Thursday, February 26, 2015

12 Applying Economics to Forestry-III: Social weighting and management decisions

Full paper available here (pdf)

Social benefit stream and forest economics

A consideration that may come to the rescue of the long rotations and slow conversion rates of existing crops may be the indirect services that are expected to flow from such natural crops, but this is likely to support longer rotations only if the stream of such benefits is shown to increase with age of the crop. If not, as in the case of carbon sequestration, it may also come about that a series of fast-growing crops may capture more carbon in a given time period, than keeping the already locked-in carbon in standing trees. Samuelson feels that such decisions should be left to “the electorate, by that same pluralistic process” which determines other fiscal decisions and allocation of budgets (Samuelson, 1974, p.486).

Distribution considerations and economic criteria

We may however argue that there is an alternative to this laissez-faire approach:  that is if the polity decided (through a democratic -- or maybe a revolutionary-- process!) to actively favour certain classes, usually the poor or otherwise disadvantaged, bringing us to social cost-benefit analysis (SCBA), in which a positive weight is attached to income or consumption increments accruing to the poor, which of course is not allowed in neo-classical economics where inter-personal utility comparisons are not admitted (see Squire & van der Tak, 1975, for a primer on SCBA; Price, 1989 for forestry applications). Then products which flow differentially to these favoured classes will be ascribed a social value that may be higher than signalled by market prices alone. In our case study, this possibility is explored by ascribing such social weighting to non-teak smallwood (and a small portion of the non-teak timber as well), which local poor are assumed to consume directly. That is, we explore the possibility of making the consumption increments of the poor our ally in defending sustained yield against the ‘heartless’ application of financial criteria.

Rather than having to undertake a special exercise to compensate the ‘losers’ in each project, SCBA seeks to do this on a societal and economy-wide basis. In a departure from this neutral stance of neo-classical utility theory, we posit that just as the marginal utility of consumption of an individual is assumed to diminish with level of consumption of a commodity, from the point of view of society as a whole, “an extra rupee is better given to a poor man than to a rich man” (Little & Mirrlees, 1974). One function required for this is the social elasticity of the marginal utility of consumption, denoted by the Greek symbol  η (eta), which denotes the (proportional) change in marginal social utility for a corresponding (proportional) change in consumption at different income levels. Then the relative weight di attached to an incremental rupee of consumption at a consumption level ci, is related to the average consumption level ĉ (or any other consumption level, for that matter), by the formula

di =  ( ci ∕  ĉ ) η
(η being negative usually)

Of course, in order not to make the assigning of relative weights completely arbitrary, some or other reasoning is advanced. Fellner (1967) suggested that the value of η could be approximated by the ratio of the income elasticity of consumption of ‘Food’ (usually positive), to its pure price elasticity (usually negative). The higher the income elasticity, the more pervasive is poverty assumed to be (denoting that there is a greater slack to be made up), and the higher will be the number for η (of course with a negative sign). As  an example of this type of estimation of the parameter, using estimates of income and prie elasticity of food grains consumption by Raj (1966),  η works out to -0.6 or -0.7, which portrays only a mildly progressive distributive orientation. If we separate out the elasticities for the rural and urban sectors, we get the numbers for η as -1.12 for the rural sector, and -0.15 (amounting to almost neutrality to distributional interests) for urban. For a really strong pro-poor bias,  η would have to be closer to, say, -2, which would denote that as consumption level doubles,  the value of an incremental rupee becomes a quarter.

This detour was only to give an idea of the computational results for η, the social elasticity of the marginal utility of consumption. But the real interest lies in the implications for the economic analysis of sustained yield forestry decisions as laid out in our case study of the teak forests in Karnataka. In doing our social cost benefit analysis (SCBA), let us assume that a value for η of -2 represents this strong distributional bias. By itself, using SCBA on the lines outlined here does not materially alter the optimal rotation decisions for maximum NPV (details in Dilip Kumar, 1988).  For a SQ III hectare, for example, using -2 for η, and ascribing full cost of labour (shadow wage rate SWR = 1), the optimal rotation of a single rotation remains at or above 75 years up to a discount rate (STPR) of 4%, but falls to 55 years at 5%, 35 years at 6%, and 10 years at 10%. For an infinite series of rotations (soil expectation value, SE) the optimal rotation falls away from 75 years to 30 years at 5%, i.e. a little faster than the single rotation case. If we take the rather extreme case of SWR =0.25 (since wages are presumably going to very poor persons), the optimal rotation for one rotation still follows the same pattern with rising discount rate, while the rotation for maximum SE falls a little sooner, from 75 years at 3% to 30 years already at 4% rather than at 5% (because the cost of postponing future returns looms larger as initial afforestation costs become lower). All this does not give much succour for long rotations per se.

