Natural Capital: From Metaphor to Measurement

1. A Theory of Natural Capital Pricing

Let x(t), either a vector or a scalar, represent individual or collective choices related to consumption of market and nonmarket goods in the economy. Behavioral choices imply potentially implicit demand for consumption of the resource. In practice these choices are rarely chosen in a way that maximizes the net present value of the objective function underlying capital valuation (e.g., profits or economic surplus). Instead these choices reflect the shortcomings of “kakotopia” (Dasgupta 2001), with inefficient management institutions, cultural constraints, information shortages, and behavioral departures from rationality all shaping choices. We refer to the totality of these conditioning factors as “societal constraints” and represent them by the notation . Conditional on these “societal constraints,” behavior, x(t), can be characterized as a feedback rule of the state of natural capital, s(t).³ This feedback can occur through direct effects of human capital on decision making as well as indirect effects of changes in the natural capital stock on management policy and hence elements of . Let be the mapping that describes this feedback rule—the “economic program” structured by the societal constraints . To reduce notation we will treat the dependence on societal constraints as implicit and represent the mapping functionally as x(s(t)).

We make the common assumption that an economic program is time autonomous, an assumption that describes many, but not all, economic programs. This assumption is not completely innocuous; calendar date, phenology of stocks, exogenous technological or ecological changes, or other nonautonomous dynamics could be important. Nevertheless, time autonomy covers a large number of cases. Furthermore, when the economic program is nonautonomous, the model of the bioeconomic system can often be mapped into an autonomous system through a redefinition of state variables (Arrow et al. 2003), and Asheim (2000) provides a blueprint for incorporating nonautonomous dynamics.

With the economic program defined, the state of natural capital changes according to

2222

Let W(s(t), x(t)) be an index of the net benefits accruing to society (or the subset of society that is counted for purposes of capital valuation) at time t. We assume that W(s, x) provides a stable monetary index of social welfare at different levels of s and x so that discounting at a constant exponential rate is justified (Dasgupta, Maler, and Barrett 1999). At time t, the present value of net benefits is

2222

2222

2222

Following Dasgupta and Maler (2000) and Arrow et al. (2003), we assume that V is differentiable and differentiate V(s(t)), using its definition on the right-hand side of equation (2), with respect to t. We suppress the dependence of s on t where doing so does not cause confusion. The result can be expressed as

2222

The time derivative of equation (4) can also be expressed as

2222

2222

Rearranging equation (6) yields

2222

2222

2222

Equation (9) is an equation of motion for the price of the natural asset given the value function (2) conditional on the economic program. Equation (9) is the adjoint equation associated with maximization of the current value Hamiltonian when behavior x(t), and hence management institutions , are chosen optimally. However, this derivation is more general and shows that the equation of motion for the natural capital price, equation (9), holds for any time-autonomous economic program—optimization is not required. However, the actual evolution of the price of natural capital is coupled with the system dynamics (include the policy choices) and the initial conditions of the system.

The net present value (NPV) approach is the standard rule for pricing capital in the deterministic case (Dixit and Pindyck 1994). In the context of natural capital assets that may be held unchanging and in perpetuity, the NPV rule is operationalized as an annuity by dividing the marginal benefit from ecosystem service flows resulting from a marginal stock increase by the discount rate (Barbier 2011). Equation (9) can be viewed in light of the NPV rule by rearranging it as follows, where subscripts represent partial derivatives:

2222

Equation (10) corresponds to Jorgenson’s (1963, 249) equation for the value of invested capital. Jorgenson’s equation, expressed using our notation and setting his “rate of direct taxation” to zero, is

2222

Equation (10) says that the price of a natural capital asset equals the marginal ecosystem service flow, W_s(s, x(s)), adjusted by anticipated price (scarcity) changes (i.e., capital gains or losses) divided by a discount rate adjusted for the overall effect on natural capital growth from adding a little more natural capital. Since the economic program is substituted in prior to taking derivatives, the stock changes include both natural (e.g., through density dependence) and human-induced changes through behavioral feedbacks. The adjustments to the discount rate in the denominator of equation (10) are the net rate of natural capital productivity (NRNCP). This adjustment term creates a wedge between the rate of return to holding natural capital and . If G_s(s) > 0, then the effective discount rate, the denominator, adjusts downward to reflect the productivity of the renewable natural capital. If increases in natural capital increase anthropogenic degradation, f_s(s, x(s)) > 0, then the discount rate is adjusted upward. In all but special cases, marginal annuity estimates (Barbier 2011), for example, , can be misleading because they ignore both and the NRNCP.

