Sustainability and the measurement of wealth: further reflections

The June 2012 issue of Environment and Development Economics published a symposium with considerable focus on our paper, ‘Sustainability and the measurement of wealth’. The Symposium also contained five articles in which other researchers offered valuable comments on our paper. The present note replies to those comments. It clarifies important issues and reveals how important questions relating to sustainability analysis can be fruitfully addressed within our framework. These include questions about the treatment of time, the use of shadow prices and the treatment of transnational externalities. This note also offers new theoretical results that help substantiate our earlier empirical finding that the value of human health is something very different from the value of the consumption permitted by health and survival. 1. Background The move from theory to measurement in economics is almost always fraught with difficulty and its attendant compromises. The exercise in Environment and Development Economics 505 Arrow et al. (2012) was no exception. There we reviewed (and to some extent extended) the theoretical finding that movements in intergenerational wellbeing are tracked by movements in a comprehensive notion of wealth. We also identified conditions under which the finding could be sharpened to imply that wealth per capita and intergenerational wellbeing averaged over the generations track one another exactly; that is, wealth per capita increases if and only if intergenerational wellbeing averaged over the generations increases. We then put the theory to work by estimating movements in wealth per capita over the period 1995 to 2000 in five countries (Brazil, China, India, United States and Venezuela). Our choice of countries was in part designed to reflect different stages of economic development and in part to focus on particular resource bases. We are particularly grateful to the Editor, Anastasios Xepapadeas, and the participants in the symposium that Professor Xepapadeas built around our paper (Duraiappah and Munoz, 2012; Gundimeda and Shyamsundar, 2012; Hamilton, 2012; Smulders, 2012; and Solow, 2012) for their reflections on the methods we used to estimate wealth and its movements in our sample of countries. In this note we take the opportunity to clarify some of our methods and offer a few observations that may prove to be useful in future work. 2. Shadow prices as marginal rates of substitution The objects that link intergenerational wellbeing to wealth are shadow prices. Because they combine ethical values with forecasts of future economic possibilities, shadow prices have long proved to be contentious – for example, in social cost-benefit analysis.1 Problems are compounded in sustainability analysis, because in estimating wealth one is obliged to impute prices to stocks of capital assets. Moreover, the notion of wealth that has to be deployed requires that we estimate shadow prices not only of reproducible and human capital, but natural capital too. For many types of natural capital there is a paucity of good data on physical stocks. And attaching shadow values to those stocks is exceptionally difficult because of the prevalence of externalities associated with the use of their services. Because of data limitations, the types of natural capital we were able to include in our study were restricted to land, forests as stocks of timber, sub-soil resources and carbon concentration in the atmosphere. A good portion of our paper was devoted to estimating shadow prices. As in Dasgupta and Mäler (2000), we developed our account of shadow prices in the context of imperfect economies. That meant we had to consider marginal variations from an existing path (and its extension into the future) which is itself not optimal.2 In policy analysis the variations are 1 Continuing debates over the magnitudes of ‘consumption discount factors’, which are shadow prices of future consumptions relative to current consumption, illustrate this. 2 In this context, optimality requires that the forecast is that of an economy that follows a consumption path which maximizes intergenerational wellbeing (defined 506 Kenneth J. Arrow et al. induced by marginal policy changes at a point in time; in sustainability analysis (the concern in our study) the variations are caused by the sheer passage of time. Solow (2012: 354) draws attention to the fact that we evaluated the variations in terms of marginal rates of substitution (MRSs), not marginal rates of transformation (MRTs). Although he suggests this as a problem, it should be seen as a virtue. Had we been studying perturbations from an optimal path, a change could have been evaluated using either the MRSs or the MRTs, since the two would be equal. However, as we were in fact studying variations around non-optimal paths – in particular, paths that are called ‘business as usual’ – the MRTs do not determine shadow prices, as they do not reflect the change in utility from a perturbation from the business-as-usual path. In contrast, the MRSs do measure the utility change. The variations to be studied need to be feasible. Variations in quantities of goods and services in our study actually occurred, so their feasibility shouldn’t be in question. But estimating shadow prices today even of past stocks requires peering into the future. We took market prices of reproducible capital assets to reflect their shadow prices, assuming implicitly that markets in each of the countries aggregated information concerning the feasibility of future economic trajectories. In estimating the shadow prices of human and natural capital, we implicitly assumed that the forecasts were feasible. That move isn’t unique to sustainability analysis; it is an implicit requirement in any exercise involving the future. Smulders (2012: 369–370) is right to remind readers that forecasts can’t be built on air. Good forecasts require the forecaster to attend to counterfactuals (what would the forecast be if the inherited stock of assets were to have been otherwise?). Smulders is in favour of arriving at shadow prices on the basis of explicit intertemporal models (e.g., computable general equilibrium models) and says that, if we had them in hand, it would have been far simpler to use the outcomes of the models to directly calculate movements in intergenerational wellbeing. So he asks if there is any need to resort to shadow prices. The intertemporal modelling approach endorsed by Smulders is a complement to our approach, not a substitute. In intertemporal simulation models, one assesses the impact on intertemporal wellbeing of a perturbation in the initial stock of each capital asset. For each asset, this impact