Unit Root Analyses of the Causality Between Japanese Money and Income

Abstract

Unit root techniques and cointegration analysis have developed considerably in the last ten years. At the same time, the nonstationary test for Granger causality has been developed. We shed some new light on Japanese money supply and income causality by using nonstationary techniques. We specify univariate ARMA models of money, income, GNP deflator and rate of interest, initially by using the Dickey and Fuller (DF) or the augmented DF (ADF) tests. Two diagnostic tests are applied to each selected ARMA regression. One is the residual DF test, and the other is the moving average (MA) unit root test of residuals. After selecting the ARMA model, some causality tests are applied to the error correction model (ECM) of a vector autoregression (VAR) one of which is ordinary least squares (OLS) and another is the maximum likelihood (ML) method. The former requires only the standard F-test on the deleted variables in the ECM. The latter requires the Johansen’s ML method in estimating cointegration. Causality is found to go from income to money supply but not the other way. Appendices include a simple implementation of the MA unit root test, a pedagogical proof of the Granger causality tests developed by Toda and Phillips (1993) and an interpretation of the test proposed by Toda and Yamamoto (1995). KEYWORDS: causality, non-stationarity, money, income, cointegration. JEL Classification Numbers: C32, E50.