The Tracking Ability of the Divisia Monetary Aggregate Under Risk

This paper attempts to establish a link between aggregation and index theory, which exists under perfect certainty, but is not known to exist under risk aversion. The paper develops a consumer based demand for money problem where the consumer is risk averse and has a known theoretical monetary aggregate. This dynamic optimization problem's solutions are approximated by the numerical Parameterized Expectation Approach and used to calculate the theoretical and Divisia monetary aggregate. The paper shows that for certain model parameter values the approximated rational expectation solutions cause the Divisia aggregate to closely track the theoretical monetary aggregate, and hence, establishes a link between aggregation and index theory when risk is present. Unfortunately, for other parameter values the Parameterized Expectation Approach fails to provide adequate solutions to conclude that this tracking continues when the level of risk aversion is large or when a different theoretical monetary aggregate exists.