Migration flows have increased in many European countries after the extension of the free movement of persons (FMP) to new EU members and associate countries. Little is known about how this affects the distribution of wages. This paper focuses on the case of Switzerland, a country that adopted the FMP principle only recently. We combine a wage decomposition method with a structural econometric model in order to determine to what extent the FMP can be made responsible for the observed changes in the wage structure of natives in Switzerland. First, we identify the changes in returns to observable and unobservable skills of natives between 2002 and 2010, using non parametric and parametric decomposition techniques. Second, we estimate a structural model of the Swiss labor market in order to simulate the changes in returns to skills that would have been observed in the absence of the FMP. Third, we combine the two types of analyses and discuss whether the FMP can be considered as being a main cause of the increasing polarization of the Swiss wage distribution.