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Estimating a New Zealand NAIRU - WP 04/10

4.2  Kalman filter NAIRU estimates

In general, the results in Table 2 suggest that Model 1 is better fit than Model 2 according to the values of log likelihood function. Furthermore, the estimates and z-statistics of the coefficient on the unemployment gap are more significant in Model 1 than in Model 2. The results support a fairly strong negative relationship between the unemployment gap and inflation except for the CPIG based inflation measure for Model 2.

Table 2 – Models estimated using the Kalman Filter
Dependent Variable  CPIX  CPIG  COND
Model 1      
0.43***(4.32) 0.45***(3.73)  
-0.15**(-2.04) -0.22*(-1.77) -0.55***(-4.89)
Δ Import prices     0.06**(2.06)
Δ Oil prices 0.03***(3.50) 0.04**(2.46)  
Rate of change in Local Authority Rates 0.03***(2.64)    
Log Likelihood -89.4 -111.3 -119.8
Model 2      
0.45***(4.44) 0.47***(3.64)  
-0.12*(-1.64) -0.17(-1.40) -0.53***(-4.53)
Δ Import prices     0.06*(1.92)
Δ Oil prices 0.03***(3.50) 0.04**(2.44)  
Rate of change in Local Authority Rates 0.03***(2.79)    
Log Likelihood -90.3 -112.6 -121.4

Z-statistics are in parentheses. *** significant at 1 % level, ** significant at 5% level and * significant at 10% level.

Figure 1 shows various Kalman filter smoothed NAIRU estimates. The resulting NAIRU estimates show large variation over time. In general, the NAIRU estimates derived from Model 2 display more variability than those obtained from Model 1. However, all the estimates rose during the first half of the 1990s and reached a peak ranging from 6% to 7.8% in 1994. For the latter half of the 1990s, the NAIRU profiles diverged slightly, especially for the COND-based NAIRU. Both CPIX and CPlG based NAIRUs declined since 1995 and flattened off during the 1997-2000 period, declining again thereafter. The period in which the fall in NAIRUs was temporarily halted, coincided with the onset of the Asian Crisis and two consecutive droughts. Hence, the flattening in NAIRUs may be attributable to the omission of supply shocks caused by the two droughts in the estimation (Buckle, Kim, Kirkham, McLellan and Sharma 2002). At the end of the sample period, the estimated NAIRUs ranged between 4.9% to 4.3% for both CPIX and CPIG based inflation measures.

Figure 1 – NAIRU estimates from the three inflation measures and two models
Figure 1 – NAIRU estimates from the three inflation measures and two models - graph 1.
Figure 1 – NAIRU estimates from the three inflation measures and two models- graph 2.
Figure 1 – NAIRU estimates from the three inflation measures and two models - graph 3.
Source: The Treasury

Like other estimates of NAIRUs, the COND-based NAIRU estimates fell for the latter half of 1990s but the main difference is that the flattening period did not start until 1999, reaching a sample low of 3.8% and 3.6% for Model 1 and Model 2 respectively.

4.3  Comparing the Kalman filter NAIRU estimates to HP filter estimates

In the rest of this section, we compare Kalman filter estimates of NAIRU based on Model 1 (our preferred model) with the HP filter NAIRU estimates. In this paper, the HP filter NAIRU estimates are derived using the λ of 1600, which is commonly used for quarterly data. Figure 2 presents the NAIRU estimates using the HP filter.

Figure 2 – Kalman and HP filter NAIRU estimates
Figure 2 – Kalman and HP filter NAIRU estimates.
Sources: Statistics New Zealand and The Treasury

The key difference between the HP filter and the Kalman filter is that the HP filter NAIRU estimates move more closely with the actual level of unemployment. As a result, the size of unemployment gaps is smaller than those estimates based on the Kalman filter (see Figure 3).

Furthermore, some important economic insights can be drawn from the difference in the unemployment gaps between the HP filter and Kalman filter. According to the Kalman filter, disinflation policy, fiscal reform, and the world recession had a greater negative impact on demand during the early 1990s, than would have been suggested if the HP filter is used. The unemployment gap required to lower inflation was much larger according the Kalman filter estimates than the HP filter estimate. Chapple (1995) argued that the increase in New Zealand’s unemployment rate between the mid-1980s and early 1990s could not be explained by an increase in the NAIRU. The Kalman filter unemployment gap estimates are generally consistent with Chapple’s (1995) argument in that the rise in unemployment was largely due to aggregate demand failing to expand sufficiently, with a smaller impact from a rising NAIRU. As the level of structural unemployment in the early 1990s is much smaller using the Kalman filter based measures in comparison with the HP filter base measures, consequently, the fall in the structural unemployment is also smaller for the Kalman filter based measures during the second half of 1990s.

Figure 3 – Comparison of the unemployment gaps derived from different NAIRU estimates
Figure 3 – Comparison of the unemployment gaps derived from different NAIRU estimates.
Source: The Treasury

In order to test which unemployment gaps are better in explaining the movement of inflation, the estimated unemployment gaps derived from both the Kalman filter and the HP filter are included in Equation (3), which is then estimated by OLS. Table 3 presents the results of the estimation. The fit of the estimated equation is a much better using the Kalman filter gaps than the HP filter gaps.

Table 3 – Estimating Equation (3) with OLS using the Kalman filter unemployment gaps and the HP filter unemployment gaps
   CPIX CPIG  COND
  Kalman HP Kalman HP Kalman HP
0.36*(3.76) 0.51*(5.59) 0.42*(3.73) 0.44*(3.91)    
-0.23*(-3.36) -0.26(-1.37) -0.27*(-2.77) -0.77**(-2.38) -0.66*(-7.34) -1.27*(-4.01)
Δ Import prices         0.07*(3.30) 0.06**(2.41)
Δ Oil prices 0.03*(3.77) 0.03*(3.40) 0.04*(3.05) 0.03*(2.74)    
Rate of change in Local Authority Rates 0.03*(2.61) 0.03*(2.72)        
Adjusted R-squared 0.54 0.47 0.43 0.41 0.40 0.09

t-statistics are in parentheses. * significant at 1 % level, ** significant at 5% level and *** significant at 10% level.

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