The determinants of foreign direct investment (FDI) are explored with gravity models, using a Poisson estimator and a linear estimator, both with fixed effects. The heterogeneity of product market regulations has a large and robust impact on cross-border investment: a reduction of regulatory divergence by one fifth could increase FDI by about 15%. In particular, the divergence of command and control regulations and of protection of incumbents (antitrust exemptions, entry barriers in networks and services) reduce cross-border investment. In addition, countries with higher employment protection have both less inward and less outward FDI, and there is some evidence that more complex regulatory procedures reduce inward FDI.