This paper also explores possible heterogeneity in agglomeration effects by the development level of countries and between countries and subregions with distinct historical and institutional backgrounds. The results show that agglomeration effects on firm innovation are prevalent across developing Asia; they are present in both upper-middle income and low and lower-middle income country groups, as well as in China, India and Southeast Asian countries, each considered separately.

Finally, using a widely cited ranking of universities and majors (QS 2019a and QS 2019b), it is possible to identify which cities are home to one or more of the top 500 ranked Asian universities as well as universities with a major in the top 500 global ranking of major fields of study. The presence of a top university is found to be positively and significantly associated with firm innovation, and having a university with a top 500 globally ranked engineering major even more so. These results indicate an important role for locally available human capital, especially that which relates to technical fields, as a channel through which agglomeration affects innovation.<sup>3</sup> It must be noted that the analysis here does not estimate the causal effects of city size on innovation. To do so would require instruments that affect current city size but are unrelated to unobserved city characteristics that impact innovation. Given the difficulties in finding plausible instruments, especially in a cross-country setting, this paper focuses on establishing important associations and exploring potential heterogeneity in the relationship between city size and firm innovation while controlling for various city and firm level characteristics.

This paper is closely related to two strands of literature. The first is on the measurement of urban agglomeration economies. Most of the empirical evidence in this strand has focused on whether city size and/or density affect firm and worker productivity.<sup>4</sup> Studies examining urban agglomeration economies associated with innovation-related activities are limited. Nevertheless, the available evidence—mostly for developed countries—suggests that innovation in a given country is heavily concentrated in a few cities, and that a city’s size or density plays a role in boosting innovation activity within that city. Ó hUallachain (1999) find that large metropolitan areas in the US dominate patenting, with patenting increasing with the size of the metropolitan area. Feldman and Audretsch (1999) also find that innovation appears to be a phenomenon of large cities: less than 4% of innovations occurred outside of the metropolitan areas in which 70% of the country’s population reside. Carlino, Chatterjee, and Hunt (2007) estimate the elasticity of patenting per capita with respect to employment density to be approximately 20% in metropolitan areas in the US. Carlino et al. (2009) further confirm the earlier results by weighting patents with the number of times they are cited. In a more recent study covering 30 OECD countries, Paunov et al. (2019) find that 64% of patent applications from 2010 to 2014 are

> 3 There are two specific ways universities influence innovation via their effect on the stock of human capital.  First, they expand the supply of skilled workers who can undertake innovation in a given location.  Second, they may influence innovation through the research of faculty via spillovers of knowledge or directly via technical collaborations with firms. For both, the evidence from developed countries suggests a strong local effect.

> 4 See Rosenthal and Strange (2004), Melo, Graham, and Noland (2009), Puga (2010), and Baum-Snow and Ferreira (2015) for extensive surveys of methodology and evidence.

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