This paper investigates the optimal monetary instrument in a New-Keynesian model with multiple monetary assets. We compare a standard interest rate rule to a k-percent rule for three alternative monetary aggregates determined within our model: the monetary base, the simple sum measure of money, and the Divisia measure. Welfare results are striking. While the interest rate dominates the other two monetary aggregate k-percent rules, the Divisia k-percent rule outperforms the interest rate rule. Next we study the ability of Granger Causality tests – in the context of data generated from our model – to correctly identify welfare improving instruments. We find the interest rate Granger Causes both output and prices at extremely high significance levels. The same result is obtained for monetary base and the simple-sum monetary aggregate. The test results for Divisia are the weakest as Divisia fails to Granger Cause prices. We conclude that if the choice of instrument is based solely on its propensity to Granger Cause macroeconomic targets, a central bank may choose an inferior policy instrument.

Historically, attempts to solve the liquidity puzzle focus on narrowly defined monetary aggregates, such as non-borrowed reserves, the monetary base, or M1. Many of these efforts fail to find a short-term negative correlation between interest rates and monetary policy innovations. More recent research uses sophisticated macroeconomic and econometric modeling. However, little research has investigated the role measurement error plays in the liquidity puzzle, since in nearly every case, work investigating the liquidity puzzle has used one of the official monetary aggregates, which have been shown to exhibit significant measurement error. In this paper, we examine the role that measurement error plays in the liquidity puzzle by (i) providing a theoretical framework explaining how the official simple-sum methodology can lead to a liquidity puzzle, and (ii) testing for the liquidity effect by estimating an unrestricted VAR.