THE BRAZILIAN CASE STUDY

The model adopted, as said before, calculates the depreciation under the optimal use of an exhaustible resource, employing the Hotelling rule relationship and arriving into some estimations of depreciation approximated by the Hotelling rent, as proposed by Vincent (1997).³⁰ The main objective of this case study is to estimate depreciation values of forests in the Amazonian Region, a typical frontier area where user cost perception fades. It is assumed that timber is a non-renewable resource based on the fact, already discussed in Section 1, that forestland conversion in this frontier area is mostly devoted to agricultural production and cattle raising and the possibilities for second growth forest are almost nil. Consequently, our depreciation values will not consider any charges for forest regrowth.

As it was seen in the previous section, there are basically three shortcuts to calculate the depreciation of natural capital: the net price (NPM), user cost (ESM) and H&V approaches. The latter, is a generalization of the other two in the sense that, assigning different values to the parameter β , would provide us with the other two specific formulas. As discussed before, the theoretical advantage of the H&V approach is that it enable us to use data on the average cost, multiplying it by a conversion factor without getting an upward bias on the depreciation. This would yield, under optimal use of the resource, an accurate estimation of the scarcity rent since it is the Hotelling rent, and not the total rent, that is equivalent to the depreciation under optimal conditions.

The timber industry in the Amazon can be classified in two main activities: timber harvesting and wood processing. Generally the timber is harvested and transported to the sawmill where it is sold with the cut and the transport activities being performed by the same economic agent. In some regions, there is a third economic agent in the process, the "bufeteiro". He is a truck driver who gets the wood in the forest, transports it to the saw mills and sells it. More recently, this industrial structure has changed. There has been a trend of vertical integration taking place in the region with the increase participation of sawmills in the extraction process.³¹

Theoretically, the calculation of scarcity rents depends critically on the prevailing property right’s regime in the region. If there exist an open access situation, over extraction of timber is very likely to occur, causing the dissipation of rents. Despite the fact that property rights are not secure in the Amazon, there is some belief that it is not the case of the existence of an open access regime of exploitation. Consequently, the timber extraction would yield positive rents from the extractive activity.

The formula used to calculate scarcity rents is the generalized formula from H&V:. It can be observed in the formula that the exhaustion period,, enters the calculation in an exponential way. This would make it the leading parameter in the final result. Any large exhaustion period would result into very low scarcity rent.

Previous studies³² have already identified very large exhaustion periods for forestland conversion in the region. Being the largest tropical forest in the world, it is not surprising that, even at the actual extraction rates, it would still take some time to completely excerpt all kinds of timber available in the forest. This is basically the main problem when we perform these kind of calculations for the timber production in the Amazonian region as a whole. It seems as we could still harvest it for many years before scarcity is perceived. Because of this "bias" caused by the still enormous size of the Amazon,³³ we have also calculated the scarcity rent for a specific species of wood under threat of extinction and tried to observe how scarcity rent estimates alter in cases of lower available stock.

The selected wood species was mahogany. Being the royal wood exploited in the region for many years, counting for almost 50% of the Brazilian timber export value, its stock has been decreasing rapidly during the past decade. Recently, its log and exports were temporally banned by the Brazilian Ministry of the Environment in 1996. As will be seen, mahogany prices are by far higher than any other timber variety.³⁴

In this study, the all timber variable is a composite good for which the data on cost and output is not differentiated among species³⁵. Consequently we treat timber as a single stock with an unique exhaustion time. Mahogany estimates, on the other hand, are specific for this specie and reflects its greater scarcity.

Although mahogany is part of the all timber composite good, its user cost is dissipated when we aggregate it with the all timber. Consequently, results on Table 4 show an aditivity bias. As it will be observed, for all values of the elasticity of the marginal extraction cost greater than zero, the depreciation value for all timber is lower than mahogany depreciation. This occurs because as the elasticity of the marginal extraction cost increases, the exhaustion period becomes the driving factor in the depreciation result. When mahogany is included in the all timber variable, the average exhaustion period increases and its greater relative scarcity fades away.³⁶

Implicitly, we are assuming for the all timber measurements that loggers see timber stock as a whole and do not differentiate species in their decisions on exploitation levels. If exploitation of species are treated separately, each specie’s user costs, as those estimated for mahogany, should be separately measured and then added up.

Apart from depreciation calculation for all timber and mahogany separately, we also apply the three depreciation valuation approaches presented above. Based on the generality of the H&V formula, values of the elasticity of the marginal cost curve are set to zero for the NPM, infinity for the ESM and intermediate values for the H&V approaches. Finally we undertake a sensitivity analysis with discount rates of 2%, 4% and 10% to enable us to analyse the differences in the scarcity rents due to differences in time preference.³⁷ All estimation cases are carried out only for the years 1990 and 1995 due to data availability, although it covers an important and recent period of forest conversion in the region.

