SIMULATION STUDIES ON CAPITAL STOCK OF MACHINERY AND EQUIPMENT

Transcription

1 SIMULATION STUDIES ON CAPITAL STOCK OF MACHINERY AND EQUIPMENT Introduction 1 This paper presents the results of four simulation studies carried out by the Singapore Department of Statistics (DOS) to assess the sensitivity of the capital stock of private sector machinery and equipment to the following: changes in asset service lives; different index number formulae; alternative retirement patterns; alternative depreciation patterns. 2 The results of the studies are mostly in line with the predictions of theory and are summarised as follows: there is a direct relationship between the level of capital stock and the length of asset service lives, provided the service lives of all asset types are changed in the same direction; chaining tends to produce growth rates which are lower than those obtained using the fixed-weighted Laspeyres volume index formula; the simultaneous retirement pattern produces the highest level of gross capital stock amongst the retirement patterns used for most years; the straight-line depreciation method results in the highest level of capital stock relative to the other depreciation methods. These results are also broadly consistent with the findings of other related sensitivity studies. Present method of computing capital stock 3 DOS uses the perpetual inventory method (PIM) to compute estimates of capital stock for the Singapore economy using the following assumptions: simultaneous retirement pattern; straight-line depreciation;

2 average service lives which are fixed over time. The existing average service lives were determined after a study of service lives for similar assets in other countries. Presently, the PIM and the above assumptions are mostly applied to highly aggregated asset types, such as the entire group of machinery and equipment. Real growth rates of capital stock are obtained using the fixed-weighted Laspeyres index formula. 4 It is recognized that the use of a standard service life for highly aggregated asset groups is rather unsatisfactory given the wide variety and expected change in the profile of these assets, especially machinery and equipment, over time. In addition, the assumption of a simultaneous retirement function is highly inappropriate as it is not likely for all assets of a particular vintage to be retired from the stock once they reach the average service life for that asset type. 5 To remedy the above deficiencies, we have been conducting an ongoing review to improve the quality of our capital stock estimates. The review encompasses: the use of distinct average service lives for more disaggregated asset classes; the use of more plausible retirement patterns; the feasibility of using other types of depreciation patterns in the measurement of capital stock. The progress of our review so far is encapsulated in the following simulation studies. Simulation Study 1 (Single-life versus Separate-lives computation) 6 The first study examined the impact on the level and growth rate of capital stock arising from the use of separate, rather than single, average asset service lives. For simplicity, we computed alternative measures of the gross capital stock of private sector machinery and equipment using the following asset service life assumptions and the simultaneous retirement pattern: 2

3 (a) present single average service life of 15 years for the entire category of machinery and equipment; (b) separate average service lives for the different types of machinery and equipment; (c) weighted average service life for the entire category of machinery and equipment. For the purpose of exposition, the gross capital stock estimates computed using the single service life assumption in (a) will be referred to as single-life estimates; those computed using separately assigned service lives in (b) are labelled separate-lives estimates; while those obtained using the weighted average service life in (c) are described as weighted single-life estimates. 7 The single-life estimates represent the present measure of our capital stock series. To determine the service lives in (b), we first did a study to determine the machinery asset classes for which past estimates of gross fixed capital formation (GFCF) are available on a consistent and systematic basis so that the PIM can be applied to these asset classes. Based on this criterion, we managed to decompose the estimates of private sector GFCF in machinery and equipment into the 17 different types shown in Table 1, which also presents the average service life of each asset class. The average service life of each asset type was obtained as the simple average of the service lives for broadly similar asset classes from the following sources: Inland Revenue of Singapore Authority (IRAS); US Bureau of Economic Analysis (BEA); Statistics Canada; Statistics Netherlands. As can be observed from the table, most of the asset classes have an average service life which is less than the present 15 years used in (a). Lastly, the weighted average service life in (c) was computed by taking the weighted average of the service lives for the different types of machinery in (b), using the 1990 estimates of GFCF in these assets as weights. The weighted average service life is 12 years, which is less than the 15 years in (a). 3