2. From Theory to Measurement

Most terms on the right-hand side of (10) can be measured and frequently are the subject of, often decoupled, research programs in natural science and economics. For natural resources that are extracted and traded commercially W_s(s, x(s)), the marginal static net benefit from an increase in the stock, is the effect of the change in the stock on economic surplus measures (e.g., net revenues in a commercial fishery with a competitive output market). Many natural capital stocks provide benefits, ecosystem services, to society that market transactions do not directly reveal. For example, wild populations provide recreational hunting, fishing, and viewing opportunities as well as non-use values, and wetlands provide flood control and water filtration—showing the vital importance of nonmarket valuation techniques (Freeman 2003) for quantifying W_s(s, x(s)). Nevertheless, (10) also shows that improving measurements of W_s(s, x(s)) is only one part of better valuing natural capital.

The estimation of G(s) and G_s(s) are important aspects of ecology, while f(s, x(s)) is addressed in multiple disciplines and interdisciplinary work (Ludwig, Mangel, and Haddad 2001; Smith 2008). The expression G(s) is the ecological production function, and G_s(s) is the marginal productivity of natural capital in the absence of human impact. The function f is a production function for anthropogenic impacts on the stock of natural capital; f_s(s, x(s)) is the marginal product of increased natural capital stocks on how humans affect the stock of natural capital. In commercial extraction cases x(s) is directly targeted at resource consumption, making the specification of f(s, x(s)) conceptually straightforward but perhaps empirically challenging (Tsoa, Schrank, and Roy 1985; Zhang and Smith 2011). In most cases, the human behavior embodied in x(s) is not directly focused on extracting resources. Instead, consumption of the resource is a factor of production for the final good or service (e.g., catch of fish as an input to a recreational fishing trip) or a by-product (e.g., reductions in air quality from visiting a national park; Bockstael and McConnell 1981; McConnell and Bockstael 2006). The explicit capital-theoretic foundation for valuation in equation (10) reveals why good biophysical science matters for valuation. Valuing natural capital requires interdisciplinary research beyond that required for the valuation of ecosystem services alone.

Both W(s, x(s)) and f(s, x(s)) are functions of the economic program . The derivatives of ecosystem service flows and human impacts to changes in natural capital in (10) must therefore include the feedbacks of human adaptation to the change. This implies that measuring human behavioral responses to changes in natural capital given management institutions is a critical aspect of natural capital valuation. In particular, failing to incorporate behavioral adaptation into the marginal valuation of ecosystem service flows may lead to misguided estimation of the value of natural capital.

The remaining terms on the right-hand side of equation (10) are the discount rate and the capital gains term. Appropriate discount rates for natural resources are hotly debated (e.g., Heal 1998; Dasgupta et al. 1999; Carpenter, Brock, and Ludwig 2007; Dietz and Stern 2008; Sterner and Persson 2008; Abbott and Fenichel 2014). Many natural capital stocks are probably best viewed as potentially long-lived public capital—therefore suggesting that natural capital should be discounted similarly to other long-lived public investments with similar risk profiles (e.g., infrastructure). In the absence of strong agreement on an appropriate discount rate, a pragmatic, consistent approach is to employ rates dictated by public accounting authorities such as the Office of Management and Budget (OMB).⁶

The capital gains term is the final numerator term on the right-hand side of equation (10). If this term were recoverable from data, then equation (10) would provide a formula for computing the value of natural capital. However, this term is not directly recoverable from data because natural capital prices are not observable. This fact has been a barrier to measuring the value of natural capital. We provide a solution to this problem. The structure of equation (10), and the observable terms, make it possible to use function approximation (Miranda and Fackler 2002) to approximate .

The approximation procedure is as follows.

First, the expression for the autonomous economic program x(s(t)) must be found conditional on the societal constraints, . In the case of an optimized system, this feedback rule may be derived from the optimization itself. In applications it may be estimated or calibrated from data. The economic program is then substituted into both W and f so that they are both functions of s(t) alone. Therefore, equation (10) can be expressed as

2222

Second, let

2222

Third, choose a number of distinct evaluation points (i.e., approximation nodes) for s. These can be selected in a number of ways, but at least N points are needed to provide solutions for the coefficients of a N−1 degree Chebyshev approximation.⁷ Once the approximation nodes for s are chosen, evaluate the expressions , G_s, and in equation (10) but maintain the dependency on s(t).

