A bidimensional reformulation of location quotients for generating input–output tables

ABSTRACT

The difficulties in obtaining input–output tables at subnational levels have led to multiple methodological developments in order to obtain local technical coefficients using semi-survey approaches. A widely accepted method is based on the use of location quotients (LQ) according to Flegg's formula (AFLQ). However, it makes the adjustment of purchasing sectors proportionally to the productive specialization, which has significant implications for the estimation of domestic coefficients. In this paper, an alternative formulation is presented as a generalization of Flegg's methodology, characterized by using a bidimensional approach that provides better results, as shown in the empirical application implemented.

KEYWORDS:

• location quotients
• regional economies
• input–output tables

JEL:

• C13
• C67
• R19

ACKNOWLEDGEMENTS

We would really like to thank the work of the three anonymous referees and the editor for their help and their valuable feedback and suggestions.

DISCLOSURE STATEMENT

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

Notes

1 Which also helps to reduce the discontinuity when $SL{Q}_i$ approaches 1.

2 Although there could be an alternative formulation incorporating a third dimension for the regional size explicitly, the proposed 2DLQ captures this dimension through the different sectoral sizes in $w{x}_j$.

3 AFLQ and FLQ are basically the same method with an augmented part when $SL{Q}_j>1$, correcting for McCann and Dewhurst’s (1998) criticism. For those regions with higher specialization in a particular production regarding the national context, the AFLQ allows the method to have a regional coefficient higher than the national one. The FLQ does not. The literature shows that the FLQ and the AFLQ have a better performance than the most simple LQ approaches (Bonfiglio & Chelli, 2008; Flegg & Tohmo, 2013b, 2013a; Flegg & Webber, 2000). The most recent piece of related work (to our knowledge) is by Lamonica and Chelli (2018), who conclude that although there is no method that accurately estimates the true coefficients, the FLQ and AFLQ produce the best approximation. They also argue that both methods have very similar results, which might also be translated into the fact that the AFLQ is at least as good as the FLQ.

4 U and U* are based on mean absolute distance (MAD) indicators, but for the particular case of matrices.

5 Scalar field is a mathematical term referring to the representation of parameter values in every point in a space (physical or not).

6 Which is the expected result if we consider that the AFLQ (and similarly the FLQ) establish β as 1, as shown in the second section of the generalization of the LQ techniques. The AFLQ minimizes the WAPEs on the optimal value of δ, while the 2DLQ minimizes the WAPEs on α and β, which naturally produces lower values of the objective function.

7 Calculated by multiplying the estimated regional coefficients by the total output of each industry.