4 Table 1 Average Service Lives of Machinery and Equipment in the Private Sector Average service life Asset type (years) Power generating machinery 18 Agricultural & Food processing machinery 11 Office, computing & accounting machinery 8 Metalworking machinery 12 Textile, leather working & printing machinery 16 Construction machinery 11 Heating and cooling machinery 11 Pumps and centrifuges 11 Mechanical handling machinery 11 Miscellaneous non-electrical machinery 16 Electric machinery 18 Telecommunications equipment 12 Scientific & medical equipment 12 Tools 12 Photographic & cinematographic equipment 11 Metres and counters Miscellaneous equipment Private Sector Machinery and equipment (weighted average) 12 8 The impact on the level of gross capital stock arising from the use of the above service lives is shown in Chart 1, while Chart 2 shows the impact on the growth of gross capital stock at 1990 market prices. In addition, Tables 2A and 2B show the relative differences arising from a bilateral comparison of the three series for selected years. Table 2A Relative Differences in Stock Levels with respect to Single-Life Estimates Relative differences in Stock Levels with respect to Single-Life Estimates (percent) Year "Weighted Single-Life" Estimates "Separate-Lives Estimates

5 Table 2B Relative Differences in Stock Levels with respect to Separate-Lives Estimates Relative differences in Stock Levels with respect to Separate-Lives Estimates (percent) Year "Weighted Single-Life" Estimates The level of single-life estimates is consistently higher than the weighted single-life method s level (Chart 1). The gap between the two series has widened with the passage of time. In particular, the relative difference has mostly exceeded 10 percent in the nineties (Table 2A). This result of gross capital stock changing in the same direction as changes to asset service lives is generally in agreement with those obtained by Koumanakos (1998) for the gross capital stock of the Canadian manufacturing industry and Meinen, Verbiest and de Wolf (1998) for the stocks of machinery in the Dutch chemical industry and is not entirely unexpected since implicitly, all the asset classes in the weighted single-life method have average service lives (12 years) which are considerably less than those in the single-life method (15 years). The higher average service life used in the single-life method increases the length of time an asset stays in the stock and hence its level. 10 What is also noteworthy is the behaviour of the separate-lives series relative to the weighted single-life series and that of the single-life series versus the separate-lives series. The level of single-life estimates is consistently higher than the separate-lives estimates (Chart 1 and Table 2A). This behaviour is, however, not observed in the bilateral comparison of the separate-lives and weighted single-life series (Chart 1 and Table 2B). Instead, the level of separate-lives estimates is consistently higher than the weighted single-life estimates up until 1992, but from 1993 onwards, we observe the level of the latter overtaking the former. The difference in 5

6 outcomes could be because unlike the earlier bilateral comparison, average service lives for all asset types are changed in different directions in the latter two comparisons. Hence, the extent of the changes in service lives of the affected asset classes as well as the relative importance of these asset classes could also have an impact on the overall level of capital stock. 11 To elaborate, the assumed average service life of 15 years for all asset types in the single-life method is considerably higher than the average service lives of 13 out of the 17 asset classes in the separate-lives method (Table 1). Only four asset types in the latter have average service lives which exceed 15 years, two of them only slightly. Apparently, the higher levels of gross capital stock of these four asset groups arising from the application of longer service lives are inadequate to offset the lower levels of capital stock of the other 13 asset groups due to the use of much shorter service lives. This causes the level of the aggregate single-life estimates to be consistently higher than the separate-lives estimates. 12 In contrast, the assumed average service life of 12 years for all asset groups in the weighted single-life method is less than the average service lives of four out of the 17 asset classes in the separate-lives method. A quite significant 12 asset classes in the latter have average service lives of 10 to 12 years, which are equal or slightly less than the service life of 12 years in the former. Only one asset class (office, computing and accounting machinery, or OCAM) in the separate-lives method has an average service life (8 years), which is considerably less than the assumed 12 years in the weighted singlelife method. Thus, the lower level of the separate-lives estimates relative to the weighted single-life estimates post-1992 could probably have been caused by the relatively much lower level of OCAM in the former. This, in turn, reflects the rising intertemporal importance of OCAM in investment. 13 The use of the three methods has an unpredictable effect on growth rates (Chart 2). This rather unsystematic outcome could probably be due to the uneven revisions in growth rates of the various machinery asset classes as a result of the changes in their respective service lives. Upward revisions to the growth rates of relatively more of the asset classes, especially the more important ones, could have caused the growth rate of one series to be higher than the other. Conversely, downward revisions to the growth rates of the more important asset classes could have resulted in the opposite effect. 6

