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

6.2  Evidence on relative factor prices

What does the evidence suggest about the relative price of labour to capital? New Zealand appears to have a consistently lower price of labour relative to capital than Australia, as shown in Figure 17. Furthermore, this gap has persisted for over a decade and has widened over time. This would in part explain both the observed lower capital intensity in New Zealand, and the fact that the capital intensity has continued to fall relative to Australia (see Figure 9). The IMF (2002) concluded that the existence of different capital intensities between New Zealand and Australia reflects different relative factor costs. They also concluded that the difference in the relative factor prices is due mainly to the higher relative wage growth in Australia.

Figure 17: The relative price of labour to capital in Australia and New Zealand: 1987 - 2002
The relative price of labour to capital in Australia and New Zealand: 1987 - 2002
Source: OECD and Statistics New Zealand.

Another way to view the relative factor prices is to plot the ratio of the factor prices in New Zealand relative to Australia. This is done in Figure 18 where we see that while the relative prices were comparable at the end of the 1980s, by 2002 the ratio in New Zealand had fallen to about 60 percent of the comparable level in Australia. In short, labour has continued to become cheaper relative to capital in New Zealand, encouraging firms to use more labour relative to capital than in Australia, and arguably leading to a lower capital intensity in New Zealand.

Figure 18: Ratio of the factor prices in New Zealand relative to Australia
Ratio of the factor prices in New Zealand Relative to Australia
Source: OECD and Statistics New Zealand.

To what extent is the difference in relative prices being driven by the lower wage growth in New Zealand? Table 7 shows that, in 2002, the gap in relative prices between New Zealand and Australia was mainly due to a lower wage rate in New Zealand (63%), with 37% of the difference due to a higher return to capital in New Zealand. Black et al (2003) also point out that, along with the implementation of the ECA which was at least in part responsible for lower real wage growth in New Zealand relative to Australia after 1991, lower skilled workers finding employment in the 1990s could have contributed to the lower labour productivity growth in New Zealand relative to Australia. This in turn would imply lower real wage growth in New Zealand compared with real wage growth in Australia.

Table 7: The contributions to the gap in relative prices between New Zealand and Australia
2002
Relative w/r in New Zealand (Australia=100) 63
Relative wage rate in New Zealand (Australia=100) 74
Relative return to capital in New Zealand (Australia=100) 119
New Zealand-Australia Gap in w/ra -0.47

Made up of (%):

w 63
r 37

a: This value is the logarithm of relative prices (w/r) ratio for New Zealand minus the logarithm of relative prices in Australia, both measured for 2002. The negative sign reflects the fact that the Australian relative price ratio was some 47% higher than in New Zealand in that year.

To this point we have explored differences in the capital intensity that might have arisen due to differences in relative factor prices. However as shown in Figure 12, differences in the capital-labour ratio could also reflect differences in the underlying production function.

A key parameter that characterises a production function is the elasticity of substitution between labour and capital. This parameter describes how the capital intensity responds to changes in the relative price of labour to capital. For example if the real wage rises relative to the cost of capital, do we observe firms moving to a more capital intensive form of production by substituting capital for labour? The elasticity of substitution is defined as:

(7)     

where w/r is the relative price of the factors with w the real wage rate and r being the cost of capital. We test for differences in the elasticity of substitution in the following section.

It should be noted that the concept embodied in the term r is typically defined as the post tax cost of capital. Ideally we want a measure that is relevant to those taking the decisions on the mix of capital and labour to employ. As investment in capital is undertaken with a horizon spanning several years, then arguably an appropriate measure would be the expected return to capital. In this study we have used estimates of the realised return to capital as the proxy for the variable r. This measure will incorporate unanticipated variations due to changes in economic conditions not foreseen at the time the initial investment was made. In the long run one would expect these unanticipated elements to cancel out. Using our proxy for the cost of capital (operating surplus divided by the capital stock), Australia’s real cost of capital in 1999 was 91% of New Zealand’s real cost of capital. This is broadly in line with that estimated by Lally (2000) combining the real cost of debt capital with the (estimated) real cost of equity capital; he found that the real cost of capital in Australia was 93% of New Zealand’s real cost of capital.

6.3  Do the Underlying Production Functions Differ?

The Cobb-Douglas functional form is the most widely known and perhaps still the most widely used model to represent the production structure in economic theory. However, it has sometimes proved inadequate in empirical studies. Diewert and Lawrence (1999) conclude that “The Cobb-Douglas functional form is simply not flexible enough to model adequately trends in the New Zealand economy.” The simple Cobb-Douglas production structure is inflexible in two separate ways: (a) it imposes an elasticity of one between each pair of inputs and (b) it does not allow for differential rates of technical progress across inputs and outputs (Diewert and Lawrence, 1999). Szeto (2001) tested empirically the hypothesis that New Zealand has a unitary elasticity of substitution. He found that the Cobb-Douglas production structure is not empirically valid for the New Zealand economy, and subsequently estimated an elasticity of substitution of approximately 0.5.

As our concern here is to estimate the elasticity of substitution and in particular to explore if the value for New Zealand differs from that in Australia, we need to adopt an approach that does not constrain the value to be the same in both countries. To this end we have used a Constant Elasticity of Substitution (CES) form of the production function. In this case, the degree of substitutability between the inputs is always the same, regardless of the level of output or input proportions, but is not constrained to be equal to unity as in the case of a Cobb-Douglas production function.

The CES production function may be written in the form[9]:

(8)    

where Y is output, A is a measure of exogenous technical progress, L is labour input, K is capital input, λ and μ are the rates of labour and capital augmenting technical progress, α is the share of labour used in production, and the elasticity of substitution (δ ) is equal to .

Including labour and capital augmenting technical progress allows us to control for the “identification problem in CES production function analysis” (Johnson 1972). The identification problem arises because the biased efficiency growth and the elasticity of substitution are both varying simultaneously over time, and one must be held constant to isolate or “identify” the other. By defining efficiency units in terms of relative productivity (as in equation 8), the shift in the isoquant is now normalised, and the marginal rate of substitution between the factors remains the same for constant ratios of the factors measured in efficiency units. Efficiency growth is now embodied in the factors of production. This allows us to define an equation for estimating the elasticity of substitution.

Taking the firm’s cost minimisation problem (equating marginal products to real factor costs) and assuming that firms take factor prices as given, we get the following relationship:

(9)     

Taking logs we get the following linear equation:

(10)     

where .

Notes

  • [9]This form assumes that there are constant returns to scale in production.
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