Improving the estimates of the UK capital stock.

Introduction

There is a widespread view that official estimates of the capital stock in the UK may be subject to substantial error. However, until recently making any major improvement would have incurred costs beyond any reasonable budget, so the Central Statistical Office has only been able

to make relatively marginal changes despite its continuing concern about the problem. Now, as the result of the computerisation of asset records and modern accounting requirements, a radical change from existing indirect estimates towards direct estimation is possible. This note, drawn from the results of a recent research project,(1) appraises the problem, suggests how the estimates of the capital stock in the UK might be improved using existing methods and then shows how direct estimation could be used to derive improved current and retrospective estimates.

Estimates of the capital stock of a country are required for a number of purposes:

* to provide estimates of capital consumption for National Accounting purposes;

* for modelling and forecasting the behaviour of the company sector;

* to assist in the estimation of the efficiency of operation of industry and the assessment of productivity;

* to help estimate the productive potential of the economy and its ability to respond to cyclical shocks and opportunities;

* to measure the contribution of capital to production and growth;

* to act as a base from which to assess the potential yield from capital and wealth taxes;

* to enable the assessment of national income, through providing the necessary information to determine the contribution of current activities to altering the value of net wealth;

* for international comparisons of rates of return on capital.

For some of these purposes such as explaining cross country differences in the level of productivity it is very important to have reliable estimates of the level of some measure of the capital stock.(2) Whereas for other purposes, such as accounting for growth in a single country, it is the growth rate of the capital stock over time that is more important. Unfortunately there are reasons for a lack of confidence in both the level and the time series profile of the official estimates of the UK capital stock that are currently produced.

Methods of estimation

There are two broad approaches to estimation of the capital stock: direct estimation and the perpetual inventory method (PIM). It is PIM which is used by the CSO and by most statistical offices in other countries. PIM uses estimates of gross domestic fixed capital formation over a long time period combined with assumptions over the length of asset lives and the pattern of the retirement of assets in a simple model. Direct estimation, as its name implies, involves measuring directly the stock of capital available to industry. One of the earliest attempts at measuring capital stock in the UK, that of Tibor Barna, working from the National Institute in the 1950s, was based on direct estimates. However, this approach has hitherto been generally thought to be prohibitively expensive as a method of data collection, particularly by comparison with PIM.

In our view it appears that the perpetual inventory method, as it has been implemented in the UK, has produced data series which probably bear little resemblance to what they are attempting to measure. The case for some form of direct estimation is overwhelmingly strong by comparison, in particular to establish a definitive benchmark relating to existing assets. At the very least the results from a one-off enquiry could be used in combination with a modified PIM. We conclude that a direct capital stock enquiry is likely to be successful, after appropriate pilot testing.

The purpose of the current paper is to summarise the methods by which estimates of the capital stock are currently obtained and examine the sensitivity of the estimates to a number of assumptions that underlie their construction. In addition we consider a variety of evidence to assess the accuracy of the estimates of the capital stock as published by the CSO. This analysis points to a number of deficiencies with the current approach which need to be remedied. We then go on to discuss a strategy for the direct estimation of the stock intended to improve the quality of the estimates at low cost to government and business.

The definition of the capital stock

Controversies about the appropriate definition of capital and indeed whether it is right even to attempt to measure it are not now as heated as they once were.(3) Nevertheless there is no single correct measure of capital and the choice will depend largely on the use to which it is put.(4) There are a number of options both with respect to the values that are attributed to different items of capital (book values, current values, replacement cost, second hand values, constant prices) and to any allowance that might be made for depreciation.

The CSO estimates the capital stock in gross and net terms--before and after estimating depreciation--and at current and constant replacement cost. These are disaggregated by asset, sector and industry and published in the Blue Book. It is beyond the scope of this note to discuss whether alternative definitions of capital might be estimated. Instead we focus on improving the measurement of capital on the basis of existing definitions, which conform with the internationally accepted UN System of National Accounts.

The perpetual inventory method

Ignoring problems of valuation and aggregation for the moment, suppose we require estimates of the gross capital stock, K. The gross capital stock is a measure of all capital in existence and may be compiled as

|K.sub.t~ = |K.sub.t-1~ + |I.sub.t~ - |R.sub.t~(1)

where |I.sub.t~ is new investment (the inflows to the stock of capital) and |R.sub.t~ represents retirements of capital (the outflows from the stock). By substituting for |K.sub.t-1~ this may be written as:

|K.sub.t~ = |summation of~ (|I.sub.t-s~ - |R.sub.t-s~) + |K.sub.t-B~ where s = 0 to B - 1 (2)

where |K.sub.t-B~ represents the starting value of the capital stock where B might be chosen as the number of years since a benchmark estimate of the capital stock or be sufficiently far in the past that it can be largely ignored.

Measuring the capital stock by way of equation (2) requires historical information on both acquisitions and retirements of capital expressed in the same units. However, information is not available in this form. Gross domestic fixed capital formation (GDFCF) is measured by the purchase of new assets and second hand assets net of sales of fixed assets.(5) But for use in (2) a disposal would need to be valued at the same price at which it appears as an investment to ensure that it cancels out in the measurement of the stock.

Without the necessary information on retirements, some assumptions need to be made to implement the perpetual inventory method. This involves estimation of the average length of life of the assets in particular groups created in each time period (L(t)). If all assets in each group and period lasted for exactly that average time then we could form a continuing series for the capital stock out of the investment figures--hence the name 'perpetual inventory'. Each investment added to the capital stock in year t would be subtracted again L(t) years later. (L(t) is usually referred to as the service life of the asset.)