7 Simulation Study 2 (How does chaining affect the growth of capital stock?) 14 The decomposition of private sector GFCF in machinery and equipment into the above asset classes with their own average service lives also gave us the opportunity to conduct an experiment to assess the impact on the growth of capital stock arising from the use of chain volume indexes. Using the results for the separate-lives method in the first simulation study, we computed alternative series for gross capital stock of machinery and equipment in the private sector using different index number formulae. The results of this experiment are presented in Chart Chaining results in growth rates which are mostly lower than those obtained using the present fixed-weighted Laspeyres index formula. The results are mostly consistent with the predictions of index number theory. The reduction in growth rates is especially considerable in recent years, ie the further the series are from the base year (1990) used for the fixed-weighted Laspeyres volume index series. It is also worth noting that these results were generated using only 17 machinery asset classes, many of which are not entirely homogeneous, so that only the upper-level substitution bias has been removed. Assuming we could obtain consistent historical estimates of finer asset classes for machinery and equipment in future, chaining would be expected to produce a further reduction in growth rates. Simulation Study 3 (Alternative Retirement Patterns) 16 Our third study investigated the sensitivity of capital stock to the use of alternative retirement functions in the PIM. The following types of retirement distributions were used in the simulation: linear; delayed linear; bell shaped (normally distributed); Winfrey S3; simultaneous. 17 To make the analysis more manageable, we confined our study to computing alternative estimates of the gross capital stock of private sector metalworking machinery. For consistency, an average service live of 12 years 7

8 was assumed in all the retirement patterns. For the delayed linear, normallydistributed and Winfrey S3 retirement patterns, assets were assumed to be retired over the period from 50 percent to 150 percent of their average service life, while for the linear retirement pattern, assets were assumed to be discarded at the same rate each year from the start of installation until twice the average service life. 18 Chart 4 shows the level of gross capital stock for private sector metalworking machinery at 1990 market prices, while Table 3 shows the relative differences of gross capital stock calculated using the various retirement patterns for selected years. Table 3 Gross capital stock of private sector metalworking machinery at 1990 market prices Relative differences in Stock Levels with respect to simultaneous retirement (percent) Year Linear Delayed linear Normally distributed Winfrey S The Winfrey and normally distributed retirement patterns produce very similar levels of capital stock. This is because both are essentially bell-shaped in nature. 20 The level of capital stock computed using the simultaneous retirement pattern is mostly higher than those computed using the other retirement patterns, but there are occasions, especially in the mid-nineties, where its level is lower than those produced by some of the other retirement patterns. This could be due to the generally falling GFCF found in past vintages of the asset. 21 The linear retirement pattern tends to produce the lowest level of gross capital stock amongst all the retirement patterns. This could reflect the fact that retirements in this method begin much earlier than in the other methods. 8

9 Simulation Study 4 (Alternative Depreciation Patterns) 22 Our fourth and last study examined the sensitivity of capital stock to the use of alternative depreciation functions in the PIM. The following types of depreciation functions were used in the simulation: straight-line; sum-of-digits; finite geometric (à la Statistics Canada); infinite geometric (à la BEA); geometric cum straight-line. 23 For simplicity, we restricted our study to computing alternative estimates of the net capital stock of private sector metalworking machinery. For consistency, an assumed average service live of 12 years was used in all the depreciation patterns. The derivation of the finite geometric depreciation rates followed the method used by Statistics Canada as outlined in the OECD s draft manual on capital stock. For the geometric cum straight-line depreciation method, geometric depreciation is first employed. Straight-line depreciation is utilised when it is greater than the corresponding declining balance calculation. This ensures depreciation is not infinite. For all the three geometric depreciation patterns, we used the declining balance rate used by the US BEA for metalworking machinery. 24 Chart 5 presents the level of net capital stock for private sector metalworking machinery at 1990 market prices, while Table 4 shows the relative differences of the various depreciation patterns with respect to the straight-line depreciation pattern for selected years. 9

