A new proposal to model regional input–output structures using location quotients. An application to Korean and Spanish regions

This paper is based on the use of Flegg's location quotients (FLQ) and proposes a novel procedure for the estimation of the unknown parameter δ in regions with and without input–output frame availability. Applied to data for the Korean regions for the year 2015, firstly the determination of the optimal δ is addressed by solving a general optimization problem and, secondly, a regression equation is proposed to estimate the value of δ from the explanatory variables of interregional road freight transport (IRFT) and imports from the rest of the world (IROW). The results obtained show a lower bias in regard to the true values of the regional inputs coefficients in relation to other methods based on location quotients. Este artículo se basa en el uso de los cocientes de localización de Flegg (FLQ, por sus siglas en inglés) y propone un procedimiento novedoso para estimar el parámetro desconocido δ en regiones con y sin disponibilidad de un marco de input–output. Aplicado a datos de las regiones coreanas para el año 2015, en primer lugar se aborda la determinación del δ óptimo mediante la resolución de un problema de optimización general y, en segundo lugar, se propone una ecuación de regresión para estimar el valor de δ a partir de las variables explicativas del transporte interregional de mercancías por carretera (IRFT, por sus siglas en inglés) y las importaciones del resto del mundo (IROW, por sus siglas en inglés). Los resultados obtenidos muestran un menor sesgo respecto a los valores reales de los coeficientes de insumos regionales en relación con otros métodos basados en cocientes de localización. 本稿は、Freggの立地係数(FLQ)の使用に基づいて、産業連関表のフレームの利用可能性のがある領域とない領域における未知パラメータδの推定のための新しい方法を提案する。2015年の韓国の地方のデータに適用し、はじめに一般的最適化問題を解くことによって最適δを決定し、次に地域間道路貨物輸送(IRFT)と外国からの輸入(IROW)の説明変数からδ値を推定する回帰方程式を提案する。得られた結果から、立地係数に基づく他の方法に関連して、地域投入係数の真の値において低いバイアスが示された。 The construction of input–output tables on a regional level can be undertaken by means of a search process of all the statistical information (survey methods), which implies a significant cost in terms of both money and time, or alternatively from operations on national input–output tables (non-survey or semi-survey methods). This second option has the great advantage of approaching knowledge of reality with a high degree of reliability, although less accurately, at a very low cost in comparison to the first option. This allows for the rapid construction of regional tables and their integration into the national table. The use of location quotients is an appropriate tool in cases where no regional input–output framework is available (Flegg et al., 1995). In a relatively simple way and with reasonable and available information needs, the regional table can be estimated in the absence of survey data, although the result obtained must be reviewed by the analyst and refined in order to obtain the best possible approximation of the inter-industrial economic reality of the territory analysed (Flegg & Webber, 2000). Based on simple location quotients, regionalization methods have been implemented which include variants on these quotients. This is in an attempt to overcome initial shortcomings related mainly to the assumption of similarity in production technology between regions and nations, as well as the underestimation of inter-regional trade. From the abundant literature available on this regionalization methodology (Bonfiglio & Chelli, 2008; Flegg et al., 1995, 2016; Flegg & Tohmo, 2016; Flegg & Webber, 2000; Lamonica & Chelli, 2018; Lampiris et al., 2019; Mastronardi & Romero, 2012), it could be concluded that the use of Flegg's location quotients (FLQ) is the most appropriate of the available location quotient (LQ) techniques. However, this assertion is not without its critics as it relates to the practical impossibility of its proper implementation (Lahr et al., 2020). Likewise, Fujimoto (2019) showed that LQ approaches underestimate regional trade and overestimate regional output multipliers as a result of the underestimation of cross-hauling. Furthermore, the works of Lamonica and Chelli (2018), Riddington et al. (2006), and Hermannsson (2016) presented several criticisms of the use of LQs. However, it can be argued that the FLQ is a well-known technique which often provides satisfactory results; its application is straightforward and requires only the use of readily available data. All of the above justifies the focus on this technique in the contributions of this paper. As previously stated, this paper focuses on the use of FLQs and the estimation of the unknown parameter δ. The objective of this work is to provide a proposal for estimating the parameter δ by means of a regression that uses variables whose information is usually available as regressors. The validity of this proposal is tested using data from the multiregional input–output matrix for Korea in 2015 and some regional input–output matrices for Spain. The determination of the parameter δ has become a crucial element in the widespread application of FLQ as a regionalization technique (Flegg & Tohmo, 2019; Flegg & Webber, 2000; Kowalewski, 2015; Lamonica & Chelli, 2018; McCann & Dewhurst, 1998; Zhao & Choi, 2015). These works that attempt to establish a parameterization of δ, which contains information on interregional trade, are applied in contexts where survey tables are available and the authors make the unknown parameter δ depend on variables that are difficult