Long-Run Neutrality in a Long-Memory Model

In this paper we use a bivariate, fractionally integrated, autoregressive, moving average model of money and real output to extend Fisher and Seater (1993) long-run neutrality requirements to long-memory processes. We derive new restrictions on the order of the nominal and real variable and discuss their implications when long-run neutrality is tested with a reduced form econometric model. These new restrictions show how finding money to be nonstationary is not sufficient for testing long-run neutrality. A long-memory process can be both nonstationary and mean reverting, meaning an exogenous monetary shock has no long-run effect on money if it is such a process. We also use the fractionally integrated, autoregressive, moving average model to estimate and test the order of integration of money and real output. Since unit root tests have low power against long-memory processes, directly estimating the differencing parameter is more robust to the presence of short and long- memory. Lastly, we apply our long-memory framework to a century worth of annual money supply and real output data for Argentina, Australia, Canada, Italy, Sweden, the UK, and the US and discover that long-run neutrality is testable in six of the seven countries and holds in five of the six countries.