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

5  Returns to Capital

5.1  Theoretical Considerations

In a basic model of economic growth where capital is perfectly mobile, capital will flow to countries with the highest rates of return. With the assumption of diminishing returns to capital, these countries will be the ones which are relatively capital shallow. This can be shown with the help of Figure 11. If we assume that New Zealand and Australia have identical production functions, then New Zealand, with a lower capital-labour ratio than Australia, will lie at some point B. At this point it can be seen that there is a higher return to capital; that is, the slope of the tangential line at point B is higher than at point A.[6]

Figure 11: Differences in capital intensity: the case of identical production functions
Differences in capital intensity: the case of identical production functions

Alternatively, the different capital intensities might arise from differences in the underlying production functions, despite both countries facing the same relative prices for labour and capital. This case is illustrated in Figure 12. A country lying at any point along the lower production function has a lower multifactor productivity level, as any given amount of capital per unit of labour will produce less output per unit of labour. In this case, both countries may have the same return to capital (points A and C), but the country at point C has a relatively low capital-labour ratio due to its relatively low MFP. Alternatively, the country with a lower MFP level may also have a higher return to capital, thus lying at point D in the diagram. In this case there could be a “wedge” that impedes capital flows to the country at point D.

Figure 12: Differences in capital intensity: the case of different production functions
Differences in capital intensity: the case of different production functions

5.2  Empirical Evidence

Our previous investigation suggests that New Zealand may have a somewhat lower level of MFP compared to Australia (see Table 5). Therefore, the question which remains is whether New Zealand is at point C or point D in Figure 12. Both points C and D correspond to a lower capital intensity in New Zealand compared to Australia.

As a first step in this section we estimate the returns to capital in New Zealand and several other OECD countries by looking at the real operating surplus (converted to US dollars using PPPs) divided by the capital stock. Ideally, we would like to assess the rate of return which firms use when deciding whether to invest. That is, we want to look at an ex ante (expected) marginal return to capital investment. However, the Operating surplus divided by the capital stock is a realised rate of return and as such is only a proxy for the expected return. Also, the operating surplus divided by the capital stock is a measure of the average return, rather than the marginal return which arguably governs decisions to undertake additional capital investment. In a Cobb-Douglas production function, the average and marginal returns are the same so this is not an issue. In the case of the constant elasticity of substitution production function, the average return is directly related to the marginal return[7]; thus the measure of operating surplus to the capital stock provides us with a reasonably good proxy of the return to capital which firms are facing.

Figure 13 shows the rate of return to capital in New Zealand, Australia, the UK, and the US, together with the OECD average. Until the early 1990s, New Zealand had a relatively similar rate of return to that of Australia, the UK, the US and the OECD average. Since 1993 New Zealand has had a higher rate than Australia, the UK and the OECD average, and since 1999 higher than the US as well.[8] This suggests that New Zealand may lie at the point D in Figure 12 when compared with Australia.

Figure 13: Average annual rates of return to capital for selected countries: 1978 - 2002
Average annual rates of return to capital for selected countries: 1978 - 2002
Source: OECD.

5.3  Adjusting for Sole-Proprietors

The 1993 System of National Accounts treats the labour income of the self-employed as capital income. As a consequence it is included in the measure of Operating Surplus instead of more logically as Compensation of Employees. Thus our estimates of rates of returns (calculated as Operating Surplus divided by the capital stock) will be overestimated. In this section we use a method proposed by Gollin (2002) to adjust our estimated rates of return to account for sole-proprietors’ income, and assess if this has much impact on the conclusions drawn in the previous section.

Figure 14 shows the adjusted rates of return for New Zealand and selected OECD countries. It is only possible to make the adjustment for New Zealand from 1987. However the adjusted rates of return show a similar pattern to those seen for the unadjusted rates, in that the real rate of return on capital in New Zealand appears to have been rising over the 1990s to end the period as the highest among the selected countries. Thus our conjecture from the previous section (that New Zealand may lie at point D in Figure 12 when compared with Australia) still holds when we adjust the Operating Surplus for sole-proprietors’ income.

Figure 14: Annual average rates of return adjusted for the income of sole proprietors: 1978 - 2002
Annual average rates of return adjusted for the income of sole proprietors: 1978 - 2002
Source: OECD.

However, these results must be treated cautiously. If we instead compare New Zealand to the US, New Zealand has a similar rate of return but a much lower capital-labour ratio. However, returns are only one part of the story – the capital-labour ratio depends not only on the price of capital but also on the price of labour (discussed in the next section). Thus we are concerned with the relative price of capital to labour, and in particular the difference in New Zealand’s relative prices compared to those in Australia.

Notes

  • [6]In this Solow-Swan framework, the country at point B will also have either a higher labour supply growth rate or a higher capital depreciation rate (or both) in equilibrium. See Solow (1956) for details.
  • [7]The marginal revenue of capital in a CES production function is equal to where is the average return.
  • [8]Rates of return that are computed neglecting inventories will be overstated, according to Diewert and Lawrence (1999), since the opportunity cost of capital due to holding inventories at the beginning of the period is neglected.
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