A comparison of deflation methods for carbon footprint calculations using Japanese data

Abstract

An embodied CO₂ emissions intensity database estimated from input–output data at current prices is now available in Japan. This study compares two non-survey methods: The double-deflation (DD) method and an elaborated approach combining the DD method with the generalized RAS method to deflate an input–output table (IOT). We used these methods to estimate new datasets of embodied CO₂ emission intensity data in Japan, utilizing Japan's IOTs for 2005, 2011, and 2015 at constant prices in 2015. Furthermore, we compare the estimated data of 367 commodity sectors for a specific year (2005 or 2011). The results reveal that the intensity for certain aggregated sector groups, such as non-ferrous metals and finance and insurance, exhibits higher uncertainty owing to the extreme price homogeneity assumption associated with the DD method. Consequently, we recommend that life-cycle-assessment practitioners use an open database when analyzing changes in the carbon footprint of products over time.

KEYWORDS:

• Embodied emission intensity
• double-deflation method
• GRAS method
• uncertainty

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 When defining the economic transaction matrix, which includes intermediate and final commodity deliveries to producers and final consumers at current prices as ${\mathbf{Z}}^{\mathrm{curr}}=(Z_{\mathrm{ij}}^{\mathrm{curr}})$, the economic transaction matrix at constant prices can be easily obtained as ${\mathbf{Z}}^{\mathrm{DD}}=({\tau }_i{Z}_{\mathrm{ij}}^{\mathrm{curr}})=(Z_{\mathrm{ij}}^{\mathrm{DD}})$, where ${\tau }_i$ denotes the price deflator for commodity $i$. The GRAS elaboration method, i.e., the CD method, aims to determine the optimal bi-proportional coefficients $r_i$ and $s_j$ in the matrix elements $Z_{\mathrm{ij}}^{\mathrm{GRAS}}=r_i{s}_j{Z}_{\mathrm{ij}}^{\mathrm{curr}}$ under the two constraints of $\sum _j{Z}_{\mathrm{ij}}^{\mathrm{GRAS}}=\sum _j{\tau }_j{Z}_{\mathrm{ij}}^{\mathrm{curr}}$ and $\sum _j{Z}_{\mathrm{ij}}^{\mathrm{GRAS}}=\sum _i{\tau }_i{Z}_{\mathrm{ij}}^{\mathrm{curr}}$ (see Lenzen et al. (2007) for detailed mathematics).

2 From the input–output dataset estimated by the DD method, the intermediate input coefficient matrix, ${\mathbf{A}}_{\mathrm{DD}}^t=(a_{\mathrm{DD},\mathrm{ij}}^t),$ can be calculated by the equation: $a_{\mathrm{DD},\mathrm{ij}}^t=Z_{\mathrm{DD},\mathrm{ij}}^t/x_{\mathrm{DD},j}^t$, where $Z_{\mathrm{DD},\mathrm{ij}}^t$ represents the intermediate input of commodity $i$ required per unit of output of commodity $j,$ and $x_{\mathrm{DD},j}^t$ represents the gross output of commodity $j$. In the same way, we can calculate the intermediate input coefficient matrix, ${\mathbf{A}}_{\mathrm{CD}}^t,$ from the input–output dataset estimated by the CD method.

3 From the input–output datasets, the ‘non-competitive-import type' embodied CO₂ emission intensities of sectors can be estimated by the equations: ${\overline{\mathbf{e}}}_{\mathrm{DD}}^t={\mathbf{d}}^t\{\mathbf{I}-(\mathbf{I}-{\hat{\mathbf{M}}}_{\mathrm{DD}}^t){\mathbf{A}}_{\mathrm{DD}}^t{\}}^{-1}={\mathbf{d}}^t{\overline{\mathbf{L}}}_{\mathrm{DD}}^t$ and ${\overline{\mathbf{e}}}_{\mathrm{CD}}^t={\mathbf{d}}^t\{\mathbf{I}-(\mathbf{I}-{\hat{\mathbf{M}}}_{\mathrm{CD}}^t){\mathbf{A}}_{\mathrm{CD}}^t{\}}^{-1}={\mathbf{d}}^t{\overline{\mathbf{L}}}_{\mathrm{CD}}^t$, where ${\hat{\mathbf{M}}}_{\mathrm{DD}}^t$ and ${\hat{\mathbf{M}}}_{\mathrm{CD}}^t$ are the import coefficient matrices whose i^th diagonal element shows a percentage of ‘imported' commodity $i$ in the domestic demand of the commodity $i$; otherwise it is zero. It should be noted that if a country imports nothing at all, ${\hat{\mathbf{M}}}_{\mathrm{DD}}^t$ or ${\hat{\mathbf{M}}}_{\mathrm{CD}}^t$ coincides with the zero matrix. In this case, we have ${\overline{\mathbf{e}}}_{\mathrm{DD}}^t={\mathbf{e}}_{\mathrm{DD}}^t$ and ${\overline{\mathbf{e}}}_{\mathrm{CD}}^t={\mathbf{e}}_{\mathrm{CD}}^t$, and the ‘non-competitive-import type' embodied CO₂ emission intensities are exactly the same as the ‘competitive-import type' embodied CO₂ emission intensities.

Additional information

Funding

This work was supported in part by the JSPS KAKENHI (No. 20H00081) and the JST, the establishment of university fellowships towards the creation of science technology innovation: [grant no JPMJFS 2132].