The gross stock of that class of capital with service life L is then:

|Mathematical Expression Omitted~(3)

where |Mathematical Expression Omitted~ is the gross stock of capital of class L at date t, |Mathematical Expression Omitted~ is GDFCF of class L at date t-i.

Using straight line depreciation and the assumption that all investment occurs at the beginning of each year, the net stock of class L capital at date t is:

|Mathematical Expression Omitted~(4)

Thus a unit of capital remains in the gross stock until it is retired at the end of its life whereas a declining proportion of it remains in the net stock.

In practice the assumption that capital of a particular type lasts for a fixed number of years is unrealistic as the assets created in one year are retired over a number of years. Some may be retired almost immediately because of an accident or unexpected obsolescence, while others may last a great deal longer than anticipated.

A number of assumptions about the retirement pattern are made by various national statistical offices (OECD, 1993). These include simultaneous retirement of all assets at the average service life (for example, Norway), a constant proportion retired each year for a range of years either side of the average (this is currently the UK's approach), a symmetric approximately Normal distribution of retirements round the average (favoured by most OECD countries), a skewed distribution round the average (Australia, Germany, Sweden).

Whether the shape of the service life distribution is important or not hinges on the sensitivity of the resulting capital stock estimates to the underlying assumptions. The CSO amended its implementation of PIM in the mid-1970s because of the sensitivity of retirements, the amount of capital assumed to be leaving the gross stock, to the assumed service lives. In particular, computed retirements are very erratic in the period from 1974 to 1980, echoing the similarly erratic behaviour of investment in the war years and after. Capital consumption however is much smoother reflecting the fact that investment over the period from 1940 to 1946 is subtracted from the net stock over a much longer period of years, rather than all at once as with the gross stock. However, the measurement of the stock itself does not appear to be very sensitive to the annual distribution of service lives (see Mayes and Young, 1994).

Of more importance is the set of service lives assumed. The original approach of the CSO to measuring capital stock(6) was to allocate GDFCF to groups according to the assumed service lives of the assets involved and to assume that all assets within each class had identical service lives. For investment in plant and machinery it was assumed that the service life of the asset would be either 16, 19, 25, 34 or 50 years, with proportions that varied across the main industry groups. The service life of buildings was assumed to be 80 years and that of vehicles to be 10 years. The distribution is shown in Table 1.

The original service life assumptions were based on the research of Redfern (1955) who inferred the lives of assets from Inland Revenue depreciation allowances on fixed capital. These were subsequently revised upward by Dean (1964) in the light of the estimates based on fire insurance valuations compiled by Barna (1957) which were consistent with the results of Feinstein (1965).

A major revision to the CSO's approach was made in 1983 when the assumed service lives were reduced in a particular way to three-quarters of their previous level. The revised assumptions for plant and machinery capital are shown in Table 2.

There are several points to note about the way service lives were changed. First, the original assumptions are retained for plant and machinery installed before 1950. Second, the adjustment to the new set of assumptions is very gradual so that even in 2008 some 40 year old class E capital will remain in the measured capital stock. Third, as noted by O'Mahony and Oulton (1990), according to these assumptions it is not always the oldest capital that is scrapped first. In 1998 for example, class E capital of the 1950 vintage will be scrapped whereas class E capital of the 1949 vintage will continue to be used. This emphasises the most important point that the revised service life assumptions are consistent with a change in the physical characteristics of plant and machinery capital over the period from 1950-70. So that 1949 vintages of class E capital must be thought to be more durable than the 1950 vintage. Given the difficulties in measuring the capital stock and its characteristics it is very hard to believe that there is any real evidence for this.

Table 1. Proportion of GDFCF by manufacturing in plant and machinery devoted
to each class of asset

per cent

Class                    A       B       C        D        E

Service life (years)     16      19      25       34       50
Proportion               2.0     7.0     23.0     48.0     21.0

Source: these proportions are based on a simple average of the figures for the
various manufacturing industries given in Hibbert, Griffin and Walker (1977).

Chart 1 shows the effect on the estimated gross stock of the current set of service life assumptions. Also plotted are the stocks of capital measured using the original assumption of life lengths for the whole period and secondly using the revised assumptions applied for the whole period.(7) Clearly the measured stock is moving from one to the other. The implication is that the growth rate of the stock as currently measured is smaller than that generated on the basis of constant service lives. Since it is the growth rate of the capital stock that is important to researchers interested in growth accounting, the current service life assumptions are seriously misleading if there is not a good basis for the declining service life assumptions.

This raises the important question of what the CSO were attempting to remedy by changing the service life assumptions. The 1983 Blue Book suggested that the existing service life assumptions were 'too long'. In which case it is not clear why the assumptions were not simply reduced for all past time rather than just from 1950 (and 1890 for buildings). Two possible reasons are that the original assumptions were based on more detailed research than the revised assumptions and second to move straight to the revised assumptions would have led to very large revisions in the estimates of capital stock and capital consumption. This suggests that it is important to distinguish between the effects of changing asset life assumptions and assuming that asset lives themselves are changing.

Table 2. Revised service life assumptions, plant and machinery

Vintage
Class   Pre-1950   1950-54   1955-9   1960-4   1965-9   1970-

A         16          15       14       14       13      12
B         19          18       17       16       15      14
C         25          24       23       21       20      19
D         34          32       31       29       27      26
E         50          48       45       43       40      37

Average asset life assumptions

The main effect of different constant average asset life assumptions is on the level of the measured stock of capital although there may also be some second order effect on its profile. Thus the level of gross stock on the basis of constant new CSO lives is 15 per cent lower in 1989 than on the basis of constant original lives; the corresponding reduction in the net stock is 18 per cent. These estimates are similar to those provided in the sensitivity exercise of Hibbert, Griffin and Walker (1977).