10 Table 4 Net capital stock of private sector metalworking machinery at 1990 market prices Relative differences in Stock Levels with respect to straight-line depreciation (percent) Geometric cum Year Sum-of-digits Finite geometric Infinite geometric straight-line As expected, the level of net capital stock generated using infinite geometric depreciation is higher than those obtained using finite geometric and geometric cum straight-line depreciation methods. 26 Straight-line depreciation results in the highest level of net capital stock among the five depreciation methods. This outcome is expected since the other depreciation methods possess a depreciation pattern which is more accelerated than the straight-line one. This accelerated nature of geometric depreciation also probably explains why the level of net capital stock obtained using infinite geometric depreciation turns out to be lower than the straight-line depreciation method s level. Another possible contributory factor is the increasingly insignificant contribution of the earlier vintages over time. 27 On the other hand, finite depreciation results in the lowest level of net capital stock amongst the five types of depreciation methods. The difference between the capital stock derived using this method and that computed using straight-line depreciation has widened to over 40 percent in recent years (Table 4). The adjustment technique utilised in finite depreciation to ensure the full initial value of an asset is completely exhausted when its reaches the end of its average service life could have resulted in a much higher depreciation rate and hence the very low level of net capital stock. 10

11 Conclusion 28 This paper has described four simulation studies conducted by DOS as part of our on-going efforts to improve the PIM used to compute the capital stock estimates for the Singapore economy. The results of our studies are mostly in agreement with the predictions of theory as well as the findings of other related studies. 29 We recognize that the task of computing capital stock is a convoluted one fraught with numerous difficulties. The difficulties we face in striving to improve our capital stock estimates are similar to those faced by many statistical agencies elsewhere. For instance, we do not have any information on how the value of fixed assets in Singapore responds to ageing in practice. 30 One way for us to overcome our difficulties is to refer to the practices and experiences of the advanced statistical agencies. In this respect, we intend to conduct further sensitivity studies for the other types of assets by adapting the methods used by these agencies in the computation of their capital stock estimates. Benson Sim and Teck-Wong Soon Singapore Department of Statistics October 1999 References Commission of the European Communities, International Monetary Fund, Organisation for Economic Co-operation and Development, United Nations, World Bank (1993), System of National Accounts 1993, Brussels/Luxembourg, New York, Paris, Washington, D.C. Fraumeni, Barbara M (1997), The Measurement of Depreciation in the US National Income and Product Accounts, Survey of Current Business, Vol 77, July, p

12 Katz, Arnold J, and Shelby W Herman (1997), Improved Estimates of Fixed Reproducible Tangible Wealth, , Survey of Current Business, Vol 77, May, p Koumanakos, Peter (1998), Impact of Service Lives on Growth Rates of the Gross Capital Stock and Impact of changes in Depreciation Assumptions on Growth Rates of Net Capital Stock, Paper Presented at Second Meeting of the Canberra Group on Capital Stock Statistics, Paris, France, 29 September-1 October. Meinen, Gerhard, Piet Verbiest and Peter-Paul de Wolf (1998), Perpetual Inventory Method: Service Lives, Discard Patterns and Depreciation Methods, Statistics Netherlands. Organisation for Economic Co-operation and Development (1993), Methods Used by OECD Countries to Measure Stocks of Fixed Capital, National Accounts: Sources and Methods, No 2, Paris. 12

13 S$Million Single-Life Separate-Lives Chart 1 - Level of Gross Capital Stock of Private Sector Machinery and Equipment at 1990 market prices Weighted Single-Life

14 35 30 Percent Chart 2 - Percentage change in Gross Capital Stock of Private Sector Machinery and Equipment at 1990 market prices Single-Life Separate-Lives Weighted Single-Life

15 Percent Fixed-Weighted Laspeyres Index Chain Laspeyres Index Chain Paasche Index Chain Fisher Index Chart 3 - Comparing Growth rates of Fixed-Weighted and Chain Indexes for Gross Capital Stock of Private Sector Machinery and Equipment

16 S$Million Simultaneous Linear Delayed linear Normal Winfrey S3 Chart 4 - Level of Gross Capital Stock of Private Sector Metalworking Machinery at 1990 market prices

17 S$Million Straight-line Sum-of-digits Finite Geometric Infinite Geometric Geometric cum straight-line Chart 5 - Level of Net Capital Stock of Private Sector Metalworking Machinery at 1990 market prices