to obtain in regions where no such prior input–output frame of reference exists. In addition, the explanatory variables considered must be modified according to the application framework in order to obtain equations that reasonably explain the value sought. In this context, we propose a novel and generalized procedure for the determination of the parameter δ both in regions with and without the availability of an input–output framework, obtaining optimal results for the regional production structure. Specifically, our proposal incorporates two novel contributions, the first of which is related to the determination of the optimal values of δ (those that minimize a goodness of fit statistic of the estimation) from the resolution of a general optimization problem which is solved with the General Algebraic Modeling System (GAMS) software. These values improve on those obtained by evaluating different values of δ in the interval [0,1], since a lower value of the statistic is obtained. The second novel contribution of our proposal consists of using the interregional road freight traffic (IRFT) and imports from the rest of the world (IROW) variables as regressors in the estimation equation of δ in the different regions, variables with a high degree of availability at the regional level. We apply the procedure to the case of Korean regions in 2015 and Spanish regions in different years. The results obtained for both the Korean and Spanish regions show better results of the input coefficients obtained with better approximation to the true values. Thus, it can be stated that the equation implemented from IRFT and IROW data is an efficient generalization for those cases where regional input–output frameworks are not available. As can be seen, the alternative proposed in the FLQ and augmented Flegg's location quotient (AFLQ) methodologies has a very significant dependence on the value given to the parameter δ (Flegg & Tohmo, 2018, 2019; Kowalewski, 2015; Lamonica & Chelli, 2018; Lampiris et al., 2019), the determination of which is highly costly and complex. On the other hand, the two-dimensional location quotient (2D-LQ) (Pereira-López et al., 2020, 2021) is based on the premise that the adjustment needed in the regionalization process for the cost structure of a given industry does not necessarily have to be related to the adjustment needed in the sales structure, allowing a different adjustment parameter to be chosen for each of the two cases. This innovative approach, although extremely interesting, is more complex and its analysis is beyond the scope of this paper. A significant number of papers make explicit mention of the comparison of methodologies to the FLQ (Flegg et al., 1995; Flegg & Webber, 1997), either directly acknowledging its better goodness of fit compared to other techniques (Jahn, 2017; Lampiris et al., 2019; Morrissey, 2016) or indirectly using it as a comparative benchmark, regardless of its determination as the best estimator (Kowalewski, 2015; Lamonica & Chelli, 2018; Zhao & Choi, 2015). In this paper we consider it more appropriate to assess our methodological contribution in the area of the Flegg coefficient, which has been sufficiently evaluated at the regional level and which, in general, seems to offer better performance. As mentioned above, the determination of the parameter δ, which is a key part of the Flegg's location quotient (FLQ) method, is an open problem (Fujimoto, 2019) for which no definitive solutions have been provided. In the following, we present the different approaches that have been made thus far. Contrary to the indication given in Flegg and Webber (1997), to set the value of δ equal to 0.3, Flegg and Tohmo (2013) presented an alternative way of quantifying the δ parameter by assessing the goodness of fit over type I output multipliers for regions in Finland. Recently Flegg et al. (2021) proposed a new procedure for the estimation of regional IOTs that combines a (modified) cross-entropy procedure (Lamonica et al., 2020) with the FLQ. The procedure consists of three stages: in the first, an estimate of the regional input coefficient is obtained using the modified cross-entropy (MCE) from the national coefficient matrix and the regional sectoral total output. In the second, the parameter δ of the FLQ quotient is estimated using the matrix obtained in stage 1. Finally, in the third stage, using the national coefficient matrix, the FLQ procedure is applied with the parameter δ obtained in stage 2 to estimate the regional matrix. The authors referred to this hybrid procedure as FLQ + . This approach was tested on the South Korean interregional input–output table (KIRIOT) for the year 2005. The results obtained reflect the superiority in the accuracy of the estimation obtained by the FLQ + method over the MCE method, thus suggesting that the hybrid FLQ + method is preferable to the application of MCE alone. On the other hand, the authors also use these data to compare the FLQ + method with the FLQ that uses the so-called optimal δ parameter, selected among the 99 different values of δ in the interval [0, 1], in increments of 0.01, by minimizing a goodness of fit statistic of the estimation. They obtain similar results for the latter two methods, but the FLQ + method is applicable when regional sectoral products are the only available data, while the optimal FLQ method requires knowledge of the entire regional matrix to compute an optimal value of δ for each region. Finally, by way of summary, it can be concluded that the various attempts analysed to establish a