CHANGES IN NATURAL CAPITAL: DECOMPOSING PRICE AND QUANTITY EFFECTS 61
Annex 3.1: Decomposition Methodology Total wealth in a given year is the sum of produced capital, natural capital, net foreign assets, and intangible capital (or residual). In our database, we estimate total wealth and the different types of capital for the period 1995–2005. Hence, we are able to estimate the change in wealth between 1995 and 2005 (for Europe and Central Asia the estimate is from 2000 to 2005). Decomposition of changes in total wealth into its four major categories (produced, natural, intangible, and net foreign assets) is straightforward since these are all additive. We are interested in going one step further by carrying out decomposition of certain categories, particularly natural capital and intangible capital, into their subcomponents. Since produced capital is estimated as the accumulated stock of investment series, its decomposition would not yield new information. Decomposition of intangible capital is undertaken in chapter 5, so natural capital is our focus here. Since we build the estimates of natural capital using information on prices and on physical quantities such as area and yield, we are interested in decomposing the effects of different factors to show their relative importance. In this section we lay out a decomposition methodology adapted from Bacon and Bhattacharya (2007). Natural capital is composed of the present value of the returns to land from crops, pasture and protected areas, forests (timber and nontimber) and subsoil assets (oil, gas, coal, and minerals). Each component in turn is estimated using information on area and yield (or production), prices or unit rents, and exhaustion time. Equation (3A.1) shows how crop wealth (CW) is estimated as an example: CWt area yield real price rentalrate ␣(T, d).
(3A.1)
Wealth is expressed as the product of area cultivated, yield, real price, rental rate, and a value ␣(T, d). The term ␣(T, d) captures the effect of taking the present value of current rents. Alpha depends on the resource’s exhaustion time (when applicable) or the time span over which the present value is taken—expressed by T—and the value of the discount rate d. The logarithmic mean Divisia index (LMDI) is used to decompose change in crop wealth into the additive effects of changes in area, yield, real price, and alpha (rental rates for crops are assumed constant over time and across countries). For details, see Bacon and Bhattacharya (2007). The change in crop wealth from 2000 to 2005 can then be written as follows: 䉭CW CW(2005) CW(2000) Aeff + Yeff + Peff + Weff .
(3A.2)