where TE0 is the carryover stock at the beginning of period 0 and Lt are the losses of prior levels of TEt due to spoilage and other factors each period, and where 'ex situ collection' refers to the aggregate of all ex situ collections.

Methodology for Assessing Economic Returns to Gains to Investment in Agro-biodiversity Conservation Projects

Crop breeding research relies on the availability of genetic resources as an input. In general, given a larger stock of genetic resources, the gains to research will be higher.

The general form for a supply response function for agricultural crop output with respect to gene bank size can be written as:

Xts = f(Pt,Zt,ht,tt[TEt-s(Et-s,It-s),TEt-s-i(Ets-jJt-s-i), TE0(E0,I0),h],Ut)for t = s, ...,T

where Xf is output given the vector of expected prices P, vector of inputs Zt, vector of uncontrolled factors Ut, vector of state of technology (excluding breeding research technology), ht, state of crop breeding research technology, x, and s, the lag before accessions have impact. Note that ht appears outside the brackets as well as inside, as much research on CGRs is done using only the private collections of the breeding firm. For x 9xt/dTEt—s—1 < 0, and 9Xt/d%t > 0, i = 0

t—s. Assuming that crop breeding research technology exhibits diminishing marginal returns with respect to TE, 92x /dTE— —i < 0. At the farm level, crop breeding research related technical change can be modelled using the common specification (Norton et al., 1992) for the profit function for a perfectly competitive farm unitjas nt = g[Pt(xt), Z,,, htj, U,| m,]. For this specification xt can represent either output or input augmenting technical change. Crop breeding research can be either.

In the literature on measuring gains to agricultural research, a common practice is to assume that agricultural research induces shifts in the supply function, which then translate into changes in producer plus consumer surplus (de Gorter et al., 1992; Alston et al., 1995). While the policymaker may have objectives other than maximizing producer plus consumer surplus and while no measure is completely subjective, this criterion has the benefit of being reasonably general and objective. Fisher and Hanemann were the first to apply this criteria in the context of agro-biodiversity. In a two-period model for measuring the option value of saving an identified native landrace, they model the benefits of saving a native corn landrace by assuming this a priori identified landrace impacts the corn supply curve through the intercept. This chapter will use the criterion of producer plus consumer surplus (denoted as W) maximization as the policymaker's objective function, but in a more generalized form that formally models the change in accessions as a function of conservation investment, models the impacts of the change in agricultural supply as a function of the change in accessions, and allows for economic uncertainty as well as multiple time periods.

Suppose that due to the new biodiversity conservation investment I", the supply curve shifter g0 decreases to y1, i.e. g 1 = f[x (TEt|It — I")] and g0 = f[xt(TEtIIt — I']), where I' is the base level, I" > I' (where g 1 and g0 are the intercept results from the summation (whether vertical or horizontal) of the supply functions of each farm unit maximizing n. above, and g 1 and g0 > 0). Considering for the moment only the welfare of developed countries making this expenditure, their change in welfare in period t when g0 decreases to g 1 is denoted as A Wt.

Since one would expect that the benefits of the investment It would be felt in successive periods, the net present value in rich countries of an agro-biodiversity investment It can be written as:

Another way to treat the problem is explicitly write y as a function of TEt_s from equation (8), the total size of the ex situ collection at time t-s, which in turn is a function of past levels of It_s, It_s_ 1 I0. Doing so also allows consideration that desired traits may be drawn not only from one accession, but also from a combination of accessions. Net present value is then:

= ^AWs+t(gs+,(TEtjIt = I"; I0 1-); gs+t,o(TEtjIt = I'; I0, ...,IM))

The summation over A Ws+t in equation (11) is the value associated with keeping alive the option of being able to use existing uncollected CGRs that would be lost without the investment plus the value of new CGRs that are developed due to the investment.

Assume that the government body is given an amount:

that it can spend on field programmes to reduce the erosion of biodiversity. In a world without uncertainty and irreversibility, the policymaker uses the net present value (NPV) rule and makes the investment now if the present value of the benefits minus the costs is greater than zero. However, as stated earlier, the standard NPV rule ignores the fact that expenditures are largely irreversible, i.e. they are a sunk cost that cannot be recovered. It also ignores the investor's option to delay and to wait for new information about markets and agro-biodiversity conditions before making the investment. This aspect of the problem is incorporated into the model by borrowing the approach used in much of the commodities literature to address investment under uncertainty and irreversibility. In the context of this paper, irreversibility refers to both irreversible loss of genetic resources as well as potentially irreversible conservation investments. The specific approaches are too lengthy to discuss in this chapter and are covered in detail in the paper that this chapter is drawn from.

