Using newly available investment data from the World Bank’s World Development Indicators database we provide an update and an extension of the aggregate capital stock estimations provided in (Berlemann, M. and J.-E. Wesselhöft (2014): Estimating Aggregate Capital Stocks Using the Perpetual Inventory Method: A Survey of Previous Implementations and New Empirical Evidence for 103 Countries, Review of Economics 65(1), 1–34). The new database contains comparable unbalanced panel data for 122 countries and the period of 1960 to 2016.
For a long period of time, the absence of internationally comparable capital stock data has been a major obstacle to empirical studies of the contribution of the capital stock to economic growth and related studies. While the OECD maintains a database of international capital stock data of its member countries, the data is a mixture of data collected from the national statistical offices and own estimations of the OECD. The OECD therefore recommends to be very careful in using the data for international comparisons.  Since the 8.0 version of the Penn World Tables capital stock data is also available from this source, however, in an attempt to construct a database covering a large range of countries and long periods of time, data from very different sources which were constructed with differing methods were merged.  While this approach has its obvious merits, the high number of applied country-specific corrections and assumptions is not unproblematic for cross-country studies.
An alternative to using the two mentioned databases is to use investment data to construct capital stock data with the Perpetual Inventory Method. While doing so helps to overcome the problem of incomparability, constructing capital stock data is quite time-consuming. Moreover, the existing studies  differ to quite some extent, especially in the way the initial capital stock is estimated.  Against this background Berlemann and Wesselhöft (2014) proposed a unified approach of applying the Perpetual Inventory Method. Based on this approach and employing investment data from the World Bank’s World Development Indicators database, the authors construct an unbalanced panel dataset of aggregate capital stock data for 103 countries over the period of 1970 to 2010 and made it publicly available. As the database has been employed quite frequently  and thus proved to be useful we decided to update the data. While we stick to the methodological approach developed in Berlemann and Wesselhöft (2014) we make some further extensions. First, we extend the dataset back to 1960 where possible. Doing so leads to considerably longer time series for the referring countries which might be useful for many applications. Second, we updated the investment time series from the World Banks’s World Development Indicators database. Doing so allows us to extend the data to 2016. Third, as the newest investment data is available for more countries we added numerous countries to the dataset. The new panel data now covers as many as 122 countries.
This article describes the update and summarizes the main features of the new dataset. Section 2 outlines the unified approach of constructing aggregate capital stock estimates using the Perpetual Inventory Method proposed in Berlemann and Wesselhöft (2014). Section 3 describes the employed data sources and gives an overview on the development of the number of sample countries over the sample period. Section 4 presents and discusses the basic results. Section 5 concludes.
2 “Unified” estimation approach
Almost all capital stock estimations make use of the Perpetual Inventory Method.  The Perpetual Inventory Method interprets an economy`s capital stock as an inventory which is feed by new investments while written-off capital leaves the inventory. In order to be able to apply the idea of the Perpetual Inventory Method strictly we would need information on the whole history of past investments (I). However, time series of investments typically cover only the (very) recent part of the capital stock history. Whenever the available time series of investments is incomplete (as almost always in practice), we nevertheless can calculate the current capital stock accurately whenever the initial capital stock at the beginning of the investment time series, , and the depreciation rate δ are known. We then can calculate the capital stock at time t as
Thus, the capital stock in period t is a weighted sum of the initial capital stock and the known history of capital investments. The weights result from the geometric depreciation function.
In order to be able to apply this method three sorts of information are necessary. First, it is necessary to have a time series of investment data. Second, information on applicable depreciation rates has to be available. Finally, we are in need of data on the initial capital stock at the time when the investment time series starts. While information on investments and depreciation rates can be obtained from various sources (we discuss the employed sources in the third subsection) there is obviously no database on initial capital stocks. To solve this problem we calculate the initial capital stock Kt0 from the investments It1, the long-term growth rate of Investments gI and the rate of capital depreciation δ:
In order to avoid that the calculations depend on a single observation of investments, which might be an outlier, we derive the initial investment value It1 from a regression approach. We therefore use the whole time series of investments, ranging from time t2 to T. In order to do so, we regress the time series of log investments ln(Ii,t) for any country i on time t. Thus, we estimate the equation
using the OLS method. In a next step we calculate the fitted value for period t1, thereby using the estimated parameters αi and βi, i.e.
