ON THE PARAMETERIZATION OF TECHNIQUES FOR REPRESENTING REGIONAL ECONOMIC STRUCTURES

Abstract

This paper is concerned with two parameterized methods of regionalising input–output coefficients: the Flegg et al. Location Quotient (FLQ) and its augmented version (AFLQ). For applying the two techniques, a parameter δ has to be estimated. In this regard, the paper faces two matters that are still open in the literature: the existence of a range of δ that can be used in different regions and the estimation of the most appropriate value of δ. For this aim, a Monte Carlo simulation has been carried out in order to generate ‘true’ multiregional I-O tables randomly. From the simulation, analyses based on probability distributions and regression were also carried out. Finally, these simulation results have been compared with those of an empirical case. Results confirm that there is actually a range of values of δ within which the best δ is more likely to fall. For the FLQ, this range is centred on 0.3 with an associated probability of 33% (if the width of the range is set at 0.1), whereas, for the AFLQ, the relevant range is between 0.3 and 0.4 with a probability by 38%. Finally, this paper provided a way to estimate the best δ for a given region, without knowing the relevant and detailed economic structure at sectoral level.

Keywords:

• Non-survey techniques
• Input–output matrices
• Monte Carlo simulation

Notes

¹Further analyses related to the FLQ and the AFLQ can for example be found in Bonfiglio and Chelli (2008).

²Non-linear fitting process used to estimate coefficients of Gaussian functions is based on the minimization of a reduced chi-square function taking the form: , where n is the number of observations, p is the number of parameters, n–p is the number of degrees of freedom, w _i is the weight given to observation i, Y _i is observation i, f is the fitting function, is the row vector of independent variables for observation i, is the row vector of parameters to be estimated. In order to estimate parameters an iterative strategy is adopted. This process starts with some initial values for parameters. With each iteration, a χ² value is computed and then parameter values are adjusted so as to reduce χ². When the χ² values computed in two successive iterations are small enough, the fitting procedure is said to converge. Adjustment of parameters is made by the use of the Levenberg-Marquardt (L-M) algorithm (Marquardt, 1963). Identification of the best fitting functions and estimation of coefficients of Gaussian functions were made through the use of the data analysis and graphing software OriginPro 8.

³The choice of an old I-O table depends on two reasons. Firstly, the latest survey-based I-O tables of some of the Italian regions were constructed in the 1970s. Since then, the I-O tables have been derived from non-survey or hybrid methods. Secondly, the few existing survey-based I-O tables are not readily accessible. Therefore, we were forced to use the only one available.

⁴The most specialized sectors of the Marche region are those where SLQ _i  ≥ 2.