AGGREGATION VERSUS DISAGGREGATION IN INPUT–OUTPUT ANALYSIS OF THE ENVIRONMENT

Abstract

Analysts carrying out input–output analyses of environmental issues are often plagued by environmental and input–output data existing in different classifications, with environmentally sensitive sectors sometimes being aggregated in the economic input–output database. In principle there are two alternatives for dealing with such misalignment: either environmental data have to be aggregated into the input–output classification, which entails an undesirable loss of information, or input–output data have to be disaggregated based on fragmentary information. In this article, I show that disaggregation of input–output data, even if based on few real data points, is superior to aggregating environmental data in determining input–output multipliers. This is especially true if the disaggregated sectors are heterogeneous with respect to their economic and environmental characteristics. The results of this work may help analysts in understanding that disaggregation based on even a small amount of proxy information can improve the accuracy of input–output multipliers significantly. Perhaps, these results will also provide encouragement for preferring model disaggregation to aggregation in future work.

Keywords:

• Aggregation
• Disaggregation
• Environmentally-extended input–output analysis
• Stochastic experiments

Notes

¹ Personal communication Glen Peters (CICERO, Oslo, Norway, 9 March 2010) and Christopher Weber (Carnegie-Mellon University, Pittsburgh, USA, 9 March 2010). In their study on regional aggregation, Andrew et al. (2009) found that in constructing an MRIO, modelling a Rest-of-World (RoW) region on the basis of many countries' input–output tables is preferable to choosing a ‘representative’ country.

³ Note that aggregators G for the input–output table parts and G ^(m) for the multipliers are different – see point 6.2 below.

⁴ This is because aggregation involves summing, and the RSE of a sum of random variables is smaller or equal to the average of the RSEs of summands.

⁵ One cannot directly compare m ⁽¹⁾ and m*, even though these multipliers are the ones that would be used in input–output analyses, because these vectors are not equally classified, i.e. they do not contain multipliers for identical sets of sectors.

² Whilst there is only one aggregator matrix G, there are, in general, different disaggregator matrices for the various tables Q, T, y, etc. This was pointed out by Editor Bart Los. For example one can aggregate three sectors into two using the simple column-normalised matrix ; however, disaggregation can be performed using a continuous range of matrices of the shape , row-normalised through . The value of a and b will in general differ in D ^(Q), D ^(T) and D ^(x), because two sectors generally have different shares of environmental impacts, intermediate demand, and gross output. In the numerical experiments described in Section 2.2, we will call the normalised D matrices ‘maps’. Further, we will not use a disaggregator D ^(x), but only a disaggregator D ^(y) for final demand y, and calculate disaggregated gross output residually via x = T1 + y. D ^(x) is used here only to simplify the mathematical notation.

⁶ This formula is an approximation of a more general relationship assuming zero covariance, and truncating a Taylor series at second- and higher-order terms.

⁷ Because of its magnitude, and its relationship with macroeconomic quantities such as GDP, gross output is usually well measured (Bullard and Sebald, 1988).

⁸ A number of authors (Dietzenbacher, 1995, 2006; Ten Raa and Rueda-Cantuche, 2007) deal with the bias of multipliers as such, due to the non-linearity of the Leontief inverse. This circumstance does not affect the findings of this work.

¹⁰ For example a proxy variable for disaggregating water use by crop could be irrigated area by crop.

¹¹ Latin letters denote true quantities, Greek letters denote estimates.

⁹ In the following, R[MIN,MAX] shall denote a random number drawn from a rectangular distribution across [MIN,MAX], and N[MEAN,STDEV] a random number drawn from a normal distribution with mean MEAN and standard deviation STDEV. Further, all disaggregated quantities are denoted by a star superscript above their aggregated counterparts.

¹² This finding is in agreement with results from a study by Su et al. (2010), who also conclude that disaggregation is preferable to aggregation, albeit only on the basis of measuring emissions embodied in trade.