Comparing structural decomposition analysis and index

doi:10.1016/S0140-9883(02)00059-2

Energy Economics

Volume 25, Issue 1, January 2003, Pages 39-64

https://doi.org/10.1016/S0140-9883(02)00059-2 Get rights and content

Abstract

To analyze and understand historical changes in economic, environmental, employment or other socio-economic indicators, it is useful to assess the driving forces or determinants that underlie these changes. Two techniques for decomposing indicator changes at the sector level are structural decomposition analysis (SDA) and index decomposition analysis (IDA). For example, SDA and IDA have been used to analyze changes in indicators such as energy use, CO₂-emissions, labor demand and value added. The changes in these variables are decomposed into determinants such as technological, demand, and structural effects. SDA uses information from input–output tables while IDA uses aggregate data at the sector-level. The two methods have developed quite independently, which has resulted in each method being characterized by specific, unique techniques and approaches. This paper has three aims. First, the similarities and differences between the two approaches are summarized. Second, the possibility of transferring specific techniques and indices is explored. Finally, a numerical example is used to illustrate differences between the two approaches.

Introduction

SDA uses the input–output model² and data to decompose changes in indicators while IDA uses only sector level data. These two fields of decomposition analysis have developed independently, with the result that they are characterized by different approaches and techniques. Generally speaking, the literature on IDA has extensively studied the implications of index theory and the specification of the decomposition, whereas the SDA literature has focused attention on distinguishing a large number and specific determinant effects.

This paper has three aims:

1
To summarize the fundamental differences and similarities between structural decomposition analysis and index decomposition analysis.
2
To transfer decomposition techniques and indices between the two methods.
3
To compare the SDA and IDA techniques in the context of a numerical example.

Section 2 presents a general overview of the differences and similarities between SDA and IDA. Section 3 discusses the transfer of IDA decomposition techniques to an SDA context. Section 4 discusses the use of SDA techniques in the IDA setting. Section 5 illustrates the results of and differences between the various decomposition forms using a numerical example. Section 6 concludes.

Section snippets

Fundamental differences

SDA and IDA are decomposition methods that are used to assess the effect of certain driving forces on indicator changes. Historical data are used, usually from two periods, to analyze which determinant changes have contributed most to a change in an indicator. For example, many studies use SDA or IDA to gauge the influence of technological and economic changes on energy use. In their review of SDA, Rose and Casler (1996) briefly discuss SDA and IDA. They note that if input–output information

IDA index approaches transferred to SDA

In this section the index approaches from the IDA literature are transferred into the SDA setting. The following indices approaches will be discussed:

1
Multiplicative decomposition of the intensity indicator
- •
  Parametric method one (conventional Divisia index)
- •
  Non-parametric method one (refined Divisia index)
- •
  Parametric method two (Laspeyres, Marshall–Edgeworth, Paasche indices)
- •
  Parametric method one and two combined (adaptive weighting Divisia index)
2
Additive decomposition of the absolute indicator
- •

Additive decomposition of the absolute indicator, using Dietzenbacher and Los (1998)

There is only one index approach that is unique to SDA and has not been implemented in the IDA (proposed in Dietzenbacher and Los, 1998). They note that if it is assumed that each of n determinant variables can either be weighted by the Laspeyres or Paasche weights, then there are n! different complete decompositions possible. In the IDA setting the base equation for the absolute indicator is: $m= ∑ i x_{i} x · m_{i} x_{i} ·x= ∑ i s_{i} ·r_{i} ·x$ This may be decomposed into the following determinant effects.⁹

Comparing SDA and IDA: a numerical example

In this section a hypothetical numerical example from Ang (1999) is expanded to illustrate the differences in SDA and IDA (Table 3). The bold information is from Ang (1999) while the input–output information (normal font) has been added. All information is in monetary units, except for the indicator m (in brackets) (e.g. joules, BTUs or man hours). The different decomposition techniques and indices were applied to these data and the results are shown in Table 4.

Table 4 shows that the

Conclusions

A number of conclusions can be drawn from the previous analysis. Firstly, there are two streams of historical decomposition methods that can analyze the determinant effects using sector level data. SDA uses the input–output model while IDA uses more aggregated sector data. As a result, SDA is capable of more refined decompositions of economic and technological effects but IDA is capable of more detailed time and country studies because of the availability of data. The two fields of

Acknowledgements

The authors are grateful to Erik Dietzenbacher, Bert Balk and Marcel Boumans for useful comments.

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View full text

Comparing structural decomposition analysis and index

Abstract

Introduction

Section snippets

Fundamental differences

IDA index approaches transferred to SDA

Additive decomposition of the absolute indicator, using Dietzenbacher and Los (1998)

Comparing SDA and IDA: a numerical example

Conclusions

Acknowledgements

Energy Econ.

Energy

Res. Energy

Energy Econ.

Decomposition methodology in energy demand and environmental analysis

Decomposition of aggregate energy and gas emissions intensities for industry: a refined Divisia index method

Energy J.

Axiomatic price index theory: a survey

Int. Stat. Rev.

Carbon dioxide emissions in the US economy

Environ. Resour. Econ.

Labor productivity in Western Europe 1975–1985: an intercountry, interindustry analysis

J. Reg. Sci.