# 6.4  Allowing for dynamic effects

While equation (10) represents a long-run equilibria position, it may well be the case that there are lags in reaching a new equilibrium level of the capital intensity following a change in factor prices. We would not expect firms to be able to adjust instantaneously when the price of labour changed relative to the cost of capital. It is likely therefore, that the ability to change in the short run as depicted by the elasticity of substitution, would be less than the adjustment we would observe in the long-run. Therefore, we allow for lags in adjustment by estimating the following regression equation for both New Zealand and Australia:

(11)

This specification is useful because both the long-run and short-run estimates of the elasticity of substitution are easily extracted.[10] The short-run elasticity is given by the estimate of β1 while the long-run elasticity is calculated as .

An important issue when dealing with macroeconomic time series is the problem of spurious regression. If the time series used in the analysis are non-stationary, the results of the estimation could be spurious as the classical t and F tests are based on the assumption that the variables are stationary.

Szeto (2001) notes that there are three approaches to the problem of spurious regression. The first approach is to difference the data before estimating. The second approach is to add the lags of the dependent variable. Finally one may consider the cointegration approach.[11] In our specification we include the lag of the dependent variable so as to estimate the long-run elasticity of substitution. Therefore we estimate the model in levels rather than in differences. We present unit root tests in Appendix 2, and also test the sensitivity of our results by running the relationship in first differences, as well as in an Error Correction (cointegration) framework.

The results of estimating equation (11) with annual data from 1987 to 2002 are given in Table 8. The short run elasticities are similar in magnitude for the two countries, at 0.30 for Australia and 0.31 for New Zealand. However, in contrast to that for New Zealand, Australia’s short-run elasticity is not statistically different from zero.

Table 8: Estimates of the short and long-run elasticity of substitution between capital and labour for Australia and New Zealand
Dependent variable: ln(K/L) Australia New Zealand
Coefficient Estimate t-ratio Coefficient Estimate t-ratio
Log of relative prices (β1) 0.30 1.58 0.31*** 4.28
Time Trend (β2) 0.003 0.58 0.007*** 3.90
Log of lagged capital-labour ratio (β3) 0.62*** 3.10 0.61*** 5.88
Long-run elasticity of substitution 0.78* -1.40a 0.79*** -3.40a
Breusch-Godfrey (order 1) 6.82*** 0.47

*= 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.

The long-run elasticities are also very similar. The results presented in Table 8 indicate that for a 10 percent change in relative prices, both Australia’s and New Zealand’s capital-labour ratios will adjust by 8 percent in the long run. Both long-run estimates are significantly different from one, indicating that the Cobb-Douglas specification (with a unitary elasticity of substitution) may not be appropriate for both countries.

The results in Table 8 were generated using data for the period 1987 to 2002. This allowed for the adjustment to be made for the earnings of sole-proprietors. The same model was re-run using unadjusted relative prices for the period 1978 to 2002. The results of this estimation are given in Appendix Table 1. Both the short-run and long-run estimates of the elasticity of substitution are very similar for both New Zealand and Australia, and the long-run estimates are both significantly lower than unity.

Both countries have implemented a series of economic reforms which one might have expected would have enhanced the responsiveness of the productive sector to changes in its operating environment. In a world of highly regulated labour and capital markets with limited access to foreign capital, it would seem plausible that the capacity of firms to adjust to changes in the economic environment would be more constrained. They would have greater difficulty in obtaining finance and restructuring their labour force in order to take advantage of new circumstances.

On the other hand, a deregulated environment introduces new sources of uncertainty, and it is entirely conceivable that economic agents will hesitate to make significant new investments until they feel sufficiently certain about the future expected payoffs. This could mean that initially it would take longer for a change in relative factor prices to trigger new capital investment or hiring; or alternatively that the same changes in relative factor prices would generate a smaller response in the capital intensity.[12]

Ultimately, the effect of the economic reforms on the responsiveness of firms, as measured by the elasticity of substitution of capital for labour, becomes an empirical question. In order to test whether the responsiveness has in fact varied over time, we re-estimated equation (11) by adding a term for the interaction between time and the relative factor price as follows:

(12)

The results for this estimation are summarised in Table 9. It is found that the coefficient on the interaction term is not significant for New Zealand or Australia, suggesting that the responsiveness in both countries is not changing over time. Naturally one should exercise caution when interpreting this result. We have no basis for extrapolating beyond the sample period to argue that the elasticity of substitution will continue to remain constant in both countries. Also, we cannot make any judgement as to whether the elasticity has been changing prior to 1987 (the beginning of our sample period).

Table 9: Estimates of the short run elasticity of substitution allowing for variation over time
Dependent variable: ln (K/L) Australia New Zealand
Coefficient Estimate t-ratio Coefficient Estimate t-ratio
Log of relative prices (β1) 0.19 0.99 0.30** 2.61
Time trend (β2) -0.07 -1.29 -0.005 -0.07
Log of lagged capital-labour ratio (β3) 0.43 1.80 0.60*** 4.96
Long-run elasticity of substitution 0.33*** -6.76a 0.74** -2.64a
Interaction time trend term (t*log of relative prices) (β4) 0.02 1.35 0.003 0.17
Breusch-Godfrey (order 1) 5.68** 0.57

Note : Based on equation 12.

*= 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.

# 6.5  Assessing the contribution from relative prices on the capital-labour ratio gap between New Zealand and Australia

We also follow Rao, Tang and Wang (2003) and re-estimate equation (11) as New Zealand relative to Australia:

(11)

This equation may be interpreted with the help of Figure 19 below.

If the long-run coefficient () is equal to one, this implies that for any change in the relative prices in New Zealand relative to the prices in Australia, the gap in the capital-labour ratio will increase or decrease by the same amount. For example, if wages in
New Zealand increase by 10% relative to wages in Australia (holding the price of capital constant in both countries), the gap between the capital-labour ratios will decrease by 10% (that is, the capital-labour ratio in New Zealand will increase relative to the capital-labour ratio in Australia).

The significant coefficients presented in Table 10 suggest that the capital intensity gap between New Zealand and Australia will in part be determined by the gap in the relative prices between the two countries. As the relative factor prices in New Zealand increase relative to Australia (a movement to the right along the horizontal axis in Figure 19), there will be a less than proportionate change in the capital intensity relative to Australia. This follows from the estimated long-run coefficient of 0.5 (Table 10). This finding is consistent with the fact that differences in the trends of the relative prices in New Zealand and Australia played a significant role in the widening of the capital intensity gap between the two countries. As the price of labour decreased in New Zealand relative to that in Australia, the capital intensity gap increased (see Figures 9 and 18).

Table 10: Response of capital intensity in New Zealand relative to Australia.
Dependent Variable: Relative capital-labour ratio Coefficient Estimate t-ratio
Short Run Real price of labour relative to capital in New Zealand relative to Australia (β1) 0.19*** 4.77
Lagged relative capital-labour ratio (β2) 0.62*** 5.29
Long Run Real price of labour relative to capital in New Zealand relative to Australia 0.50 -