# «ENVIRONMENT AND DEVELOPMENT The Changing Wealth of Nations ENVIRONMENT AND DEVELOPMENT A fundamental element of sustainable development is ...»

■ The volatility of consumption. To solve this problem we used the five-year centered average of consumption for each one of the three years: 1995, 2000, and 2005.

■ Negative rates of saving adjusted for depletion of produced and natural capital.

When depletion-adjusted saving is negative, countries are consuming natural resources, jeopardizing the prospects for future consumption. A measure of sustainable consumption needs to be derived in this instance.

**Hence, the following adjustments were made:**

● Wealth calculation for 2005, for example, considered consumption series for 2003–07.

● For the years in which saving adjusted for depletion of produced and natural capital was negative, this measure of depletion-adjusted saving was subtracted from consumption to obtain sustainable consumption, that is, the consumption level that would have left the capital stock intact.

● The corrected consumption series were then expressed in constant 2005 U.S. dollars. Deflators are country-specific: they are obtained by dividing gross domestic product (GDP) in current dollars by GDP in constant dollars. This rule was also applied to natural capital and net foreign assets.

● The average of constant-dollars consumption between 2003 and 2007, for example, was used as the initial level of consumption for wealth calculation of 2005.

## BUILDING THE WEALTH ESTIMATES: METHODOLOGY 143

For computation purposes, we assumed the pure rate of time preference to be 1.5 percent (Pearce and Ulph 1999), and we limited the time horizon to 25 years. This time horizon roughly corresponds to a generation. We adopted the 25-year truncation throughout the calculation of wealth, in particular, of natural capital.Machinery, Equipment, and Structures For the calculation of physical capital stocks, several estimation procedures can be considered. Some of them, such as the derivation of capital stocks from insurance values or accounting values or from direct surveys, entail enormous expenditures and face problems of limited availability and adequacy of data.

Other estimation procedures, such as the accumulation methods and, in particular, the Perpetual Inventory Method (PIM), are cheaper and more easily implemented since they require only investment data and information on the assets’ service life and depreciation patterns. These methods derive capital series from the accumulation of investment series and are the most popular. The PIM is, indeed, the method adopted by most OECD (Organisation for Economic Co-operation and Development) countries that estimate capital stocks (Bohm et al. 2002; Mas, Perez, and Uriel 2000; Ward 1976).

We also use the PIM in our estimations of capital stocks. The relevant expression for computing Kt, the aggregate capital stock value in period t, is then given by Kt It i (1 ) (A.2) i0 where I is the value of investment in constant prices and is the depreciation rate. In equation (A.2) we implicitly assume that the accumulation period (or service life) is 20 years.2 The depreciation pattern is geometric, with 5 percent assumed to be constant across countries and over time. Finally, note that equation (A.2) implies a “one-hoss-shay” retirement pattern, that is, the value of an asset falls to zero after 20 years.

To estimate equation (A.2) we need long investment series or, alternatively, initial capital stock.4 Unfortunately, initial capital stocks are not available for all the countries considered in our estimation, and even in the cases in which published data exist (as for some OECD countries), their use would introduce comparability problems with other countries for which data do not exist.

For the countries with incomplete series of gross capital formation data, investment series were estimated if we had data on output, final consumption expenditure (private and public), exports, and imports for the missing years.

With this information we can derive investment series from the national accounting identity Y C I G (X M) by subtracting net exports from gross domestic savings. In all cases, the ratios of the investment computed this way and the original investment in the years in which both series are available are

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very close to one. Still, to ensure comparability between both investment series, the investment estimates derived from the accounting identity were used only if the country-specific median of these ratios, for the period 1960–2006, was close to one. For the rest of the countries for which complete investment series are still not available, data on gross fixed capital formation are used for the missing years. Complete investment series for the 19 years preceding 1995, calculated using the three methods listed above, were available for 107 countries, while complete data series for 125 countries were used to calculate produced capital for the years 2000 and 2005.For 20 countries for the year 1995 and two countries for 2000, all still missing complete investment series, produced capital is estimated after adjusting the values obtained using a lifetime assumption of 14–19 years (as the case may be). The adjustment made is that values obtained using less than 20 years are multiplied with the median of the ratio of capital obtained from 20 years to that obtained from less than 20 years (over 1960–2006). For the remaining countries, we tried to overcome the data limitations by using a quite conservative approach. We extended the investment series by regressing the logarithm of the investment output ratio on time, as did Larson et al. (2000). However, we did not extrapolate output, limiting the extension of the investment series to cases in which a corresponding output observation was available. In particular, the 20-year service lifetime assumption was used to estimate capital stocks from investment series predicted from a regression of the ratio of the log of investment to GDP on time. Produced capital estimates for 6, 27, and 34 additional countries were obtained using this method for the years 1995, 2000, and 2005, respectively.

Urban Land In the calculation of the value of a country’s physical capital stock, the final physical capital estimates include the value of structures, machinery, and equipment, since the value of the stocks is derived (using the Perpetual Inventory Method) from gross capital formation data that account for these elements. In the investment figures, however, only land improvements are captured. Thus, our final capital estimates do not entirely reflect the value of urban land.

Drawing on Kunte et al. (1998), we valued urban land as a fixed proportion of the value of physical capital. Ideally, this proportion would be country-specific.

