## 5/15/11

### Validation of the New Zealand GDP model

Following the post on the German real GDP per capita, we revisit the 2008 model for New Zealand. It was also obtained by the trial-and-error method. Empirical constant A and the specific age, Ns, in the defining equation:
g(t) = dlnG(t)/dt  = A/G(t) + 0.5dlnNs(t)/dt                                            (1)

have been varied in order to fit amplitude and major features of the observed curve. The best fit annual increment value is A=\$220 (1990 US\$, as published by the Conference Board).  The specific age population in New Zealand is 14 years. The age pyramid enumerated by the 2006 census was extrapolated in the past and in the future in order to estimate the number of 14-year-olds in (1).
Figure 1 presents the observed and predicted GDP growth rates for New Zealand as obtained in 2008. Both curves are characterized by high-amplitude oscillations likely associated with measurement errors. Therefore, in Figure 2 we present both annual curves smoothed with MA(5) and MA(3), respectively. The upper panel in Figure 2 reproduces the 2008 model and the lower one – the 2010 model (one should notice the difference between various vintages of GDP estimates published by the Conference Board). One can conclude that our prediction from 2008 was correct and real GDP per capita in New Zealand actually fell to zero. This is the best validation of our model for NZ and we will continue tracking the fit.
As before, one can expect that  there is no danger of a deep recession in New Zealand, but the rate of real economic growth will be very low (on average ~0.5% per year) in the years to come.
Figure 1. Observed and predicted growth rate of real GDP per capita in New Zealand between 1980 and 2010.
Figure 2. The observed curve is smoothed with a 5-year moving average. The predicted rate is smoothed with MA(3). The upper panel displays the 2008 model and the lower panel – the 2010 model.  (We present two figures because the GDP estimates vary with data vintage.) One can observe an outstanding accuracy of GDP prediction for 2009 and 2010 (between the smoothed curves).