sample and the one on R&D two-thirds of the full-sample estimate. Thus, the firm innovation gradients seem ubiquitous along the city size distribution in the region.<sup>23</sup> In addition, to test if results are sensitive to the definition of innovation, two alternative measures of the dependent variable are used. The first indicator concerns whether the product innovation is “also new to the establishment’s main market”. Answers to this question are expected to be more reliable as the question requires the respondents to think more about their answer to the preceding question regarding general product innovation; it also gets at the importance of an innovation. As expected, this follow-up question yields a lower percentage of positive responses reported in the sample—20.5% as opposed to 35.7% for the general question on product innovation. The regression results in column (7) of Table 4 show that doubling city size is associated with a 3.0 percentage point or 22% increase in the propensity of main market product innovation, higher than 13.5% increase in propensity using the general product innovation measure.

The second alternative measure of innovation takes a value of 1 if a firm conducts either product or process innovation. The sample average, equal to 57.5%, is greater than the averages of product innovation and process innovation and smaller than the sum of the two. This implies that respondents were able to differentiate between the two types of innovation and a fair proportion of firms engaged in only one of the two. The estimated marginal effect is 4.5 percentage points, or a 7.8% increase over the predicted propensity, also with 1% statistical significance.

# **4.3. Heterogeneity by Development Level and Country**

The 25 Asian countries included in the analysis are at distinct stages of development. It is possible to examine whether the relationship between agglomeration effects and firm innovation varies with the level of development by dividing the overall sample into upper-middle income countries and low and lower-middle income countries based on the latest World Bank country classifications.<sup>24</sup> Probit regressions are estimated for both subsamples and results are reported in Table 5.

For low and lower-middle income countries, encompassing about 75% of firm observations in 345 cities, the agglomeration effects for product innovation and R&D are positive and comparable to the estimates from the full sample with 1% statistically significance. For process innovation, the marginal effect is estimated at 0.019, around half of that for the full sample, with 5% statistical significance.

> 23 The sensitivity of estimates to the exclusion of small cities which have only a small number of firms surveyed by the WBES is also considered using thresholds of 10 and 20 firms per city. The former yields 264 cities and around 20,000 firms and results are close to baseline estimates; the city size coefficients for all three innovation categories are positive and significant at 1% level. The more aggressive exclusion results in a subsample of 193 cities and around 19,000 firms. The estimate for product innovation remains almost identical to the full sample estimate. For process innovation and R&D, however, both coefficients halve in size and are marginally significant.

> 24 The World Bank defines low income economies as those with a gross national income (GNI) per capita of $1,025 or less, lower-middle income economies between $1,026 and $3,995, and upper-middle income economies between $3,996 and $12,375.

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