Changing service lives

The CSO assumption that service lives have declined over time is not inconsistent with the work of other researchers (see Muellbauer (1986), for example). But the usual argument is that the decline in service lives has come about unexpectedly because of unforeseen changes in relative prices or contractions in demand which render certain types of equipment prematurely obsolete. The appropriate way to allow for this is clearly different to the CSO approach which assumes that the decline in service lives is known from the date capital is installed.

In general firms may be expected to choose the service lives of their capital period by period in the light of economic incentives. In order to quantify the importance of this (however imprecisely) it is possible to use the vintage production function for manufacturing that is used in the National Institute's domestic macro-econometric model. This assumes that capacity (or potential) output is the output that would be produced if all vintages of capital available were used in production. Given information on capacity output, constructed using information from the CBI survey (see Minford, Wall and Wren-Lewis, 1991), past investment and factor prices, it is possible to calculate the age of the oldest capital in use. This is shown in Chart 2.

Suppose that this profile is an accurate representation of the way that service lives have changed over recent years. To incorporate this into the capital stock model requires further information. It is of some importance whether the change in service lives reflects unplanned obsolescence or is a consequence of a decline in the physical durability of capital. To show this two separate cases are considered. Both assume that the service lives of capital fall permanently from 1974 in line with the behaviour of the series shown in Chart 2 (smoothed slightly). The first approach assumes that this reflects an earlier change in the physical durability of capital. The second approach treats the change as a response to changed economic circumstances.

Chart 3 shows the gross stock of capital in manufacturing under both of the above assumptions and compares these with current CSO estimates of the gross stock. The level of both of the new series is obviously lower than the official series. This is a consequence of the shorter asset lives assumed. The series corresponding to the assumption that asset lives have shortened because of a decline in the physical durability of capital is much smoother than the series where asset lives are shortened for economic reasons. This is a consequence of the fact that when physical durability is lower the effects are distributed over a number of years: if service lives fall for vintages constructed in 1950 this will affect retirements from 1962 to 2010 with the old distribution assumptions. But if asset lives are reduced in 1974 say because of a change in economic circumstances in that year, then all assets of the appropriate age (16 year old capital built in 1959, 19 year old capital built in 1956, 34 year old capital built in 1941 and so on) will be affected so that retirements are much larger and more erratic.

None of this is meant to imply that one of these estimates is better than another but the sensitivity of PIM based estimates illustrates how bad these estimates can become when the asset life assumptions that underlie them are incorrect. In order to judge whether this is a problem in practice requires an assessment of the independent evidence on the level and profile of the capital stock. This is available from a number of sources including company accounts, fire insurance valuations, trade surveys, expert opinion, the evidence from other countries and the consistency of aggregate capital stock estimates with other macroeconomic evidence. These are discussed below.

Evidence from company accounts

One of the main stumbling blocks in using the estimates of capital assets recorded by companies in their accounts is that these are usually at historic cost. Inflation therefore leads to significant under-recording of capital in the balance sheet and depreciation in the profit and loss accounts. However Wadhwani and Wall (1986) and Smith (1987) were able to make use of the current cost accounts drawn up by many companies in the early-1980s to provide estimates of the capital stock. Wadhwani and Wall focused particularly on changes in the capital stock over time (1972 to 1982) and Smith concentrated on measuring the level of the capital stock in 1983.

Smith found substantial disparities between the official and company accounts based estimates of the capital stock in 1983 with the official estimate of the stock of equipment in manufacturing exceeding the accounts based estimate by 36 per cent and the disparity in non-manufacturing being 16 per cent. Although the data source was the same, Wadhwani and Wall's study was more extensive, involving some 333 companies in manufacturing industry. Their analysis, which also requires assumptions concerning asset lives, reinforces the earlier suggestion that the results are very sensitive to the assumptions made giving estimates using the 1972 CSO figures as a starting point which vary from 10 per cent to 35 per cent below the CSO estimates 10 years later.

The Wadhwani and Wall analysis emphasises a possibility which is sometimes overlooked, namely, that historic cost accounts can also be used as a means of estimation. Two relevant items of information are recorded in company accounts, fixed assets at historical cost and investment. This provides an opportunity to invert the PIM procedure. In PIM we know investment, make an assumption about asset lives and hence compute the capital stock. This time we have an estimate of the capital stock and investment which we can use to estimate asset lives (Jaffey, 1990). This method has been used in Canada and in France (see also Mairesse (1972), Atkinson and Mairesse (1978), Tarasofsky et al. (1987) and Lette and Szpiro (1988)).

The evidence from company accounts may be more informative about changes in the capital stock and asset lives than their levels. It is well known that the asset life assumptions that underlie company accounts are around half those in the national accounts. But the assumptions about depreciation made by companies are not necessarily any more reliable. Accountants may have reasons to be cautious as to the likely lives of capital assets when drawing up accounts as they do not wish to include capital on the balance sheet when it has already been scrapped.

Macroeconomic evidence on the accuracy of the estimates

There are two principal sources of macroeconomic evidence on the rate of scrapping: the first comes from survey evidence on the level of capacity utilisation and the second from information on the level of output and the use of other factor inputs.

