same pattern, although with no statistical significance, with a positive price elasticity of .006, a negative markup elasticity of -.006, and marginal cost elasticity of .013. These findings are consistent with a higher degree of competition in cities putting pressure on mark-ups, and that rising costs are the principal driver of the price elasticity. Only in Chile, are the price and marginal costs elasticities actually negative and significant, -.022, -024 respectively significant, suggesting that being in cities reduces costs, consistent with having the only positive TFPQ elasticity in the group.

Figure 2 summarizes the results graphically by plotting the elasticities of wage, Foster et al TFPQ measure and marginal cost for the four countries against the log of GDP per capita. The dotted lines are “fitted” to indicate the trends with level of development. Again, consistent with the literature, the wage elasticities do appear to be higher for lower income countries, falling with development with Chile which shows “advanced country” magnitudes. However physical productivity is not driving these high wage elasticities. TFPQ elasticity is negative for Ethiopia and Indonesia and rises through Colombia to Chile. Again, TFPQ rises below wages and, for Colombia and Ethiopia, is not significantly different from zero. Using TFPQ à la De Loecker et al. the estimates generate no significant values, although, with the exception of Chile, they generate the same ranking across countries.

# Robustness checks

We check the robustness of our results in several ways: instrumenting for endogeneity in quantity and quality of plants and labor, adjusting for quality in the price indexes to narrow the bounds on the TFPQ; and testing for sensitivity to alternative sample periods.

# _Addressing endogeneity issues_

Because a positive elasticity may simply reflect the reverse causality that more productive agglomerations attract a larger number of plants and workers, we follow the literature (e.g., Rosenthal and Strange, 2008; Combes et al., 2010) by instrumenting density using geological variables including soil composition or erodability, depth to rock, water capacity, and seismic and landslide hazard. The assumption is that these characteristics are predetermined yet correlated with the current density only through their importance to agricultural settlement and subsequently manufacturing and services (Combes and Gobillon 2015).<sup>14</sup> The estimated wage elasticities presented in table 2 panel b confirm our previous OLS findings although the coefficients are generally larger, perhaps due to reduced measurement error. Similarly, the instrumented TFPR estimates are slightly higher for Chile and more so for Indonesia, but they remain statistically insignificant for Colombia and Ethiopia. The

> 14 However, it should be noted that the IV strategy using natural features as instruments captures not only the relationship between city size that is endogenous (following the demand for labor) but also the size that is driven by an exogenous labor supply component. That is, it may possibly affect productivity as well, in which case the IV estimates may not be an improvement over OLS.

10