New Estimates of Government Net Capital Stocks for 22 OECD Countries 1960-2001
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: kamps@ifw.uni-kiel.de

The issue of whether government capital is productive has received a great deal of recent attention. Yet empirical analyses of public capital productivity have generally been limited to the official capital stock estimates available in a small sample of countries. Alternatively, many researchers have investigated the output effects of public investment-recognizing that investment may be a poor proxy for the corresponding capital stock. This paper attempts to overcome the data shortage by providing internationally comparable capital stock estimates for 22 Organization for Economic Cooperation and Development (OECD) countries.

Abstract

The issue of whether government capital is productive has received a great deal of recent attention. Yet empirical analyses of public capital productivity have generally been limited to the official capital stock estimates available in a small sample of countries. Alternatively, many researchers have investigated the output effects of public investment-recognizing that investment may be a poor proxy for the corresponding capital stock. This paper attempts to overcome the data shortage by providing internationally comparable capital stock estimates for 22 Organization for Economic Cooperation and Development (OECD) countries.

I. Introduction

The issue of whether government capital is productive has received a great deal of recent attention. In his seminal contributions, Aschauer (1989a,b) found large positive output effects of government capital in the United States. His results further suggested that government capital was even more productive than private capital. However, the large body of empirical literature that developed after Aschauer’s early studies challenged these results. This literature—surveyed, for example, in Gramlich (1994), Sturm, de Haan, and Kuper (1998), and Seitz (2001)—concludes that although there is evidence for positive output effects of government capital, the magnitude of these effects is in general much smaller than Aschauer reported.

The lack of public capital stock data for a large number of Organization for Economic Cooperation and Development (OECD) member countries has forced most empirical studies to focus on the United States. Few studies have investigated the productivity of government capital for other OECD countries: examples are Ford and Poret (1991), as well as Evans and Karras (1994). Both groups of authors drew their data from earlier volumes of OECD (1997) that assembled capital stock series for 12 countries over the period 1970–1996, provided directly by the national authorities. However, these data were not internationally comparable because estimation methods differed widely across countries.2 This was one of the reasons why the OECD suspended the publication of capital stock series after 1997 and cofounded the Canberra Group on Capital Stock Statistics whose activities resulted in the publication of a manual on the measurement of capital (OECD, 2001a). Thus far, only a few countries have adjusted their estimation methods; internationally comparable capital stock data are still not available.

In spite of these constraints, the analysis of public capital productivity has continued to be an active area of research. Most recent studies use an approach based on vector autoregressive (VAR) models (for example, Mittnik and Neumann, 2001; and Voss, 2002) that—unlike the earlier production function and cost function approaches—do not impose causal links among the variables under investigation. The main disadvantage of this approach is that it generally requires large data samples for conventional lag lengths. For this reason, most researchers employing the VAR approach have used data on public investment instead of data on the public capital stock. This choice has been dictated not only by the lack of capital stock data for a large number of countries, but also by the fact that public investment data are usually available each quarter, whereas public capital stock data are available only every year. One drawback of this choice is the implicit assumption that the effects of public investment are independent of the level of the corresponding capital stock. Economic theory suggests that this assumption is dubious. According to the law of diminishing returns, an increment to the public capital stock (that is, public investment corrected for fixed capital consumption) would have a small/large output effect if the capital stock in the previous period were large/small. There is indeed evidence for a fast decline in the marginal productivity of public capital (Demetriades and Mamuneas, 2000, p. 702). This paper provides internationally comparable annual capital stock estimates for 22 OECD countries for the period 1960–2001, calculated using the perpetual inventory method based on a geometric depreciation pattern.3 Capital stock data are estimated for three categories of investment: (1) private nonresidential gross fixed capital formation, (2) private residential gross fixed capital formation, and (3) government gross fixed capital formation. A sensitivity analysis explores the robustness of the capital stock estimates by varying the main estimation assumptions for two reference countries, the United States and Canada, for which public capital stock estimates from official sources are available. The results of this sensitivity analysis suggest that the benchmark capital stock estimates are robust. Finally, the paper reports and compares estimation results for the production function approach, using three alternative measures of the public capital stock: (1) author’s own estimates; (2) estimates from national authorities; and (3) estimates from OECD (1997). The regression results confirm previous results in the literature based on the production function approach and show that the elasticity of output with respect to public capital is positive and statistically significant, but quite large for most countries. According to estimates based on a simple panel data model, the elasticity of output with respect to public capital is on average 0.2 in OECD countries.

The remainder of this paper is organized as follows: Section II describes the investment data used in the estimation of capital stocks; Section III describes the estimation methodology; Section IV presents the estimation results; Section V explores the robustness of the capital stock estimates by varying the main estimation assumptions; Section VI estimates elasticities of output with respect to public capital according to the production function approach for alternative capital stock measures; and Section VII concludes.

II. Data

The basic ingredient for the estimation of capital stocks is historical data on gross investment. These data are taken from the June 2002 version of the OECD Analytical Database.4 The estimation is carried out for the following 22 OECD countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.5 The series retrieved from this database expressed in constant prices and in national currencies are (OECD code in parentheses) the total gross fixed capital formation (ITV), total private gross fixed capital formation (IPV), private nonresidential gross fixed capital formation (IBV), private residential gross fixed capital formation (IHV) and government gross fixed capital formation (IGV).

This paper uses public investment data from the OECD Analytical Database because apart from providing long-time series for a large panel of countries, the data are categorized by institutional sector and are more comparable internationally than data from national sources. Table 1 gives details about the institutional coverage of the public investment series. This information is important because the definition of the public sector underlying the investment series varies not only across sources for a given country, but also across countries for a given source. Three definitions regarding the coverage of public investment are used by the countries under investigation:6 (1) public investment of the general government; (2) public investment of the nonfinancial public sector (general government plus nonfinancial public enterprises (NFPEs)); and (3) investment carried out by economic units engaged in activities labeled “Public administration and defense services, compulsory social security services” (narrow definition) and “Public administration, educational services, and health care and social assistance” (broad definition) according to the International Standard Industrial Classification (ISIC). Whereas the first two definitions categorize by institutional sector, the latter two definitions categorize by type of economic activity. The ISIC category “Public administration, educational services, and health care and social assistance” comes close to the definition of the nonfinancial public sector, but it also includes private spending on education, which may, for instance, be important in some countries such as Canada.

Table 1.

Coverage of Government Gross Fixed Capital Formation

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Notes: The general government sector comprises the central, local, and state government subsectors including social security funds. The public sector comprises the general government and nonfinancial public corporations. See IMF (2001) for details. The column “OECD ADB” refers to the OECD Analytical Database, which provides the investment series used in the calculation of author’s own capital stock estimates. The column “National data” refers to government capital stock data available from national authorities (see Appendix for details) and the column “OECD FSFC” refers to the OECD (1997) publication Flows and Stocks of Fixed Capital 1970–1996. In Section III, the author’s own capital stock estimates will be compared to data from these sources.

Public administration and defense services, compulsory social security services (ISIC category).

Public administration, educational services, and health care and social assistance (ISIC category).

Public administration, educational services, and health care and social assistance provided by the government (no private provision included) plus investment in infrastructure provided by public corporations.

Producers of government services. The coverage of “PGS” is somewhat smaller than that of the general government since the latter also includes departmental enterprises (Florio, 2001, p. 185). Moreover, capital stocks in OECD (1997) were based on classifications of government activities according to the 1968 System of National Accounts whereas recent national data are based on classifications according to the 1993 System of National Accounts.