Minford, Wall and Wren-Lewis (1991) use information from the CBI survey to construct estimates of manufacturing capacity. These can be interpreted loosely as estimates of the capital stock if capacity tends to be proportionate to the capital stock. Chart 4 compares the manufacturing capacity series with the gross capital stock generated on the basis of constant original CSO service lives (the Minford, Wall, Wren-Lewis series begins in 1966, earlier figures are based on a centred moving average of manufacturing output). According to these figures, the capital stock is seriously over-estimated by the PIM with constant original service lives. The over-estimation reaches a peak of 44 per cent in 1986.

However the relationship between the generated capacity series and the true capital stock may change over time thus invalidating the above approach to calibrating the capital stock. An alternative approach is to look in broad terms at the relationship between employment, the capital stock and output. Chart 5 plots the capital labour ratio in manufacturing and compares it with a trend fitted up to 1973.(8) The capital stock is measured on the basis of constant original CSO lives. This shows a step change in the capital output ratio centred on 1981. This in itself is not evidence that the capital stock is over-estimated. It is generally more difficult to adjust the capital stock than it is to adjust employment and it is quite possible that when there is a shock to factor demands the measured capital stock remains in place but is under utilised whereas employment is reduced but fully utilised. However if capital were not scrapped and merely under-utilised it is likely that when the recession ended the measured capital labour ratio would fall back to its trend level as firms raise employment and increase the utilisation of their existing capital. This did not happen. Instead firms increased investment in the recovery so that the measured capital labour ratio remained substantially above the previous trend. This evidence is suggestive of substantial capital scrapping in the 1980 recession.

A similar pattern can be discerned from the behaviour of the capital output ratio in manufacturing shown in Chart 6. The capital output ratio rose sharply in the recession beginning in 1980. But rather than reverting to trend in the recovery as it had done in previous cycles, it remained substantially above trend. This again suggests that much of the capital that was included in the measured capital stock was scrapped. If it can be assumed that the true capital output and capital labour ratios revert to the trends shown in the chart, then the figures shown there suggest that the measured capital stock (on the basis of constant original service lives) over-estimated the true stock by about 25 per cent in 1986.

The difficulty with this type of macroeconomic evidence is that it can never be conclusive as it is really testing the evidence provided by the CSO against particular theories of production and interpreting any inconsistency as a failure of the evidence rather than the theory. It is fortunate therefore that there are other sources of evidence concerning the level and profile of certain parts of the capital stock.

Evidence from trade surveys

Surveys are undertaken for Metalworking Production at five year intervals in the UK to obtain estimates of the size and age distribution of machine tools. Similar surveys are undertaken for the American Machinist in the United States, by VDW, the trade association in Germany (VDW, 1980), MITI in Japan (MITI, 1983) and BIPE in France (BIPE, 1982). (Other surveys also exist, see example for Italy in Bacon and Schianchi, 1978.)

The survey evidence may be used to illuminate changes in the age distribution of the capital stock over time as well as be used to assess the plausibility of the PIM assumptions by comparing the age distribution of capital implied by the PIM with the results of the surveys. For this purpose we have constructed estimates of the age distribution of the stock of plant and machinery for manufacturing industry as a whole using the PIM with the original CSO service lives assumed constant but normally distributed around their mean. We have repeated the exercise assuming that service lives are normally distributed about the average calculated by Smith (1987). A similar analysis was carried out by Prais (1986) who assumed a constant rate of retirement using the 'reducing balance' method. The results are shown in Table 3 and compared with the results of the survey.

Table 3. Age distribution of manufacturing capital stock, 1961-87

              Under 10 years   10-20 years   Over 20 years

1961 survey          44            36            20
PIM                  48            26            26
PIM (short)          69            27             4
1971 survey          43            36            21
PIM                  48            33            19
PIM (short)          66            32             2
Prais                47            23            30
1976 survey          40            36            24
PIM                  45            35            20
PIM (short)          63            34             3
1982 survey          39            29            32
PIM                  40            39            21
PIM (short)          57            39             4
Prais                40            27            33
1987 survey          51            22            26
PIM                  37            41            21
PIM (short)          55            41             4

Notes:

(1) The survey refers to machine tools only.

(2) The PIM estimates are based on investment in plant and machinery in
manufacturing industry.

(3) The Prais estimates are based on a 2.5 per cent retirement rate.

(4) The Smith service lives assumptions are labelled '(short)'.

Looking at the results of the surveys for individual years the original CSO service life assumptions imply an age distribution of capital equipment that is similar to that revealed by the 1961 survey. The main difference is that the PIM estimates indicate that a higher proportion of the capital stock is over twenty years old and a lower proportion is in the middle age range. This would be consistent with actual service lives being slightly shorter than the original CSO assumptions. Calculating the PIM on the basis of shorter service lives fails utterly to reflect the information in the survey.

The 1971 survey and the PIM are in virtual agreement. Estimates by Prais on the basis of a 2.5 per cent retirement rate underestimate the proportion of capital in the middle age range at this time. This suggests that his assumption of a constant rate of retirement does not adequately characterise the pattern of retirement in the years leading up to 1971.

The 1976 survey and the PIM are again in broad agreement. If anything the PIM suggests a relatively younger capital stock than the survey. By 1982, the survey suggests that this process has gone further with a higher proportion of capital in the oldest age group and rather less in the middle age group. The age distribution in the survey is virtually identical to that predicted by Prais on the basis of a 2.5 per cent retirement rate.

