5 Empirical analysis

5.1  Estimates of the output gap and potential growth

Figure 3 presents the model's estimate of the output gap as well as the confidence band around the estimate. For comparison, we also report other output gap estimates (Multivariate filter,[4] MV, and Hodrick-Prescott, HP filter). The value of lambda is set at 1600 for both HP and MV filters. It appears that before the GFC, all the output gap measures moved together in broad terms and their differences were not statistically significant in general.

However, the crisis might have changed the dynamics of the economy. As a result, the output gap generated from the model over the post-crisis period is statistically different from the HP and MV filter output gap measures. However, caution is required in using the estimated confidence band to interpret the level of uncertainty, particularly at the end of the observation period. It will be shown in Section 6.4 that the estimated confidence band overstates the precision of estimates at the end of the sample.

According to the SMM, the estimate of the output gap troughs at about 2.7% in 2009Q2, which is slightly larger than the trough of 2.5% at the time of the Asian financial crisis. Furthermore, the SMM's estimate of the output gap remains negative at around 2% through the post crisis period, suggesting that there is spare capacity in the New Zealand economy.

This contrasts to the MV and HP filter gaps which were -1.7% and -2.7% respectively at the trough of the last cycle in 2009Q2 and converged back quickly to their trend. Currently, both the HP and MV gaps are positive, which suggests that there is no spare capacity in the economy.

The output gap estimates from the SMM suggest that care must be taken in using both the HP and MV filter to assess the level of potential output at the current juncture because the extent of the slack could be underestimated using the HP and MV gaps

Figure 4 shows the estimated annual growth rate of potential output with confidence bands from the model, together with the growth rates stemming from the HP and MV measures of potential output. Like the output gap measures, all the measures of potential growth show a similar pattern over the pre-crisis period. However, both the HP and MV potential growth measures are below that of the SMM for most of the period 2007-2011, which leads to the divergence of the output gap between the SMM model and the HP/MV measures.

All the measures indicate that potential output growth has declined since 2003, well before the onset of GFC. According to the SMM, the rate of growth of potential output has fallen from a peak of 3.8% in 2003 to a trough of 1.1% in 2009. Currently, the growth rate of potential output is estimated at 1.8% with a 95% confidence band of 1.1% to 2.5%. The estimate is currently below the steady-state value of potential output growth of 2.5%. Labour input and labour productivity are assumed to contribute 1% and 1.5% to potential output growth in the steady state respectively. It is important to note that the current estimate is not a permanent state. However, the estimated parameter of equation (3) means that the speed of converging to the steady state is very slow.

Figure 3 - Measures of the output gap with its confidence interval

Figure 4 - Potential growth rates (annual percentage change)

5.2  Inflation and output gap

Figure 5 shows that there is a reasonably strong relationship between the inflation rate and the estimated output gap from SMM. In particular, inflation falls sharply a year after the onset of the GFC, which corresponds well with the development of the negative output gap. Overall, the degree of movement in inflation is closely in line with the evolution of the output gap.

Figure 5 - Inflation and the output gap (lagged 3 quarters)

To test whether the SMM output gap outperforms the other output gap measures in explaining inflation, we use the cross-correlation coefficients between inflation and the output gap. Figure 6 presents the cross-correlation between inflation and the various output gap measures.

In general, the cross correlation coefficients indicate that both the MV filter and SMM output gaps move more closely with inflation than the HP filter output gap. The MV filter output gap records the largest value of cross-correlation of 0.56 at lag 3. If we restrict the sample size to the last 10 years of observations, the performance of the SMM output gap is still similar to that of the MV filter in tracking the movement of inflation.

With regard to timing, the largest value of the cross-correlation coefficient for the SMM output gap is 0.53 which also occurs at lag 3, indicating that inflation lags behind the SMM output cycle by 3 quarters. However, the contemporary correlation coefficient of 0.36 is rather large, reflecting that the model output gap has a positive impact on inflation in the same quarter.

Figure 6 - Cross-correlations between inflation and output gaps