Long-run neutrality in a fractionally integrated model

In this paper we use a bivariate, fractionally integrated, autoregressive, moving average (ARFIMA) model of money and real output to extend Fisher and Seater's [Long-run neutrality and superneutrality in an ARIMA framework. American Economic Review 83 (1993), 402-415] long-run neutrality requirements to long-memory processes. We derive new restrictions on the order condition of the nominal and real variable and discuss their implications for long-run neutrality. These new restrictions show for instance how finding money to be a nonstationary, non-mean reverting process and real output to be a nonstationary, mean reverting, long-memory process is a sufficient condition for long-run neutrality to hold. We apply our new restrictions by estimating and testing the order of integration in a univariate ARFIMA model of money and output, and by computing the impulse response functions of a bivariate fractionally integrated vector autoregressive model for Argentina, Canada, Italy, Sweden, the UK, and the US. Long-run neutrality is found to hold in every country except Sweden. However, even when money has no lasting long-run impact on real output we find positive monetary shocks having a significant and persistent positive effect on the level of output.