Averaging over the first four surveyed years produces an estimate from the PIM using constant original CSO service lives that is virtually identical to that from the survey. The PIM produces a distribution (45:34:22) that is slightly younger than that revealed by the survey (42:34:24). Further, in contrast to the PIM estimates, the survey indicates that the capital stock is becoming older over time. On the basis of this evidence, it is clear that if there is any useful information in the survey it indicates that the original service lives assumed by the CSO were not too long and that actual lives got longer rather than shorter over this period.

The results from the 1987 survey are particularly interesting. They show a much larger rise in the proportion of capital that is under 10 years old than would be predicted by the PIM. This is consistent with a significant amount of scrapping of older equipment. However, what is not clear is why premature scrapping was not detected by the 1982 survey. This is a puzzle because all of the estimates of excess scrapping that use aggregate data indicate that it was well under way by 1982.

One appealing explanation for this that fits in with other evidence (see Oulton, 1987, Smith, 1986 and Baden-Fuller, 1989) is that any excess scrapping that did take place after the beginning of the recession that started in 1980 was achieved through plant closures rather than by piecemeal scrapping of their oldest equipment by continuing plants. This would explain why the stock of equipment did not appear to be significantly younger in the 1982 survey than previously: the age of capital had not changed significantly in the plants sampled, but this took no account of the wholesale scrapping of equipment in plants that closed down and therefore were excluded from the sample.

This possibility is consistent with the evidence of Wadhwani and Wall referred to earlier. They noted that the information that they collected from company accounts for the early-1980s did not show the large falls in the capital stock claimed by others. However they also observed that their sample was unrepresentative in the sense that it excluded firms that were liquidated. Therefore it is possible to infer that if there had been large scale scrapping in manufacturing it had not come about by scrapping in continuing firms but by plant closures. Smith (1988) also found that capital output ratios changed little among existing firms in the early--1980s while the ratio for industry as a whole rose substantially. This is again consistent with the hypothesis of capital scrapping being associated with plant closures.

It would also explain why the age of the capital stock was much younger in 1987 than suggested by the PIM estimates. As output recovered from the recession, the opportunities faced by the surviving plants were greater because of the closure of their competitors. They could expand capacity and the new investment represented a substantial proportion of their capital. This behaviour is consistent with the sharp rise in the investment output ratio over the period.

Thus the evidence from the survey and from the aggregate information discussed earlier suggests that the original service life assumptions of the CSO were adequate until some time between 1976 and 1982. A period of substantial capital scrapping took place around the time of the recession that began in 1980 and this is likely to have taken the form of plant closures.

Evidence from other countries

It might be thought that since producers in the major industrial countries are subject to the same influences, the service lives of assets would also be similar across countries. In practice the assessment of assets lives elsewhere, as in the UK, has tended to be based on very soft estimates which have not been revised on a systematic basis. Just looking at the distribution of the assumptions used by the various OECD countries is inadequate as several of them have been through the same exercise and have based their estimates on those used by other countries. Bunching of estimates does not therefore imply some consensus in observed behaviour, merely a common source to the assumptions. Thus changing UK estimates to the average of OECD or to the average of the EC would not necessarily be a very helpful move. It would merely make UK estimates more comparable with those of other countries.

Table 4. Average service lives of machinery and equipment in manufacturing
activities in other countries in 1990

                             years

Canada                         22
United States                  17
Japan                          11
Australia                      19
Austria                        18
Belgium                        15
Finland                        17
France                         18
Germany                        15
Ireland                        22
Italy                          17
Norway                         25
Sweden                         23
United Kingdom                 26

Source: Blades (1991).

Indeed Prais (1986) on the basis of the machine tool surveys referred to above observed that the average age of capital in the UK is if anything younger than in other countries except Japan. Since the average age is consistent with the longer service lives that used to be assumed by the CSO it is quite possible that the shorter service lives assumed by other countries are mistaken. In matched sample studies undertaken at NIESR (for example, Daly et al. (1985), Steedman and Wagner (1987, 1989), Prais and Wagner (1988), Jarvis and Prais (1989) and Mason et al. (1992)) the age of the machinery in use was similar across industries as diverse as engineering, furniture, clothing, biscuits and hotels. It seems unlikely that the UK should stand out from the other OECD countries in the way it appears to.

Fire insurance valuations

Before embarking on the expense of direct estimation of the capital stock it is essential to be convinced that all the other options for improving estimates have been explored and that they are insufficient to meet the need. One possibility which has looked promising in the past has been valuations for fire insurance purposes as this would provide a revaluation of the stock with a considerable element of replacement cost included.

In the work of Barna (1961) and subsequently that of Smith (1986) it was clear that many firms had straightforward inventories and insurance policies which would enable the necessary identification. However, this has become increasingly difficult because of the rising trend of self insurance, particularly among large companies. Secondly it has become clear that there is substantial under-insurance, not just in the sense that values are generally insufficient but that some items are not insured at all. Gaps would therefore occur in the estimates not in the more trivial end of the distribution but among the major asset holders, thus considerably complicating any estimation process. Smith looks in detail at results for Finland, Sweden and Norway, comparing PIM estimates with those based on fire insurance valuations. No simple lesson emerges. In Sweden the two sets of estimates have tended to diverge (by as much as 70 per cent in the case of buildings), while in Norway they have oscillated, being within 10 per cent of each other by 1983. Finland on the other hand shows PIM values falling relative to the fire insurance estimates, so that by 1978 they were lower than the fire insurance valuations.

Interestingly enough, problems of undervaluation are less worrying as it is possible to get a clear impression from loss adjusters and the insurers themselves about the extent of undervaluation and how it might be changing over time. Indeed it may be possible to simplify the enquiry even more dramatically by directing it towards the insurers rather than the insured.

