VAR ANALYSIS, NONFUNDAMENTAL REPRESENTATIONS, BLASCHKE MATRICES

Macroeconomic models may produce ARMA structures where the determinant of the MA matrix polynomial has some roots inside the unit circle. This implies that the impulse-response functions are no longer identified and may vary in an infinite-dimensional space. This paper deals with this problem in the VAR, or structural VAR, framework. We provide a method to strongly limit the research for economically interesting nonfundamental impulse-response functions and show how to construct such representations from estimated VAR coefficients. We also give two empirical applications: GNP-unemployment, USA data, and interest rate-inflation, French data.