6.2.1 Method
We employ the traditional method of Development Accounting.1, complemented with the ad-ditional input factor natural resources. Natural resource input is disaggregated into input from subsoil and non-subsoil resources. Output in countryi is produced according to the following Cobb-Douglas production function
Yi = Kiαi(AiHi)βiR(s)γ(s)i iZ(ns)γ(ns)i i (1)
1For a thorough discussion of this method, see Caselli [2005]
124 6.2. METHOD AND DATA
whereYi denotes output of the economy, Ki is the physical capital stock andHi the human capital stock. The exponents, which may vary across countries, sum to one, so there are constant returns to scale. Natural resource input is split up into two components. We distin-guish between input from subsoil and non-subsoil resources. Whereas we consider the stock of non-subsoil resource capital (Z(ns)) to be productive (forests, agricultural land, etc.), we argue that in the case of subsoil resources it is the rent flow which enters the production func-tion (R(s)). A more detailed discussion follows in secfunc-tion 6.2.2. Accordingly in equafunc-tion (1) R(s)γ(s)i i denotes input from subsoil resources, whereas Z(ns)γ(ns)i i denotes input from non-subsoil resources.
The above can be rewritten as
yi = A
where lower-case variables are per worker. We write the production function in terms of the capital output ratio to account for the fact that this variable is invariant to productivity in the steady state of a neoclassical growth model (Hall and Jones [1999]).
Then we can write
i.e. A is the “residual”, the part of output unexplained by the given factors. Of course A as defined by equation (6.3) is affected by measurement units. In order to be informative, A is traditionally regarded in relation to a chosen reference point, such as the corresponding level of the US (see for example Hall and Jones [1999]). The relative contributions to output in country 1 are then given by:
y1
Consequently, the data necessary to perform development accounting consists of: output y, human capital h, produced capital k, natural capital z and r (all in per worker terms), and the respective exponentsα, β, γ(s) and γ(ns). Note that under the assumption of perfect competition on factor markets these exponents are given by the income shares of the respective input.
CHAPTER 6. THE MISSING INPUT: ACCOUNTING WITH AND FOR NATURAL
CAPITAL 125
6.2.2 Data
This section describes our data sources as well as various transformations undertaken, as the case may be. In this chapter we consider a cross section of up to 94 countries for the year 2000. In the following we describe which data we use and how we manipulate it, if at all.
• y is GDP per worker from Heston et al. [2006] (Penn World Table (PWT) 6.2, base year 2000) in international dollars.
• h is human capital per worker computed following Caselli [2005] using data on educa-tional attainment from Barro and Lee [2001], for the year 2000:
We assume that
h = eφ(s) (5)
where s is average years of schooling in the population over 25 in the year 2000. This production function for human capital assumes that all returns to accumulation of this factor are internalized and implies that the percentage difference in human capital, log(h) − log(h′) equals the percentage difference in wage, log(w) − log(w′), which in turn equals φ(s) − φ(s′). φ(s) is piecewise linear with slope 0.134 for s ≤4 (the return to an additional year of schooling in sub-saharan Africa), 0.101 for 4< s ≤8 (the average return in the world) and 0.068 fors >8 (the average return in the OECD). This captures decreasing returns to education.
• k is the physical capital stock per worker computed from PWT 6.2 data using the per-petual inventory method. The aggregate physical capital stock is
Kt= It+ (1 − δ)Kt−1. (6)
HereItis real aggregate investment in PPP.2K0 is chosen to beI0/(g + δ), where g is the average geometric growth rate between the first year with available data and 1975.
The depreciation rate δ is chosen to be 6% per year. The construction of the variable follows exactly the methodology of Caselli [2005].
The World Bank [2006b] provides information on different types of natural capital. In partic-ular there is separate information on subsoil resource capital, timber land, non-timber forest resources, protected areas, cropland and pasture land. As we argue above, for inputs in pro-duction we use the natural capital data provided in this World Bank data set for non-subsoil re-sources (timber land, non-timber forest products, protected areas, cropland and pasture land).