Figure 1 displays the evolution of the public investment–GDP ratio for the earlier-mentioned countries over the period 1960–2001. The subplots of Figure 1 for the individual countries show the public investment–GDP ratio for the data from the OECD Analytical Database as well as—if available—for data from national sources7 and from OECD (1997). The public investment–GDP ratio has in general declined over the sample period. In some countries such as Austria or Ireland, the decline has been particularly pronounced. Notable exceptions to the general pattern include Greece, Portugal, and Spain where public investment–GDP ratios have increased considerably since accession to the European Community in the 1980s. A comparison of the data from different sources reveals that the ratios calculated for data from OECD Analytical Database coincide with data from national sources, except for Belgium, Canada, Italy, Japan, and Spain. The differences in the data from these two sources and those from the OECD (1997) are quite large in most of the cases, partly reflecting that OECD (1997) data are based on the 1968 System of National Accounts, while the other two sources rely on the 1993 System of National Accounts.8 To a certain extent, the difference is also due to data revisions since the publication of OECD (1997). However, the most important reason for the discrepancy in the data from alternative sources seems to be different coverage of public investment.

Figure 1.
Figure 1.

Real Government Gross Fixed Capital Formation in 22 OECD Countries 1960–2001

(As a percentage of real GDP)

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Sources: Series labeled “OECD ADB” are taken from the OECD Analytical Database, Version June 2002. Series labeled “National source” are estimates from national authorities. Series labeled “OECD FSFC” are calculated as follows: the gross investment series are taken from the OECD (1997), Flows and Stocks of Fixed Capital 1970–96, and divided by GDP series taken from the OECD (1998), National Accounts Vol. 1, Main Aggregates, 1960–96.
Figure 1 (continued).
Figure 1 (continued).

Real Government Gross Fixed Capital Formation in 22 OECD Countries

(As a percentage of real GDP)

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Sources: Series labeled “OECD ADB” are taken from the OECD Analytical Database, Version June 2002. Series labeled “National source” are estimates from national authorities. Series labeled “OECD FSFC” are calculated as follows: the gross investment series are taken from the OECD (1997), Flows and Stocks of Fixed Capital 1970–96, and divided by GDP series taken from the OECD (1998), National Accounts Vol. 1, Main Aggregates, 1960–96.

III. Methodology

The methodology applied here in the estimation of capital stock data draws in large part on OECD (2001a) and on the U.S. Bureau of Economic Analysis (1999). The estimation exercise is comparable to that performed by Jacob, Sharma, and Grabowski (1997), who estimate capital stocks by industrial activity according to the ISIC. Here, however, the aim is to obtain estimates by institutional sector—with a special focus on the public sector—rather than by industrial activity. Other precursors of the present study include Berndt and Hansson (1991), who estimate the public capital stock for Sweden; Sturm and de Haan (1995), who estimate the public capital stock for the Netherlands; as well as Boskin, Robinson, and Huber (1987), Holtz-Eakin (1993), and Munnell (1990), who estimate the capital stock for local and state governments in the United States. This paper employs the same estimation approach as those studies: the perpetual inventory method. The net capital stock is estimated for the three subcategories of gross investment available from the OECD Analytical Database: (1) private nonresidential gross fixed capital formation; (2) private residential gross fixed capital formation; and (3) government gross fixed capital formation.9

The basic idea of the perpetual inventory method is that the net capital stock at the beginning of the following period, Kt+1, can be expressed as a function of the net capital stock at the beginning of the current period, Kt, of gross investment in the current period, It, and of depreciation10 in the current period, Dt:

Kt+1=Kt+ItDt.(1)

If one further assumes geometric depreciation (that is, the capital stock depreciates at a constant rate, δ) then the capital accumulation equation can be rewritten as

Kt+1=(1δ)Kt+It.(2)

The method is called “perpetual” because all assets are forever part of the inventory of capital stocks. Of course, the quantity of services provided by an asset declines as it ages, but it never reaches zero. This can be seen by repeatedly substituting equation (2) for the capital stock at the beginning of period t:

Kt+1=i=0(1δ)iIti.(3)

This expression shows that the capital stock at the beginning of period t +1 is a weighted sum of past investment where the weights are a decreasing function of the distance between the current period and the investment period. In practice, an infinite number of past investment flows is not available so that equation (3) is replaced by the following expression:

Kt+1=(1δ)tK1+i=0t1(1δ)iIti,(4)

where K1 is the initial capital stock at the beginning of period 1.

According to equation (4), the application of the perpetual inventory method requires the following inputs. First, a time series on gross investment flows is needed. The estimations in this paper rely on investment data from the OECD Analytical Database described in Section II. Second, the estimations necessitate an initial capital stock, in our case the capital stock at the beginning of 1960. Third, an assumption on the size and the time profile of the depreciation has to be made. Finally, a depreciation method has to be chosen. This study relies on geometric depreciation.

There is no official information on the magnitude of the initial capital stock for any country except the United States. This paper follows an approach similar to that applied by Jacob, Sharma, and Grabowski (1997, p. 567) in order to estimate the initial capital stock. For that purpose, an artificial investment series for the period 1860–1959 is constructed for each country by assuming that investment increased by 4 percent a year during this period, finally reaching its observed level in 1960.11 The rationale for this assumption is that total gross investment in the 22 OECD countries under consideration grew by 4 percent a year on average during the period 1960–2001. It is, of course, highly improbable that investment in the earlier period grew at the same rate as during the period 1960–2001, and that investment growth was the same for all countries. However, as historical information—especially on public investment—is not available for most of the countries under consideration, this study opts for an equal treatment of all countries.12 The results of a sensitivity analysis reported in Section V suggest that the assumption on the initial capital stock does not affect the dynamics of the resulting capital stock series to a large extent. Also, the importance of the initial capital stock on the level of the capital stock series fades over time. Its contribution to the level of the capital stock at the end of the sample is less than 10 percent for the average OECD country.

This assumption implies that investment and the capital stock grew smoothly over the period 1860–1960, a simplification that needs to be justified, especially since some countries in the sample experienced severe damage during World War II.13 The question arises whether the effects of war damage on the capital stock were persistent enough to affect our estimate of the initial capital stock at the beginning of 1960. There are at least two reasons why war damage might have had little effect by 1960. First, the countries that experienced the largest war damage grew much faster after World War II than the countries that suffered little or no war damage.14 Thus, real GDP in countries subject to severe war damage might well have returned to its long-run trend by 1960.15 Second, the strong rise in GDP after World War II in these countries was accompanied by fast increases in investment and in the capital stock.16 As a consequence, the capital stock might also have returned to its long-run trend by 1960.17 All in all, there are hints that the effects of war damage on the capital stock in countries that were most severely affected had disappeared by 1960, the starting year for our capital stock estimates. The strong growth performance in the quarter century following World War II, often referred to as “growth miracle,” was distributed unevenly among OECD countries. As Broadberry (1988) states, the countries most hit by war damage like Japan and Germany grew much faster than countries that were “hardly affected by war damage, such as the United Kingdom and the United States.” The evidence presented in Maddison (1982, p. 55) and Eichengreen and Ritschl (1998, p. 32) further suggests that by 1960 real GDP in OECD countries was close to the level implied by its long-run growth path. Moreover, the analysis in Eichengreen and Ritschl (1998, p. 8) shows that the strong growth performance in Germany was not impaired by a lack of capital due to war damage. Based on these considerations we choose not to correct the capital stock estimates at the beginning of 1960 for war damage.

The next assumption in the estimation relates to the size and the time profile of the depreciation rate. In this study it is assumed that the depreciation rate is time-varying for the public capital stock and the private nonresidential capital stock and constant for the private residential capital stock.18 This assumption allows taking into account the empirically observed pattern of aggregate depreciation rates.19 Figure 2 shows the implicit scrapping rate for the real government net capital stock, the real private nonresidential net capital stock, and the real private residential capital stock in the United States for the period 1960–2000. The implicit scrapping rate is calculated as the quotient of depreciation in period t and the net capital stock at the beginning of period t (data from the U.S. Bureau of Economic Analysis):

Figure 2.
Figure 2.

