Welfare persistence is estimated in and compared between Swedish-born and foreign-born households. This is done within the framework of a time-stationary dynamic discrete choice model controlling for the initial condition and unobserved heterogeneity. Three different types of persistence are controlled for in terms of observed and unobserved heterogeneity, serial correlation, and structural state dependence, the focus being on the latter measure. In a second step we analyze the long-run effects of receiving social assistance on future household earnings and disposable income. The results show that state dependence in Swedish welfare participation is strong in both Swedish-born and foreign-born. However, the size of the effect is three times as large for the latter group. When the effect is distributed over time, it disappears after three years for both groups. The effect of structural state dependence is decomposed into a number of observed explanatory factors. Surprisingly small effects are found from typical foreign-born factors such as time in the country and country of origin, both important determinants for welfare participation in general. When investigating the effect of social assistance participation on future earnings, we find a strong and persistent effect over the whole observation window, while no such effect could be found for disposable income. This indicates that the economic incentives to leave the dependency are very weak. The picture is similar for both Swedish-born and foreign-born, even though the negative earnings effect is somewhat larger for the latter.