We compare two methods of motivating money in New Keynesian dynamic stochastic general equilibrium models—money‐in‐the‐utility function and the cash‐in‐advance (CIA) constraint—as well as two ways of modelling monetary policy: the interest rate feedback rule and money growth rules. As an aid to model selection, we use a new econometric measure of the distance between model and data variance–covariance matrices. The proposed measure is useful in distinguishing between alternative general equilibrium models. Drawing on our econometric analysis, we argue that the CIA model, closed by a money growth rule, comes closest to the data.