Fourth, substitute for into equation (10) to yield

2222

2222

3. Applications

The capital theoretic framework expressed in equation (10) combined with our numeric approximating method for recovering can be used in practice to recover accounting prices. To show the validity of our numerical approximation method, we first apply it to cases where the accounting prices are known and can be compared to our recovered values. Generally speaking, accounting prices are only known for optimized systems. Therefore, our first application is a version of the classic nonlinear commercial fisheries problem (Clark 2005). We use the known solution for this case to simulate the time path of natural capital, human behavior, and the adjoint. We then apply our approximation approach and compare the results to the known adjoint variable values (a second known example is provided in the appendix). Second, we demonstrate how real-world data can be used to apply the approach to the Gulf of Mexico reef fish complex. Our application to the Gulf of Mexico reef fish complex provides a credible price function that has properties consistent with theory.

3.1. A Known Example

We model harvest as , where q is a catchability coefficient and x is a measure of effort. This generalized Schaefer specification of harvest has the attractive feature of diminishing returns to fish stock and effort. Assume

2222

2222

where the market price is m = 10, cost of effort is c = 10, the stock follows logistic growth with an intrinsic growth rate r = 0.5 and carrying capacity k = 1,000. We assume . Formally, the social planner’s problem, replicating the outcome of a dynamically efficient market, is expressed as

2222

The current value Hamiltonian for this problem is

2222

where p is the adjoint variable. The first-order necessary and adjoint conditions that are necessary for an optimal solution to the infinite horizon problem are

2222

and

2222

The infinite horizon nature of the problem and joint concavity of the Hamiltonian ensure that setting and equal to zero and using results in a system of three equations in three unknowns whose solution is the long-run optimal equilibrium (fig. 1A). This system can be linearized around this equilibrium. The eigenvalues associated with the Jacobian matrix are real and of mixed signs, indicating a conditionally stable saddle point. The eigenvector associated with the negative eigenvalue is followed to perturb the system from equilibrium to initiate numerical simulations backwards in time (fig. 1). The solution to the problem in state-control space, which is the economic program for this example, is illustrated in figure 1A by the saddle path leading to the optimal long-run equilibrium. All numerical work was conducted in Mathematica 9.0 (Wolfram Research).

Having solved this standard bioeconomic model and simulated its solution, we sample 160 points, evenly spaced in time, along the simulated saddle paths to collect “data” and record the actual numerical value of the adjoint variable at each of these points. The black dots in figure 1B are actual values of the adjoint variable. We sampled 160 values of h(x(s)), W_s, F_s(s, x(s)) for points along the saddle path (fig. 1), and using a 15th-order Chebyshev polynomial for , we minimize the sum of square deviations associated with equation (12). The solid curve in figure 1B is the approximate value of natural capital using equation (11). The real and recovered values hardly differ, with a mean approximation error of 0.007%.

Consider alternative approximation approaches. If only were ignored, thereby implicitly assuming , then the general pattern of accounting prices overestimates the adjoint variable values for stocks below the steady state and underestimates for stocks greater than the steady state (fig. 1B, gray dot-dashed curve). Adjusting for the NRNCP but omitting the influence of capital gains has fairly small errors for stock sizes close to the steady state but yields larger errors otherwise, particularly at low stock levels. Treating the value of natural capital as a marginal shift in an annuity, and using as the value of the natural capital, results in estimated accounting prices almost an order of magnitude greater than the true value due to the substantial negative value of the NRNCP (fig. 1B). Unlike omitting capital gains, the effects of failing to correct the rate of discount for the net rate of natural capital productivity do not dissipate near bioeconomic equilibrium.

3.2. A Nonoptimized System: The Gulf of Mexico Reef Fish Complex

The Gulf of Mexico reef fish stock is a substantial regional resource that consists of 62 jointly managed species. Six species make up most of the catch: gag grouper, gray triggerfish, greater amberjack, red grouper, vermilion snapper, and red snapper. Reef fish are caught using a range of gears, most commonly handline. The fishery is a mixed species fishery with imperfect selectivity across species. Historically, many species in the reef fish complex were overfished. In 1984, a fishery management plan (FMP) was adopted to rebuild stocks “on the basis of maximum sustainable yield (MSY) as modified by relevant economic, social, or ecological factors.”⁸ The FMP was enforced using a complex set of regulations involving entry restrictions, catch per trip limits, season closures, and spatial closures based on information from stock assessments. Some of these restrictions were loosened in 2007 and 2010 with the staged introduction of individual tradable quotas, ITQs, for key reef fish species.

