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Abstract
Flegg A. T. and Tohmo T. Estimating regional input coefficients and multipliers: the use of FLQ is not a gamble, Regional Studies. This paper re-examines the Finnish evidence presented by Lehtonen and Tykkyläinen on the use of location quotients (LQs) in estimating regional input coefficients and multipliers. They argue that the choice of an LQ-based method is a gamble and that there is no single method that can be recommended for general use. It is contended here that this evidence is erroneous and that the FLQ (Flegg's location quotient) yields results far superior to those from competing formulae, so it should provide a satisfactory way of generating an initial set of input coefficients. The choice of a value for the parameter δ is also examined.
Flegg A. T. and Tohmo T. 评估区域投入系数与乘数：运用 FLQ 并非一场赌注，区域研究。本文再次检视 Lehtonen与 Tykkyläinen 在评估区域投入系数及乘数时所使用的区位商数法 (LQs) 中呈现的芬兰寻证。他们主张，选择以区位商数为基础的方法是一场赌注，且没有任何单一的方法可以推荐作为普遍使用。我们则于本文中主张，此一证据是错误的，且 FLQ (Flegg的区位商数法) 所产生的结果，远较其他竞争的公式更为优异，因此该方法应当提供做为生产一组初始投入系数组合的满意方法。本文并检验係数δ的价值选择。
Flegg A. T. et Tohmo T. Estimer les coefficients d'entrées et les multiplicateurs régionaux: l'emploi du FLQ n'est pas un risque, Regional Studies. Cet article examine de nouveau les preuves provenant de la Finlande et présentées par Lehtonen et Tykkyläinen sur l'emploi des quotients de localisation (location quotients; LQs) pour estimer les coefficients d'entrées et les multiplicateurs régionaux. Ils affirment que le choix d'une méthode fondée sur les LQ est un risque et qu'il n'existe pas de méthode unique qui se généralise. On soutient ici que ces preuves sont erronées and que le FLQ (quotient de localisation de Flegg) fournit des résultats qui dépassent de loin ceux qui proviennent des formules concurrentes, donc il devrait fournir un moyen satisfaisant de construire un premier ensemble de coefficients d'entrées. On examine aussi le choix d'une valeur pour le paramètre δ.
Flegg A. T. und Tohmo T. Schätzung von regionalen Inputkoeffizienten und Multiplikatoren: Die Verwendung des FLQ ist kein Lotteriespiel, Regional Studies. In diesem Beitrag werden die von Lehtonen und Tykkyläinen vorgestellten finnischen Belege über die Verwendung von Standortquotienten zur Schätzung von regionalen Inputkoeffizienten und Multiplikatoren erneut untersucht. Lehtonen und Tykkyläinen bezeichnen die Wahl einer auf Standortquotienten beruhenden Methode als Lotteriespiel und argumentieren, dass sich keine einzelne Methode für einen generellen Einsatz empfehlen lasse. In diesem Beitrag wird dagegengehalten, dass diese Belege fehlerhaft sind und dass der Fleggsche Standortquotient (FLQ) zu deutlich besseren Ergebnissen führt als konkurrierende Formeln und somit eine zufriedenstellende Methode zur Erzeugung eines ersten Satzes von Inputkoeffizienten darstellen sollte. Ebenso wird die Auswahl eines Werts für den Parameter δ untersucht.
Flegg A. T. y Tohmo T. Cálculo de los coeficientes de entrada y multiplicadores regionales: el uso del FLQ no es una lotería, Regional Studies. En este artículo reexaminamos la evidencia finlandesa presentada por Lehtonen y Tykkyläinen sobre el uso de cocientes de localización en el cálculo de los coeficientes de entrada y multiplicadores regionales. Los autores consideran que la elección de un método basado en los cocientes de localización es una lotería y que no existe un único método que pueda recomendarse para uso general. Aquí argumentamos que esta evidencia es errónea y que el cociente de localización de Flegg (FLQ) produce resultados muy superiores a los de otras fórmulas, por lo que debería proporcionar un método satisfactorio de generar una serie inicial de coeficientes de entrada. También analizamos la elección de un valor para el parámetro δ.
Acknowledgements
The authors wish to express their appreciation to the anonymous referees, and to Peter Bradley, Artjoms Ivlevs, Julia Kowalewski, Tobias Kronenberg, Leo Mastronardi, Carlos Romero and Chris Webber for their helpful suggestions, which led to substantial improvements in this paper.
Notes
1. Lehtonen and Tykkyläinen do not, in fact, explicitly give formulae pertaining to multipliers, so it was necessary to adapt the expressions for coefficients given in their table 1.
2. Note that:
where r is the correlation coefficient between and mj (cf. Theil et al., Citation1966, pp. 29–30).
3. The results of Lehtonen and Tykkyläinen for UM are odd in the sense that the means are all well above unity, which is inconsistent with the properties of equation (12). This may have occurred because n2 = 676 rather than n = 26 was used as a divisor in the calculation of MSE (see formula 13). Also, the average rank attained by the FLQ in Ahvenanmaa should be 2.00 and not 2.25.