Implicit Scrapping Rates for the United States 1960–2000

(In percent)

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Sources: U.S. Bureau of Economic Analysis (BEA) and author’s calculations.
st=DtKt100.(5)

Figure 2 reveals that the implicit scrapping rates differ considerably across the three types of capital. The implicit scrapping rate is highest for private nonresidential capital and lowest for private residential capital. Whereas the scrapping rate of private residential capital has remained roughly constant over the period 1960–2000, the scrapping rates of private nonresidential capital and of government capital have tended to rise over time. The increase is especially pronounced in the case of the private nonresidential capital stock, its scrapping rate having risen from about 4½ percent in 1960 to about 9½ percent in 2000. Two developments may partly explain the rise in the scrapping rate: First, it may reflect an increasing weight of assets with relatively short asset lives; second, it may also reflect to a certain degree a shortening of asset lives. Both developments are characteristic of ICT-related assets that are part of the private nonresidential capital stock and—to a lesser extent—of the government capital stock. A similar pattern for implicit scrapping rates can be observed for other countries. For example, Canadian and Australian data reveal that implicit scrapping rates of private nonresidential and government capital have also risen since the 1960s.

Based on this evidence, this paper makes the following assumptions about the time profile of the depreciation rates: For the period 1860 to 1960, the depreciation rate is assumed to be 2½ percent for government assets, 4¼ percent for private nonresidential assets, and 1½ percent for residential assets. For the period 1960–2001, it is assumed gradually to increase from 2½ percent to 4 percent for government assets and from 4¼ percent to 8½ percent for private nonresidential assets,20 and it is assumed to be a constant 1½ percent for private residential assets (see Figure 2). Equation (6) formalizes the time profile of the depreciation rates:

δtj=δminj((δmaxjδminj)141)t2001+41for all t=1960,1961,,2001,(6)

where δminj is the depreciation rate of asset type j in 1960 and δmaxj is its depreciation rate in 2001.

Finally, the real net capital stock at the beginning of period t + 1 for investment category j can be expressed (see also Bureau of Economic Analysis, 1999, p. M-5) as

Kt+1j=i=1860t1[k=i+1t(1δkj)] (1δij2)Iij+(1δtj2)Itj=(1δtj)Ktj+(1δtj2)Itjfor all t=1860,1861,2001.(7)

Note that the capital stock at the beginning of the initial period, K1860, is set equal to zero. Equation (7) differs from equation (4) in two respects in order to increase the realism of the estimates. First, as discussed earlier, the equation incorporates time-varying depreciation rates. Second, new investment is assumed to be placed in service at midyear instead of at the end of the year as implied by equation (4). Investment typically occurs throughout the year, not only at the end of the year. Equation (7), in conjunction with the assumptions about the depreciation patterns, serves to estimate net capital stocks for government assets, private nonresidential and private residential assets.

An attractive feature of the approach followed in this study is that the estimated public net capital stock is equivalent to the so-called productive capital stock (OECD (2001b, p. 62–63). The latter capital stock is the appropriate measure of capital input for productivity analyses because it reflects the flows of services provided by capital more appropriately than either the net or the gross capital stock. Only for a homogenous asset and geometric depreciation does the distinction between the productive capital stock and the net capital stock vanish.21 For lack of disaggregated data, the present study treats public investment as a homogenous asset.

To sum up, the application of the perpetual inventory method requires three important assumptions. First, an initial capital stock has to be constructed, here for the beginning of 1960. This study uses artificial investment series for the period 1860–1959 as an input for the estimation of the initial capital stock. Second, an assumption on the level and the time profile of the depreciation rate has to be made. This paper assumes that the depreciation rate is time-varying and different across the three types of investment considered, but the same for all countries. Third, a depreciation method has to be chosen. This study relies on geometric depreciation. Section V analyzes in detail the importance of each of these assumptions for the resulting capital stock estimates.

IV. Capital Stock Estimates for 22 OECD Countries 1960–2001

Figure 3 displays the evolution of the ratio of the public net capital stock and GDP, both at 1995 prices, for the 22 OECD countries over the period 1960–2001.22 The graphs for the individual countries plot not only the author’s own estimates of the public capital stock, but also—where available—estimates from national authorities and from OECD (1997). For seven countries there is no benchmark against which the author’s own estimates could be assessed.23 The same holds for Greece, in view of the very low capital stock estimate (reported by OECD, 1997) that is due to a narrow definition of public investment. For those countries where alternative estimates are available, the general picture is that—in most cases—the dynamics of the author’s own estimates resemble those of the alternative estimates. In some cases, the level of the public capital–GDP ratios is also similar, but in general there are significant differences. This, in part, reflects the fact that the initial level of the author’s own estimates depends on the artificial investment series assumed for the period 1860–1959. Yet, the differences are also due to two other reasons: (1) for some countries the investment series shown in Figure 1 differ sharply from each other (Greece); and (2) there is a wide variety of methods applied by national authorities in the construction of capital stock estimates. An attractive feature of the author’s own estimates is that they rely on the same methodology and homogenous investment data across countries, a condition that is not satisfied for the alternative estimates.

Figure 3.
Figure 3.

Real Government Net Capital Stock in 22 OECD Countries 1960–2001

(As a percentage of real GDP)

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Notes: Series labeled “National source” are estimates from national authorities. Series labeled “OECD FSFC” are calculated as follows: the capital stock series are taken from the OECD (1997), Flows and Stocks of Fixed Capital 1970-1996, and divided by GDP series taken from the OECD (1998), National Accounts Vol. 1, Main Aggregates, 1960–1996.
Figure 3 (continued).
Figure 3 (continued).

Real Government Net Capital Stock in 22 OECD Countries 1960–2001

(As a percentage of real GDP)

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Sources: Series labeled “National source” are estimates from national authorities. Series labeled “OECD FSFC” are calculated as follows: the capital stock series are taken from the OECD (1997), Flows and Stocks of Fixed Capital 1970–96, and divided by GDP series taken from the OECD (1998), National Accounts Vol. 1, Main Aggregates, 1960–96.

Table 2 displays the value of the public capital–GDP ratio for three years of reference: 1980, 1990, and 2000. The average ratio for the 22 OECD countries has declined by 6 percentage points over the period 1980–2000. Public capital as a share of GDP has declined in 13 countries since the early 1980s; it has slightly increased in four countries while it has strongly risen in Greece, Japan, Portugal, Spain, and Switzerland. It does not come as a surprise that Greece, Portugal, and Spain figure among this group, because these countries are known to have made substantial efforts to improve their infrastructure after joining the European Community. Furthermore, it is well known that during the 1990s the Japanese government repeatedly attempted (in vain) to reinvigorate the sluggish economy with the help of large spending programs focusing on construction. According to the estimates, in 2000 Japan had by far the largest public capital–GDP ratio among the OECD countries considered in this study, while Ireland had the lowest. The large decline in the public capital–GDP ratio in Ireland during the 1990s mirrors the strong fall of public investment as a share of GDP during this period. Fitz Gerald and others (1999) state that the Irish government views the lack of infrastructure as one of the major impediments to growth.

Table 2.

Government Net Capital Stock in 22 OECD Countries

(As a percentage of GDP, both at 1995 prices)

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Source: Author’s own estimates and calculations.

The columns labeled “Ratio” give the ratio of the government capital stock and GDP (in percent).

The columns labeled “Rank” give the ranking of the countries according to the size of their capital to GDP ratio, the country with the highest ratio ranking first.

