Natural capital in cross country income
differences
Abstract: This paper examines the role of natural capital in an evaluation
of cross country incomes differences. To this end the productive
capac-ities of various types of produced and natural capital, as inputs to the
production process, are assessed. A development accounting exercise is
used to ascertain the importance of the various types of capital. This
re-quires that the data is harmonized for cross country comparisons, while
allowing all the capital types to be consistently comparable to the each
other. The results show that for several countries, large improvements to
the understanding of income differences can be achieved.
Daan Freeman
Contents
1 Income Differences (Introduction) 3
2 Development accounting (cross-country setting) 6 2.1 Capital Stocks . . . 8 2.2 Income shares . . . 11
3 Synopsis 16
4 Data Sources 18
5 Analysis & Results 25
5.1 Variance Decomposition . . . 25 5.2 Productivity Differences . . . 27
6 Conclusion 36
2 LIST OF FIGURES
List of Figures
1 Percentage adjustment to 2011 Relative Estimated TFP Differences (compared to United States) - For Produced capital (blue) & Natural capital (green), sorted
from most negative to most positive . . . 5
2 2011 Relative TFP Differences - ’Traditional’ (Yellow) & Produced Capital (Blue) (USA = 1) . . . 30
3 2011 Relative TFP Differences - Produced capital (Blue) & Natural Capital (Green) (USA = 1) . . . 31
4 2011 Relative TFP Differences - ’Traditional’ (Yellow) & Produced Capital (Blue) (USA = 1) - Using an Internal Rate of Return . . . 33
5 2011 Relative TFP Differences - Produced capital (Blue) & Natural Capital (Green) (USA = 1) - Using an Internal Rate of Return . . . 34
6 2011 Changes to Relative TFP differences - Contrasting the External (purple) with the Internal Rate of Return (yellow) . . . 35
7 Hierarchy of types of capital . . . 41
List of Tables
1 Natural capital Lifetimes . . . 192 Depreciation Rates . . . 20
3 Real internal rate of return (for 2011) . . . 21
4 Per Capita Stocks of Assets (mil. 2011 USD PPP) . . . 23
5 capital output ratios and correlation to per capita income for 2011 . . . 24
6 Variance Decomposition for 2011 . . . 25
7 Variance Decomposition for 2011, using the internal rate . . . 26
8 NPVStock divided by Stock . . . 38
9 Per Capita Stocks of Assets (mil. 2011 USD PPP), valued using the internal rate of return . . . 39
1
Income Differences (Introduction)
Large income differences exist across different parts of the world, leading to a great deal of inequality between people from different countries (Caselli, 2005). Living in a country in which incomes are low is often disastrous, forcing people to endure poverty without respite. Addition-ally, of the all the income inequality in a global sense, inequality between rather than within countries is the greater contributor (Milanovic, 2016). Understanding the reasons for the large income differences across the world is vitally important to address these issues.
The development accounting method can be used to account for income differences by ex-amining production in many countries. Development accounting evaluates income differences between countries using information about the inputs of the production processes. The result is that income differences are attributed to differences in inputs, or to differences in the pro-ductivity with which inputs are used. More specifically, propro-ductivity is measured as a residual; the part of income differences that can not be explained by the differences in input factors. The measure of productivity differences is very important to asses the causes of the income differences, and can potentially guide efforts to reduce differences in income. Because of this potential, it is important that the productivity residual is measured in as much detail as pos-sible. To achieve greater detail, the standard methodology is improved here by adding more detail and variety to the input measures that are used.
4
Recent advances data allow to add extra detail to the measure of the produced capital stock, as well as to include natural capital. This paper combines the more detailed produced capital data with the natural capital data, and incorporates them into the development accounting framework. To achieve this addition, the framework used will be adapted to include more heterogeneity in the measure of produced capital, along the lines of Mutreja (2014) and to some extent Caselli and Feyrer (2007), though the focus of the latter is on the addition of natural capital. Which is the second issue; the measurement and inclusion of natural capital (Brandt, Schreyer, and Zipperer, 2013), as well as including agricultural land (Vollrath, 2009). A final challenge is how to relate the various types of capital to each other, as well as to make them internationally comparable (Diewert and Fox, 2015).
Natural capital is a particularly interesting addition to the model as it is an important part of income for many countries; in fact many countries are very much reliant on the their reserves of natural resources to maintain their spending patterns (i.e. fiscal spending as well as imports). Furthermore, natural capital makes up a large part of the capital stock, especially for low income countries. This means that a model including of natural capital should account for more of the variation in income than if only produced capital would have been included.
This paper uses a cross-section of 113 countries (for the year 2011) starting at a ’traditional’ estimate of productivity differences, moving through an estimate employing heterogeneous pro-duced capital measures, to end up at an estimate that accounts for the importance of natural capital. Figure 1 shows the change of productivity relative to the United States. There are two cases; the percentage change to the estimates when improved produced capital estimated are included (blue), and when natural capital is taken into account (green). For example, the largest upward blue bar shows that the estimate for Venezuela’s productivity, relative to that of the United States is increased by over 100% when heterogeneous produced capital is taken into account. The green bars in figure 1 show greater values, especially for the OPEC countries, and generally stronger downward tendencies. When natural capital is included, sticking to the same example, the downward bar of Venezuela shows that the estimated TFP share would decline with over 120% compared to the traditional value. The countries are split into OPEC and non-OPEC members, since the effects are largest for natural capital reliant countries, of which the OPEC members are prime examples.
Figure 1: Percentage adjustment to 2011 Relative Estimated TFP Differences (compared to United States) - For Produced capital (blue) & Natural capital (green), sorted from most neg-ative to most positive
−150 −100 −50 0 50 100 % Change Non−OPEC OPEC
using a production function containing the various capital types. This comparison is a ’measure of success’ (Caselli, 2005) indicating how well the variation of incomes is explained by the es-timation of the production function, assuming equal productivity across countries. The results of the variance decomposition generally find little change in the level of ’success’ when the new measure of produced capital is added, but the addition of natural capital appears to counter these effects.