It is important to note that we are not estimating depreciation values for a single state or region, we are looking at the Brazilian Amazon as a whole. We are interested in the national macroeconomic perspective since the depreciation calculated would be deducted from the national GDP to incorporate a sustainability perspective in national accounts. Consequently, we are taking into account the fact that economic agents perceive stock of wood across political frontiers as equally accessible.³⁸ Naturally, if we had studied a highly cleared area, we would have obtained high depreciation values, but this verification would not yield any perspective on the Brazilian sustainability issue, unless the region had the majority of the timber extraction and could be regarded as a closed economy.

The study area will be the so-called Legal Amazon, only excluding the State of Mato Grosso due to the lack of data on timber stocks.³⁹

As mentioned in Section 1, timber extraction in Brazil takes place mainly in the Amazon from primary forests, accounting today for more than 75% of the Brazilian production of logs. The State of Pará alone produces almost 80% of the timber output in the region. However, data on the timber sector in the region is very scattered, particularly economic information on the production side. Due to its enormous size, ecological complexity and economic dispersion, it is extremely difficult to perform any systematic survey of the sector. When data is available, it does not usually follow the same pattern and, consequently, aggregation becomes a very complex task.

Two kind of data were used in this study: official aggregated data from the National Statistical Office (IBGE) and specific and punctual studies undertaken for academic and research purposes with a more limited coverage. There is a trade-off in using each one of these sources. The official aggregated figures, although reliable, do not go in details for species and locations and are based on declarations which certainly avoid not legal output. On the other hand, specific studies present good data and particular information, but the generalization of this information for the Amazon as a whole has to be done carefully.

As it was presented in the previous sub-section, the data required for the estimation sets, following the generalized formulae, are log prices, output, average cost, stock and the elasticity of the marginal cost curve.

The extraction of timber and the production of sawnwood in the Amazon is very diversified. Not only it takes place in many of the states, but it is also carried out by many economic agents. A great variety of trees are harvested in a very heterogeneous way and, consequently, it is very hard to monitor the extraction of logs and its processing. As a result, a general database containing prices of wood, quantity extracted, extraction costs and stock of timber in the Amazon is not available.

It was possible to define two procedures to identify price series. One was the use of data from the IBGE on quantity extracted and value of production, dividing the former by the latter to obtain an implicit price for wood. This data was available on a time series and it would enable us to observe the evolution of the implicit price of wood through time. However, the estimated implicit prices appeared to be very erratic and with no relationship to export prices and other sources. The shortcoming of this source seems to be related to the lack of reliability on the figures on production value. Moreover, data is aggregated with no identification of species.

Another procedure used was based on two regional studies. The first one was Stone (1998) which utilises data from field surveys in the Paragominas region (State of Pará) elaborated by the Imazon (Instituto do Homem e Meio Ambiente da Amazônia) in 1990 and 1995. The survey included 33 wood processing firms in 1990 and 40 firms in 1995. Given the predominance of the Pará wood industry in the region, these values can be considered to be fairly representative for the Amazon as a whole.

Stone (1998) presents an average price of logs and sawnwood and classifies them in five groups based on the value of the wood, from high to very low valuable wood.

The second regional data source was a study on wood extraction in the State of Rondônia conducted by the consultancy firm Tecnosolo-DHV (1997) which presents a very detailed wood price list. Although it is a very rich database, generalization with prices from Rondônia is less reliable due to the small representativeness of its timber industry in comparison with Pará. Nonetheless, cross checking with Stone (1998) data showed consistency if one takes into account the division of wood types.

Estimates of costs of extraction and processing of wood in the Amazon are very rare.

Once more, we have relied on Stone (1998) which presents average extraction costs and transportation costs for 1990 and 1995 for both small and large firms.

For the logging activity, the difference between small and large loggers is based on the number of chain saws, trucks, bulldozers and log-lifters used in the extraction process. For the sawmills, the size is determined in the sample, by the number of band-saws. Small mills operate with one band-saw while large mills operate with two or more. The data on the cost structure of logging for 1990 is based only on small firms. This is the only data presented in Stone (1998). This would not cause a huge bias since the majority of firms operating in 1990 were small (approximately 80%). However for 1995, we had data available for small and large firms. To calculate the unit cost, we created a composite cost as the average of costs from small and large firms, weighted by their relative contributions to the total production volume.