The column labeled “Reliability” gives the contribution of government investment in the period 1960–1999 to the net capital stock at the beginning of 2000 (in percent). The difference between 100 percent and this figure reflects the contribution of government investment in the period 1860–1959, for which official data are not available.

Unweighted average.

The last column of Table 2 shows the contribution of government investment in the period 1960–2000 to the government net capital stock in the year 2000. As explained in the previous section, assumed investment data for the period 1860–1959 are used in order to estimate the initial capital stock at the beginning of the year 1960. The contribution of the assumed investment data to the initial capital stock is 100 percent, but their influence gradually fades and is quite small at the end of the sample. The capital stock estimates for the year 2000 are largely unaffected by the assumption on investment during the period 1860–1959, for which no data from official sources are available. Investment from 1960 onwards contributes an average 92 percent to the net capital stock in the year 2000, implying that the average contribution of the assumed investment data is only 8 percent.24

Another way to compare the government capital stock across countries is to look at its absolute value for each person. For an international comparison of real capital stock, three conditions have to be met (OECD 2002a, page 8). First, the definition of the capital stock must be the same. This condition is fulfilled since for all countries the investment data used in the capital stock estimations are compiled according to the 1993 System of National Accounts. Second, the capital stock must be expressed in the same currency and third, the price level at which the capital stock is valued must be the same. The second and third conditions are not fulfilled since the capital stock estimates are expressed in national currency and valued at the national price. These data can be converted to a common currency and revalued at a common set of prices using so-called purchasing power parities (PPPs). Unfortunately, PPPs for the public capital stock are not available. Instead, a proxy for this measure has to be used. The OECD (2002a) provides PPPs for GDP and for total gross fixed capital formation. In the following PPPs for GDP for 2000 from the OECD (2002b) are used in order to convert the public capital stock estimates to U.S. dollars.25

Table 3 gives the real per capita public net capital stock expressed at 2000 PPPs for GDP in U.S. dollars for the years 1980, 1990, and 2000. The average capital stock for each person for the 22 OECD countries has increased by 30.9 percent over the period 1980–2000 (that is, by 1.4 percent per year). This growth rate has been lower than that of real GDP, implying that the public capital–GDP ratio has declined on average during this period in the OECD, as shown in Table 2. A comparison across countries reveals that the public capital stock per head is by far the highest in Japan, exceeding the average by more than 160 percent in the year 2000. As regards the ranking of the countries, the United States ranks considerably higher than in Table 2, but Greece, Portugal, and Spain rank much lower. This discrepancy can be explained by the level and the change in real GDP, respectively. Output growth in the United States was very fast in the second half of the 1990s, implying a decreasing public capital–GDP ratio during the 1990s, even though public capital expanded substantially at the same time. In the cases of Greece, Portugal, and Spain, both public capital per head and real GDP per head remain low in international comparison.26 However, public capital per head has increased on average much faster in these countries than in OECD countries over the period 1980–2000, reflecting the strong efforts to enhance public infrastructures in connection with their accession to the European Communities.

Table 3.

Government Net Capital Stock per Head in 22 OECD Countries

(At 2000 PPPs in U.S. dollars)

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Sources: author’s own estimates and calculations.

The columns labeled “Capital” give the level of the government net capital stock per head at 2000 purchasing power parities (PPP) for GDP in U.S. dollars. Purchasing power parities for GDP in national currency per U.S. dollar are taken from the OECD (2002b). Population figures are taken from the OECD Analytical Database, Version June 2002.

The columns labeled “Rank” give the ranking of the countries according to the level of public capital per head, the country with the highest level ranking first.

Unweighted average.

V. Robustness of the Public Capital Stock Estimates

The key assumptions made in the construction of the public capital stock estimates are the following: (1) investment in the period 1860 to 1959 is assumed to have grown by 4 percent per year to finally reach its observed level in 1960; (2) the depreciation rate is time-varying and assumed gradually to increase for all asset types except residential assets; and (3) depreciation is assumed to be geometric. This section assesses the effect of these three assumptions. For that purpose, alternative public capital stock series are estimated for two reference countries, the United States and Canada, modifying in turn each of the assumptions. These alternative estimates are then compared with the benchmark estimates and with estimates from official sources. The results of this exercise are depicted in Figure 4.

Figure 4.
Figure 4.

Government Net Capital Stocks for Alternative Estimation Assumptions

Citation: IMF Working Papers 2004, 067; 10.5089/9781451848939.001.A001

Notes: Series labeled “BEA estimate” are from the U.S. Bureau of Economic Analysis (BEA). The series for Canada except the one labeled “own estimate” are from Statistics Canada. See Appendix for details.

The upper row of Figure 4 shows public capital stock estimates for alternative assumptions on the initial capital stock in 1960 for the United States, as well as the official capital stock estimate from the U.S. Bureau of Economic Analysis. The benchmark public capital stock estimate relies on the public investment series provided by the U.S. Bureau of Economic Analysis for the period 1914–60 and assumes that public investment grew by 4 percent in the period 1860–1914.27 The figure also shows an estimate that relies on the assumption that—as is assumed for all other countries—public investment in the United States grew by 4 percent in the period 1860–1959. In addition, Figure 4 shows an estimate that differs in the way the initial capital stock is constructed. This estimate of the initial public capital stock is constructed directly following a “steady-state approach” (Fuente and Doménech, 2002, p. 47). It follows from equation (2) that the growth rate of the capital stock can be expressed as

gtK=Kt+1KtKt=δ+ItKt.(8)

Thus, the capital stock at the beginning of period t can be calculated as investment in period t divided by the sum of the depreciation rate and the growth rate of the capital stock in period t :

Kt=Itδ+gtK.(9)

As the growth rate of the capital stock is unknown a priori, an assumption about its magnitude is needed. Neoclassical growth theory suggests that investment and capital grow at the same rate in the steady state. Thus, the growth rate of capital can be approximated by the growth rate of investment. As it is improbable that the U.S. economy was in a steady state in 1960, the growth rate of capital is instead approximated by the average growth rate of investment over the period 1960–2001. This growth rate was 2.7 percent in the case of government investment, 5.4 percent in the case of private nonresidential investment, and 2.5 percent in the case of private residential investment. Finally, the investment series is filtered using a Hodrick-Prescott filter in order to remove its cyclical component.

Figure 4(a) shows that assuming a constant 4 percent growth rate of public investment over the period 1914–59 instead of using the historical Bureau of Economic Analysis (BEA) investment growth rates does not significantly affect the resulting public capital stock series. For the period of interest, 1960–2000, the levels and the dynamics of both series are almost indistinguishable. Pronounced differences occur over the period 1940–50 only because the public capital stock based on BEA investment takes account of the large increase in public investment during World War II, whereas the alternative estimate does not. Yet the effect of this difference is short-lived. The figure also reveals that although the level of the public capital stock estimates is lower than the capital stock series reported by the BEA, the dynamics are very similar, as witnessed by the strong comovement of the growth rates of the public capital stock series. Furthermore, formal tests for equality between the means and the variances of the author’s own estimates and of the BEA series fail to reject the null hypothesis of equality.28 Figure 4(a) also depicts the author’s own estimate of the public capital stock relying on the steady-state approach. The time profile of this estimate differs considerably from that of the other series shown in the figure. While the level of the initial capital stock at the beginning of 1960 is higher than that of the BEA reference series, its level at the beginning of 2000 is comparable to that of the author’s own estimate and thus lower than that of the BEA series. Furthermore, the dynamics of this estimate are significantly different from that of the other series, as can be seen in the figure. This visual impression is confirmed by a formal test for equality between the means and variances of the growth rates of this estimate and of the BEA series. These results suggest that the benchmark assumption on the initial capital stock made in this paper seems to be a reasonable way to proceed.

