Interpreting reduced form cointegrating vectors of incomplete systems. A labour market application

This paper explores the issues arising when the reduced form cointegrating vectors are obtained from an incomplete VAR with omitted endogenous variables. Reconsidering some Wickens' (1996) results, we show that the specification of an incomplete VAR model, based on variables of the reduced form cointegrating vectors, produces an approximation of the long run coefficients. We also show that in certain circumstances this problem does not arise. An example concerning the estimation of the NAIRU is provided suggesting the empirical relevance of our criticism. We use a numerical example with simulated data to illustrate the potential pitfalls.