After transforming the fitted value using the exponential function we end up with a time series of investments ranging from t1 to T. We then use the first (and thus the fitted) value of this time series to calculate the initial capital stock in period t0. Moreover, we use the estimated parameter βi as estimator for the long-run growth rate of investments gI.
Rather than assuming a constant rate of depreciation, as it is often done in the related literature (for reasons of convenience) we use time-varying depreciation schemes, which seem to be the more plausible variant. As Kamps (2006) we base our assumptions on capital depreciation schemes on US data, provided by the U.S. Bureau of Economic Analysis (see Figure 1). Instead of defining a synthetic mathematical function which delivers a similar pattern as the observed values, we estimate the depreciation rates for the period of 1950 to 2014 in three separate linear OLS regressions (private non-residential, private residential and government fixed assets). The estimation results are summarized in Table 1.
|Private non-residential fixed assets||Private residential fixed assets||Government fixed assets|
|Constant||‒77.6376*** (3.2015)||‒24.4737*** (0.8411)||17.0076*** (4.4565)|
|Time||0.0429*** (0.0016)||0.0134*** (0.0004)||‒0.0064*** (0.0020)|
“***”: significant on the 99% confidence level, “**”: significant on the 95% confidence level, “*”: significant on the 90% confidence level; values in brackets are standard errors
|Country||First year of data||WDI classification|
|Albania||1996||Upper middle income|
|Algeria||1969||Upper middle income|
|Antigua and Barbuda||1981||High income|
|Argentina||1960||Upper middle income|
|Armenia||1990||Lower middle income|
|Azerbaijan||1990||Upper middle income|
|Bahamas, The||1989||High income|
|Bangladesh||1980||Lower middle income|
|Belarus||1990||Upper middle income|
|Belize||1981||Upper middle income|
|Bolivia||1960||Lower middle income|
|Botswana||1974||Upper middle income|
|Brazil||1970||Upper middle income|
|Brunei Darussalam||1989||High income|
|Bulgaria||1980||Upper middle income|
|Burkina Faso||1983||Low income|
|Cambodia||1993||Lower middle income|
|Cameroon||1975||Lower middle income|
|China||1978||Upper middle income|
|Congo, Dem. Rep.||1993||Low income|
|Congo, Rep.||1985||Lower middle income|
|Costa Rica||1960||Upper middle income|
|Cuba||1970||Upper middle income|
|Czech Republic||1990||High income|
|Dominican Republic||1960||Upper middle income|
|Ecuador||1965||Upper middle income|
|Egypt, Arab Rep.||1982||Lower middle income|
|El Salvador||1965||Lower middle income|
|Equatorial Guinea||1980||Upper middle income|
|Gabon||1980||Upper middle income|
|Gambia, The||1966||Low income|
|Guatemala||1960||Lower middle income|
|Honduras||1960||Lower middle income|
|Hong Kong SAR, China||1973||High income|
|India||1960||Lower middle income|
|Indonesia||1979||Lower middle income|
|Iran, Islamic Rep.||1960||Upper middle income|
|Jordan||1976||Upper middle income|
|Kazakhstan||1990||Upper middle income|
|Kenya||1979||Lower middle income|
|Korea, Rep.||1960||High income|
|Kyrgyz Republic||1990||Lower middle income|
|Lebanon||1994||Upper middle income|
|Lesotho||1970||Lower middle income|
|Macao SAR, China||1982||High income|
|Macedonia, FYR||1990||Upper middle income|
|Malaysia||1960||Upper middle income|
|Mauritania||1965||Lower middle income|
|Mauritius||1976||Upper middle income|
|Mexico||1960||Upper middle income|
|Moldova||1991||Lower middle income|
|Morocco||1966||Lower middle income|
|Namibia||1980||Upper middle income|
|New Zealand||1970||High income|
|Nigeria||1981||Lower middle income|
|Pakistan||1960||Lower middle income|
|Panama||1980||Upper middle income|
|Paraguay||1991||Upper middle income|
|Peru||1960||Upper middle income|
|Philippines||1960||Lower middle income|
|Puerto Rico||1971||High income|
|Romania||1990||Upper middle income|
|Russian Federation||1990||Upper middle income|
|Serbia||1995||Upper middle income|
|Sierra Leone||1980||Low income|
|Slovak Republic||1992||High income|
|South Africa||1960||Upper middle income|
|Sri Lanka||1960||Lower middle income|
