Application and improvement of the DO index in measuring industrial Co-agglomeration: The case of the BTH region in China

Industrial co-agglomeration is the most prominent geographical feature of economic activities and also a worldwide phenomenon, yet existing methods primarily rely on discrete spatial units such as administrative divisions, causing issues like the Modifiable Areal Unit Problem (MAUP). To address this, Duranton and Overman proposed the DO index. Building on this, the study develops an improved framework incorporating three dimensions—intensity, scale, and location—and applies it to analyze spatiotemporal patterns and features of manufacturing co-agglomeration in the Beijing-Tianjin-Hebei (BTH) region. Results show: (1) In intensity, the overall pattern remains stable with a slight decline, exhibiting a Matthew effect. (2) In scale, dominant co-agglomeration distances shifted from 25 to 68 km in 2008 to both within 55 km and 75–103 km in 2018, indicating a simultaneous contraction of intra-provincial collaboration radius and strengthening of inter-regional co-agglomeration. (3) In location, the proportion of the scope of occurrence of agglomeration decreased from 44.40 % to 39.76 %, reducing the overall scope of agglomeration, and the spatial pattern evolved from a dual-core (Beijing-Tianjin) concentration to a more polycentric, resulting in a more balanced distribution. (4) Methodologically, this study enhances the DO index by optimizing threshold selection, reducing kernel density partitions, increasing the critical co-agglomeration value, and incorporating location information. These improvements provide methodological references for similar studies and empirical evidence for exploring mechanisms and optimization paths of industrial co-agglomeration.