We consider the fishery prior to the introduction of ITQs—a time when the most prominent stocks in the complex were generally considered overfished. During this period stocks and catch were relatively stable (fig. 2).⁹

Our objective is to obtain an accounting price for an in situ living pound of reef fish vulnerable to fishing gear conditional on the nonoptimized management that persisted in the fishery at this time. We follow Zhang and Smith (2011) and model the vulnerable reef fish complex as a single stock growing logistically. Zhang and Smith (2011) estimate

2222

where s is the stock of reef fish in pounds.¹⁰ The second right-hand side term in equation (15) is the generalized Schaefer harvest function, where x is fishing effort measured in crew-days. The catchability coefficient, q = 3.17 × 10⁻⁴, is calibrated to replicate pre-2005 average catch per unit effort levels observed in National Marine Fisheries Service logbooks from the fishery at the equilibrium catch and effort levels defined below. The technology parameter, , is set to Zhang and Smith’s estimated value for handline gear. Zhang (2011) estimates the empirical effort response function—the “economic program,”

2222

with conditional on pre-ITQ management. We calibrate the parameter y = 0.157 so that the system equilibrates at the mean level of biomass harvest between 1986 and 2004—implying a stock at 24% of carrying capacity (fig. 3, solid curve). This calibration reflects the judgment that managers were implicitly (whether intentionally or not) targeting sustained yields and stocks significantly below the stated MSY goals of the FMP (or there were substantial “relevant economic, social, or ecological factors”). This judgment is supported by the fairly stable pattern of overall reef fish catch and biomass over these years (fig. 2). This pattern is consistent for many of the commercially valuable individual stocks. The effort response model empirically builds in behavioral responses to changes in the fish stock and implicitly accounts for contemporary management institutions in a reduced form manner through the values of its parameters. This provides a model of the economic program. The term W is defined as in equation (13). We use National Marine Fisheries Service logbook and trip cost survey data to calibrate m = $2.70 per pound of reef fish, and c = $153 per crew-day in 2005. We follow OMB’s 2012 appendix C for 30-year plus projects and use an annual discount rate of 0.02. We then contrast our results to OMB’s base case discount rate of 0.07. Our qualitative results are not overly sensitive to this range of variation in the discount rate.

We choose 500 stock sizes between 500,000 pounds and carrying capacity as the roots of a 500th-order Chebyshev polynomial. Next we use a 50th-order Chebyshev polynomial to approximate . The average deviation per simulated data point is 5.4 × 10⁻⁶. Increasing the polynomial order had no measurable effect on the quality of approximation.¹¹ A summary of results at the steady state and at 50% of the steady state for the annuity approach, an approximation ignoring price changes, and the complete approximation are shown in Table 1.

Natural Capital Valuation Approach	Natural Capital Marginal Value, p	Stock Capitalization Value, ps
Marginal annuity approach:
Steady state	$36.55	$3.156 billion
50% of steady state	$18.94	$818 million
Ignoring price changes:
Steady state	$3.08	$265.5 million
50% of steady state	$9.98	$431 million
Full approximation approach:
Steady state	$3.08	$265.5 million
50% of steady state	$4.11	$177 million

View Table Image

The value per pound of in situ reef fish conditional on pre-2005 management institutions varies with stock size from $1.80/lb to over $10/lb (fig. 4)—with a value of $3.08 at the steady state. As expected, the accounting price function is downward sloping in stock. Ignoring overestimates the accounting price at low stocks and underestimates it at high stocks (fig. 4). It is interesting to compare these accounting prices to the share trade prices after ITQs were introduced to the red snapper fishery in 2007. The ITQ policy allocated fishermen transferable rights to shares (percentages) of the total allowable catch; the transfer price of these shares should reflect the present value of expected future profit flows (Newell, Sanchirico, and Kerr 2005). Prices for shares of red snapper, one of the more highly valued species of the six that we aggregate over, have steadily increased over successive seasons. The equivalent price per pound transferred was $8.73 in 2007 and $25 in 2011.¹² Theory suggests that ITQs should alter the economic program, including potentially altering the economic (m and c), technological (q and ), and behavioral (y and ) parameters of the model through changes along the extensive and intensive margins of effort (Smith 2012) and thereby raising the value of the stock. Such share prices suggest that our substantially lower recovered accounting prices—reflecting comparatively poor management institutions—are reasonable. The marginal annuity approach substantially overestimates accounting prices per pound, as in the prior example, but also results in an upward-sloping accounting price function (in fig. 4 in $ × 10), which is driven by the economic program. Specifically, the upward-sloping price function associated with the annuity approach results from the slope and curvature of the generalized Schafer production function when combined with the estimated behavioral response (economic program) of fishermen.

