Nonparametric Testing for Long-Run Neutrality with Applications to US Money and Output Data

We consider a nonparametric testing procedure for long-run monetary neutrality using spectral approaches. Long-run effects between bivariate integrated series are represented as the spectral density matrix of their first-differences evaluated at the zero frequency. The long-run neutrality, the core issue in this work, reduces to zero power of the cross spectral density function near the origin. We propose a statistic based on a kernel-based cross spectral density estimator. As designed to be consistent against cross correlations of unknown forms, the test differentiates it from tests based on parametric regression models. In implementing the tests, some feasible bandwidth selection procedures are detailed in terms of mean squared error criteria and of type I and type II errors criteria. Our testing procedures can be a complementary approach for neutrality testing. Simulation studies are shown to support theoretical results. Our methods are applied to testing long-run neutrality in the US nominal money and real output quarterly data from the first quarter of 1959 to the third quarter of 2009. Our tests unanimously reject the long-run neutrality for M2 regardless of the choice of bandwidths and of kernels.