for China and India. Using comparable regression specifications, Chauvin et al. (2017) report an elasticity of nominal wages with respect to population density of 4.6 percent for US Metropolitan Statistical Areas (MSAs), 19.2 percent for a sample of Chinese provincial and prefectural level cities, and 7.6 percent for the urban parts of Indian districts. Meanwhile, the estimated elasticities of the city premium with respect to average years of schooling and market access for our sample of 16 LAC countries are 62 percent and 4 percent respectively.

While the above correlations are suggestive of the ability of the three theories of urban success to explain variations in sub-national underlying productivity, it is also the case that population density, average years of schooling and market access are all positively correlated with one another. Hence, more densely populated areas tend to exhibit both higher average years of schooling and market access.<sup>28</sup> To disentangle the relative importance of the three theories of urban success, we estimate equation 5. Table 5 shows the results. Columns 1-3 report the results of regressions of the estimated city premium on population density, average years of schooling, and our measure of market access. In these regressions, we also control for mean air temperature, terrain ruggedness and total precipitation, physical geographical conditions that could be correlated with both city premiums and the main explanatory variables.

In column 1, we see that the estimated elasticity of the city premium with respect to population density declines to 4.9 percent once we control for geographic conditions. Although this estimate remains statistically significant, it is less than the estimated elasticity of 5.3 percent that we reported above when not controlling for geography. Once we also introduce average years of schooling, in column 2, however, both the estimated size and statistical significance of the elasticity of the city premium with respect to population density fall dramatically. Including market access in column 3 then leads population density to lose its statistical significance completely.<sup>29</sup> Although both average years of schooling and market access are significant, the former has a much larger effect on underlying productivity. While an increase in average years of schooling from the 25<sup>_th_</sup> to the 75<sup>_th_</sup> percentile in our sample implies an estimated productivity increase of 23.4 percent, moving from the 25<sup>_th_</sup> to the 75<sup>_th_</sup> percentile for market access implies a productivity increase of only 4.1 percent. The point estimate for the elasticity of underlying productivity with respect to average years of schooling is 0.57. This implies, at the overall average level of education of 8.6 years, that an increase in one year of education is associated with an increase in wages of

> 28The Pearson correlation coefficient for population density and average years of schooling is 0.30, while that for population density and market access is 0.67. For average years of schooling and market access, the correlation coefficient is 0.32. All estimated correlation coefficients are significant at the 5 percent level.

> 29 Robustness tests were implemented to test a possible non-linear relationship of the variables. Results are available from the authors. We find a positive quadratic relationship (a U shape), which contrasts with the inverted U shape more commonly found in the literature (Desmet and Rossi-Hansberg, 2014). Instead of the optimal density of a city (Au and Henderson, 2006) after which cities become too congested, this would suggest a minimum density threshold in cities after which agglomeration economies start emerging (or overcoming congestion costs). This could be affected by relatively low levels of infrastructure and institutional quality compared to those in developed countries. However, these results could be a consequence of pooling different years and countries. Future work testing this relationship independently by country could shed light on the agglomeration vs congestion costs relationships in developing countries, which the literature has not fully addressed simultaneously (Desmet and Rossi-Hansberg, 2013; Desmet and Henderson, 2015; Duranton, 2016; Akbar and Duranton, 2017; Hanlon and Tian, 2015).

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