Long-run Identification in a Fractionally Integrated System

Abstract

We propose an extension of structural fractionally integrated vector autoregressive models that avoids certain undesirable effects for impulse responses if long-run identification restrictions are imposed. We derive its Granger representation, investigate the effects of long-run restrictions and clarify their relation to finite-horizon schemes. It is illustrated by asymptotic analysis and simulations that enforcing integer integration orders can have severe consequences for impulse responses. In a system of US real output and aggregate prices effects of structural shocks strongly depend on integration order specification. In the statistically preferred fractional model the long-run restricted shock has only very short-lasting influence on GDP.