6
2
Development accounting (cross-country setting)
As briefly outlined above, development accounting is used to explain income differences between countries. To achieve this, income differences are evaluated using the variation of available the production inputs between different countries. The inputs are evaluated by choosing a produc-tion funcproduc-tion that reflects economy-wide producproduc-tion as best as possible. Using such a producproduc-tion function, differences in income are accounted for by differences in the availability of inputs. Of-ten, after all the variation in inputs has been taken into account, some residual part of income remains unexplained. The residual is often interpreted as differences in productivity, or more formally, total factor productivity (TFP). Standard development accounting assigns up to 50% of income differences to the residual, which means that in some cases 50% of income differences would be due to more efficient use of inputs! Alternatively, and perhaps more appropriately, TFP is also sometimes called a “measure of our ignorance” (Caselli, 2005) recognizing that it is essentially comprised of all the factors that are excluded from the production function, but that nevertheless influence income (differences). This paper aims to reduce ’our ignorance’ by incorporating inputs that are normally not (explicitly) included into development accounting exercises.
Stated before, the new addition to the framework is natural capital, which is added alongside the usual produced capital. The other main component that is always used as an input for production in development accounting is a measure of the labour force. The labour force measure reflects the size of the labour force, often augmented by a measure of human capital, reflecting productivity of the average worker. To show how the development accounting method uses these inputs, the simple Cobb-Douglas function is used here for illustration. Traditionally, the Cobb-Douglas is the most used production function in development accounting, and it explains income by produced capital, human capital and TFP1 (Caselli, 2005; Hsieh and Klenow, 2010):
Yi = Ai∗ Kiα∗ (hiLi)β
Yi = Ai∗ Kiα∗ (hiLi)β∗ Niγ
(1)
Where in the first equation, Y is income, and K is the produced capital stock. L is a measure of the labour force, which is modified by the (average) level of human capital per worker h. The
1
subscript i indicates that this is the function for a country i. The parameters α and β are the output elasticities relevant for produced capital and human capital. In practice these elasticities are approximated by using the share of total income accruing to that particular input. The income shares are used to ‘weigh’ the effects of the input factors (produced and human capital) on income. Finally, A is a measure of TFP, which modifies the effects of the weighted inputs to end up with total income Y . The second line of equation 1 adds natural capital N , which is weighted with γ; its output elasticity (or income share). The Cobb-Douglas function can be used to explain differences in incomes between two countries by dividing the production function of one country by that of another. After dividing, the equation can then be specified such that TFP differences between two countries depend on differences in income and inputs. A more detailed explanation of the application is provided later.
After having chosen the functional form, the other critical aspect of the development ac-counting exercise is the measurement of the production inputs that have to be included in the production function. In this case the production function will be specified using the three types of capital introduced above, produced, natural, and human capital. These need to be combined with information on their respective output elasticities (represented by α, β and γ in equation 1). Besides rewriting equation 1, filling in the unknowns and backing out values for Ai (Ai/Aj),
the TFP (differences), there are other ways to evaluate the explanatory success of development accounting. A variance decomposition approach is used by (Caselli, 2005) to evaluate the per-formance of the development accounting framework under different choices of parametrisation and data. The variance decomposition measures the explanatory power of the model by dividing the variance of factor input-predicted income by the actual income observed in the data. The result then is a measure of ‘success’, indicating what percentage of the variation in income is explained by variation in the input factors.
The variance decomposition uses the Cobb-Douglas functions presented in equation 1, which can be rewritten as:
var(log(Y )) = var(log(Yv)) + var(log(A)) + 2cov(log(A), log(Yv)) (2)
Where Yv is the predicted income based solely on the factors, leaving productivity, and
8 Capital Stocks
ShareAccounted = var(log(Yv))
var(log(Y )) (3)
It needs to be made clear at this point, that development accounting examines proximate causes of income, as opposed to ultimate causes. As is illustrated in (Hsieh and Klenow, 2010), development accounting uses the different types of capital as inputs to explain income. The quantities and qualities of the inputs themselves are likewise influenced by many differ-ent drivers, which include geography, institutions (see for example Robinson, Acemoglu, and Johnson (2005), or simply luck. The deeper drivers are referred to as ‘ultimate’ sources and makes the different types of capital used here, ‘proximate’ sources of income. This has led Hsieh and Klenow (2010) to term the method used here “proximate development accounting”. The ultimate causes are not explicitly taken into account here as the focus is primarily on different types of capital. This focus on proximate causes does not mean of course, that the underlying ultimate drivers are not relevant.
A final note on the development accounting method is that it unfortunately does not estab-lish clear causal relationships. As Hsieh and Klenow (2010) state for instance, there could well be indirect effects of TFP via produced, or even human capital on income. If this is indeed the case, it could lead to the understatement of the importance of the TFP, in its effect on income. If the indirect relationships would affect various countries in different ways, this leads to biases in estimates of productivity differences in the cross country framework adopted here.
2.1 Capital Stocks
more extensive review of the literature on the resource curse can be found in Smith (2015). A further point tied in with the Dutch-disease argument is that sectors that extract natural capital are often highly productive sectors. The productivity of the natural capital sectors does not only reduce opportunities for other (export) sectors to develop, but also leads to problems when attempting to measure economy-wide productivity. The estimates of productivity could be biased if natural capital is not properly taken into account, this is one of the problems that this paper aims to address.
Venables (2016) points out that the fluctuation of commodity prices is another problem associated with reliance on natural capital. These fluctuations are a huge problem for economies that are highly dependent on the income from export of resources. primarily, because the price volatility makes it difficult to maintain prudent fiscal policies. The price fluctuations of natural capital also lies at the heart of another measurement problem. The valuation of the stock of natural capital is based on expected future revenues over the lifetime of the stock, if the revenues fluctuate heavily over time, the valuation of the stock becomes less accurate. Equation 4 displays how the value for a stock of an asset a of natural capital is determined (Lange, Hamilton, Ruta, Chakraborti, Desai, Edens, Ferreira, Fraumeni, Jarvis, Kingsmill, and Li, 2011).
Vat= Rta1 +1 r 1 − 1 (1 + r)T (4)
Where Vat and Rta are the value of the stock and the revenues of natural capital type a, at time t. Equation 4 builds on the restrictive assumption that revenues are constant over time, and therefore also that the extraction path is optimal (Lange et al., 2011; Diewert and Fox, 2015). To this end, it is interesting to examine whether the value of the natural capital stock, based on equation 4, corresponds to the value in case sufficient time has passed to examine the ex-post value, based on the realized revenue streams. In the latter case the actual revenue streams are simply discounted using the rate of return. Some tentative statistics with regards to this are presented in the appendix; table 8.