|Sudan||1976||Lower middle income|
|Tajikistan||1986||Lower middle income|
|Thailand||1960||Upper middle income|
|Trinidad and Tobago||1980||High income|
|Tunisia||1965||Lower middle income|
|Turkey||1987||Upper middle income|
|Ukraine||1990||Lower middle income|
|United Kingdom||1970||High income|
|United States||1960||High income|
|Uzbekistan||1990||Lower middle income|
|Venezuela, RB||1960||Upper middle income|
|Vietnam||1994||Lower middle income|
|West Bank and Gaza||1994||Lower middle income|
According to our findings, the depreciation rate of private non-residential fixed assets (PNA) increases from roughly 6.0% in 1950 to 8.8% in 2014. For private residential fixed assets, we find the depreciation rate to increase moderately from 1.6% to 2.5%. For government fixed assets (GA) we find a negative trend of the depreciation rate. The depreciation rate falls from 4.6% in 1950 to 4.2% in 2014. As we have no comparable data for the other sample countries we follow Kamps (2006) in assuming that these depreciation rates apply to all countries in the sample. 
In order to construct an adequate aggregate depreciation rate we calculate a weighted average of the three depreciation rates of private residential, private non-residential and government fixed assets. As weighting factor we use the average mix of all 22 OECD countries in the OECD Economic Outlook database.  The resulting depreciation rate, which is shown in Figure 2, is then applied to all sample countries.
3 Sample countries and data
In order to construct time series of capital stock data for a large sample of countries without having to rely country-specific and thus likely incomparable data sources, we rely on aggregate investment data provided by the World Bank in the World Development Indicators (WDI) database.  The investment data  includes land improvements (fences, ditches, drains, and so on), plant, machinery, and equipment purchases; the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings and commercial and industrial buildings. According to the 1993 SNA, net acquisitions of valuables are also considered as capital formation. Data are in constant 2010 USD. 
While the WDI database of the World Bank contains aggregate investment data on a large number of countries, the starting dates of the data differ heavily from country to country. We only included countries in our dataset, for which at least 20 observations of investment data were available and we thus can construct reasonably long time series of capital stock data. Nevertheless, the resulting dataset is highly unbalanced. Figure 3 illustrates aggregate data availability. For 32 countries, the investment time series start out as early as in 1960. Major increases in the number of countries, for which data is available are 1965 (6 countries), 1970 (13 countries), 1980 (10 countries), 1990 (14 countries) and 1995 (5 countries). The 14 countries added in 1990 are primarily East European transformation countries. Since 1996 the number of countries, for which data is available, amounts constantly to 122. A table with more detailed information can be found in the Appendix.
The country sample consists of countries on quite different levels of development. According to the World Bank classification four types of countries are distinguished: low, lower middle, upper middle and high income countries.  As Figure 4 reveals, most countries for which data is available come from the high income group (45 countries, 37%) while the low income countries represent only 10% of the whole sample (13 countries). However, as it is shown in Figure 5, the share of the four country groups in all countries is very similar in our dataset as compared to the full WDI dataset of countries (which includes 218 countries).
4 Capital stock estimation results under the unified approach
In the following we give an overview on the most important results of our aggregate capital stock estimations.  Due to space restrictions we concentrate on reporting the estimation results for the absolute aggregate capital stocks, capital intensities (capital per worker), and capital coefficients (capital per unit of GDP).