is its shadow price. However, the estimates obtained from intertemporal models are only as good as the technological and behavioural assumptions built into them. The information underlying those assumptions may be good, but it will be less than perfect. Our approach relies on a different (and also imperfect) source of information, namely, the information inherent in today’s market prices. Using both approaches should be expected to offer more insights than relying entirely on one. in our paper as the present discounted value of momentary utilities or ‘felicities’), subject to technological and ecological constraints. Environment and Development Economics 507 In several cases, estimating shadow prices compelled us to rely on important theoretical predictions about economic equilibrium. For example, we assumed that the scarcity rent for crude petroleum will rise at the rate of return on reproducible capital. This is a central prediction in the theory of optimum extraction (Hotelling, 1931). Hamilton (2012: 358–359) suggests that this move on our part went against the emphasis we placed when developing the theory underlying our empirical exercise that the economies being studied were imperfect. However, the empirical evidence on movements of their market prices, reported periodically since the classic by Barnett and Morse (1963), is remarkably varied. To be sure, the price of extracted crude oil has not been rising at the rate of interest. A number of factors – including technological changes that lower extractions costs, as well as changes in market structure and discoveries of new deposits – have influenced the time path of extracted crude oil. It is very difficult to discern what component of that price is the scarcity rent. Still, to assume (in keeping with the Hotelling Rule) that the scarcity rent has tended to increase at the rate of interest would seem to be at least as reasonable a basis for a forecast on which to have built our empirical work than any of the very many ad hoc rules we could have followed. 3. Is time an asset? Solow (2012: 354) takes issue with our decision to model time as a capital asset on the grounds that one cannot choose to alter the stock of time, which simply ‘marches on’ exogenously. What should be included on the list of capital assets is in part a matter of convenience. One could, for example, regard knowledge and institutions as assets. After all, people use the term ‘institutional capital’ often enough, and ‘knowledge capital’ is a commonplace term today. If in the absence of an overarching social theory it is assumed that they change exogenously over time, knowledge and institutions would be mathematical transformations of time itself. In that case, to regard knowledge and institutions as capital assets would in effect be to add ‘time’ to the list of state variables. This is sometimes done by analysts when the systems they are studying are non-autonomous. Alternatively, those exogenous changes could be absorbed in the way we measure the more grounded categories of assets, namely, (i) reproducible capital, (ii) human capital and (iii) natural capital. The idea is to measure stocks of assets in efficiency units. That makes the dynamical system appear as autonomous. Shadow prices are then defined for the qualityadjusted assets, and wealth is defined as the sum of the shadow values of quality-adjusted assets.3 3 The above remarks are not limited to exogenous changes in institutions and knowledge; they are valid for any variable that changes exogenously over time (e.g., exogenous change in the terms of trade). Population size is another variable that, in the absence of a comprehensive demographic theory, is often assumed to change over time in an exogenous manner. 508 Kenneth J. Arrow et al. In the first part of our paper, where we developed the pure theory of wealth accounting, time was taken to be an asset. We viewed time that way so as to develop the theory without modelling the economy explicitly. (The latter meant it wasn’t possible to identify how the exogenous changes in economic variables ought to translate into adjustments in the quality of the more grounded assets (i)–(iii).) However, in the second half of our paper, where we came to estimate wealth changes for the five countries in our sample, we restricted the use of the term ‘asset’ to categories (i)–(iii). The task we faced thereby was reduced to estimating the shadow prices of the quality-adjusted assets in categories (i)–(iii). The two methods are equivalent. We illustrate this by way of a simple, imperfect economy. Assume population to remain constant over time. Output Y (t) at time t is taken to be a power function of an aggregate (scalar) index of capital stocks in categories (i)–(iii), which we write as K (t). Thus Y (t) = A(t)K (t), 0 < α ≤ 1. (1) A(t) is total factor productivity (TFP) at t . It reflects the economy’s institutions and knowledge base. Imagine that A(t) grows at a constant, exogenous rate γ . If consumption is a constant proportion, (1-s), of output, the dynamics of the economy would be given by the equations dK (t)/dt = s A(t)K (t), 0 < s < 1, (2) dA(t)/dt = γ A(t). (3) One way to interpret the dynamical system (1)–(3) is to regard both A and K as state variables. In that view of things, the model has two capital assets. Intergenerational wellbeing, which we write as V , is therefore a function of A and K : V (t) = V (A(t), K (t)). (4) Shadow prices of the pair of assets are then, respectively, PA(A(t), K (t)) = ∂V (A(t), K (t))/∂A(t), (5a) PK (A(t), K (t)) = ∂V (A(t), K (t))/∂K (t). (5b) Comprehensive wealth at t , which we write as W (t), is W (t) = PA(A(t), K (t))A(t)+ PK (A(t), K (t))K (t). (6) Taken together, equations (1)–(5a–b) appear to be an autonomous dynamical system. But that is an illusion, inasmuch as we have merely re-measured time for our purposes (equations (3) and (5a)). Equation (5a) is then to all intents and purposes the shadow price of time. In estimating comprehensive wealth (equation (6)), we would then be required to Environment and Development Economics 509 estimate the shadow value of time, a feature of the theory that Solow (2012: 354) found distinctly odd.4 However, there is an alternative way to express equations (1)–(5a–b). It would be to acknowledge that there is a single quality-adjusted capital asset. The task would then be to estimate the shadow price of that single asset. That is what we did in the empirical part of our paper. The idea is to create a single capital asset out of A and K by measuring the quantity of K in efficiency units. To see what that involves, define the variable A∗ as A∗α = A. (7) Using equation (7) we may then re-write equation (1): Y (t) = [A∗(t)K (t)]. (8) Now define the variable X as