10 Capital Stocks
of natural capital is vital because natural capital consist largely of non-renewable resources. A link to sustainability can also be made in the current work, where the importance of natural capital in total income differences is used. The importance of natural capital could provide an indication of the sustainability of current income levels for certain countries that depend to a significant extent on natural capital.
Returning to the valuation of stocks of assets, Arrow et al. (2012) employ what they call ‘shadow prices’, which are the prices that reflect the social costs of the consumption of a certain asset. The shadow prices are defined as the contribution of a certain asset type to ‘comprehensive wealth’, which itself is defined as a measure that reflects the ability of a country to generate income, now and in the future. When shadow prices have been estimated, a capital asset can be valued to indicate how consuming it affects comprehensive wealth. evaluating all assets using the appropriate shadow price allows for comparability between the effects of consuming different kinds of assets. Comparability between assets implies substitutability between assets, however, some argue that this is not at all appropriate (Arrow et al., 2012). If substitutability is not possible, the optimum consumption of some assets must be (close to) zero, in order to ensure sustainability of future consumption. Other views argue that any such calculation to estimate sustainability is difficult and relies too heavily on assumptions about realism of expected prices in the first place (Smulders, 2012). These arguments are again relevant for the valuation of natural capital presented in equation 4, assuming for the purposed of this paper that all assets can indeed be compared through such methods.
land is included as a factor of production.
Having discussed the valuation of the natural capital stock, the other inputs of the pro-duction function, human and produced capital, deserve additional elaboration. Human capital covers the size and quality of the labour force. It is common in development accounting to augment measures of the labour force with estimates of the average level of human capital, which is strongly based on educational attainment. Examples of how to deal with this come from Caselli (2005) and Hsieh and Klenow (2010), who choose a particular functional form to operationalize human capital, which is shown in equation 5.
h = Be(φ(s)) (5)
Where h is the human capital per person, s is the years of schooling, and B captures additional factors of human capital accumulation. The function φ(.) is the ’Mincerian return’ function (Hsieh and Klenow, 2010), which essentially puts a value on the number of years of education. The return is an increasing function for education, but at a decreasing rate2.
Finally the stock of produced capital is rather more difficult to value exactly, because of the difficulty of measuring all the buildings and machines within a country. Instead the investments over a long period of time (corrected for depreciation) are added up to estimate the stock of produced capital. This methods is called the perpetual inventory method and is shown in equation 6 (Feenstra, Inklaar, and Timmer, 2015)
Ka,t= (1 − δa)Ka,t−1+ Ia,t (6)
Where Ka,t and Ka,t−1 are the values of the capital stock at time t and t − 1 for asset a.
Ia,t is the investment at time t, and δa is the depreciation rate, both for asset a. Assuming
some starting stock, or starting from a point in time that is sufficiently long ago, and working forward in time will result in an estimation of the current capital stock.
2.2 Income shares
Equation 1 showed the simple Cobb-Douglas function to illustrate development accounting. Now, to delve deeper into how the process will work, the actual production function is pre-sented. The production function that will be used is the so-called translog function (Diewert
2
12 Income shares
and Morrison, 1986). The translog function is a more general form of the Cobb-Douglas func-tion, the benefit of this function is that it can be specified in a more suitable way for international comparisons. This is due to the function not only taking the individual factors of production into account, but also their cross products3. Equation 7 shows the translog function including the three broad types of capital.
ln Yi= α1iln (Ki) + α2iln (hiLi) + α3iln (Ni) + β11ln (Ki)2+ β22ln (hiLi)2+ β33ln (Ni)2
+β12ln (Ki) ln (hiLi) + β13ln (Ki) ln (Ni) + β23ln (hiLi) ln (Ni)
(7)
Or, in a more general and compacted shape:
ln Yi(Vi) = α0i+ L X l=1 (αliln vli) + 1 2 XL l=1 M X m=1 (βlmln vliln vmi) (8)
Where Vi = (v1i, v2i, v3i) is the vector of endowments of capital, representing stocks of
produced, human and natural capital, in country i. Note also that βlm= βml, which is why the
second term is divided by two, and that the β’s are assumed to be the same for all countries (Feenstra et al., 2015). Using this function, the productivity differences between a country i and a country j can be expressed as:
Ai = (Yi(Vi)) (Yj(Vi)) or Aj = (Yi(Vj)) (Yj(Vj)) (9)
The first equation 9 states that the productivity difference Ai between country i and j can
be derived by dividing the production of country i by the production of country j, if country j had the factor (capital) endowments of country i. The second part, Aj, does the same but
uses the endowments of country j in both cases. Both equations are valid expressions of the productivity difference between country i and j, so they are combined (Feenstra et al., 2015):
ln (AiAj)
1 2 = 1
2(ln Yi(Vi) − ln Yj(Vi) + ln Yi(Vj) − ln Yj(Vj)) (10) Now, ln Yj(Vi) and ln Yi(Vj) cannot be observed, being the counter-factual situations in
which either country produces with the endowments of the other country. However, using
3
equation 8, equation 10 can re-written into equation 11, following Diewert and Morrison (1986) and more closely Feenstra et al. (2015):
(AiAj)
1
2 = (Yi(Vi))/(Yj(Vj))/QT(Vi, Vj, wi, wj) (11)
Where the QT is the T¨ornqvist quantity index of capital endowments, which is defined in
equation 12. ln(QT(Vi, Vj, wi, wj)) = L X l=1 h1 2 wlivli P m=1wmivmi +P wljvlj m=1wmjvmj lnvli vlj i (12)
Where wli is the price for capital l in country i, which means that P wlivli
m=1wmivmi is the share
of income accruing to capital type vl, in country i4. The final term of equation 12 (lnvvlilj)
represents the difference in various assets of the human, produced, or natural capital stocks between country i and j .
