Ordinary least squares (OLS) regression has a breakdown point of 0%, whereas the least median squares (LMS) method and the corresponding reweighted least squares (RLS) method can withstand a substantial number of outliers in the data. In this paper the LMS/RLS method is extended to robust estimation of a distributed intercept model, and an algorithm for this situation is proposed. This method is applied to estimation of earnings functions with different intercepts for industries, based on data from five countries. Contrary to a widely shared view, the patterns of interindustry wage differentials seem to be different across the countries.