Abstract
In order to analyse the historical changes in economic, environmental, socio-economic and energy indicators, it is useful to identify, separate and evaluate the macroeconomic forces that contribute to those changes. Basically, the literature records four paradigms that may be used in order to decompose the change experienced by an indicator. These are (a) econometric analysis, (b) analysis based on aggregate data, (c) index-based analysis (Index Decomposition Analysis, or IDA), and (d) structural analysis (Structural Decomposition Analysis, or SDA).
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Notes
- 1.
Sun’s original contribution only considers additive decompositions.
- 2.
SDA is the technique most frequently used in decomposition studies based on input–output tables, and therefore it is sometimes known as input–output decomposition analysis.
- 3.
- 4.
In this regard, a line integral is said to be independent of its path in an open region S in \({\Re^{n} }\) if (for \(\varphi\) continuous on S, with x and y being two points in S):
$$\int_{{\,\varGamma \left( {x,y} \right)}} {\,\,\,\,\,\varphi \,{\text{d}}\alpha \left( t \right)} = \int_{{\,\varGamma_{1} \left( {x,y} \right)}} {\,\,\,\,\,\,\,\varphi \,} {\text{d}}\beta \left( t \right)$$for all paths \({\alpha \left( t \right)}\) and \({\beta \left( t \right)}\) describing curves \(\varGamma\) and \({\varGamma_{ 1} }\) such that \({\varGamma \subset S}\), \({\varGamma_{ 1} \subset S}\), \({\alpha \subset \varGamma }\), and \({\beta \subset \varGamma_{ 1} }.\)
- 5.
The term ‘adaptive’ refers to the fact that the parameters are not fixed in advance. Instead, they are determined by the levels of the magnitudes in periods 0 and T.
- 6.
Törnqvist et al. (1985) argue that the above logarithmic function was originally proposed by Törnqvist in (1935), though it is in their 1985 work where it was eventually specified that:
-
(a)
\(x\) and \(y\) should be positive numbers,
-
(b)
if \({x \ne y}\) the range of function \({L\left( {x,y} \right)}\) should be \({\left( {\left( {xy} \right)^{ 1/ 2} ,\left( {x + y} \right)/ 2} \right)}\).
-
(a)
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Fernández González, P., Landajo, M., Presno, M. (2014). Literature Review and Methodology. In: The Driving Forces of Change in Environmental Indicators. Lecture Notes in Energy, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-07506-8_1
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