Equations 11 and 12 will be used to compute the productivity differences. The differences will be calculated by consistently taking the United states as the base country, i.e. to be country j5. The results of the productivity differences presented will be the differences of any country i with respect to the United States. Different specifications of equation 12 will be used to evaluate the effect of including natural capital on productivity differences.
To estimate productivity differences, equation 12 uses the income shares of each asset of the various capital types. To compute the income shares the amount of income derived from each of the assets needs to be examined. The income derived from a stock of assets depends on the size of the stock, but also on its productive capacity. Consider for example the productivity of computer, and compare these to that of a building. This seems difficult enough, next consider the productivity gains of a stock of computers and a stock of buildings of identical value. Comparing one computer to (part of) a building of the same value is rather nonsensical. To remedy this problem of compatibility, information is required about the user costs of the assets. The user cost includes the factors that govern the relation between the capital stock and the which income derived from it. Combining the stocks with user costs will result in the flows of income derived from the stocks, these flows are called capital services (OECD, 2009).
The user cost takes different shapes for produced and natural capital. For produced capital
4
For the derivation of equation 12 see Feenstra et al. (2015).
5An additional specification was run using Australia as the base case, which mostly did not impact the
14 Income shares
the user cost is calculated using the original purchasing price; the rate of return, or opportunity costs; and the capital gains, or asset revaluation. By attaching user costs to the stock of each respective type of capital, the capital service flows of different capital types can be compared with one another. Equation 13 shows the user cost for a certain asset (a) of produced capital as (OECD, 2009):
U CCa= ra+ δa− ia (13)
Where ra is the real rate of return, ia is a revaluation term reflecting asset price changes,
and finally, δa is depreciation rate. The rate of return can be interpreted as an opportunity
cost, or a lower-bound return of any asset. The revaluation is defined as the price change of assets; this is different from general inflation. If stocks are already valued at market prices, the revaluation is the difference between price change of assets and general inflation. The term reflecting depreciation is an indication of the wear an tear by usage of the asset6. Applying the
user cost requires the assumption that marginal costs equal marginal benefits to make the capital services appropriate as a measure of income. As an alternative, instead of directly measuring the capital service flow, Brandt et al. (2013) assume that capital flows are proportional to their stock. Therefore, they assume that the rate of change in the stock equals the rate of change in services, this assumption removes the need to specify a user cost.
Moving now to natural capital, there are some differences with produced capital. Usage of produced capital leads to depreciation, but this is not the case for natural capital. In the case of natural capital, depreciation is equivalent to depletion, i.e. the extracting of a type of assets from a stock of natural resources. The special characteristic of many types of natural capital is that they are non-renewable. Consider a sub-soil stock of oil, once all the oil is extracted and used for production (in this case likely for fuel), it will be impossible to extract it again. This can be contrasted with produced capital, which can be replaced. If a factory building is worn down, it is relatively easy to replace it by building another factory. Diewert and Fox (2015) derive two alternative measures for the user cost of non-renewable resources. Their preferred option is the traditional user cost, which is similar to equation 137 and is defined for an asset a of natural capital in equation 14.
6several choices can be made regarding depreciation paths, see OECD (2009) for details 7
U CNat= (ra− ia+ (1 + ia)δa∗) (14)
Which is very much like equation 13, but defines δ∗ as the depletion rate, and not the depreciation rate as in the user cost for produced capital.
Alternatively, Diewert and Fox (2015) derive a measure based on the work by Brandt et al. (2013) and Lange et al. (2011), which implicitly uses input and output prices (unit costs and unit price). This second way of defining the user cost is termed the “World Bank” approach since it is readily applicable using data available at the from the World Bank (Lange et al., 2011). By using information on depletion and total revenue for an assets of natural capital a, the user cost can be calculated, as is shown in equation 15.
U CNa= Rta/(Sat−1− Sat) (15)
Where St−1 and St are the stocks of natural resources (expressed in units of extracted resources) at the beginning and end of a period t. St−1− St therefore corresponds to the
extracted resources during period t. Rt is defined as the total net revenue of the extracted resources8. While equation 14 is perhaps theoretically more sound, equation 15 presents the more useful specification of the user cost because, as will become apparent below, the data that is used, assumes it implicitly. Diewert and Fox (2015) argue that the two equations are equivalent if some conditions are met. Firstly, the unit rents of the resource need to equal the user costs. Diewert and Fox (2015) show that this holds, if the resource extraction path is optimal9. Secondly, equivalence of equations 14 and 15 requires that expectations about depletion, revenues, and therefore also prices, on which equation 15 is based, are realized. While this can be considered a strong assumption, it is necessary to employ said data.
The structure of human capital is fundamentally different from produced and human capital. Concepts like the depreciation, depletion, or rate of return are much more difficult to apply. Because of these difficulties, a ’user cost’ for human capital hardly seems appropriate. Luckily, the income that accrues to human capital is easier to observe than are the incomes accruing to the other capital types. Income derived from human capital is available in the shape of data on the total labour income.
Having expressions for the user costs and stocks of the different types of capital, it is possible
8more formally: R = (p − c)q where p, c and q are the price, cost per unit, and the quantity produced 9
16
to aggregate them to form total income. This makes it possible to derive the shares of each asset, by dividing each of the separate asset’s income stream by the total income. Equation 16 shows a decomposition of the total capital flow of income R, along with the shares of each of the parts of income.
R = RL+ X n (Rn) + X a (Ra) sharen= Rn/R sharea= Ra/R shareL= RL/R (16)
Where Rnand Raare the flows of capital services for each individual type of produced capital
n and natural capital a. The shares are then obtained by dividing each capital type’s income by the total income. Computing the income shares of each assets using capital services allows for more detail in the income shares; each type of capital can be assigned an income share. Traditionally, only the income share of labour is used in development accounting; aggregate capital is then assigned the residual share.
