The aggregation problem: Implications for ecological economics

Fix, Blair Working Paper The aggregation problem: Implications for ecological economics Working Papers on Capital as Power, No. 2018/03 Provided in Cooperation with: The Bichler & Nitzan Archives Suggested Citation: Fix, Blair (2018) : The aggregation problem: Implications for ecological economics, Working Papers on Capital as Power, No. 2018/03, Forum on Capital As Power - Toward a New Cosmology of Capitalism, s.l., http://bnarchives.yorku.ca/543/ This Version is available at: https://hdl.handle.net/10419/179420 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ No. 2018/03 The Aggregation Problem Implications for Ecological Economics Blair Fix May 2018 http://www.capitalaspower.com/?p=2486 WORKING PAPERS ON CAPITAL AS POWER The Aggregation Problem: Implications for Ecological Economics Blair Fix⇤ May 3, 2018 Abstract This article discusses the aggregation problem and its implications for ecological economics. The aggregation problem consists of a simple dilemma: when adding heterogeneous phenomena together, the observer must choose the unit of analysis. The dilemma is that this choice affects the resulting measurement. This means that aggregate measurements are dependent on one’s goals, and on underlying theory. Using simple examples, this article shows how the aggregation problem complicates tasks such as calculating indexes of aggregate quantity, and how it undermines attempts to find a singular metric for complex issues such as sustainability. Keywords: aggregation; GDP; capital stock; natural capital; sustainability indexes ⇤Author contact: [email protected] Introduction 2 1 Introduction Aggregation — the practice of summing heterogeneous things — is used in all aspects of science. Aggregation occurs when a physicist sums the mass of many different particles, or when an ecologist sums the energy consumption of an ecosystem. The use of aggregation is so commonplace that its epistemology is often given little thought. This is particularly true in economics — a field that tends to hide epistemological questions under a fog of mathematics (Mirowski, 1991;Keen,2001). Aggregation is often portrayed as a purely objective process. After all what could be more objective than the simple arithmetic act of adding things up? The purpose of this article is to show that aggregation, like any act of measurement, is never a purely objective process. This is because underlying every measurement are assumptions about what is to be quantified, and why the quantification is being made. Giampietro, Allen and Mayumi (2006) call this the “epistemological predicament associated with purposive quantitative analysis” — “the observer always affects what is observed when defining the descriptive domain”. This is another way of saying that no measurement is theory free. In the natural sciences (particularly physics), the inter-connection between theory and observation is often undiscussed because there is a consensus that core theories are correct (and these theories are backed by overwhelming evidence). For instance, if a physicist wants to measure the inertia of a system, Newton’s laws make it clear that he/she should aggregate the system’s mass. But when we move into fields like ecological economics that study more complex phenomena, theory is less clear. For instance, what does it mean to measure ‘sustainability’? What is it that is to be sustained? And what are the units of measurement? If ecological economics is to be a “science of sustainability” (Dodds, 1997), then these epistemological questions must be addressed. This article makes three main points. First, when it comes to aggregation and objectivity, less is more. When faced with theoretical uncertainties, less aggregation will generally lead to more objective analysis. Second, it is best to avoid aggregation that uses ‘real’ monetary value. The problem is that numerous subjective decisions must be made when attempting to ‘correct’ for inflation. Moreover, existing price-index methods (that underpin national accounting systems) are strongly informed by neoclassical economic theory. If one wishes to challenge neoclassical theory, then these methods should be avoided. Lastly, when we aggregate complex phenomena guided by theories that are either unclear or contested, we should acknowledge that the resulting measurement con- The Aggregation Problem 3 tains an inescapable political element. This likely means abandoning the use of aggregation to search for ‘optimal’ policy decisions. 