The middle row of Figure 4 shows public capital stock estimates for alternative assumptions on the time profile of the depreciation rate and again contrasts these estimates with the official estimate reported by the BEA. The benchmark estimate assumes a time-varying depreciation rate increasing from 2½ percent to 4 percent, as explained in Section III. Figure 4(b) also shows the public capital stock for a depreciation rate that—based on implicit scrapping rates for the total capital stock—gradually increases from 3 percent to 6 percent over the period 1960–2001. It also shows the public capital stock for a depreciation rate that is constant over time and equal to the average implicit scrapping rate empirically observed for the United States (3½ percent for government assets). The figure reveals that these two estimates exhibit dynamics that differ significantly from those of the BEA series and of the benchmark estimate. The reason is that the estimate assuming a constant depreciation rate considerably overestimates the growth of public capital in the 1990s, whereas the estimate relying on a steeper time profile of the depreciation rate underestimates the growth of public capital in the 1970s and in the early 1980s. All in all, the benchmark assumption on the depreciation rates based on empirically observed implicit scrapping rates for the United States seems to be the most sensible approach, given the alternatives.

Finally, the lower row of Figure 4 depicts the influence of alternative depreciation methods. Unlike the previous two sensitivity analyses, this exercise is not based on author’s own estimates, but on official estimates for Canada.29 Statistics Canada provides public capital stock estimates for three alternative depreciation methods—straight-line, hyperbolic, and geometric. Figure 4(c) shows that hyperbolic and geometric depreciation result in quite similar capital stock estimates, whereas the estimate based on straight-line depreciation differs considerably both in levels and dynamics. The level of the author’s own estimate based on geometric depreciation is in general lower than the Statistics Canada series based on the same depreciation method, but higher than its series based on linear depreciation. The dynamics of the author’s own estimates are similar to that of the Statistics Canada series based on geometric depreciation except for the 1960s. A formal test for equality between the means and variances of the growth rates of these two series cannot reject the null hypothesis of equality. Thus, the benchmark estimates seem sensible in the case of Canada also.

To sum up, this section has shown the effect of various assumptions on public capital stock estimates. Visual inspection and tests for equality between the benchmark estimates and reference series reported by the U.S. BEA and Statistics Canada reveal that the benchmark estimates of public capital seem quite plausible. The properties of the capital stock estimates based on the various assumptions are further explored in the next section, where these estimates are used as explanatory variables in regressions according to the so-called production function approach.

VI. Evidence for the Production Function Approach

This section uses alternative capital stock measures in order to estimate the elasticity of output with respect to public capital, applying the production function approach. Section VI.A presents regression results for the various capital stock estimates for the United States and Canada, and thus supplements the sensitivity analysis presented in the previous section. Section VI.B presents regression results for 22 OECD countries for capital stock estimates from different sources (that is, for author’s own benchmark estimates, for estimates from national sources and for estimates from OECD, 1997).

The production function approach is one of three main approaches that have been employed in the empirical literature on the macroeconomic effects of public capital. The other approaches are the cost function approach and the vector autoregressive (VAR) approach.30 This study concentrates on the production function approach both because it is the simplest among the three approaches and because it still remains widely applied in the empirical literature. Even recent studies relying on the less restrictive VAR approach often provide additional estimates according to the production function approach as a benchmark against which to evaluate the VAR results (Ligthart, 2002). Thus, there is ample evidence against which the regression results of this study can be evaluated.

The starting point of empirical applications relying on the production function approach is an aggregate production function of the form Y = AF (KP,L), where Y is output, KP is the private capital stock, L is labor input, and A is an index representing multifactor productivity. This expression is extended by including the public capital stock (KG) so that the aggregate production function can be written as Y = AF (KP ,L, KG). Using the Cobb-Douglas form and taking the natural logarithm yields the regression equation that is typically employed in empirical studies relying on the production function approach:

yt=a0+a1t+αlt+βktP+γktG+εt,(10)

where yt is the log of GDP, lt is the log of labor input, ktP is the log of private capital, ktG is the log of public capital, and εt is a disturbance term. As in Aschauer (1989b), a constant, a0, and a time trend, t, are introduced as a proxy for multifactor productivity. The parameters α, β, and γ can be interpreted as elasticities of output with respect to the factors of production.

An important issue raised by this specification is that of potential nonstationarity of the variables included in the regression. A large number of alternative unit root tests are designed to discriminate between nonstationary and stationary processes (Survey in Phillips and Xiao, 1998). We use the popular Dickey and Fuller (1979, 1981) test in order to determine whether the model variables are nonstationary. This test is applied to a total of 165 variables that are used in the individual-country regressions reported in Sections VI.A and VI.B.31 The test results indicate that the vast majority of variables is nonstationary; only 10 variables appear to be stationary in level. Among the variables that are nonstationary many seem to be integrated of order two rather than of order one according to the test results. Yet it is well known that unit root tests have low power to discriminate between unit root and near unit root processes (Enders, 1995, p. 251–54).32 This problem is especially pronounced for small samples (Campbell and Perron, 1991). One way to alleviate the problem is to make use of the cross-sectional dimension of the data and to apply panel unit root tests to the variables. The results of two popular panel unit root tests suggest that the variables are integrated to the first order.33 The individual-country regressions are thus also based on this finding.

Since the variables are nonstationary estimation of equation (10) makes sense only if the variables are cointegrated. There are many alternative methods that can be used to test for cointegration (see the survey in Dolado, Gonzalo, and Marmol, 2001). In this paper the two-step procedure initially proposed by Engle and Granger (1987) is applied. In the first step, equation (10) is estimated by ordinary least squares (OLS) and in the second step an augmented Dickey-Fuller test is performed on the residual sequence {ε^t} in order to determine whether it has a unit root. The null hypothesis of the test is that the residual sequence has a unit root or, in other words, that the variables are not cointegrated. Note that the critical values of the Engle-Granger test are larger in absolute value than those of the standard Dickey-Fuller test because the sequence {ε^t} is generated from a regression equation. The appropriate small-sample critical values can be derived from MacKinnon (1991). If the variables are cointegrated, the OLS estimates from regression (10) will be superconsistent, in the sense that they converge faster to their true values in probability than in OLS regressions using stationary variables (Stock, 1987). However, if the variables are not cointegrated, estimating equation (10) in levels might give rise to a spurious-regression problem. Instead, it is appropriate to difference the variables in order to induce

stationarity. In this case the regression equation takes the form

Δyt=a1+αΔlt+βΔktP+γΔktG+υt,(11)

where Δ is the first-difference operator and υt is a disturbance term.

A. Estimates of Public Capital Productivity for Alternative Capital Measures

This section supplements the sensitivity analysis and reports estimates of the elasticity of output with respect to public capital for the United States and Canada, using the various public capital stock estimates discussed in Section V. Real GDP and employment data are taken from the OECD Analytical Database; public and private capital stocks are estimates calculated using the alternative assumptions on the initial capital stock and the depreciation rate and depreciation method considered in the previous section. The private capital stock is the sum of private nonresidential and private residential capital. The private capital stocks are estimated using exactly the same method as the estimation of government capital. The benchmark estimation assumes that the depreciation rate increases from 4¼ percent to 8½ percent for private nonresidential assets, although it is assumed to be constant for private residential assets (1½ percent). Two alternatives are considered regarding the time profile of the depreciation rate. The first alternative assumes that the depreciation rate increases from 3.0 percent to 6.0 percent over the period 1960–2001 for all assets. The second alternative assumes that the depreciation rate is time-invariant and—based on average implicit scrapping rates for the United States—is equal to 6.0 percent for private nonresidential capital and 1½ percent for private residential capital. Finally, the capital stocks for Canada for alternative depreciation methods are official estimates provided by Statistics Canada.