Computing an accounting price for reef fish facilitates including the reef fish stock, as a capital asset, in a comprehensive wealth measure or the NIPA, conditional on the current management. For instance, the pre-2005 management equilibrium (24% of carrying capacity) leads to an accounting price of $3.08/lb using a 2% discount rate and $2.54/lb using a 7% discount rate. Valuing the entire stock at this marginal price implies a total stock capitalization or the component of “comprehensive wealth” (Arrow et al. 2012) attributable to the stock of between $265.5 million (2% discount rate) and $219.1 million (7% discount rate).¹³ Alternatively, at equilibrium where there is only a dividend flow of ecosystem services but no change in natural capital stocks or prices, the annual net benefits that flow from the fishery are $24.7 million (2% discount rate), which yields a net present value, V, of $1.24 billion (2% discount rate) or $353 million (7% discount rate). These provide measures of the value of the fishery that are only valid at equilibrium.

A management action or positive environmental shock that made the stock less scarce and increased the vulnerable stock to the level supporting MSY (at half of carrying capacity), without altering the nature of the fisher response function, would reduce the accounting price to $2.33/lb but would increase the asset value to $418.9 million (assuming a 2% discount rate). This range of capitalization is on par with “small caps” publicly traded companies. Such changes should be accounted for in adjusted net or comprehensive investment measures as well as the NIPA. Given the lack of management change—so that stocks will eventually be fished back to their pre-intervention equilibria—realizing MSY represents a temporary increase of $153.4 million in natural capital holdings using the capitalization value. Figure 4 suggests that ignoring price changes still gives qualitatively accurate results. However, if capitalized value is used as a metric, which may be the case in wealth accounting, the NIPA, or the measurement of comprehensive wealth (Arrow et al. 2012), then Table 1 shows that ignoring price changes could lead to qualitatively different conclusions about whether a change in the stock is wealth enhancing.

Given that the application of the model only considered ex-vessel prices and harvesting costs, these capital values only reflect the value of fish capital for the harvesting sector, holding all other human, fishing, or processing capital constant. They are not a measure of consumer surplus in the final product market or processor-related producer surplus. Therefore, our marginal accounting prices, like the ITQ share price, are lower bounds for the marginal social value of natural capital in this system. Nevertheless, our approach can readily be extended to include nonmarket values conditional on available estimates.

The finding that the current value Hamiltonian is the current rate of return on the value function implied by the economic program, , suggests that the CVH is an appropriate instantaneous index for comparing the net benefits resulting from alternative economic programs. The current value Hamiltonian captures the idea that the instantaneous flow of benefits in a given period from natural capital depends on both its ecosystem service dividends and wealth accumulation associated with net investments in natural capital, changes in fish stock, multiplied by p.