4. The use of ŨS and ŨM rather than US and UM had a negligible impact on the rankings.
5. Although the mean sectoral difference between Lehtonen and Tykkyläinen's figures for national transactions by aggregated sector and the true figures was a relatively small 2.0%, some of the individual sectoral differences were substantial, with a range from –24.2% to +40.0%. The mean absolute error was 7.3%. Likewise, for the sectoral sums of intermediate inputs, the individual differences ranged from –24.4% to +31.5%. The mean error was 0.6% and the mean absolute error was 6.4%. Supporting calculations are available from the authors on request.
6. For a numerical example, see Miller and Blair (Citation2009, pp. 324–327). The detailed results of Sawyer and Miller (Citation1983) provide a very clear illustration of the point that errors in coefficients are likely to be far greater than those in multipliers.
7. MPE was estimated using the formula:
where z is the number of zero values for rij. Such cases were excluded from the calculations. A disadvantage of this measure, in the context of coefficients, is that it is inflated in situations where rij is close to zero. This facet is illustrated by the relatively large values of MPE displayed in .
8. The propensity to import from other regions is expressed as a proportion of gross output. The mean value of this propensity for all 20 Finnish regions in 1995 was 0.1870.
9. The intercept has changed by –1.5834 ln0.187 = 2.6548, where 0.187 is the sectoral mean propensity to import from other Finnish regions in 1995.
10. It is also possible to rewrite equation (28) as:
where i is the sectoral mean intermediate use for the region, which has not been divided by the corresponding national figure. The constant differs from that in equation (28) by 2.8812 ln0.3991 = –2.6465, where 0.3991 is the sectoral mean ratio of intermediate use to gross output for Finland in 1995.
11. PROP is the proportion of a region's total intermediate inputs that is purchased from other regions, whereas p in equation (28) is the proportion of a region's total gross output that is bought from other regions. RSRP is the ratio of total regional to total national intermediate inputs. By contrast, R in equation (28) measures regional size in terms of output or employment.
12. Using data from Kowalewski (Citation2013, table 1), the following estimate of δ was derived for Baden-Wuerttemberg in 1993:
Here the state's share of total German employment (Kowalewski, Citation2013, p. 5) has been used as a proxy for RSRP. An even more negative result was obtained for Uusimaa in 1995:
In this instance the outcome reflects the fact that Uusimaa is by far the largest Finnish region. It also has the lowest value of PROP. For the other 19 regions, Bonfiglio's method generated positive values of , as required.
13. Using equation (28), along with data from Kowalewski (Citation2013, table 1 and p. 10), the following estimate of δ was derived for Baden-Wuerttemberg in 1993:
Kowalewski found that the optimal value of δ varied from 0.11 to 0.17, depending on which statistical criterion was used to evaluate the estimated multipliers (Kowalewski, Citation2013, table 3). It is reassuring that 0.151 falls within this range. Some further evidence is furnished by Flegg et al. (Citation2014) for the province of Córdoba in Argentina. Using detailed survey-based regional data for 2003 and the equation given above in note 10, they derived the following estimate of δ:
This estimate of δ is close to the optimal values of 0.134 and 0.123, respectively, that the authors derived for multipliers when using STPE and U criteria (Flegg et al., Citation2014, table 4). Note that 0.422 is the sectoral mean intermediate use for Córdoba, which has not been divided by the corresponding figure for Argentina.
14. shows, for each region, the value of δ yielding MPE ≈ 0.
15. The use of δ = 0.244, rather than δ* ≈ 0, in the calculations reported in and for Uusimaa can explain the comparatively poor performance of the FLQ in that region. The fact that δ* ≈ 0 for Uusimaa is a surprising outcome; it suggests that CILQ (with SLQs down the principal diagonal of the adjustment matrix) is the best method and that no extra allowance for imports from other regions is required.
16. Sector 59 in the 2002 tables (Private households with employed persons) has no intermediate transactions, so it was aggregated with sector 58 (Other service activities).
17. The study commenced in June 1997, with the aim of collecting data pertaining to 1996. It was assumed that no change in trade flows had occurred between 1995 (the base year of the regional tables) and 1996 (Kauppila, Citation1999).
18. lnH and lnD had near-zero t ratios when they were added to regression (26). This finding suggests that these variables have minimal additional explanatory power and that the effects of location and specialization have already been allowed for via the inclusion of lnR, lnP and lnI.
19. These initial coefficients should always be evaluated by the analyst on the basis of informed judgement, surveys of selected industries, etc., rather than taken at face value (Flegg and Tohmo, Citation2013b, p. 718). It should be noted that the FLQ should preferably be applied to national input–output tables that exclude imports from abroad; where such imports are included, Kronenberg's CHARM method can be used for purposes of regionalization. The type of table that is used would depend on the aim of the study. The FLQ is suitable for estimating output and employment multipliers, whereas CHARM is suitable for estimating the supply multipliers of concern in environmental studies (Kronenberg, Citation2009, Citation2012; Flegg and Tohmo, Citation2013a).