3
Synopsis
This section outlines the expectations with regard to the estimated productivity differences when the current development accounting frame work is used. Starting from the point of the traditional capital-labour development accounting, two major changes are implemented that can affect the estimation of the productivity differences. These changes are the disaggregation of the capital term, and the addition of natural capital to the framework. The effects of the two changes can largely be considered separately in their effects of the estimated productivity differences. While an aggregated capital term is the norm, disaggregating the capital term has been done before (Mutreja, 2014; Caselli and Wilson, 2004). A common conclusion is the observation that the composition of the capital stock is very diverse between countries.
capital stocks. The capital quality here is reflected in the size of the new capital stock vs. the old estimates. The contribution of the composition and the efficiency run through the addition of the user costs. The user cost effectively weighs the capital assets in the overall stock on the one hand; on the other hand, using the relative user cost takes cross country efficiency differences into account. The authors find that disaggregating the capital capital stock has the potential to account for some of the estimated productivity differences between countries. In fact, the results suggest that up to an additional 10% of variation in incomes can be accounted for, on top of the traditional estimates. Combining these two views results in the expectation that splitting up the capital stock could yield reduced estimates of productivity differences by bringing the productivity estimates of different income groups closer together. In a more technical sense, if a relatively small stock of capital is responsible for the generation of a relatively large share of income, then the miss-estimation from using an aggregated capital stock would be largest.
18
differ. It is expected therefore, that explicitly taking the natural capital stock into account will reduce the productivity of richly endowed countries compared to their less well-endowed counterparts.
4
Data Sources
Having defined the production function and discussed the required variables, data needs to be gathered for the necessary terms of Equations 11 and 12. First, Yi(Vi) and Yj(Vj) are the
GDP of countries i and j respectively, data for which is obtained from the Penn World Table 9 (PWT9). (Feenstra et al., 2015). The data from PWT9 is GDP at current PPPs, in 2011 dollars, but price level data are available, should transformation be required. For Equation 12, the income shares of the different types of capital are required, as well as measures for the stocks of the different types of capital.
Firstly, all stocks of capital are transformed to per capita form, dividing the stock of each asset by the total population, data for which is available from PWT9. An alternative would be to use per worker values of capital (Caselli, 2005) which would not make a large difference to the overall results. The data for human capital are obtained from PWT9 where estimates for the workforce, the average hours worked, as well as the level of human capital are available. These estimates are in the form outlined in equation 5 and can be used as such10.
Second, natural capital data is from the World Banks wealth accounting dataset (Lange et al., 2011). This dataset contains data on three broad categories of natural capital, which are forestry, minerals, and energy. These categories can be again subdivided into multiple different types of natural capital which are shown, along with the types of produced capital in figure 7. The natural capital data includes the net revenues derived from each asset, which therefore corresponds to equation 15 (Brandt et al., 2013; Diewert and Fox, 2015). One additional type of natural capital is added to the dataset that is not featured in the World Bank dataset; agricul-tural land. Data for this is obtained form FAOSTAT (Food and Agriculture Organization of the United Nations, 2016), this resource includes data about gross production value of agricultural sector and the land area allotted to agriculture. The data do not include net production values for a limited number of countries, which are necessary to obtain the income shares derived from agricultural land. Lange et al. (2011) assume that the cost of agriculture is 30% for all countries,
10See http://www.rug.nl/research/ggdc/data/pwt/v90/what_is_new_in_pwt90.pdf for a more detailed
Table 1: Natural capital Lifetimes Reserve Lifetime Agriculture 25 Timber 25 Energy Oil 16 Gas 38 Hard Coal 63 Soft Coal 456
Metals and Minerals
Bauxite 97 Copper 33 Gold 17 Iron Ore 88 Lead 16 Nickel 25 Phosphate 37 Tin 45 Silver 14 Zinc 21
Source: Lange et al., 2011
this method however leads to incomes from agricultural land that in some countries rival the size of total GDP. To bring the estimates of income from agricultural land more in line with expectations, the costs in agriculture are instead set equal to the share of labour income in total income. Assuming that labour makes up the lions share of the costs in agriculture, as well as, that the share of labour income in agriculture is similar to the overall share of labour income in the economy.
To enter natural capital data into the comparison in equation 12, the data need to be adapted. This is done by estimating the present value of the stock of natural capital. For this estimation, data on the lifetimes of the different stocks of natural capital is required (see table 1), along with the rate of return. Several assets like coal and bauxite have lifetimes that far exceed the average; however, following Lange et al. (2011) lifetimes are capped at 25 years in the calculation of asset stocks. The figures in table 1 are based on World Bank estimates of the median lifetimes over all the available years and countries11. The rate of return is assumed here to be equal to either an external rate of return of 4%, or to an estimated internal rate of return (see below). These rates of return, in either case, are assumed to be equal for all the types of natural and produced capital. The estimation of the value of a stock of natural capital is shown in equation 4 (Lange et al., 2011).
11
20
Thirdly, the measure of produced capital also uses data from PWT9. Data is available for nine different types of capital stocks, the detailed composition of the capital stock employed in this paper can be found in figure 7. The data on capital stocks is denominated at current cost, fortunately, price indexes are available, allowing international comparisons to be made more easily.
In addition to the data on capital stocks, the income shares for each capital type are required. This data is available for human capital, as total payments to labour as a share of GDP, from PWT9. However, the income shares of the various types of produced and natural capital are computed using the flow of capital services, or rents, from each of the stocks of the capital types. For natural capital, the data are available as the total rent derived from each capital, and can therefore be readily applied here. For produced capital, however, the user costs needs to be separately calculated, which is done using equation 13. The data on pricing of the stocks is already obtained, still leaving the other components of the user cost to be collected. In accordance with equation 13 the depreciation rate, revaluation term, and rate of return are still required.
The depreciation for specific assets is assumed not to depend on the country that the capital happens to be located in. Depreciation rates are taken from Feenstra et al. (2015) who base their data on Fraumeni (1997). The specific depreciation rates for each asset type that together make up produced capital are shown in table 2. The revaluation term is the price change of produced capital, data for which is adapted from PWT9.
Table 2: Depreciation Rates
Asset type Sub-type Depreciation Machinery IT 31.5 CT 11.5 Other 12.6 Building Residential 1.1 Non- Residential 3.1 Transport Equipment 18.9 Other Software 31.5 Other 15
country, it is out of the scope of this paper. Instead, following Lange et al. (2011) a real rate of return of 4% is assumed for all countries. The alternative, an internal rate of return can be estimated by solving for the rate of return from total income. Equation 17 decomposes GDP into incomes from labour RL, produced capital RN and natural capital RA.
