12We are aware that GDP per capita is an indirect proxy for income. Unfortunately, data on income at NUTS2 are available only for a shorter period (i.e. from 2000 onwards). Yet, the simple correlation between GDP per capita and income (computed on those years in which data are available at NUTS2 level) is 0.92 and significant at 1% level. By substituting GDP per capita with income and running regressions on the subsample for which income data are available, findings are qualitatively unchanged. Appendix A.3 reports the results of this robustness check. Therefore, given the high consistency of findings obtained by using the two variables, we opted for the largest temporal coverage and used GDP per capita data.
On a purely theoretical ground, we cannot exclude endogeneity concerns in the form of sorting effects, i.e. satisfied people are more likely to move to happier/wealthier cities. This issue is discussed in depth in the companion paper Lenzi, Perucca (2016b), reporting no substantial evidence of endogeneity and sorting effects, albeit using a different dataset enabling a direct comparison of life satisfaction between natives and migrants. The present dataset, unfortunately, does not allow recording such information in a longitudinal way, even if we are aware that it would add robustness to our findings. In absence of a direct statistical test excluding the presence of endogeneity, however, our estimates are better to be interpreted as robust partial correlation coefficients rather than causally.