Taken together the various different sources of evidence give little cause for comfort over the appropriateness of the service life assumptions now used by the CSO. Given what we know about the sensitivity of PIM based estimates to these assumptions we feel that it is important to assess the possibility of using direct methods to measure the capital stock. Even if these direct estimates are used only to provide a new benchmark and picture of the age structure of the current stock of capital it will enable substantial improvement in the estimates for previous and future years for some time to come.

Direct estimation of the capital stock

Only the Netherlands is to our knowledge conducting comprehensive surveys of the capital stock among the OECD countries at present (Japan used to use this approach and some work is being undertaken in Canada, primarily to determine the distribution of asset lives, and a full survey is undertaken periodically in South Korea) and it is looking very hard at ways to cut the cost and implement a much simpler system. However, the experience of the Netherlands shows that it is possible to conduct a progressive survey of the stock in order to improve existing PIM based calculations (Frenken, 1992). This exercise is particularly interesting as it presents a strategy which tries to get the maximum improvement in the statistics at an early stage. We have conducted a small but successful pilot study to establish that this methodology appears to be readily transferable to the UK.

What this and other surveys show, however, is that it has not been possible to get accurate results from written enquiries to the firms. While it may be possible to list the assets, firms have problems in valuing them and hence a very clear inventory is required. This suggests therefore that on the first occasion a visit to the business is normally going to be necessary. However, whereas the Dutch thought at the outset that they would need very considerable detail in order to provide accurate estimates (they initially sought data on over three hundred types of capital) they have come to the conclusion that it is not necessary to extend the breakdown beyond a handful of major categories. Since most businesses have asset registers which contain some considerable detail, usually in computerised form, such lists including date of acquisition and historic cost appear to be readily available.

Variations between industries according to the different types of equipment they have can be picked up simply by sufficient disaggregation according to industry. Ownership of carpet making machinery, for example, will be confined almost entirely to the carpet making industry, there is therefore little point in trying to get data on it from other industries, while there is little value in knowing how important the component types of machinery are within carpet manufacturing if service life and mortality distributions are only going to change slowly. It is only where a small number of firms or industries are sampled in detail with a view to using their results across firms as a whole that such a disaggregated approach could be useful.

Even direct estimates do not need to be comprehensive surveys of every business in the country. In the same way that very accurate estimates of production can be obtained by a census of the largest firms and a sample survey of the smaller firms--the smaller the size of the firm the smaller fraction required--so quite accurate estimates can be obtained of the capital stock for most industries. Large firms and plants tend to dominate capacity and production.

The appropriate strategy is clearly to begin with a careful pilot study to obtain more accurate estimates of the difficulty and costs of obtaining the information, the accuracy of the method and the burden on business. The results will also help establish the appropriate sample size for the various steps in the analysis. Then one can TABULAR DATA OMITTED proceed in a manner which will result in the ability to alter the overall estimates at an early stage. This involves examining a sample of industries which can in some sense be thought to typify others within their general group. This will provide a range of estimates of the average service lives of the various categories of the capital stock, which will, through the extent of its variance, give an indication of the extent to which it is necessary to conduct a careful analysis of each industry group. The Dutch strategy was to start with the most capital intensive industries so as to cover as much of the ground as quickly as possible with the minimum number of interviews. (Capital intensive industries are by and large also relatively concentrated so that the number of firms to interview within each industry were relatively low.) Then they surveyed industries at a level of detail equivalent to the 3-digit level of NACE, using a five year programme, such that all were covered in turn.(9)

We anticipate that, even in the first year, it would be possible to make a general readjustment across the whole of industry on the basis of the sample if it indicated substantial errors in asset lives. However, this re-estimate would not involve a proper rebasing, just a recomputation of PIM using new parameters. The Dutch were slow to do this, having considerable doubts about the extent to which results could be extended from one industrial sector to another. The reason for this was that while all the direct estimates were higher than their PIM counterparts their ratio varied considerably. Ignoring the extreme ratio of 11.66 the distribution of the ratio of direct to PIM estimates for the 128 industries is shown in Table 5.

Land and buildings are most accurately estimated by PIM while computers are most heavily underestimated. No direct inference can be made for the outcomes in the UK as the Dutch do not use the same parameters in the calculation of PIM. However, in crude terms, the shorter the expected asset life, the greater the errors made under PIM are likely to be.

Making these estimates only once does not really show where PIM breaks down. We need to survey again--in five years time if we take the Dutch example--and compare the original direct estimate, updated by PIM for 5 years, with the new direct estimate. The range of results was still surprisingly large in the Netherlands, although there seems to be a learning process and more recent PIM augmentation of the five year old direct estimates appear to be more accurate. There is clearly more work to be done here to try to improve the PIM augmentation. It is also necessary to develop the appropriate grossing up factors to be used to enlarge the estimates obtained from the sample of larger firms in the industry which have been surveyed to estimates for the whole industry, containing the smaller firms and the other non-sampled firms as well.

It is not necessary to replicate the Dutch approach as our own investigations with companies suggests that those with computerised asset registers would be able to keep their capital stock estimates up to date as their own accounting procedures require them to record the assets which are scrapped or sold each year and the acquisitions of new or already existing assets. Even if only a representative panel of businesses provides this information then it would become much easier to spot and quantify episodes of accelerated or delayed scrapping and hence avoid what appears to be the very wide variations in PIM estimates from actual behaviour that seemed to have occurred in the past.