2 The Aggregation Problem Any act of aggregation requires making two types of decisions. First, one must choose what is to be included in the aggregation and what is to be excluded. This is often called making boundary decisions. Second, one must choose a method for converting qualities into quantities. For simplicity, I call this choosing the ‘unit’ of analysis. Note that I mean this in the sense of choosing the conceptual unit (as in mass), not the literal measurement unit (as in kilograms or pounds). This article focuses on the ‘unit’ aspect of aggregation analysis, rather than on boundary decisions. This is because boundary problems have already been extensively discussed in ecological economics literature. For instance, a common criticism of aggregate measures of output (i.e. real GDP) is that they do not include externalities such as environmental degradation or social ‘bads’ (Daly and Cobb,1994;Kubiszewski et al.,2013). Similarly, ecological economists have criticized measures of the capital stock because they do not include the stock of natural resources, or ‘natural capital’ (Daly,2011;Dixon and Hamilton, 1996;Costanza and Daly,1992). While it is important to debate boundary decisions, my aim here is to show that even if there is a consensus on what system boundaries should be, the act of aggregation still involves subjective (theorydependent) decisions about the unit of analysis. Moreover, these subjective decisions affect the measurement itself. 2.1 An Example: Aggregating Apples and Bread The best way to understand how units affect the aggregation process is through a simple example. Suppose you are a shopkeeper who has a stock of apples and bread slices. Like many shopkeepers, you are not satisfied to state that you have xapples and yslices of bread. Instead, you want to know the size of your total inventory. How do you go about calculating this quantity? Let’s set aside the fact that most shopkeepers care about the monetary value of their stock. (I will deal with monetary value later). Instead, let’s assume that you are a former natural scientist, and you want a physical measure of the size of your stock. This is simple enough to do — all that is required is for you to choose a unit of analysis. Table 1shows realistic values for the average mass, volume and energy content of apples and bread slices. You simply choose one of The Aggregation Problem 4 these units, and use it to aggregate your total stock. But herein lies the problem. The choice of units is subjective — it depends on your goals. Yet this choice plays a crucial role in determining the measurement results. Table 1: Measuring apples and bread slices using different units Mass (g) Volume (cm3) Energy (cal) Apple 75 104 39 Bread Slice 30 52 79 To understand this dilemma, it is helpful to reflect on what a unit does. In an aggregative analysis, a unit determines the relative weights assigned to the different elements being added together. In our example, the unit determines how we weight apples relative to bread slices. The problem is that different units lead to different weightings. Using the values in Table 1, we can see that using mass, volume, or energy leads to the following (different) weightings between apples and bread slices: Mass: 1 apple =2.5 bread slices (1) Volume: 1 apple =2.0 bread slices (2) Energy: 1 apple =0.5 bread slices (3) These different weightings can lead to wildly divergent measures for the aggregate stock of apples and bread slices. A clear way to illustrate the problem is to construct an indexed time series of aggregate quantity (an extremely common practice in economics). Suppose that over the course of 30 hours, the individual stock of apples and bread slices changes as shown in Figure 1A. Assuming that apples and bread slices are uniform, we can objectively state that the stock of bread slices increases by 164%, while the stock of apples decreases by 70%. There is no ambiguity here. We would get the same result, no matter what unit of analysis we choose. However, this is not true when we move to an aggregate analysis. Figure 1B shows the results of aggregating the stock of apples and bread slices using units of energy, volume, and mass (with values from Table 1). Suddenly there is significant ambiguity in the indexed growth of the aggregate stock. When measured in terms of caloric energy, the size of our apple-bread stock increases by 86%. Yet when measured in terms of mass, the same stock appears to decrease in size by 3%. This large discrepancy occurs because when we change units, we The Aggregation Problem 5 ● ●●●● ● ● ●● ●● ●● ●● ●● ● ● ● ●●●● ● ● ● ● ● ● ● ●● ● ● ●● ● ●● ● ● ● ● ● ● ●●● ● ● ● ● ●● ● ● ● ● ● Bread Slices Apples +164% −70% Energy Volume Mass +86% +8% −3% 50 100 150 200 250 1.0 1.2 1.4 1.6 1.8 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Time (hrs) Time (hrs) Number Indexed Aggregate Stock A. Disaggregated Stock of Bread and Apples B. Aggregated Stock of Bread and Apples Figure 1: Conflicting aggregate measures of a stock of apples and bread slices This figure shows how the choice of (conceptual) unit affects aggregate measures of quantity. We imagine that a shopkeeper has a stock of apples and bread slices. Panel A shows how the number of apples and bread slices changes over a period of 30 hours. Panel B shows three different indexed aggregate measures of the same stock, calculated using units of energy, volume, and mass (with values from Table 1). Different units lead to a different weighting between apples and bread slices, which causes divergent measures for the growth of the aggregate stock. Notes: this figure is inspired by Fig. 8.1 in Nitzan and Bichler (2009). Monetary Value: The Changing Meter Stick 6 change the relative weighting