The Cross-Euler Equation Approach in Estimating the Elasticity of Intertemporal Substitution for Food and Non-Food Consumption in Japan

We use the standard two-good version of the life cycle/permanent income model in analyzing the intratemporal and intertemporal aspect of food and non-food expenditure in Japan. The empirical dilemma in identifying and estimating the parameters governing the intertemporal elasticity of substitution (IES) is addressed. In overcoming this empirical dilemma we employ the Cross-Euler equation approach proposed by Nishiyama (2005). The IES parameters are estimated by exploiting the cointegration restriction implied by the Cross-Euler equation and also from the standard Euler equation using GMM. Further, by comparing the IES estimates from the Cross-Euler equation to those from the standard Euler equation, we formally test the hypothesis whether food and non-food expenditure in Japan is affected by some factors that cause misspecification in the standard Euler equation approach, such as liquidity constraints or habit formation.