GDP = RL+ X n (Rn) + X a (Ra) (17)
The capital services (or rents) of labour and natural capital are available from the data (see above), the rents of produced capital are the services derived from produced capital and are defined as their user costs multiplied by the stock of assets. This means that, using equation 13, equation 17 can be solved for ri, which in this case is the internal rate of return. This implies
that the internal rate of return will therefore be defined for each country, but be applied to all capital types within that country.
GDP = RL+ X n (Rn) + X a (Ka∗ (ri+ δa− ia)) (18)
The results of the estimation of the internal rate of return are summarized in table 3. The first row shows the rate of return is only the stock of produced capital is taken into consideration. The second row shows the rate of return when natural capital is also added. It shows that the average rate is considerably higher than the 4% assumed before. The difference between the countries is quite large at times too; ranging from several values that are slightly negative, to the highest value of over 50% for Zimbabwe. The difference between the two rows is also interesting suggesting that when natural capital is included the average rate declines, but also the variation of the across countries. This is a similar finding to Caselli and Feyrer (2007) who find that the marginal return to capital is much more equalized across countries if natural capital is taken into account.
Table 3: Real internal rate of return (for 2011)
Variable Obs Mean Std. Dev. P10 P90 Produced Capital 113 .188 .208 .039 .454 Produced & Natural Capital 113 .118 .132 .028 .221
22
terms need to be transformed to uniform purchasing power parities (PPP’s). Depending on data availability, the transformation requires slightly different approaches for data from each of the different sources. For the produced capital stocks, the initial data is denominated in current local currency units. The first step to transform this data is to convert it to a common currency, in this case U.S. Dollars at 2011 prices, and by using the appropriate PPP estimates. Data for both of these are available for each of the asset types, for the same source as the data on the assets stocks (Feenstra et al., 2015). Secondly, the data is corrected for the relative user costs, to reflect differences in the utilisation costs of the different assets. The user costs defined in equation 13 are used for this purpose. The final data at PPP valued at 2011 U.S. dollars, to which all data needs to be transformed.
Data on the natural capital stock (except agricultural land) is estimated as the present value of the revenue streams which available in current dollars (Lange et al., 2011). This data made constant over time by using a general GDP deflator to obtain values in 2011 dollars. The cross country correction is made using the relative user cost of each of the types of natural capital to make them comparable. The exception to this is the data on agricultural land, for this data, the user costs are difficult to estimate, as no data on the (unit) costs are available. Fortunately, the data on total agricultural production value from Food and Agriculture Organization of the United Nations (2016) are are available in 2004-2006 constant international dollars. These are reshaped into suitably comparable data using pricing data available from the same source.
The primary examination of the data will be done for 2011, as most data is available for this year. The resulting dataset contains 113 countries that sport data on labour, produced capital and at least one category of natural capital. For some countries, data on natural capital contains only limited assets since only a few are actually present. Table 10 in the appendix presents a list of countries that have been included.
Tables 4 and 9 (appendix) show summary statistics for the values of the stocks of assets in 2011. The table shows the average value of the stocks of assets (in millions of dollars PPP), standard deviation and the number of countries for which the data is available. Clearly there is a lot of variation between and within the values different stocks of capital, evident from the high standard deviations. The number of observations for each type show how many countries have values for each of the stocks.
Table 4: Per Capita Stocks of Assets (mil. 2011 USD PPP) Variable Mean Std. Dev. N
Resid. 49322.6 57696.4 113 Gas 38443.8 164388.8 71 Non-Resid. 24455.8 29370 113 Oil 23951.4 77076.8 73 Iron 5165.2 17432.4 36 Agriculture 4157.4 3594.7 113 Other Mach. 3799.2 4825.1 113 Intel. Prop 2244.1 6437.1 113 Copper 1915.9 6591 40 Transport 1292.2 1999.7 113 Timber 1227.8 2281.1 113 Hard Coal 1204.1 2711.5 46 Comm. Tech 750.1 1573.9 113 Software 562.8 1113.8 113 Nickel 547.1 733.4 20 Gold 441.1 816.3 75 IT 359.5 583.5 113 Phosphate 256.7 497.4 33 Soft Coal 246.3 614.2 30 Zinc 163.7 321.3 37 Tin 111.5 227.9 15 Bauxite 108.4 293.3 18 Cultivated 88.3 187.6 113 Lead 56.7 106.2 29 Silver 52.9 107.8 42
agricultural land have data for all the countries included in the analysis12. For all the other
assets types, the values only cover countries which actually posses any meaningful stocks of the assets in question (Lange et al., 2011). This difference between tables 4 and 9 (appendix) is that the second presents the stocks estimated using an internal rate of return, this makes a difference for the estimation of the natural capital stocks, the future income streams of which are discounted differently.
Table 5 shows additional statistics with regards to the capital stock. The first column displays ratio of capital stock to output for each particular capital type. The second column shows the correlation of the capita output ratio with per capita income. Remarkable here is that the correlations of the produced capital stocks are almost all positive, while the correlations of natural capital tend to be more negative. This means that for countries with large stocks of natural capital, generally, incomes per capita are lower. Likewise, if produced capital stocks
12For China, Taiwan, and Sudan the FAO data does not contain full coverage, for these cases, the data is
24
relative to output are large, incomes tend to be higher.
5
Analysis & Results
5.1 Variance Decomposition
Tables 6 and 7 show the variance decomposition of the incomes across countries for the year 2011 (Caselli, 2005; Hsieh and Klenow, 2010; Feenstra et al., 2015). This is an indication of the results of the development accounting exercise for the entire cross section.
The variance of actual incomes is shown in the first row (remaining constant for all speci-fications in both tables. The second row presents the variance of incomes as estimated by the factor inputs alone (Yv), e.g. assuming common technology across all countries. The fourth
row labelled shareaccounted presents the share of variation in total income that is accounted for by the Yv, the figures in this row are according to equation 3. Additionally, the third row
presents the variance of the estimated productivity figures resulting from equation 11, which will be presented in more detail in the next section. Lastly, the final row displays an alternative measure to the share accounted by variation, which compares the 10th to 90th percentile ratios of the actual incomes with those of Yv13. This final entry has the benefit of being less sensitive
to outliers in the data, which can significantly impact the variance. Of note is that the values of this last approach are consistently lower across all specification, this suggests that the more extreme cases contribute strongly to the results of the share of variance accounted for14.