between apples and bread slices. This, in turn, affects how much we weight the increase in the quantity of bread slices against the decrease in the quantity of apples. Because the different units yield different apple-to-bread-slice weightings, the resulting indexes of aggregate quantity give conflicting results. It might seem reasonable to ask — which of these three indexes is the ‘correct’ measure of aggregate quantity? However this question is ill posed. All three measures are correct in a strictly mathematical sense. Instead, what we should ask is — which measurement is appropriate, given our goals and our state of knowledge? It is here that subjectivity enters the equation. For instance, if we want to know the scale of our apple-bread stock in the context of feeding a starving population, caloric energy content seems the most appropriate choice of unit. But if we wanted to calculate shipping costs, then mass is likely the best unit. Even when the context makes the choice of the unit seem clear, we need to remember that the aggregation process depends on a priori decisions about why we are taking the measurement. The subjective aspect of aggregation means that in matters where the appropriate unit is not clear (or when the unit is contested), aggregate analysis should be undertaken with caution. For instance, suppose that instead of aggregating bread and apples, we wanted to aggregate fresh water and bituminous coal to create an index of ‘natural capital’. It is far from clear what unit of analysis we should use, since fresh water and bituminous coal have completely different uses. Given the uncertainty in our goals and theory, the resulting aggregation would have a great deal of ambiguity. Thus, it is far more reasonable to treat fresh water and bituminous coal as separate, incommensurable entities. This disaggregated treatment will be far more objective than any aggregate analysis. To summarize, aggregation always involves theory-informed choices about the unit of analysis, and these choices affect the resulting measurement. Given this epistemological predicament, researchers need to remember that less aggregation means greater objectivity. 3 Monetary Value: The Changing Meter Stick A defining feature of economics is its focus on prices. This has led to a strong tendency to conduct aggregate analysis using units of monetary value. Unfortunately, using prices as the unit of analysis leads to its own unique set of problems. The difficulty is that prices change over time, and attempts to ‘adjust’ for this change inevitably require subjective decisions. Monetary Value: The Changing Meter Stick 7 When we use prices to measure how aggregate quantities (such as economic output) change over time, a common belief is that one can objectively account for price changes simply by adjusting for inflation (using official price indexes). However, the matter is not so simple. The problem is that price changes are not uniform. As shown in Figure 2A, historical price changes (in the US) have varied drastically by commodity. Since 1935, the price of apples increased by a factor of 50, the price of electricity increased by a factor of 7, and the price of TVs actually declined (more on this later). This divergent price change means that our unit is unstable. The effect is the same as when we literally changed units in our apple-bread example (Fig. 1). Divergent price changes cause the relative weighting between commodities to change with time. This means that our aggregate measure will be affected by the year in which we chose our prices. This problem was identified over a century ago by Francis Edgeworth (Edgeworth, 1887): If one great group of commodities varies pretty uniformly in one direction, and another in a different direction (or even in the same direction but in a markedly different degree), then the task of restoring the level of prices can no longer be regarded as a purely objective ... problem. (cited in Vining and Elwertowski (1976); emphasis added) The effect of changing prices can be clearly illustrated by calculating real GDP using different base years (in which prices are fixed). Figure 2B shows how the choice of base year affects the growth of US real GDP. This analysis indicates a 30% uncertainty in the growth of US GDP over the last 60 years. This range of estimates is conservative because it does not account for other subjective factors that enter into price adjustments. Most importantly, commodities themselves change with time. Today’s computers are drastically different from those of the 1990s. It is standard practice, in price-index methodology, to differentiate between pure changes in price (inflation) and changes in the quality of a commodity. For instance, if a computer increases in price by a factor of 2, but at the same time increases in ‘quality’ by a factor of 4, this is recorded as a decrease in price by a factor of 2. This is why Figure 2A shows such a drastic decrease in the price of computers. Virtually all of it is due to quality adjustments. The same is true of TVs (which have drastically decreased in indexed price since the advent of smart TVs). How is