Man-made capital costs of extraction and transportation average costs were also calculated with the three discount rate scenarios⁴⁰ using the same rates applied for the depreciation formula.

Data on timber output was taken from the IBGE figures, although there was some concern about their poor spatial coverage, they were the only available source for the region as a whole.

Data on the total aggregated stock of timber in the Amazon was estimated by Prado (1995) for the year 1990, based mostly on IBGE data, in fairly detailed spatial coverage but without distinction for wood species. The only caveat was the absence of data for the State of Mato Grosso. In our estimates of the stock figures, we have deducted from the physical stock all the timber stock available in conservation areas.

To estimate the 1995 stock we have used data on the quantity extracted of timber from IBGE assuming that the stock evolution was proportional to the rate of change in the log extraction. This is a strong assumption since there is illegal logging that would not be taken into account in the IBGE and output lost in the harvesting process.⁴¹ Both cases allow for an overestimation on the timber stock.

Mahogany stock and output time series were not available. However, Barros et alii (1992) has made some estimates for 1990. Consequently our calculations were restricted to 1990 in the case of mahogany.

Table 3 presents the selected data indicators for timber stock (S), output (q), price (p), average cost (AC) and net price (NP) for the years 1990 and 1995.

Table 3 Economic Indicators for Depreciation Estimation

Table 4 and Table 5 present the depreciation estimates for the years 1990 and 1995, respectively. Exhaustion time for all the timber stock in the Amazon was estimated as 258.6 years for 1990 and 242 years for 1995. For the analysis of mahogany, the exhaustion period was 42 years for 1990.

Table 4 Depreciation Estimates in the Logging Activity for the Brazilian Amazon in 1990

(1995 US$)

Notes: i = discount rate and β = elasticity of marginal cost curve.

Table 5 Depreciation Estimates in the Logging Activity for the Brazilian Amazon in 1995

(1995 US$)

Note that scarcity in the case of all timber stock in the Amazon is not a real threat considering such a large exhaustion time, as our depreciation estimates will show. Nonetheless, the mahogany case, when considered alone, will be otherwise more prone to reflect depletion costs due to the possibility of taking into account its much lower exhaustion period.

As it can be observed in Table 4, as β increases the user cost becomes larger for mahogany relative to all timber. As already discussed in Section 5.1, this is a consequence of the aditivity bias caused by the fact that mahogany specific user cost is not added up separately, but instead, aggregated into the all timber before estimating the depreciation value.

Increases in the discount rate decrease the depreciation values, as shown in Table 4. This result differ from other studies on the fact that changes in the discount rate for the net price method change the depreciation values. This could sound surprising since when β =0 the discount rate should not play a role on the depreciation calculations. Nevertheless, since we included charges for man-made capital costs (capital opportunity cost of machinery and equipments) on the calculation of total cost, discount rate will affect these charges and, consequently, net price estimates.

Therefore changes occurring to the depreciation based on the net price method is due to the differences on average costs when discounting rates varies affecting man-made capital charges and not due the adopted V&H depreciation formula which does not have any discounting on it for net price measures.⁴³ At 10% discount rate, all timber user cost and H&V values decrease significantly tending to an almost negligible value. Mahogany values are significant at all rates insofar mahogany exploitation presents lower exhaustion periods and larger net profits.

It should be noted that, even considering the underestimation of logging production figures due to illegal practices, say, exhaustion time for the total stock of timber would be still high enough to generate negligible depreciation values.

Our results are also consistent with the theory. As the discount rate increases, the present value of future flow of rents decrease, causing a substantial decrease in the depreciation measure. This result confirms the fact that depreciation values are very sensitive to the discount factor used in its calculation.⁴⁴

Observing again Table 4, for given discount rates, depreciation values decrease as the elasticity of the marginal extraction cost increases. We can easily identify these differences in our estimates. The user cost estimate (β =∞ ) is eminently lower than the estimate of the net price (β =0). This result goes in the direction expected based on other estimates of depreciation in the natural resource accounting literature.⁴⁵

The results for 1995 in Table 5 show that depreciation magnitudes are higher than the similar ones for 1990 in all cases, although still with low significance at 10% discounting. That upward variation is conformed with the adopted methodology due again to the increase in net profit magnitude and the reduction of exhaustion time. Also comparing the 1995 results across discount rate yields the same results observed for 1990, that is, increases in the discount parameter, and diminishes substantially the depreciation estimates.

In this sense, the distinction between the methods is very important as noted by Atkinson et alii (1997), "The distinction between net-price and user-cost is not just of theoretical interest: for countries with very long-lived deposits, even small discount rates will yield user costs that are much smaller than current rents."