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Capital Shallowness: A Problem for New Zealand? - WP 05/05

6.6  Adjustments to the definition of capital

It could be argued that the growth of the capital stock in the housing sector does not necessarily respond to changes in relative factor prices in a manner similar to that in other sectors of the economy. For this reason, we removed housing capital from the estimate of the total capital stock for both New Zealand and Australia. The purpose of this adjustment is to test whether our earlier findings are robust with respect to changes in the description of the capital stock. The results of re-estimating equation 11 with the revised capital stock excluding housing capital are shown in Table 11.

The effect has been to widen the gap between the estimated long-run elasticities of substitution for New Zealand and Australia. The value for New Zealand has fallen from 0.79 to 0.54, whereas for Australia the estimated long-run elasticity increased from 0.78 to 0.94 and becomes insignificantly different from unity. This suggests that the production sector in New Zealand does not respond as fast to changes in the relative price ratio as does the production sector in Australia; for a 10% change in relative prices the capital-labour ratio in the production sector adjusts by 10% in Australia but only by about 5.5% in New Zealand. However, when we re-ran our estimation using an error correction framework, Australia’s long-run elasticity estimate is 0.58 and significantly smaller than unity. Also, in both specifications, an F-test of the coefficients on interactions of a dummy variable with the log of relative prices and the log of the lagged capital labour ratio in a pooled regression (combining New Zealand and Australian data with the dummy equal to one if the observation is for Australia) failed to reject the hypothesis that both coefficients in the derivation of the long-run elasticity estimate are statistically different from New Zealand’s, indicating that the Australian and New Zealand long-run elasticity estimates are not statistically different.

It has often been argued (see IMF, 2002, extension of that report) that the different industrial structures of New Zealand and Australia could play a role in the capital intensity gap between the two countries. In particular, the Australian economy is thought to have a relatively capital intensive mining and quarrying sector that accounts for a proportionately larger share of the Australian economy than the corresponding sector does in New Zealand. Also, the agriculture, fishing and forestry sector represents a larger proportion of the New Zealand economy than the Australian economy. In addition, New Zealand agriculture may be less capital intensive than is the broad-acre cropping and grazing that characterises much Australian agriculture.

To test whether the presence of the Mining sector, and in turn the Agriculture, Forestry and Fishing sector, has an impact on our results, we reran equation 11 excluding this sector,[13] and then excluding both sectors. Table 11 compares the results of our base case to the estimation when we exclude mining, and when we exclude both mining and agriculture, forestry and fishing. New Zealand’s long-run elasticity remains significantly lower than unity for both equations. However, the results show that the long-run elasticity of substitution in Australia becomes higher than the corresponding elasticity of substitution for New Zealand when Mining is excluded. Australia’s long-run elasticity becomes significantly greater than 1 when Mining is excluded, but is once again significantly lower than unity when both Mining and Agriculture are excluded. These results may indicate that the agricultural sector in Australia is very elastic in comparison with other sectors in Australia, and outweighs the inelastic nature of the mining sector. However, when we ran our model in an error correction framework, we found that the long-run elasticity for Australia when both sectors were excluded was 1.58, statistically greater than unity. Also, an F-test from the pooled regression (of the coefficients on the interaction terms of the dummy variable with the two parameters included in the long-run elasticity computation) - in both the form of equation 11 and in an error correction framework - failed to reject the null hypothesis that both coefficients are not statistically different from zero. This result indicates that while Australia’s long-run elasticity may be greater than New Zealand’s when Mining is excluded, they are not statistically different when both mining and agriculture are excluded.

This evidence conflicts with the conclusions drawn by Diewert and Lawrence (2003), who found that excluding the Mining and Quarrying sector, although leading to a marginal increase in New Zealand’s capital intensity relative to Australia, was unlikely to lead to significant differences. They concluded the same thing when the Agriculture, Forestry and Fishing sector was excluded.

