Long run equilibrium estimation and inference: a non-parametric application

Abstract

Phillips (1988a) has demonstrated that the long run parameters of a continuous time error correction model (ECM) involving nonstationary variables can be estimated from a corresponding discrete time ECM. He suggests Hannan efficient and band spectral frequency domain procedures for estimation and inference, anticipating they would provide significant advantages over the parametric methods traditionally used for continuous time models. A further advantage of Phillips' proposed methodology is that conventional asymptotic chisquared hypothesis testing can be carried out. This paper provides an early successful application of that methodology, using Australian consumption and income data. The spectral regression estimates are relatively straight forward to compute, with only a few iterations being required. The spectral estimates are not sensitive to alternative initial estimates. The application also highlights the potential importance of non-parametric estimators. Empirically, the long run consumption function estimates obtained are sufficiently realistic for it to be worthwhile exploring conditional short run dynamic relations and other macroeconomic data sets. Our hypothesis testing procedures are consistent across the aggregate and disaggregated data sets used, and between the unit root and cointegration stages of the investigation. A surprising result is that the null of no cointegration between aggregate real consumption and household disposable income cannot be rejected.