In practice, detailed national balance sheet information with which to compute these ratios was not available. Thus, like Kunte et al. (1998), we used a constant proportion equal to 24 percent: 5 Ut 0.24Kt. (A.3)

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Energy and Mineral Resources This section describes the methodology used to estimate the value of nonrenewable resources. There are at least three reasons that such calculations may be difficult.First, it is only in the past few decades that the importance of including natural resources in national accounting systems has been widely recognized. Although efforts to broaden the national accounts are underway, they are mostly limited to international organizations such as the United Nations or the World Bank.

Second, there are no private markets for subsoil resource deposits to convey information on the value of these stocks. Third, the stock size is defined in economic terms: reserves are “that part of the reserve base which could be economically extracted or produced at the time of determination.”6 Stock therefore depends on the prevailing economic conditions, namely technology and prices.

Despite these difficulties, we assigned dollar values to the stocks of the main energy resources (oil, gas, and coal7 ) and to the stocks of 10 metals and minerals (bauxite, copper, gold, iron ore, lead, nickel, phosphate rock, silver, tin, and zinc) for all the countries that have production figures.

The approach used in our estimation is based on the well-established economic principle that asset values should be measured as the present discounted value of economic profits over the life of the resource. This value, for a particular country

**and resource, is given by the following expression:**

where iqi is the economic profit or total rent at time i, ( i denoting unit rent and qi denoting production), r is the social discount rate, and T is the lifetime of the resource.

Choice of T To guide the choice of an exhaustion time value, we computed the reserves-to-production ratios for all the countries, years, and resources.8 Where country reserves data are missing, world and regional data are substituted. Table A.1 provides the median of these ratios for the different resources, showing the abundance of energy and mineral resources relative to each other.

With the exception of the very abundant coal, bauxite, and iron, the reservesto-production ratios tend to be around 20–30 years. We chose to cap exhaustion time at 25 years for all the resources and countries.9 From a purely pragmatic point of view, the choice of a longer exhaustion time would require an increase in the time horizon for the predictions of total rents, to feed equation (A.4). On the other hand, rents obtained farther in the future have less weight since they are more heavily discounted. Finally, the level of uncertainty increases as we look toward a more remote future. Under uncertainty, it is unlikely that companies or governments will develop reserves to cover more than 25 years of production.

Timber Resources The predominant economic use of forests has been as a source of timber. Timber wealth is calculated as the present discounted value of rents from roundwood

production. The estimation then requires data on roundwood production, unit rents, and the time to exhaustion of the forest (if unsustainably managed) in the beginning year.

The annual flow of roundwood production is obtained from the FAOSTAT database maintained by the Food and Agriculture Organization of the United Nations (FAO).10 Calculating the rent is more complex. Theoretically, the value of standing timber is equal to the discounted future stumpage price received by the forest owner after taking out the costs of bringing the timber to maturity. In practice, stumpage prices are usually not readily available, and we calculated unit rents as the product of a composite weighted price and a rental rate.

The composite weighted price of standing timber is estimated as the average of three different prices, weighted by production: (a) the export unit value of coniferous industrial roundwood, (b) the export unit value of nonconiferous industrial roundwood, and (c) an estimated world average price of fuelwood.

Where country-level prices are not available, the regional weighted average is used.

Forestry production cost data are not available for all countries. Consequently, regional rental rates ([price cost]/price) were estimated using available studies and consultations with World Bank forestry experts.

Since we applied a market value to standing timber, it was necessary to distinguish between forests available and forests not available for wood supply because some standing timber is simply not accessible or economically viable.

The area of forest available for wood supply was estimated as forests within 50 kilometers of infrastructure. Data on productive areas were obtained from the FAO’s Global Forest Resources Assessments (Global FRA) for 2005 and 2000 (UNFAO 2006, 2001).11 Data for 1995 were imputed from Global FRA 2000 data by using the ratio of productive area to total forest area, which is then multiplied by total forest area in 1995 obtained from State of the World’s Forests 1997 (UNFAO 1997).

Rents were capitalized assuming a growth rate of zero and using a 4 percent discount rate to arrive at a stock of timber resources. The concept of sustainable use of forest resources is introduced through the choice of the time horizon over which the stream is capitalized. If roundwood harvest is smaller than net annual increments, that is, if the forest is sustainably harvested, the time horizon is 25 years. If roundwood harvest is greater than the net annual increments, then the time to exhaustion is calculated. The time to exhaustion is based on estimates of forest volume divided by the difference between production and increment. The smaller of 25 years and the time to exhaustion is then used as the resource lifetime.

Five-year-average values of production and unit export values are used to calculate the revenue from timber production. Data on coniferous and nonconiferous, industrial roundwood, and fuelwood production are obtained

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for the years 1991–2005 from FAOSTAT forestry data online. Fuelwood price data are also from FAOSTAT forestry data online. Roundwood export unit values are calculated from FAO online data. Studies used as a basis for estimating rental rates include those by Fortech (1997); Whiteman (1996); Tay, Healey, and Price (2001); Lopina, Ptichnikov, and Voropayev (2003); Haripriya (1998); Global Witness (2001); and Eurostat (2002).Nontimber Forest Resources Timber revenues are not the only economic contribution of forests. Nontimber forest benefits such as minor forest products, hunting, recreation, and watershed protection are significant but are not usually accounted. This leads to forest resources being undervalued. A review of nontimber forest benefits in developed and developing countries reveals that annual returns from hunting, recreation, and watershed benefits vary from $129 per hectare in developed countries to $27 per hectare in developing countries (based on Lampietti and Dixon [1995] and Merlo and Croitoru [2005], and adjusted to 2005 prices). We assume that only one-tenth of the forest area in each country is accessible for recreation.