Table 6: Variance Decomposition for 2011
Traditional Produced Capital Natural Capital
Variance(Y ) 1.314 1.314 1.314
Variance(Yv) 0.746 0.609 0.842
Variance(A) 0.101 0.207 0.057
ShareAccounted 0.568 0.464 0.641 ShareAccounted(90/10) 0.381 0.384 0.377
The two tables are differentiated by the rate of return that is applied. In either table, the rows represent the estimates using different specification of the production function. These move from the traditional estimates, to the specification that includes the inputs for separated produced, and finally natural capital. The figures in the second column are based use the
dis-13This is equivalent to the variance decomposition, only uses the 10/90 percentiles ratio (Caselli, 2005) 14
26 Variance Decomposition
Table 7: Variance Decomposition for 2011, using the internal rate Traditional Produced Capital Natural Capital
Variance(Y ) 1.314 1.314 1.314
Variance(Yv) 0.746 0.932 1.101
Variance(A) 0.101 1.167 0.098
ShareAccounted 0.568 0.710 0.838 ShareAccounted(90/10) 0.381 0.564 0.575
aggregated produced capital measures, but do not include natural capital. The third column shows the estimates also the including natural capital.
The first results is that from the first to the second column, the share that is accounted for increases across both tables and for the 90/10 ratio. The total variance shows a reduction when considering table 6. This indicates that considering the separate assets of produced capital, a larger share of the income variation is accounted for. This first step shows a significant gap between the two tables, as the estimates of produced capital show much larger shares when the internal rate is employed. These figures are in line with the results of Caselli and Wilson (2004) who also find that the disaggregation of the produced capital measure is capable of explaining significant portion of additional variation in incomes.
The changes, moving from columns 1 to 2 are due to two primary effects: a composition effect and an efficiency effect (Caselli and Wilson, 2004). The composition effect is due to composition of the capital stock varying between countries, and this can be very important. As was seen in table 5, the different capital types relate to income in different ways. The assets of produced capital are generally positively correlated with income, but also within these assets, there is variation. This means that relatively large stocks of highly productive capital will increase the overall capital stock, if their higher productivities are taken into account. Since the productive capital stocks are generally more abundant in richer countries, the overestimation of their TFP residuals is reduced.
external rate of return is used, the only cross country variation of the user costs is due to the variation in asset-price changes, as becomes clear from equation 13. Because the price changes of assets are generally lower in richer countries, the user costs tend to be higher there. Through this, the estimate of relative TFP in inflated as the productivity of the capital stock is estimated to be lower. This reduces the share of variation in incomes that is accounted for, and is likely to be the reason that this is observed in table 6. However, when the rate of return is allowed to vary, the user costs become more in line with income levels and reduce the negative efficiency effect, and indeed turn it positive, which explains the large difference between the tables.
Moving now to the final column, the differences between the two tables are smaller in terms of the changes, but the tendencies are comparable. Overall, the effect of the addition of natural capital seems to have an ambiguous effect on the share of variation accounted for. There is a distinct different between the variation measure and the 90/10 ratio. This difference indicates that some of the gain in the variance is likely to be due to countries that are at the extremes of the income distribution. This is perhaps no great surprise, as the expectation is that most of the explanatory clout of the additional of the natural capital, apply to countries at the extremes of the income distributions; i.e. poor countries heavily reliant on natural resources, but also (on average) rich countries, well-endowed with oil, gas and other valuable natural resources. The results that the addition of natural capital has relatively small effects, is in line with Brandt et al. (2013) who find similarly small overall effects when accounting for natural capital in income growth15.
5.2 Productivity Differences
This section presents the estimated productivity differences of each country with the United States Figures 2 and 3 show the productivity for each country, as a share of the productivity of the United States. The results of both these graphs use the external rate of return; the results using the internal rate are presented below. The yellow bars in figure 2 show the TFP estimated using just human capital and produced capital as the two types of capital, these estimates correspond to TFP estimates published in PWT9 (Feenstra et al., 2015). The blue
15
28 Productivity Differences
bars in tables 2 and 3 show results that still use human and produced capital, in this case however, capital is no longer one aggregated total, but disaggregated measures of produced capital are used. Finally, the green bars in figure 3 show the results when natural capital is included in the estimation of TFP differences.
Country groups are arranged conforming to broad income groups according to the classifi-cation of the World Bank (World Bank, 2016), with the addition of a separate group for OPEC countries, displayed at the far right of the graphs. Within the groups, countries are sorted according to their estimated TFP relative to the United States.
Figure 2 shows the original and revised estimates of TFP differences when introducing a more detailed measure of capital, taking into account the shares of all the different produced capital assets. There are several countries with rather large corrections, either up- or downward. It appears that taking the productivities of different types of capital into account makes quite a large difference for some countries. There are two main effects that are at work here and it is interesting to examine them with the help of some individual country examples. Firstly, the most apparent effect is the size of the produced capital stock; correcting the capital stocks for the relative user costs, leads to differences in the estimated productivity because a larger stock of capital requires less productivity to arrive at the same income. The capital stock for most countries is somewhat larger, reducing estimated productivity compared to the United States. Of course, the make-up of the capital stock the second important factor. An example for this second effect is Qatar (QTR), which shows an increase in estimated productivity compared to the United States, while the estimated capital stock remains similar. In this case, the change is due to the fact that capital assets, which represent a relatively small part of the capital stock are responsible for generating relatively large shares of income. The increase of estimated productivity in for example Ireland (IRL) is also due to this effect.
