6 Sensitivity analysis (continued)

6.3 Steady-state assumptions

In this section, we check whether the output gap estimates are sensitive to the steady-state growth rate parameter and the steady-state unemployment rate parameter. Apart from at the end of the sample period, the output gap measures are almost identical to the baseline estimates when we lower the steady-state growth rate from 2.5% to 1.5% (see Figure 14). With an assumption of lower steady-state growth rate, the size of the negative output gap in the September quarter 2012 is estimated to be 1.4% which is slightly smaller than the baseline estimate of 1.8%.

Figure 14 also shows that increasing the steady-state unemployment rate from 5% to 6% does not result in a drastic change in the output gap estimates. Overall, the level of the output gap estimate shifts upward slightly across the whole sample period in comparison with the baseline estimates.

Overall, the output gap estimates are robust to alternative steady-state growth and unemployment rate assumptions.

Figure 14 - Output gap estimates under different steady-state assumptions

6.4  Endpoint problem

Although the output gap is a useful theoretical concept, it is very difficult to measure because of the unobservable nature of potential output. It is also well known that all the statistical filters employed in measuring potential output are subject to the “endpoint problem”, reflecting the fact the future is unknown. Ideally, the output gap estimates should not be revised drastically when new observations are added into the analysis. Figure 15a and 15b illustrates how various output gaps evolve when the sample is ended at two alternative points: 2007q4 (at the peak of a business cycle) and 2010q2 (one quarter before the September 2010 Canterbury earthquake).

When the sample is ended at 2007q4, all the output gap estimates are substantially different from the full sample estimates. The model output gap is initially estimated to be 0.6% at the December quarter of 2007q4 and the estimate is subsequently revised up to 3.1%. Similarly, the MV filter and HP filter estimates are revised up from 1.1% to 3.2% and from 0.1% to 2.5% respectively.

Apart from the HP filter estimates, the divergence between the initial output gap estimate and the full sample estimate at 2010q2 is also very large. According to the SMM, the output gap is initially estimated to be negative with a magnitude of 2.5%, which is revised up to -1.1%. Likewise, the MV filter estimate is revised up from -0.5% to 0.6%.

These findings suggest that although the new methodology incorporates more structural relationships, it is not able to eliminate large revisions in the output gap when the economy is subject to large shocks such as the GFC and the Canterbury earthquake. These findings are consistent with those found by Plantier and Karagedikli (2005). Thus, the addition of structural equations does not resolve the inherent difficulty of measuring the level of output gap with sufficient reliability in “real time”.

Figure 15a - Output gap updates - sample until 2007q4

Figure 15b - Output gap updates - sample until 2010q2