Table 4 reports estimates of the elasticity of output with respect to public capital for the United States and Canada using the various public capital stock estimates. Figures in bold indicate whether the elasticity is taken from the model in levels or first differences, depending on the results of the test for cointegration. Table 4 shows that the Engle-Granger test statistic is lower in absolute value than the 5 percent critical value in all cases. The test results, thus, suggest that there is no cointegration among the variables and, by implication, that the production function as formalized in equation (10) does not constitute a stable long-run relationship. As a consequence, all estimates are based on the model in first differences.34 The estimated elasticities of output with respect to public capital are all statistically significant and have the expected (positive) sign. The estimates are, however, in general very high, ranging from 0.40 to 0.86 and thus implying what Aschauer (1995, p. 91) has called “supernormal” returns to public capital. Yet, this is a common finding in the literature. For example, Sturm and de Haan (1995, p. 64) report elasticities of output with respect to public capital of 0.67 for the United States and 0.71 for a model similar to equation (10), estimated in first differences.

Table 4.

Elasticities of Output with Respect to Public Capital for the United States and Canada for Alternative Capital Stock Measures

article image
Source: Author’s own estimates and calculations.

t-values based on the Newey and West (1987) heteroscedasticity and autocorrelation consistent covariance estimator in parentheses. * denotes statistical significance at the 5 percent level. Elasticities in the column labeled “Levels” are printed in bold if the variables are cointegrated; otherwise the elasticity for the corresponding model estimated in first differences reported in the column labeled “Differences” is printed in bold.

This paper uses the so-called augmented Engle-Granger test, performing an augmented Dickey-Fuller test on the residuals of the model in levels (equation (10)). The MacKinnon (1991) 5 percent critical value for rejection of the null hypothesis of no cointegration is -4.795 for the sample 1960–2001.

The growth rate of investment in the period 1914–59 is assumed to be 4 percent per annum. The benchmark estimates, instead, rely on historical growth rates of investment reported by the BEA.

The depreciation rate is assumed to be constant over time. Based on the average implicit scrapping rate over the period 1960–2000 the depreciation rate is assumed to be 3½ percent for government capital, 6 percent for private nonresidential capital and 1½ percent for private residential capital.

Moreover, the regressions reveal another problem associated with the production function approach: the difficulty of interpreting the regression results as representing the input elasticities of output. The estimates of the coefficient on labor input are larger than one and the estimates of the coefficient on private capital are negative in all regressions.35 Taken at face value, these results suggest not only that public capital is much more productive than private capital but also that private capital is not productive at all. Again, such a finding is not uncommon in the literature. For example, Sturm and de Haan (1995, p. 64) report that their estimates for the United States imply a large negative elasticity of output with respect to private capital. There are several reasons to be cautious in interpreting this finding: (1) the assumed functional form of the production function may not be an appropriate description of the data, (2) the exogeneity assumptions underlying the production function approach may not be satisfied, and (3) the regressions may suffer from a multicollinearity problem. This might be a reason why the coefficient on private capital is statistically insignificant in most cases and has the unexpected negative sign. Multicollinearity among the regressors is frequently cited as a problem in the empirical literature estimating production functions and cost functions for individual countries (see the survey by Sturm, de Haan, and Kuper, 1998).36 One way to deal with this problem is to exploit the cross-sectional dimension of the data and to estimate panel data models instead of carrying out individual-country regressions. The panel estimate reported in the next section indeed suggests that the implausible value for the elasticity of output with respect to private capital found in the individual-country regressions may be the result of a multicollinearity problem.

B. Estimates of Public Capital Productivity for 22 OECD Countries

Table 5 reports estimates of the elasticity of output with respect to public capital for the 22 OECD countries for equation (10) using public capital stock estimates from three alternative sources: first, author’s own estimates; second, estimates from national sources; and third, estimates from OECD (1997). The table reveals the main advantage of the author’s own capital stock estimates. Equation (10) can be estimated for 22 countries while the alternative sources allow for only 10 and 11 individual-country regressions, respectively. The estimates of the elasticity of output with respect to public capital are based on the model in first differences with one exception (Belgium) since the augmented Engle-Granger test fails to reject the null hypothesis of no cointegration in all cases but one. Most of the coefficients are statistically insignificant for the estimations based on data from other sources. This result is similar to that of Ford and Poret (1991), who estimated models based on the production function approach for 11 OECD countries using capital stock data from an earlier volume of OECD (1997). In contrast, most of the coefficients stemming from estimations based on author’s own capital stock estimates are statistically significant. Yet, in those cases where the elasticity of output with respect to public capital is significant, it is again quite large. Moreover, for some countries the coefficient on private capital—not reported in the table—is negative, making it difficult to interpret the estimated coefficients as parameters of a Cobb-Douglas production function.

Table 5.

Elasticities of Output with Respect to Public Capital for 22 OECD Countries for Capital Stock Estimates from Different Sources 1/

article image

t-values based on the Newey and West (1987) covariance estimator in parentheses. * denotes statistical significance at the 5 percent level. The model is estimated in first differences in all cases except one (Belgium for data from national sources) based on the results of Engle-Granger tests for cointegration.

The last row of Table 5 reports the elasticity of output with respect to public capital for a panel consisting of all 22 OECD countries. This estimate is based on a regression equation similar to equation (11) where the intercept is allowed to vary across countries while the input elasticities of output are assumed to be the same across countries (estimation by fixed effects).37 The advantage of the panel regression over the individual-country regressions is obviously the much higher number of observations: while most individual-country regressions have 37 degrees of freedom, the panel regression has more than 800 degrees of freedom. Consequently, the parameters of interest can be estimated much more precisely. The estimation results for the panel model indicate that the output elasticities of public capital (0.22), of private capital (0.19), and of labor input (0.61) take on sensible values.38 Not surprisingly, a test for constant returns to scale in all inputs fails to reject the null hypothesis.

VII. Conclusion

This paper provides new estimates of the government net capital stock for 22 OECD countries for the period 1960–2001. This data set has several attractive features compared to existing alternatives. First, the same estimation approach is used across all countries, ensuring a maximum degree of international comparability. Second, the estimates are based on investment data (compiled by the OECD) that are homogenous across countries. Third, these investment data have been compiled according to the 1993 System of National Accounts, whereas the data reported in OECD (1997) were compiled according to the old 1968 System of National Accounts. Finally, the dataset covers 22 countries and 42 years for each country and is, thus, much larger than any existing alternative.

The public capital stock estimates reveal that public capital–GDP ratios have tended to decline in most OECD countries since the late 1970s. The estimates further show that a considerable disparity exists in the public capital endowment of OECD countries, even though some convergence has taken place in the past two decades. A sensitivity analysis regarding the main estimation assumptions suggests that the benchmark estimates of public capital stocks are reasonable when compared to estimates from official sources for the United States and Canada. Regression results based on the production function approach indicate that the elasticity of output with respect to public capital is positive and statistically significant in most countries. This is confirmed by the results of a simple panel regression showing that public capital is productive on average in OECD countries.

The capital stock data may prove useful for applied research on the macroeconomic effects of public capital in several respects. First, they may allow an assessment of public capital productivity for countries for which such estimates have not been available so far because of a lack of public capital stock data. Moreover, they may be used in the estimation of models based on dynamic panel regression techniques aiming to uncover the average effect of public capital in OECD countries. Finally, they may be employed in the estimation of VAR models—the most commonly used framework in the recent empirical literature.