parameterization of δ (which contains information on interregional trade) show that, on the one hand, it does indeed appear to be linked to these magnitudes given that, with greater or lesser precision, they are all capable of approximating the optimal value of the parameter. However, contrasting the attempts with available survey tables led the authors to make the parameter that is being sought depend on information that is difficult to obtain when there is no prior input–output framework to serve as a reference. Moreover, successive parameterization work has shown that the explanatory variables considered must be modified in order to obtain equations that reasonably explain the value sought. In this context, our aim is to offer an improvement in the estimation procedure of the δ parameter in regions without the availability of an input–output framework by testing it in the case of Korean and Spanish regions. The proposed estimation of the parameter δ presented in this paper is based on the use of a regression model whose regressors are the inter-regional road freight transport (IRFT) flow obtained from the national traffic survey 22 https://kosis.kr/eng/index/index.do and data corresponding to imports from the rest of the world (IROW). The advantage of this proposal over other regression-based estimation methods (such as those of Flegg & Tohmo, 2013, 2019) is the availability of the data corresponding to the regressors. In line with these proposals, our regression requires the availability of regional survey tables for some regions of the country. More precisely, the proposed estimation procedure consists of two stages. In the first stage, using the survey table data available for some regions of the country, we calculate the optimal δ values for each of these regions, understood as those that produce a better estimate (based on some goodness of fit measure) of the corresponding survey table. The second stage consists of using these values as the dependent variables of a regression whose regressors are the IRFT flow obtained from the national traffic survey and data corresponding to IROW. The coefficients of this regression would then be used to calculate the value of δ that is proposed to be used in the process of estimating regional tables for regions where survey tables are not available. Compared to the Flegg's location quotient+ (FLQ+) method, our approach is much simpler, does not need the support of other complex estimation methods (such as modified cross-entropy (MCE)), and is easy and low-cost to implement, particularly in terms of time. However, the FLQ + method has the advantage that it only requires the use of the regional sectoral outputs (or sectoral employment) data of the region whose table is to be estimated. The present study uses the Korean multi-regional input–output framework 33 According to public information on the Bank of Korea website, the 2015 Korea regional tables are based on survey data (https://ecos.bok.or.kr/). for the year 2015 for 17 regions. Korea's multi-regional table for 2015 presents a 33 × 33 product breakdown for 17 regions with the flows valued in millions of won. The multi-regional table breaks down the intra-regional elements for each region and for each product, the values of transactions between each pair of regions, and the trade with the rest of the world on a product-by-product basis. For our purpose of assessing the efficiency of the different estimations, the use of type B matrices is required. 44 FLQ focuses on production and employment generated within a region and applies to national tables in which inter-industry transactions exclude imports, namely the non-competitive import-type table (type B), wherein transactions of domestic and imported goods are treated separately. For this purpose, the minimization problem of the WAPE statistic is posed and solved with GAMS software. The values thus obtained improve on those obtained by evaluation at different values of δ in the interval [0,1] in the sense that they result in a lower value of the statistic, as reflected in the tests carried out by the authors. 55 The results can be obtained on request from the authors. As shown in Table 1, the optimal (or true) δ parameter obtained for each region is the one that minimizes the WAPE and ranges between 0.186 and 0.605, corresponding to the Seoul and Sejong regions respectively, with a mean value of 0.39. It should be noted that the differences in the values of δ are due to the different propensities to import from other regions or from abroad that are not explained by the difference in regional size. In relation to the estimation of Equations (10) and (15) proposed by the creator of the FLQ (Flegg & Tohmo, 2013, 2019), we proceed in the same way. The values of δ estimated from Equations (10', 15', 11'), and (19) are used to estimate the input–output tables (IOTs) for the 17 Korean regions. Table 6 shows the WAPE values and relative differences between the WAPE values corresponding to the δ estimated from Equations (10', 15', 11'), and (19) and the optimal WAPEs, in order to compare and assess which one provides a better fit. As can be seen, all estimations produce similar results, although our proposed estimation (Equation 19) is the one that obtains, both in average and weighted average, the lowest value of the WAPE statistic. This means that the proposed estimation is the one that achieves the highest precision of the estimated input–output coefficients with respect to the survey values of the different Korean IOTs. Moreover, our proposal has, on