Inter-city firm connections and the scaling of urban economic indicators.

Cities exhibit consistent returns to scale in economic outputs, and urban scaling analysis is widely adopted to uncover common mechanisms in cities' socioeconomic productivity. Leading theories view cities as closed systems, with returns to scale arising from intra-city social interactions. Here, we argue that the interactions between cities, particularly via shared organizations such as firms, significantly influence a city's economic output. By examining global data on city connectivity through multinational firms alongside urban scaling Gross Domestic Product (GDP) statistics from the United States, EU, and China, we establish that global connectivity notably enhances GDP, while controlling for population. After accounting for global connectivity, the effect of population on GDP is no longer distinguishable from linear. To differentiate between local and global mechanisms, we analyzed homicide case data, anticipating dominant local effects. As expected, inter-city connectivity showed no significant impact. Our research highlights that inter-city effects affect some urban outputs more than others. This empirical analysis lays the groundwork for incorporating inter-city organizational connections into urban scaling theories and could inform future model development.