Conclusion

Our analysis indicates that PIM based measures of the capital stock are extremely sensitive to the assumptions that underlie their construction. The indirect evidence that we have surveyed suggests that there is no reason to suppose that the current set of assumptions have any great empirical validity. The evidence from company accounts and from the practices of official statisticians in other countries suggest that current service life assumptions are too long. By contrast the evidence from trade surveys suggest that service life assumptions were about right until some time in the early 1980s since when they have become too long. The macroeconomic evidence also indicates that the service life assumptions became too long in the early 1980s.

Putting this evidence together suggests that official estimates of the capital stock are too high and some downward revision will eventually be required. However it is of great importance how this adjustment is brought about. As was noted earlier, for many purposes the level of the capital stock is of less importance than its time series profile. If the measured capital stock has become too high because of excess scrapping in the early 1980s then this needs to be incorporated into the estimating procedure in such a way that ensures that the time series profile of the stock is as accurate as possible. As we have seen, different methods of incorporating changes in asset lives can have substantial implications for the time series profile of the stock.

We do not think that any of the evidence currently available provides estimates accurate enough to warrant specific changes in the CSO's assumptions without further investigation. After careful study of results produced by the Netherlands Statistical Office over a period of more than a decade we are convinced that the simple use of the perpetual inventory method not merely leads to an inaccurate base line for the capital stock but also to inaccurate updating, which can lead to estimates as much as 10 per cent adrift over a period as short as five years. Econometric and case study evidence makes it clear that premature retirement of the capital stock is affected by economic factors which cannot be represented by simple rules under PIM, even with sophisticated allowances for vintages. Only direct estimates provide data on the age distribution of the extant stock.

Four steps are necessary.

First, a pilot study to provide a more accurate assessment of the costs of direct collection, the burden on business, the accuracy of estimators and the feasibility of using indirect estimates from knowledgeable sources.

Second, a sample survey designed to cover the main capital owning industries with some care and the rest of industry more lightly to estimate both the size of the existing capital stock and the age distribution of assets by vintage.

Third, annual supplementation of the estimates by additional information on the capital that has been scrapped or sold.

Fourth, more use of other existing sources of information to improve the quality of estimates. The estimates can be kept up to date by a small expansion of the information required from firms in the Annual Census of Production and the equivalent enquiries of the distribution and services industries.

One of the major problems is the estimation of scrapping on the basis of assumptions rather than observation. We cannot collect observations on the past but we can provide a more coherent link with the new estimates of the current stock by deriving a new profile over previous years. Various sources of information listed above should be consulted to assess how the underlying mortality distribution has changed over time due to changes in the physical durability of equipment. These include:

a) to use the approach of Mairesse and others to exploit the information contained within company accounts. In particular, historical cost estimates of the value of capital and investment can be used to infer asset life assumptions;

b) to use information from the machinery surveys discussed above. While this is not panel information it does tend to suggest that the service life of capital owned by the representative firm did not change significantly at least until the 1980s;

c) to use surveys of expert information to discover whether practitioners perceive there to have been a change in service lives;

d) to use fire insurance valuations, perhaps in association with company accounts to see if these imply significant changes in the service lives of capital over time;

e) to classify asset types more finely so that IT equipment is distinguished from other types of capital.

As noted earlier, our impression is that the major reason for mismeasurement of the capital stock is because capital scrapped by firms going out of business remains in the measured stock. It is therefore possible, but unverifiable without direct estimates, that there has been no change in the service lives of capital used by continuing firms. Thus we consider it of major importance that some attempt be made either to estimate the capital lost through plant closures or to find direct estimates of the capital used by existing firms that may be grossed up to estimate the aggregate stock. The second route is likely to be the more feasible.

REFERENCES

Atkinson, M. and Mairesse, J. (1978), 'Length of life of equipment in French manufacturing industries', Annales de L'INSEE, no. 30-31/1978, Paris.

Bacon, R.W. and Schianchi, A. (1978), 'La strutture del parco macchinne utensili in Italia: un estensione del l'analisi', Rivista Economica e Politica, no. 3.

Bacon, R.W. and Eltis, W.E. (1974), The Age of US and UK Machinery, NEDO Monograph 3, London.

Baden-Fuller, C. (1989), 'Exit from declining industries and the case of steel castings', Economic Journal, vol. 99.

Barna, T. (1957), 'The replacement cost of fixed assets in British manufacturing in 1955', Journal of the Royal Statistical Society, Series A, 120(1).

Barna, T. (1961), 'On measuring capital', The Theory of Capital, by F.A. Lutz and D.C. Hague, New York: MacMillan.

Blades, D.W. (1991), 'Capital measurement in the OECD countries: an overview' in Technology and Productivity: The Challenge for Economic Policy, OECD, Paris.

Bureau d'Information et de Provisions Economiques (1982), Recensement du parc francais de machines-outils en 1980, Neuilly.

CSO (1985), United Kingdom National Accounts: Sources and Methods, (3rd edition), HMSO. Daly, A., Hichens, D.M.W.N. and Wagner, K. (1985), 'Productivity, machinery and skills in a sample of British and German manufacturing plants', National Institute Economic Review, no. 111, February.

Dean, G. (1964), 'The stock of fixed capital in the United Kingdom in 1961', Journal of the Royal Statistical Society, Series A (General), vol. 127, pt 3.

Economic Planning Agency (1970), National Wealth Survey of Japan, vol. 1, Summary Report, Tokyo.

Economic Planning Agency (1979), 'Non-residential business capital stock in Japan 1965-78', Tokyo.