The main impact of social criteria will be through the computation of the social discount rate (SDR). One of the effects of considering the marginal utility of consumption through a parameter like η is on the consumption rate of interest CRI or social time preference rate STPR (see Kula, 1984). Considering that per capita income is expected to grow quite slowly, however, future increments of income are not very highly discounted due to η, and it was calculated that the CRI would be only around 3.6% with η= -2, allowing for mortality (the probability of surviving to enjoy the future consumption stream being around 98.5%, which imposes a time preference rate of 1.5% by itself). A simple assumption of zero mortality (survival probability = 1) would bring the discount rate (CRI) to 2% (η being -2), or essentially 0% for η = 0. Any lower figure for η like -0.5 would likewise devalue future increments less strongly, yielding an even lower discount rate like 2%. Such results are a support for maintaining longer rotations, but as the transition to shorter rotations occurs between 3% and 5%, the optimal rotation is extremely sensitive to the precise discount rate chosen, but merely using social prices rather than market, does not render long rotations any more viable.

Conversion of natural forest and social criteria

So far we have considered the optimal rotations for a fresh plantation. As we saw before, under strictly economic analysis, there is no mitigating circumstance to come to the aid of a slow pace of conversion, and even under social CBA, the social value of the firewood and small timber coming out to augment consumption of the poor would only add to the pressures to convert the standing forest. But there may be one special circumstance in which social considerations may so support a longer conversion period. This is, if only a limited portion of the production is utilisable by the poor, each year, and any excess production over this limit would go to socially neutral uses, it may make some sense from the social angle to slow down the rate of conversion of the old growth, especially if consumption by the poor is highly valued (say η= -2).

Such an exercise was actually done in the case study of Yellapur-Mundgod (Dilip Kumar, 1988, chapter 10). The working plan estimated an annual production of 6,548 cum of teak logs and 28,293 cum of non-teak logs annually on a 30-years conversion period of the remnant existing forest. If we assume that 1.5 times this comes out as firewood, this would amount to respectively 9822 cum of teak firewood and 42,439 cum of non-teak firewood annually; the latter would just be sufficient to meet the demand based on the state-wide per-capita assessment of fuelwood consumption in the Karnataka State of Environment Report in 1977-78 (Subramanian, 1984),. A similar exercise for timber demand and potential output as per the working plan indicated that just some 10% of non-teak timber would be sufficient to satisfy local needs. If now we ascribe high social value to the non-teak timber and fuelwood that is assumed to be consumed by the poor, obviously any acceleration of conversion that is not required for the years’s local consumption would have less social value (as the local poor would not have a use for it and it would go to the general market).

On these assumptions, relative weights (di) can be calculated for the firewood and timber produced every year under the normal (sustained yield) prescriptions and under (hypothetical) accelerated  conversion rates of natural forest, based on available information on income class distributions in the area. While not describing the detailed calculations, a few sample results are presented. With a high distributive bias (η = -2), consumption increments distributed equally over the entire population would have a aggregate relative social weight (D) of around 6.1; if restricted to the classes below the poverty line it would have a higher weight of over 8.8; or if restricted to the class of workers alone, 13; and if restricted to the poorest class, it would be as high as 491.5 (Dilip Kumar, 1988, chapter 10).

In the Little-Mirrlees scheme of SCBA, these d values are not used directly to amplify the value of incremental consumption or products; one more step is involved, that of expressing values in terms of a standard measure or ‘numeraire’, v, which is defined as the value of incremental public income (in ‘border rupees’, i.e. after correcting for distortions due to local tariffs and duties). This numeraire depends on the use to which the incremental public income is assumed to be put in the economy. A simple assumption, for example, may be that it is all applied to consumption, and further that it is equal to consumption at the reference level ĉ (the average level of consumption in the economy). Then the value of a rupee of public income income would be essentially 1.0, except that it would have to be converted to border values by multiplying by some average accounting ratio or standard conversion factor (SCF) to account for duties (we used a SCF of 0.86). An alternative formulation, however, could be that the (incremental) public income is devoted partly to investment, which may yield further incomes and even further re-investments, and partly to consumption. One could even posit that public income is put to socially very high-valued uses (for instance, income supplements to the poorest classes, say below the critical or minimum level of consumption, which would inflate its social value). These different scenarios give us different estimations of v, which is then used in the formulation D/v to convert the consumption benefits from market rupees to the corresponding social value at border prices. As can be imagined, if we assume a high value for v (public income is highly valuable), then the value of consumption benefits accruing to individuals will go down even though they may be poor, with high social weightage or D values). If we assume that public income is fairly neutral in distributive effects, then the D/v value of consumption benefits will be allowed to remain at high levels.

