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.

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.