The Aggregation Problem: Implications for Ecological and Biophysical Economics

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 the 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.

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Fig. 1
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Reproduced with permission from Fig. 8.1 in Nitzan and Bichler (2009)

Fig. 3
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Notes

  1. 1.

    This position was summarized by Mill (1848) when he wrote: “There cannot ... be intrinsically a more insignificant thing, in the economy of society, than money.”

  2. 2.

    Relative standard deviation is defined as the standard deviation divided by the mean.

  3. 3.

    The relative standard deviation of adult males is roughly 4% (Smith et al. 2000).

  4. 4.

    For instance, US Federal Reserve economist Karl Whelan nicely captures real GDP uncertainty: “Take 1998 as an example: The growth rate of fixed-weight real GDP in this year was 4.5% if we use 1995 as the base year; using 1990 prices it was 6.5%; using 1980 prices it was 18.8%; and using 1970 prices, it was a stunning 37.4%!” (Whelan 2002).

  5. 5.

    For a review of the many subjective choices used in quality-change adjustments, see Nitzan (1992).

  6. 6.

    For a summary of the Cambridge debate, see Cohen and Harcourt (2003), Felipe and Fisher (2003), Harcourt (2015). For a broad discussion of the problems with measuring capital, see Nitzan and Bichler (2009).

  7. 7.

    The most famous discounting controversy is likely the debate between Nicholas Stern and William Nordhaus. This was an argument about the ‘correct’ discount rate for climate change costs. The Stern Review (2006) found that drastic action was required to avert catastrophic future costs. However, Nordhaus (2007) found that action was far less urgent. What was the main difference? The Stern Review used a discount rate of 1.4%, while Nordhaus used a discount rate of 6%. Nitzan and Bichler (2009) point out the effect this has on future costs: “One thousand dollars’ worth of environmental damage a hundred years from now, when discounted at 1.4%, has a present value of \(-\$249\) (negative since we measure cost). ... But the same one thousand dollars’ worth of damage, discounted at 6 per cent, has a present value of only \(-\$3\).”

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Correspondence to Blair Fix.

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Appendix

Appendix

Sources and Methods

See Fig. 3.

Consumer price index data comes from the Bureau of Labor Statistics database, available at https://download.bls.gov/pub/time.series/cu/. Commodities that exist in 1935 are indexed to 1 in that year. However, many commodities are introduced after 1935. I deal with these new commodities by indexing them to the average indexed price of the existing commodities in the sample.

Real GDP data comes from the Federal Reserve Bank of Philadelphia, series routputmvqd. This dataset contains ‘vintage’ real GDP calculations using different base years between 1965 and 2017. The source data does not calculate real GDP for years later than the corresponding base year. For instance, GDP data for base year 1995 ends in 1995. For comparison, I project real GDP growth up to 2017 (for all series). I do this by first calculating the difference in average growth rates between the given base-year series (\(g_{\text{base}}\)) and the 2017 series (\(\bar{g}_{2017}\)):

$$\begin{aligned} \bar{g}_{\Delta } = \left( \bar{g}_{2017} ~ - ~ \bar{g}_\text{base} \right) \bigg |_{1947}^\text{base} \end{aligned}$$
(5)

Here \(\bar{g}\) indicates the geometric mean. The average is calculated from 1947 to the base year in question. I then use the average growth rate difference \(\bar{g}_{\Delta }\) to project the base-year series up to 2017:

$$\begin{aligned} g_\text{project} = \left( g_{2017} ~- ~ \bar{g}_{\Delta } \right) \bigg |_\text{base}^{2017} \end{aligned}$$
(6)

US population data comes from the U.S. Bureau of the Census, retrieved from FRED https://fred.stlouisfed.org/series/POP. Population data prior to 1952 comes from the Historical Statistics of the United States series Aa6.

See Fig. 4

Computer quality-change adjustment are estimated as follows. We begin with the definition of price index change—the change in price less the change in quality:

$$\begin{aligned} \Delta \text {price index} = \Delta \text {price} - \Delta \text {quality} \end{aligned}$$
(7)

This implies that computer quality change is given by:

$$\begin{aligned} \Delta \text {quality}_{\text {computer}} = \Delta \text {price}_{\text {computer}} - \Delta \text {price index}_{\text {computer}} \end{aligned}$$
(8)

OECD (2004) provides the change in computer price index between 1995 and 2001 for eight OECD nations. To get the change in computer quality, we need computer price-change estimates for each country. However, this data is difficult to obtain. As an approximation, I assume that the change in computer price can be proxied by the official inflation rate in each country. This gives the following method for estimating the rate of computer quality change:

$$\begin{aligned} \Delta \text {quality}_{\text {computer}} \approx \Delta \text {inflation} - \Delta \text {price index}_{\text {computer}} \end{aligned}$$
(9)

For this estimate, I use GDP deflator data from the World Bank (series NY.GDP.DEFL.KD.ZG). Since official inflation rates in our eight OECD nations are very similar, virtually all of the dispersion in computer quality change comes from dispersion in the computer price index.

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Fix, B. The Aggregation Problem: Implications for Ecological and Biophysical Economics. Biophys Econ Resour Qual 4, 1 (2019). https://doi.org/10.1007/s41247-018-0051-6

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Keywords

  • Aggregation
  • GDP
  • Capital stock
  • Natural capital
  • Sustainability indexes