particularly important when estimating the relationship between firms’ innovation and city size.<sup>20</sup> In one, entrepreneurs do not choose among alternative locations when starting a firm; but once started by a resident entrepreneur, a firm’s subsequent decisions on innovation are dependent on city size as well as unobserved city characteristics such as the quality of the local workforce and public resources—characteristics which may also be correlated with city size. Alternatively, firms may be free to choose their locations, with more innovative entrepreneurs likely to locate in larger cities in order to access their (typically) larger pool of skilled workers, better infrastructure, and thicker markets. In both cases, but especially in the second, the common practice of using historical city size as an instrument for current city size is not likely to be helpful in solving the endogeneity problem. Instead, one would need at a minimum, instruments capturing recent immigration, fertility, or mortality shocks occurring in cities—i.e., factors that would affect current city size but be unrelated to city characteristics that impact innovation. More realistically, given that location choice is unlikely to be completely exogenous, valid instruments would need to capture the choice of entrepreneurs across cities but be uncorrelated with firms’ innovation.

Given the difficulties in finding plausible instruments, the analysis focuses on the correlation and possible heterogeneity in the relations between city size and firm innovation controlling for various city and firm level characteristics.

# **4.1. Baseline Estimates**

Table 3 presents the baseline results. The coefficients of the main variable of interest, logarithm population in 2010, are positive and significant at 1% for all three outcome variables. In other words, holding everything else constant, firms residing in cities with larger populations are more likely to implement both product and process innovations and undertake R&D. For product innovation, the predicted propensity when the independent variables are at their mean values is 31.4%. The coefficient corresponds to a marginal effect of 4.3 percentage points, or 13.5% higher from the predicted propensity. For process innovation, the estimated marginal effect is 3.7 percentage points, or 8.5% higher than the predicted propensity of 42.8%. For R&D, the estimated marginal effect is 2.8 percentage points, or 14.3% higher than the predicted propensity.

Other city characteristics are also correlated with innovation-related activities. The coefficients on average precipitation are negative and significant; coefficients on maximum temperature are positive and significant in models for process innovation and R&D; coefficients on minimum temperature are positive and significant; lastly, firms based in inland cities and/or cities with more slopes are, on average, more likely to innovate.

In terms of firm characteristics, younger firms are more likely to implement process innovations and conduct R&D. Firm size is positively associated with all three innovation-

> 20 We are grateful to a referee for this discussion on the requirements of an IV strategy. It may be noted that in an earlier version of the paper (Chen, Hasan and Jiang, 2020), the 1950s population of administratively defined cities corresponding to each natural city (sourced from the World Urbanization Prospects database) was used to instrument for the contemporary population of our natural cities. The IV estimates are largely in line with the results from Probit models.

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