The first part of the paper considers a behavioural model of trade unionism. Wages and employment are characterized as the outcome of a process by which the union maximizes an objective function containing wages and employment as arguments, and is constrained by a trade-off between these two variables as represented by the firm's labour demand function. In the second part, we apply the testing methodology developed by Johansen [Johansen, S., 1992a. A representation of vector autoregressive processes integrated of order 2, Econometric Theory 8, 188–202; Johansen, S., 1995a. A statistical analysis of cointegration for I(2) variables, Econometric Theory 11, 25–29; Johansen, S., 1997. A likelihood analysis of the I(2) models. Scandinavian Journal of Statistics 24, 433–462.] and extended by Paruolo [Paruolo, P., 1996. On the determination of integration indices in I(2) systems. Journal of Econometrics, 72 313–356.] and Rahbeck et al. [Rahbeck, A., Kongsted, H.C., Jorgensen, C., 1999. Trend stationarity in the I(2) cointegration model. Journal of Econometrics 90, 265–289.] for the presence of I(2) components in a multivariate context along with the estimation of the roots of the companion matrix [Juselius, K., 1995. Do purchasing power parity and uncovered interest rate parity hold in the long run? An example of likelihood inference in a multivariate time-series model. Journal of Econometrics 69, 211–240.]. Furthermore, structural restrictions identifying the long-run relations of interest are specified as proposed by Johansen and Juselius [Johansen, S., Juselius, K. 1994. Identification of the long-run and the short-run structure: An application to the ISLM model, Journal of Econometrics, 63, 7–36.] and Johansen [Johansen, S., 1995b. Identifying restrictions of linear equations. Journal of Econometrics 69, 111–132.] since more than one cointegrating vector is found. Applying the Hansen and Johansen [Hansen, H., and Johansen, S., 1993. Recursive estimation in cointegrated VAR-models. Working Paper, Institute of Mathematical Statistics, University of Copenhagen., Hansen, H., Johansen, S., 1999. Some tests for parameter constancy in cointegrated VAR-models. Econometrics Journal, 2, 306–333.] stability tests we show that the rank of the cointegration space is sample independent while the estimated coefficients do not exhibit instability in recursive estimation. Finally, an error correction model is estimated in order to disentangle the short-run from the long-run behaviour.