the moment when they reach the average service life for the type of asset concerned. The corresponding survival function therefore shows that all assets of a given type and vintage (i.e. year of installation) remain in the stock until time T, at which point they are all retired together. A mortality function that is often used in practice is the Winfrey curve.

At the year in which the asset enters the capital stock, its value is equal to the GFCF value. At the end of its service life the value of the asset is zero. But what are the values for the years in between? This depends on the amount of fixed capital that has been consumed. The conventional way of measuring consumption of fixed capital is to do it directly by applying a depreciation formula to the capital stock. Again, different choices are possible, the easiest of which is straight-line depreciation, in which the value of the asset – say 100 – is depreciated in equal portions over its lifetime. If we take the lifetime to be 5 years, this would amount to a consumption of fixed capital of 20 per year.

However this calculation gives rise to a bias, because the same consumption of fixed capital is imputed if the investments take place in December. Assuming an even distribution of the acquisitions of fixed assets over the year, the average of the stock of the current year T and the previous year T-1 (of course both in prices of year T-1) seems to be a better choice for the estimation. An example is given in the following table, let’s say for a “computer”.

In this example the asset “computer” enters the (gross) capital stock in year 1 and remains in service for 5 years. A factor of 1/5 is applied to the average of the capital stock for the current and previous year, which is 50 for year 1, 100 for years 2 to 5 and 50 for year 6. The net capital stock is obtained by subtracting the calculated consumption of fixed capital from the gross capital stock.

Extending the example to a series of yearly additions (“vintages”) of the same asset over a number of years is straightforward, as is demonstrated in the following table.

For each new vintage the values are shifted forward in time with one year.

Capital Services

The consumption of fixed capital measures the decline in the value of assets associated with ageing. This decline in market values can be described as the age-price profile of an asset. The age-price profile is related to, but different from, the decline in the efficiency of assets as they age. This decline is referred to as the age-efficiency profile. These two concepts are best illustrated using the example given in SNA Table 20.1, which is reproduced in the table below.

Here we do not look at GFCF (indicating the value of the asset) but at the contribution to production of the asset. First look at the diagonal values (100, 80, 60, 40, 20). Here we recognize the same straight-line depreciation with a factor 1/5 as used before, although now applied to the contribution to production. By comparing the value in year T with T-1 we get the age-efficiency profile in the last column (e.g. 0.75 = 60/80). These values represent the capital services of the asset, and thereby constitute gross operating surplus.

It is important to note that the contribution to production in year 2 (80) also increases the value of the asset in year 1, since the asset will generate production in both year 1 and year 2. The standard way of obtaining the additional value in year 1 is by calculating the present value in year 1 of the value in year 2. The idea is that one can invest money at a particular interest rate – say 5 % – in year 1 which will then yield the original amount plus interest in year 2 of 1.05 times the original value. The present value can be obtained by reversing this calculation, i.e. by dividing 80 by 1.05 we get 76 after rounding. The next entry on the diagonal, 60 for year 3, will yield a (rounded) present value of (1/1.05)*60 = 57 for year 2 and (1/1.05)* (1/1.05)*60 = 54 for year 1. This way all non-diagonal elements in the above table can be found and the asset value can be constructed by summing the columns: 282, 191, 116, 59, 20. The decline in asset values (91, 74, 57, 39, 20) represents again consumption of fixed capital and by comparing two consecutive values one obtains the age-price profile (e.g. 0.61 = 116/191).

The important point of this example is that the age-efficiency profile can be used to generate the age-price profile for assets and to then derive consumption of fixed capital indirectly as the difference between successive values of the net capital stock. This also works the other way around as is noted in SNA (section 20.15): if nothing is known about the contribution of the asset to production but the decline in the value of the asset over the five years, due to ageing, is known (the age-price profile), one can derive the same age-efficiency profile again (the tables 20.1 and 20.2 in SNA are equal).

A number of patterns can be postulated for either the age-price or age-efficiency profile. These include the straight line depreciation case. An interesting alternative are geometrically declining profiles, where the value in year T is obtained by multiplying a fixed proportion to the value of the year before. In this case the shape of the age-price profile and the shape of the age-efficiency profile are exactly the same (SNA 20.23). One consequence is that figures for capital stock adjusted for the decline in value are equal to those for capital stock adjusted for the decline in efficiency. This property is an important reason for choosing this profile in practice to determine the value of capital stock.

The “income” in the table is the amount that the owner of the asset can spend and still be as well off at the end of the period as at the beginning. For year 1 this income is 100 – 91 = 9, for year 2 it is 80 – 74 = 6. This income constitutes the return to capital or net operating surplus. This way we have established a link between the asset valuation and operating surplus, via the notion of capital services. Chapter 20 of SNA presents a detailed analysis of these capital services.

The PIM Method

In practice we want to use time-series of GFCF to generate consumption of fixed capital. This is usually done using the Perpetual Inventory Method (PIM), for which the preceding sections have already laid the foundations. This is a method to derive the gross capital stock from GFCF and then calculate CFC and net capital stock as before. PIM works by accumulating past capital formation and deducting the value of assets that have reached the end of their service lives. Both capital formation and discards of assets (“scrapping”) are revalued either to the prices of the current year (current prices) or to the prices of a single base year (constant prices). To implement PIM we need statistics on gross fixed capital formation, price indices for capital assets, and information on average service lives and on how retirements are distributed around these averages. Provided the capital stock series go back as many years as the longest-lived asset (go back “perpetually”), it is possible to estimate the capital stock without having an initial benchmark estimate. However, as the longest lived assets, usually dwelling structures, may have service lives in excess of 100 years, most countries need to start their PIM estimates with a bench-mark estimate, at least for assets with long lives. In the example below we will illustrate this. Note that PIM relates to the estimation of the capital stock and not to the calculation of CFC. The method is described in detail in chapter 6 of the OECD manual on measuring capital, to which the interested reader is referred. Here we will illustrate the method with an example.

Suppose we have time-series of GFCF values and price indexes as in table 8 below, e.g. for the asset “dental equipment”. We can then express GFCF in prices of 2005 by deflating current values with the index (e.g. 59 = 100 * 56 / 95 with rounding applied). The capital stock is then derived by adding GFCF in prices 2005 to the capital stock of the year before and CFC is derived by applying the depreciation rate (in this example again 1/5 = 0.2). Inflating CFC with the price index gives CFC at "current replacement costs" (e.g. 52 = 54 * 95/100 with rounding applied).

We have applied the OECD procedure in the following table using a simple formula that derives CFC from the net capital stock directly by applying the factor 1/5 to half the value of GFCF plus the value of the net capital stock of the year before (e.g. 56 = 1/5 *( 63 / 2 + 246) with values rounded). The factor ½ arises because of the same reason as in table 5. The net capital stock is then derived as the net capital stock of the year before plus GFCF minus CFC (254 = 246 + 63 – 56 with values rounded).

The problem is to get these calculations started by estimating the net capital stock for 1999. In the example this is done by calculating an average of the GFCF increase over the period 2000 – 2012 (0.032 = (84/56)^(1/13)-1 with values rounded). The net capital stock for the year 1999 is then derived by dividing GFCF for the year 2000 by the sum of this average increase and the rate of depreciation 1/5 (242 = 56 / (0.032 + 0,2) with values rounded). The series for the net capital stock is then build up using this initial value as starting point.