Disaggregation of sectors in social accounting matrices using a customized Wolsky method: a comment on its estimation bias

ABSTRACT

Barrera–Lozano et al. (2015) suggest an approach to disaggregate SAM matrices using a customized method based on Wolsky (1984). Starting from an aggregated sector, they propose the extraction of a branch instead of its partition. This study compares these two methods based on the magnitude of their estimation bias of the disaggregated technical coefficient matrix. From simulations of the disaggregated Leontief matrix, this work calculates linkages and multipliers for common sectors derived from using either the Wolsky (1984) sectoral disaggregation or the Barrera–Lozano et al. (2015) sectoral extraction. Results show that both approaches provide biased estimators, with the last one showing a significantly higher bias, especially in cases of incomplete information. This comparison suggests the need of additional research to provide bias corrections for input–output disaggregation methodologies.

KEYWORDS:

• Input–output analysis
• sectoral disaggregation
• sectoral extraction

JEL CLASSIFICATION:

• C63
• C67
• C15

Acknowledgement

I am grateful to Geoffrey J. D. Hewings for his extensive feedback in this study. I also thank Satish Joshi, Dusan Paredes and Andre F. T. Avelino for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Aside from disaggregation concerns are those regarding aggregation. See for example Miller and Blair (2009) for the so common “aggregation bias”, and Kymn (1990) for an extensive review of aggregation problems.

² Sectors that are not disaggregated.

³ This means that those indicators from Wolsky’s original illustration will be considered the true population parameters, as these were known.

⁴ Same simulations were performed using higher dimensions, with similar results. Estimations from Barrera-Lozano, Mainar, and Vallés (2015) start to be unbiased only for linkages in cases of full incomplete information and for higher dimensions, while results for the output multiplier remain biased independently of dimension.

⁵ Wolsky (1984) specifies upper and lower bounds for the variables and whenever the disaggregation is performed into two subsectors and the information is incomplete. See Wolsky (1984) for more details.

⁶ The conclusion is identical when adding columns instead, in which case the result will involve the variable instead of .

⁷ Common sectors may show some differences related to the inverting procedure only. However, adjustments from the inverting procedure will apply to both approaches, and beforehand there are no reasons to expect a higher impact on only one of them.

⁸ The code on R is available upon request.

⁹ Original values presented by Wolsky (1984) are used to construct these population parameters: , , , , , , , .