Validation of the formulation of location quotient methods using regression analysis

The location quotient (LQ) method, a widely used nonsurvey method, has been improved through a series of empirical studies, resulting in variations that incorporate various factors. These variations include the simple LQ (SLQ) method, which considers the concentration of the supply sector; the cross-industry LQ (CILQ) method, which considers the concentration of both the supply and purchase sectors; and Flegg’s LQ (FLQ) method, which modifies the CILQ method by accounting for regional size. However, LQ methods have long been criticized for their emphasis on mechanical convenience and lack of theoretical foundation, and previous studies have not adequately addressed these issues. In addition, the formulation of the conventional LQ method, which emphasizes simplicity, makes it difficult to statistically test the explanatory power of the factors introduced by each method. Therefore, we use regression models that generalize conventional LQ methods to elucidate the explanatory power of the included factors and test the validity of the conventional formulations. Our analysis reveals partial validation of the SLQ method, with the generalized SLQ method achieving an accuracy comparable to that of the conventional FLQ method. Furthermore, the variables introduced by the CILQ method, which represent the concentration in the purchase sector, have negligible explanatory power. Finally, the parameters of the FLQ method function primarily as constant terms and dummy variables rather than reflecting the effect of regional size.