Biodiversity Investment Under Uncertainty and Irreversibility: a Numerical Simulation

Given that even with a linear supply and demand system, A Wt is a non-linear function of the variables, evaluating A Wt at the means of A ANt and AMt is not the same as e(A Wt) given the distributions of these variables. Given these non-linearities, the most tractable method for evaluating the net present value of a particular set {Ij 0, Ij1 I, t_s} for each j = 1 Jin situ conservation areas is with a simulation approach in which repeated draws are made, as illustrated in the following section.

Obviously, maximizing equation (11) over j in this simulation framework would be laborious and require a complex non-linear programming application. However, given the lack of availability of the data necessary for estimating actual values, developing such an application would be overkill in the short term. Instead, several simplifying assumptions will provide a more tractable maximization problem that will be sufficient towards the chapter's basic goal of generating a conceptual framework for economic discussion of agro-biodiversity conservation. First, let j = 1 in situ region. Second, it is unlikely to be politically feasible to vary It (in real terms) greatly from period to period. Whether or not the programme lasts for a fixed number of years, once a programme starts, the payments are likely to continue at some fixed rate until the programme is stopped. It is unrealistic to turn on and off conservation programmes from year to year. For instance, the US farmers enrol in the Conservation Research Program under 10 year contracts at rates that are fixed for the contract period. Next, assume that the budget of the biodiversity programme is a given I that must be used in its entirety. Then, whether or not the programme enrolment is to last an indefinite period or for a predetermined number of years, the choice variable is the starting period. This strict equality constraint eliminates the trade-off between biodiversity conservation and other activities, but still allows for intertemporal tradeoffs within the sphere of this conservation activity. Given these assumptions, the maximization problem is:

where k is an index referring to one of T—s programme starting points and where d(k) = 1 when k is chosen and: 0 otherwise, where Ik, the fixed programme payment per year is chosen such that:

On the other hand, if the public agent plans an m period contract to start at some point t during the evaluation period, then Ik is chosen such that:

For the simulations, two scenarios are examined: (i) conservation programme costs that are constant per period over the planning horizon T; and (ii) a 10-period long conservation programme, starting any time from t = 0 and

Table 2.1. Base parameters used for simulation runs

Simulation time span coverage3 Interest rate per period

Discounted cost of conservation contracts (over time span T) at t = 0

Bernoulli parameter for the number of estimated total CGRs uncollected at t = 0

Bernoulli success parameter for yearly accessions given constant E, both for existing uncollected CGRs, and new CGRs

Rate of loss of in situ CGRs

Transformation of conservation investment into change in number of accessions

Parameters for conversion of total accessions into agricultural supply intercept coefficient changeb

Research lag, i.e. periods before new accessions to ex situ collections have economic impact

Agricultural demand intercept (source: Chambers and

Just)c

Agricultural demand price coefficient Agricultural supply intercept coefficient Agricultural supply price coefficient Agricultural supply and demand intercept drift parameters

Volatility of drift parameter Impact of new varieties on yt aTo increase precision of predictions, each period divided into 12 subperiods for estimation of the Brownian motion equations but is converted back to the original units elsewhere. bFor the simulations, a Cobb-Douglas type functional form is assumed fr the average number of varieties adopted by farmers in period tthat used accessions from TEt_s in the breeding process. Normalizing inputs other than TEt_s in this process to 1, %t = ffl1(TEt_s)m2. cSupply and demand coefficients are from Chambers and Just and are also used in Fisher and Hanemann and are for a simplified version of US demand and supply curves for corn (price coefficient is in dollars/bushel and quantity is measured in billions of bushels per annum).

t = T — 10. In all cases, the discounted costs of programmes are the same. Table 2.1 lists the values and the simplifying assumptions used for the simulations. Programming of the simulations was done using the GAUSS computer programming language and each of the 40 possible payments paths was simulated 500 times over the range of the planning horizon.

Simulations were conducted to examine the path of total accessions over time, with and without a 10-period conservation programme starting at t = 0, using the functional forms from the first section plus the parameter values from Table 2.1. For the simulation, the variables are drawn stochastically, where, according to equation (7):

AMt ~ NB(Bernoulli success parameter = 90, probability of failure

ANt ~ NB(Bernoulli success parameter = q>ANt, probability of failure

Yt ~ NB(Bernoulli success parameter = jYt, probability of failure

The results of the simulations show that the in situ accessions eventually fall to the same level whether or not the conservation programme is funded. However, the conservation programme succeeds in delaying genetic erosion. Thus, under the scenario in which the conservation programme is funded, more accessions move from in situ to ex situ collection before they disappear.

In computing benefit streams, the simulation results show that while the median discounted present value of the conservation investment is relatively constant over time, the upper bounds of the confidence interval around benefits become many times higher than the median or mean values. The upper bounds are more sensitive to the specification of the price volatility parameter than they are to the erosion in biodiversity coefficient.

