Method to Construct Moments in the Multi-Good Life Cycle Consumption Model

摘要

Life cycle consumption models are often estimated by using the intertemporal relationships implied by the Euler equations. In the paper the authors present a method to construct such Euler equations and, more generally, moments, if one allows for quite general formulations of the life cycle consumption model. For example, one may wish to allow for intertemporally non-additive (expected) utility or one may wish to include (next to the lifetime wealth budget constraint) additional (inequality) constraints, such as liquidity constraints. The construction of the moments will be on the basis of the first order conditions which the authors derive by application of a generalized Lagrange multiplier rule. In case of more than one good per period, the authors also allow for within period uncertainty in addition to intertemporal uncertainty. As a consequence, the first order conditions not only lead to intertemporal Euler equations but also to intratemporal moments instead of the intratemporal identities between marginal utilities which usually show up. The construction of moments is illustrated by some examples of particular multi-good life cycle consumption models.