In Figure 6 we show a map visualizing the estimated aggregate stocks for 2016. Somewhat unsurprisingly, the countries with the largest populations tend to have also the highest capital stocks, at least whenever they are at least upper middle income countries. In Figure 7 we show the 20 countries with the highest aggregate capital stocks in 2016. In fact, only two countries with less than 20 million inhabitants are among the 20 countries with the largest capital stocks: the Netherlands and Switzerland. The United States have by far the largest capital stock, followed by China, and Japan. Germany leads the following group of European countries, followed by France, Italy and the United Kingdom. Brazil, India and Canada complete the top ten countries with the largest absolute capital stocks.
Figure 8 shows the development of the aggregate capital stock for the 10 countries with the highest capital stock in 2016 over the period of 1978 to 2016. Over the entire period, the United States had the highest capital stock of all sample countries. Until the late 1990s, Japan’s capital stock developed at a similar pace as its U.S. counterpart. However, since then the difference between the U.S. and Japan grew considerably larger. The same holds true for almost all other sample countries with the exception of China and India. China exhibits a strongly upward development since 1978. In 2008, China’s capital stock exceeded Germany’s capital stock for the first time. As of 2014, China also overtook Japan and is now owner of the second largest capital stock, with the capital stock still growing at a larger pace than its U.S. counterpart. A continuation of this development would lead to a further convergence over the next years. Besides China, India also shows a strong upward trend. Starting out from a similarly low capital stock as China, India’s capital stock exceeded the one of Canada for the first time in 2014. In absolute terms, India had the 9th largest capital stock in 2016.
Over the period of 1996 to 2016 the average aggregate capital stock of the 122 sample countries almost doubled from 113.207 bn. USD in 1991 to 212.452 bn. USD in 2016 (USD of 2010). However, this increase in the mean level was not accompanied by a convergence of the capital stocks. Over the same horizon, the standard deviation of the aggregate capital stocks also almost doubled.
While absolute aggregate capital stock data are often useful for empirical analyses the capital stock available per worker,  i.e. capital intensity, is often the more interesting variable. High capital intensities indicate that the amount of physical capital  available per worker in the production process is also high.
In Figure 9 we show a world map reporting capital intensities for the year 2014. It is easily visible that the ranking for this indicator is quite different from those reported in the previous section. Especially China, but also India and to some lower extent also Brazil and Russia do not perform very well in terms of capital intensity. On the other hand comparatively small but highly developed countries like the Scandinavian countries, Belgium, Ireland, Austria and Luxemburg appear among the 20 countries with the highest capital intensities.
As Figure 10 reveals, Norway and Japan turn out to have the highest capital intensities in our sample, ranging closely to 500,000 USD per worker, closely followed by Switzerland. The next group of countries has capital of slightly more than 300,000 USD per worker and is led by Japan, followed by Denmark, Belgium, Austria, Sweden, Finland, France and Australia. Germany, the United States and Canada range only on 15th, 16th and 17th place, the United Kingdom does not even range among the first 20 countries.
It is also an interesting question, how much capital a country needs to generate the current output. This question can be answered by studying capital coefficients, i.e. the amount of available capital divided by the gross domestic product. Figure 11 shows a world map with capital coefficients. When comparing capital coefficients between countries on strongly differing levels of development, the results are not too informative as the economies structures and thus also their need of capital differ enormously. In Figure 12 we therefore concentrate on a comparison of capital coefficients in high income countries.
The country with the highest capital input per unit of GDP is Japan, where 3.8 units of capital are utilized to produce one unit of output. Capital coefficients of more than 3.5 are also prevailing in Greece, Spain, Austria, Italy, the Czech Republic and Finland. Other large industrial countries such as Germany (3.2) and Australia (2.9) turn out to exhibit somewhat lower capital coefficients. Even lower capital coefficients can be observed for China (2.8), the United States (2.7) and the United Kingdom (2.4).
5 Summary and conclusions
The lack of internationally comparable capital stock data has been a major obstacle to empirical multi-country research on the role of physical capital in the process of economic growth. The feedback on our approach to overcome this problem by delivering consistent estimates of aggregate capital stocks using the Perpetual Inventory Method (see Berlemann and Wesselhöft 2014) motivated us to deliver an update of the dataset, which now covers the time period of 1960 to 2016 for 122 countries (unbalanced). As in the previous version, the dataset can be downloaded from the authors’ internet page freely.
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