average, the smallest difference from the optimal WAPE. The smallest relative differences, ordered from smallest to largest (less than 1%), occur both in the relatively large regions of Seoul, Ulsan, Incheon, Gyeongsangnam-do, and Chungcheongnam-do, as well as in the small regions of Busan, Daegu, Jeollabuk-do, Gangwon, and On the the largest differences in order of than occur in the relatively largest region of and in the small regions of and In of the above results, the of our proposal based on the use of the FLQ as a regionalization technique is It is that it results that, on average, show a lower with regard to the rest of the with the advantage that it uses two explanatory variables that are and available in the of the regions, allowing it to be to other than and the validity of the estimating (19) proposed for Korean regions in other we use Spanish regions to estimate the values of δ. does not have a multi-regional table and the availability of regional tables is regions. For this it was to use the Spanish survey input–output table for the and 2015 as a reference table. regard to the regional IOTs in each the survey table is used for one of the in which the survey for is available. The regional IOTs for have been from the statistical or statistical of each where the is those to the year using survey methodologies The input–output survey tables for the regions of and have a different than the for Spain. For these two in which IOTs are available for the year it was to use the for corresponding to the year as a reference. However, for the that regional in terms of value have from to as well as for the that the of trade must not have in the In general the there has been no significant in trade between Likewise, the degree of of the regions has not significant in interregional trade either Table we proceed to the largest number of available regional tables in relation to the national tables as a between and For the estimation of the optimal values of δ, in the case of the largest possible number of is in each of of all the regional tables to the same number of and The for this is that into can the regionalization process (Flegg & Tohmo, and to as can be in Riddington et al. the 17 Spanish regions, of have an which allows to apply our procedure in this Table shows the optimal values and the WAPE statistic corresponding to the different Spanish regional the reference This parameter ranges from in the to in with an average value of the different of interregional and trade. Thus, regions with an of interregional and imports have a δ. The very low value for the can be explained by its as an This result is with the production structure being highly in with a high dependence on generated within the region and where the to import is to be A more for the case of can be in Fujimoto to the procedure applied to the Korean regions, the table for each of the Spanish regions is estimated the survey information of the regions. Table shows the parameter values and obtained for each of the regions. Table presents the estimated WAPE values and the relative difference with regard to the optimal WAPE. As can be seen, the average difference of the estimated values of the WAPE statistic is relatively small at average an fit to the regional input the results obtained with the application of the proposed procedure in the Spanish regions are satisfactory given that, on average, the estimation bias is relatively This that the implemented procedure is a generalization when regional input–output frameworks are not available. This paper proposes a novel approach to improve the regionalization procedure of national input–output tables (IOTs) based on the use of Flegg's location quotients for contexts where input–output frameworks not and statistical information is In the use of FLQ that depend directly on the value given to the unknown parameter δ very The for the use of this procedure in the estimation of the parameter δ, which a crucial element in the regionalization In this our aim has been to provide an improvement in the implementation of the FLQ method, two novel The first, the determination of the optimal δ from the resolution of a general optimization problem of the WAPE statistic, that the of these values by obtaining a lower value of the statistic than those obtained by minimizing the statistic on a set of different values of δ in the interval 99 values in increments of The second is using readily available explanatory variables with economic in the regression equation for δ in the different regions. We to inter-regional road freight transport (IRFT) and imports from the rest of the world (IROW). Based on data from the multiregional for Korea for the year 2015, the results of the different are procedure shows the most with regard to the optimal values. Thus, although all produce results, our estimation proposal is one that for the average and weighted the smallest difference with regard to the optimal WAPE. This the of our proposal based on the use of the FLQ as a regionalization It is that it results that, on average, show a lower with regard to the rest of the with the advantage that it uses two explanatory variables with economic and in regions without a input–output These results, by a the application of our proposal in the case of Spanish regions. These results can be as satisfactory given that, on average, the estimation bias of the parameter δ is that the implemented procedure is a generalization when regional input–output frameworks are not available

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