APPENDIX I

National Data Sources

This appendix provides summary information on 13 OECD countries for which public capital stock estimates from national sources are available. Public capital stock estimates from national sources are not available for the following countries: Austria, France, Greece, Iceland, Ireland, the Netherlands, Portugal and Switzerland. For Sweden, public capital stock data are available at http://www.scb.se/ for local governments only.

Australia

Capital stocks are estimated by the Australian Bureau of Statistics and are published in “Australian System of National Accounts.” Data are available for the period 1960–2000 at http://www.abs.gov.au/. Stocks are calculated according to the perpetual inventory method; depreciation is assumed to follow a hyperbolic pattern. Coverage: General government.

Belgium

Capital stocks are estimated by the National Accounts Institute (NAI) and are included in the National Socio-Economic Database. Data are available for the period 1970–2000 at http://www.nbb.be/belgostat/. Coverage: Public administration and defense services, compulsory social security services.

Canada

Capital stocks are estimated by Statistics Canada. Data are available for the period 1961–2001 at http://www.statcan.ca/english/CANSIM/ (CANSIM Table 031-0002). Stocks are calculated according to the perpetual inventory method; estimates are provided for three alternative depreciation schemes (straight line, geometric, and hyperbolic). Coverage: Public administration, educational services, and health care and social assistance.

Denmark

Capital stocks are estimated by Danmarks Statistics and are included in the database Danmarks Statistikbank. Data are available for the period 1966–2001 at http://www.statistikbanken.dk. Coverage: General government.

Finland

Capital stocks are estimated by Statistics Finland. Data for the period 1975–2001 were provided by ETLA (The Research Institute for the Finnish Economy). Coverage: General government.

Germany

Capital stocks are estimated by Statistisches Bundesamt. For West Germany, net capital stocks for the period 1960–95 according to the former European System of National Accounts (ESA 1979) are available at http://www-zr.destatis.de/. For Germany as a whole, only gross capital stocks are available for the period 1991–2000. These data were published in 2001 in “Hauptbericht, Fachserie 18: Volkswirtschaftliche Gesamtrechnungen, Reihe 1.3” and are not available online. Coverage: Public sector (including NFPEs).

Italy

Capital stocks are estimated by the Istituto Nazionale di Statistica (ISTAT). Data are available for the period 1980-2000 at http://www.istat.it/. Stocks are calculated according to the perpetual inventory method; depreciation is assumed to follow a straight-line pattern. Coverage: Public administration and defense services, compulsory social security services.

Japan

Capital stocks are estimated by the Economic and Social Research Institute (ESRI) and are published in the “Annual Report on National Accounts”. Data are available for 1955–2000 at http://www.esri.cao.go.jp/. Coverage: Data are available for the general government and for the public sector (including NFPEs).

New Zealand

Capital stocks are estimated by Statistics New Zealand; the most recent results were published in the “Upgraded National Accounts 2000.” Data are available for 1987–97 at http://www.stats.govt.nz/. Coverage: Public sector (General government including all government-owned producer enterprises).

Norway

Capital stocks are estimated by Statistics Norway and are published in the “Annual National Accounts.” Data are available at http://www.ssb.no/nr en/ for the period 1970–2000. Coverage: General government.

Spain

Capital stocks are estimated by the Ministry of Finance and are included in the BD.MORES database. Stocks are calculated according to the perpetual inventory method, depreciation is assumed to follow a geometric pattern. Data for the period 1964–95 are available at http://www.igae.minhac.es/. Coverage: Data are available for the general government and for the public sector (including NFPEs).

United Kingdom

Capital stocks are estimated by the Office for National Statistics (ONS) and are published in the “Blue Book.” Data are available at http://www.statistics.gov.uk/statbase/ for the period 1948–2000. Stocks are calculated according to the perpetual inventory method; depreciation is assumed to follow a straight-line pattern. Coverage: Public sector.

United States

Capital Stocks are estimated by the U.S. Department of Commerce, Bureau of Economic Analysis (BEA). Data for 1925–2000 are available at http://www.bea.gov/bea/dn/faweb/. Stocks are calculated according to the perpetual inventory method; depreciation is assumed to follow a geometric pattern. Coverage: Public sector (general government plus government enterprises).

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1

Kiel Institute for World Economics, 24100 Kiel, Germany. Tel.: +49-431-8814-266, Fax: +49-431-8814-525. The first draft of this paper was written while I was a summer intern in the Fiscal Affairs Department of the International Monetary Fund. I thank the staff of the Fiscal Policy and Surveillance Division for their hospitality and cooperation. I am especially indebted to Teresa Dabán for many helpful and clarifying discussions. I thank country desk economists for providing me with information on national data sources. I would finally like to thank seminar participants in the 2003 annual conference of the Royal Economic Society, in the 2003 annual conference of the International Institute of Public Finance and at the University of Groningen, as well as Alfred Boss, Kai Carstensen, Joerg Doepke, Joachim Scheide, Jan-Egbert Sturm, Marcel Timmer, and Bart van Ark for helpful comments.

2

Sturm, de Haan, and Kuper (1998, p. 382) draw attention to the problem that “most authors employ data in their analysis which are generally chosen on the ground of their availability, without analyzing whether their conclusions are sensitive not only to the concept of the public capital stock (narrow versus broad definition), but also to the way the capital stock has been constructed.”

3

The capital stock estimates are available upon request to the author.

4

This database includes not only investment data but also a large set of other macroeconomic variables. In addition to investment, real gross domestic product (GDPV) and employment (ET) are also retrieved from the OECD Analytical Database. Most of these data are available online at http://www.sourceoecd.org.

5

For most of these countries the data are available for the period 1960–2001. The following OECD countries are not included in the analysis because long investment series are not available: the Czech Republic, Hungary, the Republic of Korea, Luxembourg, Mexico, Poland, the Slovak Republic, and Turkey.

6

In OECD (1997), public entities are referred to as “Producers of government services.” This category in most cases corresponds to the definition of public activities underlying the investment series from national sources. An important difference, however, is that capital stocks in OECD (1997) were based on classifications of public activities according to the 1968 System of National Accounts whereas recent national data are based on classifications according to the 1993 System of National Accounts.

7

See Appendix for a description of data from national sources.

8

For details on the 1993 System of National Accounts see European Commission and others (1993).

9

All series are expressed in the constant prices of 1995. For those countries with a different base year (Australia 1999/2000; Canada, 1997; Iceland, 1990; Norway, 1997; Switzerland, 1990; and the United States, 1996) the series were rebased to 1995.

10

The terms “depreciation” and “consumption of fixed capital” are used interchangeably in this paper. This is common in economic literature. Note, however, that “depreciation” as used here differs considerably from its use in company accounts where it is calculated on the basis of historic costs rather than market prices.

11

An exception to this general rule applies in the case of the United States. The Bureau of Economic Analysis (BEA) provides investment series starting in 1914. This information is used by chaining the OECD data which are available for 1960–2001 with the BEA growth rates for 1914–60.

12

Maddison (1995) estimates gross capital stocks for six OECD countries based on investment series that in some cases start in the 19th century. However, he acknowledges that the assembly of the investment series is a major problem because historical series for different periods have to be linked and because these series rely on different weighting bases. Also, there are generally breaks in the historical investment series. Yet, most important for our purpose is that historical series on investment in general do not include a measure of government investment but only measures of private investment. An exception relates to the influential works of Feinstein (for example, 1972), who provides investment series for the public sector in the United Kingdom starting in 1856. Yet, the definition of the public sector in his studies differs considerably from that underlying the OECD series.

