Estimation of the New-Keynesian model The point of departure of this paper was the finding from previous research that the

4.5. Estimation of the New-Keynesian model The point of departure of this paper was the finding from previous research that the

elementary three-equations model (NK) is remarkably successful in reproducing the au- tocovariance profiles of its three variables i t ,y t ,π t . The obvious question is now how this compares to the matching of our Old-Keynesian model in the last two Scenarios 3a and 3b, which were equally claimed to be a good success. Such a comparison is even more meaningful as the a priori possible herding effect was not confirmed by these estimations. Hence the New-Keynesian and the Old-Keynesian models are on a similar footing and could be viewed as two variants of the New Macroeconomic Consensus. That is, they in- clude similar arguments centring around the real rate of interest, while the expectations involved in them are specified in different ways: in a so-called forward-looking manner in

31 Apart from this it is worth noting that the “aggregate” noise level σ i +σ y +σ π in the economy is similar across the Scenarios 2b, 3a, 3b, only the distribution across the three random sources

varies.

the New-Keynesian model and—in that language—a purely backward-looking manner in the Old-Keynesian approach.

Let us then reconsider the estimation of the New-Keynesian model on the 78 autoco- variance moments. The linear structure of the model is very convenient in this respect because it saves us from the sample variability across different simulation runs. In fact, the closed-form solution of such rational expectations models takes the form of a vector autoregression, so that its autocovariances can be computed analytically without having to simulate the model (they are the asymptotic moments, corresponding to an infinite simulation size in MSM; see Appendix A4 for further details). Column NK–a in Table 1 reproduces the estimation in Franke (2011b), which is the outcome from the minimiza- tion of the present loss function J (78) . Its value of 37.13 is a bit higher than in Scenarios SD–3a and SD–3b, but the difference will not be reckoned significant. So far it can there- fore be stated that the New-Keynesian and the Old-Keynesian score about equally well in matching the empirical autocovariances.

Nevertheless, the close values of J (78) in these estimations are just an overall evalua- tion, they do not mean that also the entire autocovariance profiles of NK–a and SD–3a are similar. The most conspicuous example is the following. We already know that the main

weakness of SD–3a is the relatively strong underestimation of the empirical Cov(y t ,π t− 1 ). Model NK–a, on the other hand, has no problem at all with that moment. Instead, Ta- ble 2 indicates that it cannot overcome a serious underestimation of the variance of the inflation rate, which is not perfect but still acceptable in SD–3a.

Regarding the additional moments that we consider, moment m 79 does not apply to the New-Keynesian model and can be omitted here. We can thus directly turn to the three raggedness statistics. Although there is no analytical expression for them and we cannot get around simulating them, their sample variability over our long simulation horizon of S = 10, 000 quarters is so limited that effects from different random seeds can

be neglected. Column NK–a in Table 2 shows the implications of this estimation for the time series patterns: R(y t ) is perfect, R(i t ) is still tolerable, but R(π t ) points out that the inflation rate is much too smooth as to claim it could mimic the behaviour of the empirical series to any decent degree. This failure is also reflected in the dramatically higher value

of the augmented loss function J (82) in Table 1. 32 Hence the original estimation of model NK yields a good matching of the autocovariances, whereas it is very unsatisfactory when it comes to the raggedness of the inflation rate.

It may be noted in passing in Table 1 that the estimation of those parameters that the New- and Old-Keynesian model have in common are very dissimilar in NK–a and SD–3a. The only two exceptions are the complete absence of noise in the Taylor rule (σ i = 0) and the policy coefficient on inflation µ π , which in both estimations is also

32 In order not to change or extend the numbering in the superscript of J, J (79) may be identified with J (78) for the New-Keynesian model.

not too different from Taylor’s benchmark value 1.50. The relatively low value of the Phillips curve noise level σ π in NK–a (0.429 versus 1.340 in SD–3a) is certainly the most immediate explanation for the insufficient raggedness of inflation in this estimation (in both cases the supply shocks, as a feature that is remarkable in itself, exhibit no serial correlation, so that the levels σ π are directly comparable).

As we did for the three versions of the Old-Keynesian model, we should finally include the raggedness moments in the loss function and re-estimate model NK accordingly. This procedure, which gives rise to Scenario NK–b, is successful insofar as the ragged- ness statistics are similarly good to those in SD–3b (see Table 2). In all other respects, however, NK–b is inferior to SD–3b. First of all, the minimal value of J (82) is distinctly higher (119 versus 43). Second, the extended minimization seriously deteriorates the pre- vious matching of the autocovariances; J (78) increases from 37 to 107. Third, the policy coefficients on inflation and output, µ π and µ y , are heavily affected by the re-estimation and their high values are no longer fully credible. 33

A comparison of the New-Keynesian model and the most elaborate version of the Old-Keynesian model can now be briefly summarized as follows. Both models are almost equally successful in reproducing the autocovariances of their state variables i t ,y t ,π t . The performance in this dimension can indeed be said to be rather convincing. However, the autocovariances and the raggedness R(π t ) of the inflation rate can hardly be reconciled in the New-Keynesian model. Either it produces a good match of the former and a bad match of R(π t ), or the other way around. By contrast, in the Old-Keynesian model the two types of moments are largely compatible; a good match of one type can go along with at least an acceptable match of the other type. Hence in one single sentence, if we are more ambitious concerning the features that a model should be able to reproduce, the Old-Keynesian model with the crossover random shock effects model does a better job than the New-Keynesian three-equations model.