Money and monetary policy in dynamic stochastic general equilibrium models

We compare three methods of motivating money in New Keynesian DSGE Models: Money-in-the-utility function, shopping time and cash-in-advance constraint, as well as two ways of modelling monetary policy, interest rate feedback rule and money growth rules. We use impulse response analysis, and a set of econometric distance measures based on comparing model and data variance-covariance matrices to compare the different models. We find all models closed by an estimated interest rate feedback rule imply counter-cyclical policy and inflation rates, which is at odds with the data. This problem is robust to the introduction of demand side shocks, but is not a feature of models closed by an estimated money growth rule. Drawing on our econometric analysis, we argue that the cash-in-advance model, closed by a money growth rule, comes closest to the data