It is possible to compare the relative well-being generated by two alternative economic programs, perhaps the result of alternative institutional arrangements, by comparing the value of H using the accounting prices implied by the two programs.¹⁴ To illustrate this approach consider a stylized proposed management change. In our model, a policy could alter parameters related to behavior and the fishing production function. For example, consider a new gear restriction, simulated by reducing (e.g., by 10%). The logic of a gear restriction is that it makes a unit of effort less effective, so fewer fish are caught, resulting in a larger stock size. This has the intended biological effect (fig. 3, dashed curve), but making fishing less productive will also likely encourage a behavioral response through a reduction in effort at a given stock level—modeled here as a reduction in (e.g., by 6%).¹⁵ In this particular case, together these two effects lead to an even more conservative harvest and larger equilibrium stock size (fig. 5, dotted line).¹⁶ The policy change influences the economic program and reduces p, except at small stock sizes (fig. 5). Figure 5 shows the equilibrium values (Xs on the figure) of the current value Hamiltonian. These values are nothing more than the equilibrium ecosystem service dividends because stocks are not changing. The value of H with the management change (dotted curve) exceeds the value of H without the management change (solid curve). However, simply comparing equilibria could be misleading, since it is possible that the path to the new equilibrium under the alternative economic program is more costly than remaining at the current (calibration) equilibrium. The ability to calculate a valid accounting price conditional on the stock size and economic program enables us to assess the change in the current value Hamiltonian (the annualized difference in the value function) at the calibration stock size under the alternative economic program (fig. 5, circle). Interestingly, at the calibration stock size W is less under the alternative economic program, and the top panel of figure 5 shows that p is also reduced. Yet, the change in stock size (investment) is large enough to offset this forbearance.¹⁷ The fact that at all values of the current value Hamiltonian associated with the alternative program are above the value of the baseline current value Hamiltonian suggests that such a change is uniformly welfare enhancing. This result occurs because of the depleted state of the equilibrium fish stock in the baseline economic program. Interestingly, the improvement in the current value Hamiltonian is driven by the reduction in effort at a given stock size, the reduction in . Technical change alone, the reduction in , actually reduces the value of the current value Hamiltonian unless effort is also suppressed by the technical change. These comparisons demonstrate that the method developed here to recover accounting prices not only is useful for valuing natural capital but also contributes to measuring the relative desirability of current and alternative economic programs.

4. Discussion

Natural capital may be a large share of the wealth of nations, but in many cases it remains underpriced in markets and unaccounted for in public accounts. What goes unmeasured often goes unvalued—thereby contributing to the poor management of many natural capital stocks. Failure to manage and invest in natural capital means that society is dissipating wealth, reducing future productivity, and potentially jeopardizing the sustainability of well-being and wealth of future generations.

The natural capital metaphor is a powerful communication tool. However, if “nature is capital” is to be more than a metaphor, then the valuation approach must integrate economic and natural science metrics within a rigorous capital-theoretic framework. Many critical policy questions can be framed as decisions to invest or divest natural capital, but investment decisions should be based on the totality of dividends, capital gains, and asset growth. Research is advancing the valuation of the dividends from natural capital, ecosystem services, but this is not the same as valuing natural capital. Treating the value of natural capital as an annuity of marginal ecosystem service dividends is incomplete and, our simulations suggest, potentially highly misleading. Modifying the annuity approach to account for the asset growth associated with natural capital can perform well in the neighborhood of a steady state when capital gains are small, but poorly elsewhere. We have developed and successfully demonstrated a numerical approach to approximate the rate of capital gains implicit in existing management institutions, conditional on (1) the marginal value of ecosystem services, (2) the net marginal productivity of natural capital at different stock levels, and (3) the choice of discount rate. Our numerical approach provides a linchpin for internally consistent valuation of natural capital while also suggesting important implications for future work.

First, substantial improvements in the valuation of natural capital can be made by appropriately adjusting the “discount rate” for the marginal productivity of the natural capital stock. This requires explicitly bringing biophysical science measurements into valuation computations, including the productivity of natural capital in the absence of human impact, and the effect of natural capital on human degradation of the capital stock. Natural capital valuation is fundamentally interdisciplinary—even beyond the level required for the valuation of ecosystem services.

Second, we demonstrate that both the marginal value of ecosystem services and the adjustment to the discount rate require the substitution of an “economic program” predicting the link between human behavior and the natural capital stock. Understanding the feedback between the state of natural capital and human behavior—mediated by markets, regulations, social norms, and other institutions that mold this behavior—is imperative to valuation. This necessitates an expansive role for economics in natural capital valuation extending well beyond the “normative” valuation of ecosystem services to also encompass the positive science of understanding human behavioral feedbacks in response to changes in the state of nature and the incentive structures provided by management institutions. While there is ample research considering these behavioral feedbacks for the purposes of avoiding potentially unwelcome feedbacks to natural capital stocks, this literature has largely existed outside the literature on valuation.

Finally, our framework concretely illustrates the necessity of incorporating the two-way feedbacks between natural systems and human behavior under nonidealized economic programs when valuing natural capital. Valuation without incorporating feedbacks is incomplete. So, just as understanding integrated ecological-economic systems requires valuation, valuation requires understanding feedbacks. The current value of the natural “wealth of nations” and its future rise or fall hinge critically on the wisdom of the human behavior embodied in the economic program at other values of the capital stock and the effects of this behavior on natural capital.