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A Basic Model for Thinking about Investment and Productivity

The previous section established that New Zealand appears to have a low level of capital intensity (capital per unit of labour) and MFP compared to other OECD countries. We know from the analysis above that these two gaps must account for the gap in the level of labour productivity between New Zealand and these countries. However, without an economic model, we can’t understand how these variables interact. This section lays out a basic model. The model has the following key building blocks:[3]

An economic model helps frame thoughts about capital accumulation and productivity
  • As mentioned in the introduction, MFP is mainly driven by the environment for innovation and other underlying factors. (The most important drivers of MFP are the subjects of the other Productivity Performance and Policy papers mentioned in the introduction.) The model simply assumes a level of MFP for each country (that is, MFP is exogenous).
  • An increase in MFP raises the productivity of capital and the return to investment in capital, spurring investors to increase the stock of capital. Capital may come from domestic or foreign savers.
  • There may be “impediments” that get in the way of this process of capital accumulation, preventing investors from taking advantage of profitable opportunities presented by MFP growth. Another way of defining these impediments is to say that they elevate the cost of capital above the return received by capital.
  • The model has a “long-run” focus, meaning that it abstracts from business cycle and currency fluctuation issues.[4]

Caselli and Feyrer (2006) call this the “standard neoclassical one-sector model”. Although, as we will see in a later section, it leaves out potentially important complications, the model is very useful for organising thoughts about the relationship between capital intensity and productivity and is an essential reference point in the international literature that discusses relative capital-intensity across countries. A 1990 article by Lucas, titled “Why doesn’t capital flow from rich to poor countries?” kicked off a large amount of research on this subject.[5]

Although it is enough to keep in mind the three points listed above, it is also useful to briefly discuss a graphical representation of the model. Figure 6 shows the relationship between GDP per unit of labour (labour productivity or “Y/L”) and capital intensity (“K/L”), as determined by a country’s curved “production function”. The curved shape reflects the common assumption of diminishing returns to capital.[6] (That is, each additional unit of capital adds less and less extra output if labour is not also expanded.) The height of a country’s production function reflects the country’s level of MFP: a higher production function means the same level of capital intensity produces more output per unit labour. In line with the data presented in the previous section[7], New Zealand is drawn with a lower production function than the OECD comparator country[8]. Again, the model says nothing about what makes MFP high or low, but instead gets at the interaction between capital intensity and MFP in determining labour productivity.

Figure 6: Labour Productivity, Capital Intensity, and the Returns to/Cost of Capital
Figure 6: Labour Productivity, Capital Intensity, and the Returns to/Cost of Capital.

The marginal product of capital is the extra amount of output produced by one extra unit of capital, holding labour constant. This marginal product can be read in the graph as the slope of the production function at any given point. Moving along a production function, the marginal product of capital falls as capital intensity increases (again, this reflects diminishing returns to capital). Assuming capital markets are competitive, then the marginal product of capital defines the return to capital, which in turn equals the cost of capital. In other words, investors compete hard for investment opportunities, with the result that they are willing to bid and pay for investment projects until the extra amount of output that the unit of capital will produce just covers the financing cost.[9]

The model shows how a low level of MFP can be held responsible for both low capital intensity and low labour productivity

We can use Figure 6 to consider two scenarios. First, consider the case where capital can flow freely across borders without encountering any frictions or impediments. Under this assumption, capital markets will equalize the return to capital in both countries. (In other words, savers in New Zealand wouldn’t finance any projects in New Zealand that offered lower returns than any available opportunity in the comparator country, and vice versa.) The graph shows that New Zealand’s capital intensity and labour productivity will be lower than the comparator country’s whenever the return to capital is equal in both countries (that is, whenever they are both at points where the slopes of their respective production functions are equal), as is the case where the comparator country is at point A and New Zealand is at point B. In this scenario, we can say that New Zealand’s lower level of MFP drives New Zealand’s lower level of capital intensity and thus is ultimately responsible for the entire labour productivity gap between the two countries. Note that the kind of accounting analysis discussed in the previous sections indicated that New Zealand’s low capital intensity and low MFP are both components of the labour productivity gap. The model allows us to see the deeper point that, in this scenario, low MFP is entirely responsible for New Zealand’s low labour productivity (as well as for New Zealand’s low capital intensity).

The model also shows that an elevated cost of capital can drive capital intensity below the level otherwise justified by the level of MFP

Now consider the second scenario, where investors encounter an impediment that drives a wedge in New Zealand between the marginal product of capital and the return received by the investors. For example, imagine that New Zealand has an underdeveloped financial system that adds costs as it funnels capital to New Zealand investment projects. (Note that this impediment affects all investments in New Zealand equally – no matter whether the source of the funding is from savers in New Zealand or elsewhere.) In this case, marginal New Zealand investment opportunities that have a higher marginal product than alternatives in the comparator country will not receive funding because of the costs associated with the impediment. That is, New Zealand capital intensity and labour productivity will be lower than in the absence of the impediment, as at point C. At point C, we can say that New Zealand’s low labour intensity is partly due to low MFP and partly due to the impediment. We can also say that, at point C, New Zealand faces a “high cost of capital”, has a “high marginal product of capital” or pays a “high return to capital”. These are all just different ways of stating the same thing.

To put the results from these two scenarios in yet another (more informal) way, New Zealand at point B simply lacks good opportunities for investment (that is, “lacks demand” for investment) that would allow its capital intensity to catch up with the comparator country’s. In contrast, at point C, New Zealand has relatively high value (high marginal product) unfilled investment opportunities requiring capital, but investors (both domestic and foreign) are unwilling to finance them due to the extra costs that would be caused by the impediment.

To sum up, the model has three important implications:

  • New Zealand’s low capital intensity can be thought of at least partly as a by-product of New Zealand’s low MFP.
  • There may also be impediments driving New Zealand’s cost of capital upward and driving the capital stock downward below the level that would be justified by New Zealand’s MFP.
  • Policymakers should focus on boosting MFP. (In the model, this will always lead to increases in capital intensity and labour productivity, regardless of the existence of impediments.) However an important additional goal should be the removal of impediments, if they can be identified. This is discussed further in the section on policy conclusions.

In a later section, this paper will introduce complications to the model and discuss whether they change these implications. But first, the next section asks whether it is possible to tell whether New Zealand suffers from an impediment to capital accumulation – that is, whether we can think of New Zealand as being at point B (no impediment) or point C (impediment) in Figure 6.

Notes

  • [3]This model is also discussed in Treasury (2005).
  • [4]Purchasing power parity holds and there is no consideration of separate currencies.
  • [5]Lucus (1990)
  • [6]A later section briefly discusses increasing-returns production functions.
  • [7]While the data in the previous section is for a single year and may not represent a ‘long run’ equilibrium position as the model assumes, it is a good reflection of New Zealand’s position relative to most OECD countries in terms of capital intensity and MFP performance.
  • [8]This can be thought of as a representative OECD country that has higher capital intensity and MFP than New Zealand.
  • [9]This simple model abstracts from risk and sources of firm finance (debt and equity) that feature in the weighted average cost of capital (WACC) approach.
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