Using the Toda and Yamamoto approach to test for granger causality between two sectors : the energy sector and non-energy sector

Abstract

This paper attempts to study the dynamic relationship between the price index of the energy sector and non-energy sector-specifically agriculture, fertilizers and metals & minerals- whether they are related to each other or not, using Granger causality test proposed by Toda and Yamamoto (1995) to a Vector Autoregressive (VAR (p+m)) model (description of the Energy and non-energy sector is presented in the Appendix p.38-45). Granger causality determines the causal relationship among those four endogenous variables. Under this approach, we decided to test for causality in non-stationary time series among each pair (Energy-Agriculture, Energy-Fertilizers and Energy-Metals & Minerals), where worked on the levels of the data rather than the returns. The study is conducted on 56 years data of the adjusted close monthly prices, from January 1960 to August 2016. The major findings of the study are (a) the correlation Matrix proved that there is a high correlation among the 4 sectors, (b) the Granger causality Wald test shows there is dependency among the 4 pairs translated into a one way causation from Agriculture to Energy and a two way causation among Energy-Fertilizers and Energy-Metals & Minerals ; (c) the Max. Eigenvalue cointegration test shows that there exists a long-run equilibrium relationship between the price index of Energy and Fertilizers and Energy and Metals & Minerals. Since they are cointegrated, this certifies the existence of Granger causality between them which is two ways causality. With the absence of cointegration, there is no compelling reason to crosscheck on the causality results which is the case between Energy and Argiculture where no cointegration was found, however causality took place.