this change in quality measured? Here the aggregation problem rears its head again. In order to measure quality change, we must decompose a commodity into individual components, measure the change in quality of these components, and then aggregate the result. But what unit should we chose? Non- REFERENCES 14 environmental impacts in a disaggregated manner in order to separate objective measurement from subjective decision-making. References Ackerman, Frank. Critique of cost-benefit analysis, and alternative approaches to decision-making. Technical report, London, 2008. Addison, Kenneth N. We Hold These Truths to Be Self-Evident...: An Interdisciplinary Analysis of the Roots of Racism and Slavery in America. University Press of America, 2009. BLS. “Frequently Asked Questions about Hedonic Quality Adjustment in the CPI: U.S. Bureau of Labor Statistics.”, 2010. Cohen, Avi J. and Geoffrey C. Harcourt. “Retrospectives: Whatever happened to the Cambridge capital theory controversies?” Journal of Economic Perspectives 17, 1 (2003): 199–214. Costanza, Robert and Herman E. Daly. “Natural capital and sustainable development.” Conservation biology 6, 1 (1992): 37–46. Daly, H.E. Ecological Economics : Principles and Applications. Washington: Island Press. ISBN 1-59726-681-7, 2011. Daly, Herman E. and John B. Cobb. For the common good: Redirecting the economy toward community, the environment, and a sustainable future. Beacon Press, 1994. Diamond, Peter A. and Jerry A. Hausman. “Contingent valuation: is some number better than no number?” Journal of economic perspectives 8, 4 (1994): 45–64. Dixon, John A. and Kirk Hamilton. “Expanding the measure of wealth.” Finance and Development 33, 4 (1996): 15. Dodds, Steve. “Towards a ‘science of sustainability’: improving the way ecological economics understands human well-being.” Ecological economics 23, 2 (1997): 95–111. Dore, Mohammed HI. “The problem of valuation in neoclassical environmental economics.” Environmental Ethics 18, 1 (1996): 65–70. REFERENCES 15 Eberle, W. David and F. Gregory Hayden. “Critique of contingent valuation and travel cost methods for valuing natural resources and ecosystems.” Journal of Economic Issues 25, 3 (1991): 649–687. Edgeworth, Francis Y. “Measurement of Change in Value of Money I.” First Memorandum presented to the British Association for the Advancement of Science. Reprinted in his Papers Relating to Political Economy 1 (1887): 198–259. Felipe, Jesus and Franklin M. Fisher. “Aggregation in production functions: what applied economists should know.” Metroeconomica 54, 2–3 (2003): 208–262. Forrest, Adam. “The death of diesel: has the one-time wonder fuel become the new asbestos?” The Guardian ISSN 0261-3077. Ghose, Tia. “Volkswagen Scandal: Why Is It So Hard to Make Clean Diesel Cars?”, 2015. Giampietro, M., T. F. H. Allen and K. Mayumi. “The epistemological predicament associated with purposive quantitative analysis.” Ecological Complexity 3, 4 (2006): 307–327. Harcourt, G. C. “On the Cambridge, England, Critique of the Marginal Productivity Theory of Distribution.” Review of Radical Political Economics 47, 2 (2015): 243–255. ISSN 0486-6134, 1552-8502. doi:10.1177/0486613414557915. Hodgson, Geoffrey M. “The fate of the Cambridge capital controversy.” In Capital controversy, post Keynesian economics and the history of economic thought. Routledge, pp. 112–125, 2005. Karras, Georgios. “The optimal government size: further international evidence on the productivity of government services.” Economic inquiry 34, 2 (1996): 193–203. Keen, Steve. Debunking Economics: The Naked Emperor of the Social Sciences. New York: Zed Books, 2001. Koopmans, Tjalling C. “On the concept of optimal economic growth.” Cowles Foundation Discussion Papers 163. Kubiszewski, Ida, Robert Costanza, Carol Franco, Philip Lawn, John Talberth, Tim Jackson and Camille Aylmer. “Beyond GDP: Measuring and achieving global genuine progress.” Ecological Economics 93 (2013): 57–68. REFERENCES 16 Kwerel, Evan. “To tell the truth: Imperfect information and optimal pollution control.” The Review of Economic Studies (1977): 595–601. Mirowski, P. More Heat Than Light: Economics as Social Physics, Physics as Nature’s Economics. Cambridge Univ Pr, 1991. Nitzan, J. Inflation as restructuring. A theoretical and empirical account of the US experience. Ph.D. thesis, McGill University, 1992. Nitzan, J. and S. Bichler. Capital as Power: A Study of Order and Creorder. New York: Routledge, 2009. Robinson, Joan. “The production function and the theory of capital.” The Review of Economic Studies 21, 2 (1953): 81–106. Robinson, Joan. Economic philosophy. Chicago: Aldine Pub. Co., 1962. Sandmo, Agnar. “Optimal taxation: An introduction to the literature.” Journal of public economics 6, 1-2 (1976): 37–54. Vidal, John. “The rise of diesel in Europe: the impact on health and pollution.” The Guardian ISSN 0261-3077. Vining, Daniel R. and Thomas C. Elwertowski. “The relationship between relative prices and the general price level.” The American Economic Review 66, 4 (1976): 699–708. Wills, Garry. Negro President: Jefferson and the Slave Power. Houghton Mifflin Harcourt, 2005.