13

In his estimation of nonresidential capital stocks for six OECD countries, Maddison (1991, pp. 284–92) assumed that the loss in capital stock caused by war damage amounted to 3 percent in the United Kingdom, 8 percent in France, 10 percent in the Netherlands, 16 percent in Germany, and 25.7 percent in Japan. These figures are subject to a large margin of uncertainty, though, and the war damage to productive capacities may well have been lower than assumed by Maddison. For example, Ritschl (2003, p. 11) reports that the industrial capital stock in Germany in 1945 exceeded prewar levels by one-third. This capital stock was often composed of multipurpose machinery and thus available for civil production. Likewise, Eichengreen and Ritschl (1998, p. 8) and Giersch, Paqué, and Schmieding (1992, p. 17) note that war damage to the capital stock in Germany was quite limited.

14

Maddison (1987, p. 650) reports that between 1950 and 1973 real GDP grew by 9.4 percent a year on average in Japan and by 5.9 percent in Germany, whereas the average annual growth rate was only 3.0 percent for the United Kingdom and 3.7 percent for the United States.

15

For example, long-run growth in real GDP was remarkably stable in West Germany despite the disruptions caused by World War II. Calculations based on historical GDP figures drawn from Ritschl and Spoerer (1997) reveal that real GDP grew by 2.9 percent a year on average between 1938 and 1960 and by 3.1 percent between 1960 and 1990. Of course, real GDP did not grow smoothly in the first subperiod. Real GDP in 1946 was lower than in 1938 by roughly 60 percent. Yet, real GDP growth over the period 1946 to 1960 was extremely strong, averaging almost 12 percent a year.

16

Maddison (1987, p. 657) reports that between 1950 and 1973, the private capital stock on average grew in Japan by 9.5 percent a year and in Germany by 7.2 percent. Calculations based on Luetzel (1977, p. 66) show that the total net capital stock in Germany grew by 7.9 percent a year on average between 1950 and 1960. Calculations based on Mitchell (1975) show that net investment in Germany grew by 9.7 percent a year on average between 1950 and 1960.

17

The fall in capital stocks due to wartime disruptions was less pronounced than the fall in output (Maddison, 1982, p. 55), implying that the gap between capital stock levels at the end of World War II and their long-run trend was lower than was the case for output.

18

This paper assumes that the time profile of the depreciation rates is the same across countries. Official estimates of capital stocks for different countries are in general based on different assumptions about depreciation rates. This is appropriate insofar as country-specific factors influence service lives. However, only a few countries have investigated service lives with particular care, among them the United States (OECD 2001a, p. 99). Therefore, it seems preferable to assume identical depreciation rates across countries for the purpose of international comparisons. Such a standardized approach is also adopted by Maddison (1995) and O’Mahony (1996).

19

National authorities usually estimate the contribution of investment to the net capital stock for a large number of individual assets (U.S. Bureau of Economic Analysis, 1999). For most of these assets, national authorities assume constant depreciation rates except for assets related to information and communication technology (ICT). At the same time, they assume different depreciation rates for different types of assets. As the relative importance of different assets changes with time, so does the average depreciation rate. The latter will increase over time if assets with relatively short asset lives gain in importance. This paper tries to capture this phenomenon by assuming a time-varying aggregate depreciation rate.

20

Figure 2 shows that the implicit scrapping rate calculated for BEA data sharply accelerated after 1995. To some extent, this probably reflects the growing importance of ICT assets characterized by asset lives that are much shorter than those of other assets. Because the importance of the ICT sector is considerably lower in most other industrial countries than in the United States (OECD, 2002c), we chose a flatter depreciation profile for the years 1995 to 2001 than that implicit in U.S. data.

21

This is not true for other depreciation methods, such as straight-line or hyperbolic depreciation.

22

A special problem in the estimation of capital stocks relates to German reunification. The OECD investment and GDP series cover West Germany only for the period 1960–90, but they include East Germany from 1991 on. As there is no information on the magnitude of the East German capital stock at the beginning of 1991, this paper assumes that the ratio of the East German capital stock with respect to the West German capital stock equaled the ratio of East German and West German GDP in 1991 (8 percent). In the estimation, the German capital stock at the beginning of 1991 is thus increased by 8 percent for the three asset types considered. From 1991 on, this additional capital stock depreciates at the same rate as the other assets.

23

Austria, France, Iceland, Ireland, the Netherlands, Portugal, and Switzerland.

24

The contribution of the initial capital stock varies between 14.3 percent in the case of Denmark and 3.0 percent in the case of Japan. The differences in contributions across countries are mainly due to differences in the level of public investment–GDP ratios over the sample period. For instance, the contribution of the initial capital stock is lowest in Japan because the public investment–GDP ratio there was the highest among the considered countries over the period 1960–2001.

25

The most important qualitative results reported in the following paragraph are unaffected if PPPs for total investment are used instead. Detailed results are available on request.

26

In 2000, real GDP per head amounted to 66.3 percent of the OECD average in Greece, to 72.4 percent in Portugal, and to 79.5 percent in Spain (OECD, 2002b, p. 339).

27

The official growth rates provided by the U.S. Bureau of Economic Analysis for the period 1914–60 are chained with the OECD investment series available for 1960–2001.

28

Detailed results are available upon request. These tests are carried out for the growth rates of the series because unit root tests indicate that the public capital stock series are integrated to order 1.

29

As information on asset lives at the aggregate level is not available, this study cannot provide capital stock estimates that are comparable across depreciation methods. For this reason the capital stock estimates are based on implicit scrapping rates for the United States and Canada instead. See Section III for details.

30

See Sturm, de Haan, and Kuper (1998) for a discussion of the three approaches, as well as for an overview of empirical studies.

31

Detailed results are available on request. We use the so-called augmented Dickey-Fuller test that is asymptotically valid in the presence of serial correlation in the errors, including two additional lags of the respective variable. The test is first carried out for the variables in levels. In this case the test equation includes a constant and a linear time trend. If the null hypothesis of a unit root cannot be rejected at the 5 percent significance level, the test is also carried out for the variables in first differences. In this case the test equation includes a constant. If the null hypothesis of a unit root still cannot be rejected, the test is also carried out for the variables in second differences. Small-sample critical values are derived from MacKinnon (1991).

32

The power of a test is the probability that it will correctly lead to a rejection of a false null hypothesis.

33

We use the panel unit root tests proposed by Levin, Lin, and Chu (2002) and Im, Pesaran, and Shin (2003). Detailed results are available on request.

34

As the usual inference procedures are inappropriate in the presence of nonspherical disturbances, the t-statistics reported in Tables 4 and 5 are based on the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator.

35

These estimates are not reported in Table 4. Detailed results are available on request. While the coefficient of employment is statistically significant in all cases, the coefficient on private capital is insignificant in most cases.

36

Kennedy (1998, p. 187) even cites the estimation of the Cobb-Douglas production function as “the classical example” of multicollinearity.

37

The estimation of a dynamic panel model and tests for panel cointegration (for example, in Canning and Pedroni, 1999) are beyond the scope of this study and a fruitful avenue for further research.

38

The elasticities of output with respect to private capital and labor input are not reported in the table. All elasticities are significant at the 5 percent level. Detailed results are available on request.

New Estimates of Government Net Capital Stocks for 22 OECD Countries 1960-2001
Author: Christophe Kamps
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    Real Government Gross Fixed Capital Formation in 22 OECD Countries 1960–2001

    (As a percentage of real GDP)

  • View in gallery

    Real Government Gross Fixed Capital Formation in 22 OECD Countries

    (As a percentage of real GDP)

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    Implicit Scrapping Rates for the United States 1960–2000

    (In percent)

  • View in gallery

    Real Government Net Capital Stock in 22 OECD Countries 1960–2001

    (As a percentage of real GDP)

  • View in gallery

    Real Government Net Capital Stock in 22 OECD Countries 1960–2001

    (As a percentage of real GDP)

  • View in gallery

    Government Net Capital Stocks for Alternative Estimation Assumptions