2computed as RGDP L· P OP · KI, where RDGP L is real GDP per capita using the Laspeyres method, P OP is the population and KI is the investment share in real GDP.
126 6.2. METHOD AND DATA
We denote this measure byz(ns). In particular z(ns) includes and is computed by the World Bank as follows:
• Timber wealth is calculated as the net present value (NPV) of rents from roundwood production, with an assumed lifetime of 25 years. Unit rents are calculated as the prod-uct of a composite weighted price and a rental rate. Unsustainable management of the forest is captured by a shorter time horizon. Only forests within 50 kilometers of infras-tructure are counted as being available for wood supply.
• Non-timber forest resources are benefits stemming from various activities such as hunt-ing, recreation as well as existence values. Returns per hectare per year vary from 190 US dollars in developed countries to 145 US dollars in developing countries. Further-more it is assumed that one-tenth of the forest area in each country is accessible, i.e.
brings the above-mentioned benefits. Non-timber forest resources are then valued as the NPV of benefits over 25 years.
• The value of cropland resources is estimated by assuming that the agricultural products grown on the land are sold at world prices. The return to land is thus the difference between the market value of output crops and crop specific production costs. Crops that are being taken into account are maize, rice, wheat, banana, grapes, apples, oranges (the last four as a proxy for fruits and vegetables), soybean and coffee (the latter two as a proxy for oil crops and beverages respectively). Other crops are calculated as a residual.
A country’s overall land rent is then computed by a weighted average (weighted by the sowing areas) of rents of all different crop categories. The annual return is projected for 25 years, i.e. starting from the year 2000 where values are known, until the year 2025, assuming a constant growth rate which reflects sustainable management of land. The NPV is calculated based on these assumptions.
• Pasture lands are valued at the opportunity cost of preserving land for grazing. The returns to pasture land are assumed to be 45 percent of the output value, which is based on the production of beef, lamb, milk, and wool valued at international prices. Again, annual return is projected starting from the year 2000 until the year 2025, assuming a constant growth rate reflecting sustainable grazing practices, and the NPV is calculated accordingly.
• Protected areas provide a number of benefits that range from existence values to recre-ational values (tourist industry). They are valued at their opportunity cost, i.e. at the
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minimum of the per hectare value for cropland and pasture land respectively. Again the NPV over 25 years is computed.
• Finally the World Bank also provides estimates of the stocks of subsoil resources in a country (which we denote byz(s)). Dollar values are assigned to the stocks of the main energy resources (oil, gas and coal) as well as to the stocks of ten metals and minerals (bauxite, copper, gold, iron ore, lead, nickel, phosphate rock, silver, tin and zinc). These stocks are valued measuring the present discounted value of economic profits (the total rent at some time t) over the lifetime of the resource. Note that for this method future rents of the resource have to be known. These are extrapolated from rents observed in the year 2000, assuming that future rents grow at a constant rate g. A lifetime of 20 years is assumed for all resources and all countries.
In backing out productivity levels we do not use the measure of subsoil resource stocks but rent flows (r(s) as discussed above). Therefore we use in our calculation data on subsoil resource rent, also provided by the World Bank.
Last, the income shares are calculated as follows: the labour share in GDP (β) is taken from Bernanke and Gurkaynak [2001]. In order to maximize the number of observations we do not exclude the countries where data for this variable is not available. Rather we use a geography-based method to approximate the labour shares for the countries where the observations are missing. We regress labor shares on regional dummies3 and use the corresponding predicted values as labour shares for those countries where measured data is missing.
Assuming constant returns to scale in production, the total capital share in GDP is
(total capital share) = α + γ(s) + γ(ns) = 1 − β. (7) We first back out the income share of physical capital,α (for a discussion of this method see Caselli and Feyrer [2007]). Formally the income share of physical capital is given by
α = ipkk
pyy. (8)
wherepkk and pyy is the nominal value of physical capital as well as output and i is the rental rate for capital. We also know that the total capital share is given by(1 − β), where
1 − β = i(pr(s)r(s) + pz(ns)z(ns) + pkk)
pyy , (9)
where we have assumed that all types of capital have the same rental rate.
3The R2from this regression is 0.4.