In this paper we present techniques for cointegration modeling of interrelated factor demands. These techniques respect the non-stationary character of the price and quantity data, and permit specification of general, dynamic factor demand models based on error correction forms derived from cointegration. Therefore, we do not have to assume ad hoc dynamic forms. Moreover, we ensure that estimated relations are structural, and not spurious. Cointegrating vectors are estimated subject to all standard economic theory restrictions by using a procedure, which we call dynamic SUR. We show how consistent error correction models can be specified and estimated. In addition, we test the neoclassical restrictions both in the short- and the long run. The new methods are used to shed light on the major problem of the European Union (unemployment) and its relationship with imports. The empirical analysis is conducted for five countries of the European Union with an emphasis to the south: The UK, France, Greece, Italy, and Spain.