We cite a few variants from our constructed example of conversion of old forests in the Yellapur-Mundgod division. A simple assumption could be that all the non-teak firewood and 10% of non-teak timber that are going to local basic needs, are consumed equally by all sections of the population. Our calculations show that this component would then have a social weight in aggregate (D value) of around 6.1 (assuming the parameter η= -2); because most people have low incomes, if the product is consumed by all the classes equally, the aggregate social weight is high. In contrast, if the product were distributed in proportion to existing incomes, the aggregate social weight D would be only 1.4; while if it were restricted to the really poor, say to the workers class and below, the relative weight D would be higher, around 13.1 (Dilip Kumar, 1988).

There is one more step: the  relative weight has to be converted to the numeraire by dividing it by the social value of public income v, as outlined above. If we assume that there is no reinvestment, that all is consumed at the average level of consumption, and a consumption rate of interest (CRI) of 3.56% (with expectation of mortality and η  --2), the simplest case, then v comes to around 3.3. If we assume that 15% of public income is reinvested at marginal product of 10%, and the rest consumed at the average level of consumption, then v comes out to around 4.8 (ibid., Table 8.10). The more valuable that public income is assumed to be, the lower would be the social value of consumption benefits indicated by the D/v ratios of firewood or other basic needs products (ibid.).

If we accept the scenario where incremental consumption benefit accrues to the entire population (D=6.1),  and value of public income is related to the average level of consumption (v=4.8), the accounting ratio D/v of the added consumption comes to 1.27. If we change the assumptions, the D/v ratio will also change: thus, if incremental consumption is assumed to accrue to workers only, D will be higher, 13.1, and D/v 2.7. Many more variants in assumptions regarding D or v values could be imagined, which we need not spell out here. 

Now we can try accelerating the conversion process from 30 years to say 20, 10 or even shorter periods, and see how the social value changes as diminishing proportions of the non-teak output qualify for the higher social values. For the non-teak firewood, the conversion factor (to convert value at market prices into social value in terms of the numeraire) at 30 years conversion rate (100% socially valuable) would be 1.5 using a D/v of 1.5, or 2.5 using D/v of 2.5. Under a 20-year conversion period, part of the extra firewood would go to general consumption (not 100% socially valuable), so that  falls to 1.3 (D/v = 1.5) or 1.95 (D/v = 2.5). For a 10-year conversion period, it is only 1.1 (D/v of 1.5) or 1.4 (D/v of 2.5). Non-teak timber, of which only 10% of prescribed output is socially advantageous under the 30-year period, has accounting ratios (ARs) respectively of 1.02, 0.97, 0.92 and 0.88 under conversion periods of respectively 30, 20, 10, and 3 years and D/v of 2.5 (Dilip Kumar, 1988, Table 10.5). If the consumption is assumed to accrue at lower levels, D/v may be higher, and the social accounting ratios also higher.

These accounting ratios or shadow prices are then plugged into the SCBA, under various assumptions of social discount or time preference rate (STPR) and shadow wage rate (SWR). Under our assumptions, the longer conversion period is favoured at low social discount rates and high D/v values of the non-teak component. At 3% discount rate and D/v 2.5, it is the 1-year conversion period (immediate liquidation!) that has maximum value; to favour the 30-year period, we would have to use a D/v of around 5.0. At 5% discount rate, D/v of 2.5 or even 5.0 favours still the 1-year conversion period; only if D/v were to be 7.5, does the 30-year period become favourable. In these cases, a loss in social value of the non-teak products is countered by the higher early returns from the high-price teak component. Of course, it has to be remembered that any conclusion favourable to the longer conversion periods comes about only if the afore-mentioned limits on the capacity to absorb the basic needs products is operative. If no such limit is posited, then the more that is extracted, the higher will the net social value be, and there will be no succour for the sustained yield option.

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