Table 11: Estimation of the elasticities of substitution when Residential Housing or the Mining and Quarrying Sector
or both the Mining and Quarrying and the Agriculture, Forestry and Fishing Sectors are excluded
Dependent Variable: ln(K/L) Excluding Housing Excluding Mining Excluding Mining and Agriculture, Forestry and Fishing
Australia New Zealand Australia New Zealand Australia New Zealand
Log of relative prices (β1) 0.30*
(1.91)
0.27***
(4.33)
0.57**
(2.42)
0.34***
(8.18)
0.33
(1.74)
0.33***
(7.23)
Time Trend (β2) 0.003
(0.61)
0.009***
(4.13)
-0.004
(-0.53)
0.006***
(6.66)
0.003
(0.35)
0.006***
(5.76)
Log of lagged capital-labour ratio (β3) 0.68***
(3.61)
0.50***
(4.71)
0.59**
(2.36)
0.45***
(5.46)
0.54*
(1.95)
0.42***
(4.50)
Long-run elasticity of substitution 0.94
(-0.35)a
0.54***
(-14.47)a
1.39**
(2.04)a
0.62***
(-14.88)a
0.72*
(-1.73)a
0.57***
(-16.87)a
Adjusted R-squared 0.98 0.96 0.97 0.93 0.98 0.89
Breusch-Godfrey (order 1) 5.48** 0.96 3.09* 1.99 3.66* 2.49

The t-ratios are given in parentheses below the coefficient estimates.

*= sig. at 10% level, **=sig. at 5% level, ***=sig. at 1% level

a: These t-ratios were calculated using the Delta method and indicate whether the long-run elasticities are statistically different from one.

A final test of robustness with respect to changes in the definition or measurement of the capital stock was made by re-estimating the basic model (equation 11) using a series obtained from the OECD.[14] These data comprise direct estimates of the capital stock in contrast to the estimates based on the Perpetual Inventory Method that we have adopted in this paper. The one main difference is that we used a flat 6% depreciation rate for all types of assets, whereas the new OECD capital stock uses different depreciation rates for different asset types. By using the same depreciation rate for all assets, we may be overstating the actual size of the Australian capital stock compared to New Zealand, as (in particular) Australia has more ICT capital than New Zealand, which arguably has a higher depreciation rate compared to other asset types. Thus by re-estimating our equation using the new OECD capital stock estimates, we are analysing how much of an effect the use of a constant depreciation rate has on our results.

The results are summarised in Table 12. As the OECD data excludes housing capital the relevant long-run comparisons are given by 0.94 for Australia and 0.54 for New Zealand (using the perpetual inventory method) and 0.67 for Australia and 0.93 for New Zealand based on the OECD capital stock data. Clearly this implies that the New Zealand economy (in particular the production sector) is rather more responsive to changes in the relative factor prices than given by the original estimates, while the Australian economy is considerably less responsive. In fact, our long-run estimate for New Zealand changes from being statistically different from one when we use our original data, to being not significantly different from one when we use the OECD capital stock data (and vice versa for Australia). This suggests that our assumption of a constant depreciation rate across asset types may have a significant effect on our results. However, when we ran our model in an error correction framework using this new data, we found New Zealand’s long-run elasticity to be significantly lower than unity (although still higher than the long-run estimate for Australia).

Table 12: Estimates of the short and long-run elasticity of substitution between capital and labour for New Zealand
using the new OECD capital stock data
Dependent Variable: ln(K/L) Base Case Excluding Housing Using new OECD capital stock
Australia New Zealand Australia New Zealand (adjusted)b
Log of relative prices (β1) 0.30*
(1.91)
0.27***
(4.33)
0.42***
(3.85)
0.39***
(5.01)
Time Trend (β2) 0.003
(0.61)
0.009***
(4.13)
0.004
(1.15)
0.009***
(4.35)
Log of lagged capital-labour ratio (β3) 0.68***
(3.61)
0.50***
(4.71)
0.37**
(2.39)
0.58***
(6.33)
Long-run elasticity of substitution 0.94
(-0.35)a
0.54***
(-14.47)a
0.67***
(-5.49)a
0.93
(-1.19)a
Adjusted R-squared 0.98 0.96 0.98 0.96
Breusch-Godfrey (order 1) 5.48** 0.96 4.16** 0.49

*= sig. at 10% level, **=sig. at 5% level, ***=sig. at 1% level

a: These t-ratios were calculated using the Delta method and indicate whether the long-run elasticities are statistically different from one.

b: An adjustment was made in the OECD capital stock data for New Zealand by replacing an apparent outlier in 1992 with the average values for 1991 and 1993.

Notes

  • [13]The relative prices for the regressions excluding the Mining and Quarrying Sector are unadjusted for sole-proprietors income as data on self-employment is unavailable by sector.
  • [14]Paul Schreyer, pers. comm..
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