Temporal and spatial Taylor's law: Application to Japanese subnational mortality rates

Taylor's law is a widely observed empirical pattern that relates the variances to the means of population densities. We present four extensions of the classical Taylor's law (TL): (1) a cubic extension of the linear TL describes the mean–variance relationship of human mortality at subnational levels well; (2) in a time series, long‐run variance measures not only variance but also autocovariance, and it is a more suitable measure than variance alone to capture temporal/spatial correlation; (3) an extension of the classical equally weighted spatial variance takes account of synchrony and proximity; (4) robust linear regression estimators of TL parameters reduce vulnerability to outliers. Applying the proposed methods to age‐specific Japanese subnational death rates from 1975 to 2018, we study temporal and spatial variations, compare different coefficient estimators, and interpret the implications. We apply a clustering algorithm to the estimated TL coefficients and find that cluster memberships are strongly related to prefectural gross domestic product. The time series of spatial TL coefficients has a decreasing trend that confirms the narrowing gap between rural and urban mortality in Japan.