Economic Planning Agency (1970), 'Non-residential business capital stock in Japan: concepts and methodology', Tokyo.

Feinstein, C. H. (1965), Domestic Capital Formation in the United Kingdom 1920-1938, Cambridge University Press.

Frenken, J. (1992), 'How to measure tangible capital stock? The choice between two methods', Netherlands Central Bureau of Statistics.

Griffin, Tom (1975), 'Revised estimates of the consumption and stock of fixed capital', Economic Trends, October.

Hibbert, J., Griffin, T.J. and Walker, R.L. (1977), 'Development of estimates of the stock of fixed capital in the United Kingdom', The Review of Income and Wealth.

Jaffey, M. (1990), 'The measurement of capital through a fixed asset accounting simulation model', The Review of Income and Wealth, June.

Jarvis, V. and Prais, S.J. (1989), 'Two nations of shopkeepers: training for retailing in France and Britain', National Institute Economic Review, no. 128, May.

Lette, G. and Szpiro, D. (1988), 'La duree de vie des equipements industriels sur la periode 1972-1984', Cahiers Economiques et Monetaires, no. 28, Paris.

Mairesse, J. (1972), 'L'evaluation du capital fixe productif: methodes et resultats', Les Collections de L'INSEE, C18-19, Paris.

Mason, G., van Ark, B. and Wagner, K. (1994), 'Productivity, product quality and workforce skills: food processing in four European countries', National Institute Economic Review, no. 147, February.

Mayes, D.G. and Young, G. (1994), 'The UK's Capital Stock', National Institute Research Report.

Minford, M., Wall, M. and Wren-Lewis, S. (1991), 'Manufacturing capacity: a measure derived from survey data using the Kalman Filter', Oxford Bulletin of Economics and Statistics.

Ministry of International Trade and Industry (1983), The Sixth Statistical Survey of Metalworking Equipment, 1981, Japan.

Muellbauer, J. (1986), 'Productivity and competitiveness in British manufacturing', Oxford Review of Economic Policy, 2(3), Autumn, (i)-(xxvi).

OECD (1993), 'Methods used by OECD countries to measure stocks of fixed capital', National Accounts Sources and Methods, no. 2, Paris.

O'Mahony, M. (1993), 'Capital stocks and productivity in industrial nations', National Institute Economic Review, no. 145, August.

O'Mahony, M. and Oulton, N. (1990), 'Industry-level estimates of the capital stock in UK manufacturing, 1948-85', National Institute Discussion Paper, no. 172.

Oulton, N. (1987), 'Plant closures and the productivity 'miracle' in manufacturing', National Institute Economic Review, no. 121, August.

Oulton, N. and O'Mahony, M. (1994), Productivity and Growth Study of British Industry 1954-1986, Cambridge University Press.

Prais, S.J. (1986), 'Some international comparisons of the age of the machine stock', Journal of Industrial Economics, vol. 34.

Prais, S.J. and Wagner, K. (1988), 'Productivity and management: the training or foremen in Britain and Germany', National Institute Economic Review, no. 123, February.

Redfern, P. (1955), 'Net investment in fixed assets in the United Kingdom, 1938-53', Journal of the Royal Statistical Society, Series A (General), vol. 118, Pt 2.

Scott, M. FG., (1992), 'Policy implications of "A new view of economic growth"', Economic Journal, May, no. 102.

Smith, A.D. (1986), 'The feasibility of fire insurance measures of capital stock', National Institute Discussion Paper no. 116.

Smith, A.D. (1987), 'A current cost accounting measure of Britain's stock of equipment', National Institute Economic Review, no. 120, May.

Smith, A.D. (1988), 'Changes in output, employment and the stock of equipment during the 1980s: the experience of fifty companies', National Institute Discussion Paper no. 144.

Steedman, H. and Wagner, K. (1987), 'A second look at productivity, machinery and skills in Britain and Germany', National Institute Economic Review, no. 120, May.

Steedman, H. and Wagner, K. (1989), 'Productivity, machinery and skills: clothing manufacture in Britain and Germany', National Institute Economic Review, May, no. 128.

Tarasofsky, A., Roseman, T.G. and Waslander, H.E. (1987), 'Ex post aggregate real rates of return in Canada', Economic Council, Ottawa.

United Nations (1986), System of National Accounts, Geneva.

Vereins Deutscher Werkzeugmaschinenfabriken (1980), Altersstruktur des Industriellen Werkezeugmaschinenparks in der BDR, Frankfurt.

Wadhwani, S. and Wall, M. (1986), 'The UK capital stock--new estimates of premature scrapping', Oxford Review of Economic Policy, 2(3), Autumn.

Winfrey, R. (1935), 'Statistical analysis of industrial property retirements', Bulletin 125, Iowa Engineering Experiment Station, Iowa State College.

NOTES

(1) To be published as 'The UK Capital Stock', a National Institute research report by David Mayes and Garry Young.

(2) See O'Mahogany (1993) for analysis of the sensitivity of such comparisons to estimates of the capital stock.

(3) Nevertheless theoretical disagreements continue. See Scott (1992) for an unorthodox view and Oulton and O'Mahony (1994) for a comment on this.

(4) This includes issues of valuation which are dealt with more fully in the full report on this project.

(5) See United Kingdom National Accounts: Sources and Methods 12.3.

(6) Hibbert et al (1977).

(7) That is, those given in Table 2 as being applicable from 1970 onwards.

(8) The year before the oil shock recession took hold.

(9) Thus rather than covering each 2-digit category in turn, their coverage is spread over five years with each of their component 3-digit categories being covered progressively over that period.