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Abstract
This article contributes to the debate on the role of money in monetary policy by analysing the information content of money in forecasting euro-area inflation. We compare the predictive performance within and among various classes of structural and empirical models in a consistent framework using Bayesian and other estimation techniques. We find that money contains relevant information for inflation in some model classes. Money-based New Keynesian Dynamic Stochastic General Equilibrium (DSGE) models and Vector Autoregressions (VARs) incorporating money perform better than their cashless counterparts. But there are also indications that the contribution of money has its limits. The marginal contribution of money to forecasting accuracy is often small, money adds little to dynamic factor models, and it worsens forecasting accuracy of partial equilibrium models. Finally, nonmonetary models dominate monetary models in an all-out horserace.
Acknowledgements
We would like to thank Henning Weber and seminar participants at the IMF, the Free University of Berlin, and the 2008 WEA meeting for helpful comments and suggestions. The views expressed are those of the authors and do not necessarily represent those of the IMF or IMF policy.
Notes
1 All variables of the NKM models discussed in the section ‘DSGE models’. A are expressed as deviations from their steady state levels, while the section ‘Partial equilibrium models’ as well as Appendix A use levels.
2 An alternative argument for incorporating money in the interest rate equation could be that money, for reasons not captured in the structural model, helps to forecast inflation or the central bank shares the households' preference for a stable money stock. See Andrés et al. (Citation2007).
3 The reason is that forward-looking price setters apply the households' stochastic discount factor in their dynamic optimization problem, which, in turn, is influenced by money holdings.
4 Note that the direct and indirect impact of contemporaneous money on inflation move into opposite directions, with the overall impact being a question of the underlying parameters and, thus, ultimately an empirical matter.
5 Equation Equation12 combines a number of approaches. Hallman et al. (Citation1991), for instance, assume α = 1, which seems to be in line with Reynard's (Citation2007) empirical observation that the price gap influences inflation with considerable lags and some persistence. As a rule, the P* model does not restrict the expectations term, which, in principle, could take any form.
6 Note also that Bayesian estimation allows for better treatment of expectations in a model consistent way that addresses to a greater degree potential endogeneity problems.
7 Note that the coefficients estimated for the DSGE models are semi-structural, as we do not enforce some of the restrictions implied by the deep parameters of the underlying model in the empirical implementation.
8 More specifically, the assumption of no inertia in aggregate demand is rejected by the data despite tight Bayesian priors.
9 We proceed with the GDFM forecasting in two steps. In the first step, using the dynamic techniques described in Forni et al. (Citation2000), we estimate the covariance matrices of the common and idiosyncratic components. In the second step, as the cross-section size tends to infinity and the idiosyncratic components cancel out, as they are poorly correlated, we approach the factor space. We then obtain the predictor by projecting future values of the common components on the estimated factor space.
10 Note that this convention will affect the across-the-model comparison, as it will favour the Phillips curve models. However, the within-model class comparison, which is more relevant for our analysis of the relative importance of money, is not affected. To forecast the off-model conditional variables – in particular, the output and real money gaps and long-term money growth for the Phillips curve models – we proceed in two steps. For a given forecasting window, we first calculate these variables using a standard Hodrick–Prescott filter and then forecast them up to twelve quarters ahead using an ARMA process. This process is repeated each time the forecasting window is moved and a new observation is added.
11 The fact that our simulated out-of-sample exercise is based on revised instead of real time data should have no bearing on the results. A bias (if any) in forecasting accuracy that the use of revised data may create would influence all models simultaneously, leaving their relative performance unchanged. And indeed, in a recent paper, Faust and Wright (Citation2007) show that the use of real time or revised data does not influence the relative performance of various model- and expert-based forecasts for inflation and output in the US economy.
12 further below, in addition, shows the relative rank of the models within each nested model class (see columns named ‘within model class’) based on the relative RMSE at the 12 quarter horizon and the average RMSE across all horizons, respectively.
13 Note that this is not simply an artifact of the NKM model lacking the ability to capture the persistence in the data, which may influence forecasting accuracy. In the empirical implementation, all estimated equations include lagged endogenous variables (Section III, Appendix A).
14 Additional results available on request.
15 The results from a single equation autoregressive distributed lag model containing money (not shown, but available on request), suggest that while the inflation forecast is not better than the random walk model, it is superior to the forecasts from the ARMA approach.
16 In part, this might be explained by the fact that our approach emphasizes within-class comparisons, and that we have made no effort to fine-tune the performance of a particular class of model vis-à-vis another. On the other hand, it is not immediately obvious how such an effort would alter the results.
17 In general, we follow the notation of the main text. For ease of exposition, we use Roman letters to abbreviate growth rates where required.