excluding all localities _j_ located within a 25, 50 or 75 km radius of locality _i_ , hence the reference to a ‘doughnut’.<sup>17</sup>

**The ’recursion problem’ or the structural endogeneity of market access and market potential** . When considering an explained variable which is correlated with other variables that enter the calculation of the accessibility regressor in formulas (1) or (2)—for instance when regressing total employment on market access in Equation (3)—a recursion problem is bound to emerge, even when excluding ‘own locality’ from the measure of accessibility. To see this, notice that locality _i_ ’s market access is a function of locality _j_ ’s population, which in turn is correlated with locality _j_ ’s employment, which is a function of locality _j_ ’s market access, and thus of locality _i_ ’s population. Locality _i_ ’s employment is then structurally correlated with its own market access in the absence of causal effect of market access on Fol- any employment. lowing Baum-Snow et al. (2017), we address this problem by calculating either counts of road intersections or a ‘doughnut’ of efficient road lengths in a given radius (in a similar way to the market access and market potential ‘doughnuts’).<sup>18</sup> We then use the road count or efficient road variable instead of the market access or market potential indicator, or use it to instrument market access or market potential. Sources of variations in ‘accessibility’ are then only due to variations in roads, thus avoiding the recursion problem.

The validity of our three instruments (both for market access and market potential) is tested by means of the Kleibergen-Paap statistics, which is robust in the presence of heteroskedasticity. After performing this test, we reject the hypothesis of weak instruments as the rule of thumb suggested by Staiger and Stock (1997) that the statistic must be larger than 10 is satisfied. As for the exogeneity of the instruments, we rely on the Hansen-J statistics and strongly accept the hypothesis of exogenous instruments.<sup>19</sup> The coefficients on market access and market potential are positive and statistically significant in all second stage regressions.

To differentiate the role of access to domestic and external markets, we also estimate the infrastructure model as previously discussed. In this model, domestic market access is proxied

> 17Because of the mixed nature of our sample, for metropolitan areas, we first compute these counterfactual measures at the municipality level, excluding both municipalities within a same metropolitan area and municipalities within our distance threshold. We then define the metropolitan area ‘doughnut’ as the weighted average of these municipality indices, using municipality area as weights.

18In this ‘doughnut’, the exclusion of surrounding areas addresses endogeneity of road placement. 19See Baum et al. (2017) for a detailed explanation of test implementation in stata and for references. It is worthwhile noticing that, besides being efficient, our estimation results are also consistent with respect to the absence of heteroskedasticity or autocorrelation because of the Stock-Yogo weak identification employed for the estimation. In all our iv regressions, the first stage f-statistic is large, suggesting that the instrument is strong (Stock and Yogo, 2005).

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