Of the 40 possible 10-period long investment plans, the simulations show that the welfare-maximizing plan is the one starting at the present time, a result that is no doubt influenced by the linear-over-time specification of the erosion in agro-biodiversity coefficient used here. This specification implies that the biodiversity erosion rate is high enough at present that potentially valuable accessions are being lost. The results can change if the impact of accessions on the agricultural supply is a function of age cohorts (i.e. newer accessions have a greater impact than older stocks). The same result holds with investments evaluated at their mean values of the simulations. However, if one considers the relatively large width of the 90% confidence intervals as well as their relatively flat path with respect to the median paths, the gains to starting the programme in the first period are less clear cut.

This chapter is the first to present a formal discussion of framing models for measuring gains to publicly funded research as investments under uncertainty and as irreversible decisions. This framework, which borrows from the commodities literature, can have applications in other resource topics, such as publicly funded pest control. One observation drawn from the simulation results is that mean benefits estimates may be inappropriate as they will give little idea of the large spread. Perhaps an analogy can be drawn with investments on flood control projects, for which planning decisions are not generally based on mean potential damages but on costs of extreme floods (e.g. the 100-year high vs. the yearly high).

Given the modelling framework presented in this chapter, the key areas for empirical research necessary to implement this model include:

1. Estimates of AMt, the number of existing cultivars uncollected at time t. These data are necessary to allow estimation of the rate of loss in potential accessions over time.

2. Estimation of the number of accessions obtained from both in situ stock existing at t = 0 as well as from new varieties not yet in existence at t = 0 obtained per dollar of collection expenditure (Et). As collection activities have gone on for some time, some of these data should be available, although it may be difficult to separately identify At (the number of cultivars collected from the base value AM0) from ANt, which are the cultivars not existing at period 0, but which may be developed by indigenous breeding activities subsequent to t = 0.

3. Estimation of the impact on the change in accessions obtained at time t from both in situ stock existing at t = 0 as well as from new varieties introduced after t = 0 per dollar of in situ biodiversity conservation expenditure (It). Since major in situ agro-biodiversity programmes have not yet been implemented, this estimation may have to wait some time.

4. Estimation of Tt[TEt_s(Et_!f It_), TEt_s_l(Et_s_l, Vs_1) TEo(Eo, Io), ht]

from equation (9), i.e. the impact on the agricultural supply function of publicly available accessions. Perhaps this section can be addressed through extensions of research that have been done on valuing the traits of accessions in ex situ collections (Evenson, 1996).6 Estimates of the mean arrival rate of a disease or pest-related production shocks as a function of total accessions can be included here as well, but this is probably not feasible to estimate. Another avenue of research is on research investments that can change the parameters in t.

5. Estimation of agricultural output price and quantity prices, as well as the price volatility term.

When sufficient data have been collected to make empirical estimation possible, the logical research extension is to apply the model discussed in this chapter in a multi-country, multi-crop partial equilibrium framework that can account for substitution effects and cross-price linkages. Given that farmers participating in agro-biodiversity conservation programmes may have lower output than if they were not, and to the extent that this participation increases local prices, consumers in the conservation regions may require compensation, which would be an additional component of the cost of in situ conservation programmes. In the developing country regions hosting the agro-biodiversity conservation programmes, the costs of these distributional impacts may be addressed through an application of the model in a computable general equilibrium framework.

Notes

1. This chapter is excerpted from a more detailed manuscript of the same title; contact the author for further particulars.

2. Although the term CGR is used for brevity, the same economic principles discussed in the chapter should hold for animal genetic resources for agriculture as well. Note that the term agro-biodiversity covers all plants and animals, whether wild or domestic, that are important to food and agriculture.

3. To some extent, this latter form of irreversibility (loss of genetic resources) may be analogous to asset depreciation in the case of an asset for which there may not be perfect substitutes, such as the pitching arm of a potential major league draft pick. If the arm of this player is not carefully nurtured and is damaged before the player makes the majors, whether or not he will be the next superstar is unknown.

4. The other possible discrete distributions include the Poisson and the negative binomial. The variance of a negative binomial distributed variable is greater than its mean, while the variance of a Poisson distributed variable equals its mean.

5. In calibrating the coefficients in P(01) in an empirical application of this model, it may be useful to note that with the logistic specification, the value of It where P(It < I) = 0.5 is It = — a/vI, where a = v0 + vAAt— j + vSSt, which is positive if a >0. Furthermore, for 0 < P < 1, ln((1 —P)/P) = a + v/.

6. Since the hedonic method estimates values over a path of tangencies of supply and demand, the cited study cannot be used directly to identify the supply shifter.

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