Figure 2: 2011 Relative TFP Differences - ’Traditional’ (Yellow) & Produced Capital (Blue) (USA = 1)
0
1
2
3
Low−income economiesLower−middle−income economies Upper−middle−income economies High−income economies High−Income OECD economies OPEC countries
CAF NER BDI MOZ TGO RWA ZWE TZA BEN LSO TJK BFA CIV
CMR SLE SEN KEN SDN MRT JAM HND LAO IND BRB PHL NIC CHN PRY
MAR LKA KGZ MDA COL MNG UKR ARM BOL CRI FJI DOM TUN PER ZAF SWZ GTM SRB NAM JOR EGY TTO THA HKG BRA URY PAN SVN LVA TWN MYS SVK ROU HRV MUS BGR CYP MEX LTU RUS BWA BHR TUR ARG KAZ CZE GRC HUN KOR EST PRT JPN ISR GBR ITA CHL ISL AUT LUX
0
1
2
3
Low−income economies
Lower−middle−income economies Upper−middle−income economies High−income economies High−Income OECD economies OPEC countries
CAF MOZ NER BDI ZWE TGO RWA TZA SLE BFA MRT BEN CIV LSO CMR TJK KEN SEN SDN BOL MNG KGZ LAO HND JAM NIC IND PRY UKR BRB PHL CHN PER MAR COL LKA ARM MDA FJI ZAF CRI TUN
32 Productivity Differences
The results of the specification above show some varying degree of differences concerning the addition of natural capital to the development accounting framework. It is interesting to examine how well these result hold up against different choice for certain other variables.
Recall that several choices have been made to arrive at the results that are presented above; choices, that can be altered. The estimation of natural capital stocks, and the specification of the income shares is dependent on the choice of the real rate of return. The results above use the external rate of return of 4% but an internal rate of return, in some cases can deviate strongly from this figure.
0
2
4
6
Low−income economies Lower−middle−income economies Upper−middle−income economies High−income economiesHigh−Income OECD economies
OPEC countries
Figure 5: 2011 Relative TFP Differences - Produced capital (Blue) & Natural Capital (Green) (USA = 1) - Using an Internal Rate of Return
0
2
4
6
Low−income economiesLower−middle−income economies Upper−middle−income economies High−income economies High−Income OECD economies OPEC countries
CAF NER MOZ BDI TGO RWA MRT TZA BEN BFA ZWE SLE LSO CIV CMR SEN KEN SDN TJK BOL JAM BRB LAO HND MNG PRY MAR NIC CHN IND COL PHL LKA UKR KGZ TUN SWZ DOM PER ZAF ARM MDA NAM CRI FJI
0
.5
1
1.5
2
2.5
Low−income economies Lower−middle−income economies Upper−middle−income economies High−income economiesHigh−Income OECD economies
36
6
Conclusion
The primary aim of this paper is to increase our understanding of how the endowments of various sorts of capital that a countries can posses contributes to the differences in incomes that exist between countries. To this end, a development accounting framework is used and extended by adding more detail and greater diversity to the measures of capital that are normally included in similar explorations of cross country income differences. To realize this, data from different sources on the various capital types needed to be made comparable among each other and across countries. These data are used in a variance decomposition to evaluate the ability of the model to explain income differences. Additionally, relative productivity differences with the United states as base country, have been estimated for each country separately.
The results of these exercises suggest that the changes instituted here improve the ability of the model to account for differences in incomes, compared to the traditional development accounting exercise. This hold especially true for the disaggregation of the produced capital stock. The addition of natural capital seems to make little differences for the lions share of the sample; however, specific estimates for specific countries are impacted significantly. Improve-ments are especially noted for low-income countries, and generally those whose economies are heavily dependent on natural capital.
7
Appendix
The following tables present some indicative results with respect to the valuation of the stocks of natural capital that are used throughout the paper. The method for this valuation is described in the main text; however, a reference is made to the fact that the valuation could be done using the realized revenues from natural capital exploitation. Table 8 shows for several types of natural capital the share between stock estimated using realized revenue values on the one hand, and estimated values of the stock using expected (and assumed constant) revenues, on the other.
38
Table 8: NPVStock divided by Stock
Variable Countries Mean Std. Dev. P10 P90 Stock of Soft Coal 21 11.926 30.608 .839 10.002
Table 9: Per Capita Stocks of Assets (mil. 2011 USD PPP), valued using the internal rate of return
40
Table 10: Countries included
Nr country Nr country Nr country
1 Argentina 39 Guatemala 77 Nicaragua
2 Armenia 40 Hong Kong SAR, China 78 Netherlands
3 Australia 41 Honduras 79 Norway
4 Austria 42 Croatia 80 New Zealand
5 Burundi 43 Hungary 81 Panama
6 Belgium 44 Indonesia 82 Peru
7 Benin 45 India 83 Philippines
8 Burkina Faso 46 Ireland 84 Poland
9 Bulgaria 47 Iran, Islamic Rep. 85 Portugal
10 Bahrain 48 Iraq 86 Paraguay
11 Bolivia 49 Iceland 87 Qatar
12 Brazil 50 Israel 88 Romania
13 Barbados 51 Italy 89 Russian Federation
14 Botswana 52 Jamaica 90 Rwanda
15 Central African Republic 53 Jordan 91 Saudi Arabia
16 Canada 54 Japan 92 Sudan
17 Switzerland 55 Kazakhstan 93 Senegal
18 Chile 56 Kenya 94 Sierra Leone
19 China 57 Kyrgyz Republic 95 Serbia
20 Cote d’Ivoire 58 Korea, Rep. 96 Slovak Republic
21 Cameroon 59 Kuwait 97 Slovenia
22 Colombia 60 Lao PDR 98 Sweden
23 Costa Rica 61 Sri Lanka 99 Swaziland
24 Cyprus 62 Lesotho 100 Togo
25 Czech Republic 63 Lithuania 101 Thailand 26 Germany 64 Luxembourg 102 Tajikistan
27 Denmark 65 Latvia 103 Trinidad and Tobago 28 Dominican Republic 66 Morocco 104 Tunisia
29 Ecuador 67 Moldova 105 Turkey
30 Egypt, Arab Rep. 68 Mexico 106 Taiwan, China
31 Spain 69 Mongolia 107 Tanzania
32 Estonia 70 Mozambique 108 Ukraine
33 Finland 71 Mauritania 109 Uruguay
34 Fiji 72 Mauritius 110 United States
35 France 73 Malaysia 111 Venezuela, RB
36 Gabon 74 Namibia 112 South Africa
37 United Kingdom 75 Niger 113 Zimbabwe
endix
41
Figure 7: Hierarchy of types of capital Capital Human Capital Education Natural Capital Minerals Energy Coal Gas Oil Agriculture Forest Produced Capital Other Cult Soft IPP Construction Non-Resid. Resid. Transport Equipment Machinery Other IT CT
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