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# 2  Data

## 2.1  Measuring the Capital Stock

The measurement of capital is one of the nastiest jobs economists have set to statisticians.

((Hicks 1981): 204)

### Perpetual Inventory Method

While the System of National Accounts (SNA) ensures consistent investment data for international comparisons, there are no such guidelines for producing capital stock series. Therefore we use the Gross Fixed Capital Formation series contained in the OECD national accounts to construct capital stock data.[1] The method used to construct capital stock data from investment flow data is that set out in Caselli (November 2003), using the perpetual inventory equation:

(1)   Kt = Lt + (1-δ)Kt-1

where Ltis investment and δ is the depreciation rate. The initial capital stock (K0) was calculated as:

(2)

where I0 is the value of the investment series in the first year available (1970 for all OECD countries except Czech, Hungary, Poland, and Slovak), and g is the average geometric growth rate for the investment series between 1970 and 1980. The depreciation rate δ was set to 0.06 following Caselli (November 2003).

The perpetual inventory method takes into account the continual additions to and subtractions from the stock of capital as new investment and retirement of old capital take place.

Caution must be used when analysing series created using this perpetual inventory method. While observations which occur later in the series will be fairly accurate, values near the beginning of the series should be interpreted with caution, as they are subject to the value assumed for the initial capital stock K0. Figure 1 shows the evolution of the capital stock for three different initial values.

The constructed capital stock series will also be sensitive to the choice of depreciation rate. Figure 2 shows three different capital stock series with the same initial capital stock but different depreciation rates.

The capital stock used in this paper is based on an initial value of US\$105b (for New Zealand in 1995 prices) in 1970 and a depreciation rate of 6%.

### Land and Inventories

It has been argued that land and inventories should be included in any measure of the capital stock used in production (see Diewert and Lawrence 1999, Ahmad 2004). The rationale for recognising capital services from inventories is based on the idea that the inventory holder provides security of supply or the ability to provide goods at a later date. Land also provides capital services in that it may be utilised for production at some point in the future.

However, the current SNA has no role for inventories or land as inputs into production. Standard national accounting conventions usually treat the change in inventories as an output but do not include the stock of inventories as an input. Land is not included as an input perhaps because the quantity of land in use is seen to remain relatively constant over time, and hence can be treated as a fixed, unchanging factor in the analysis of production. However, Diewert and Lawrence (2000) state that even though the quantity of land is fixed, its price is not, and so neglecting land can have a substantial effect on aggregate input growth.

As New Zealand has no official data on the stock of land, the assumption must be made that the share of land in the total capital stock is similar between New Zealand and other comparator countries. If this assumption is violated (as could well be the case given New Zealand’s large agricultural base), the resulting level comparisons will be biased.

In two separate studies, Diewert and Lawrence (1999 and 2000) examine the effect of including land and inventories on the growth of TFP, for New Zealand and Canada respectively. In their 2000 paper, they found that excluding land as a factor of production in Canada increases the average growth rate for capital services and hence decreases TFP growth. When both inventories and land were dropped as factors of production, the average growth rate for real capital services increased further, and further decreased the average TFP growth rate, since inventories have grown much more slowly than other types of capital in Canada.

In their 1999 paper, Diewert and Lawrence concluded that the impact of excluding land from the coverage of inputs had a negligible impact on TFP in New Zealand. They argued that this was because land has a relatively small (ex post) user cost and consequently has a small weight in forming the overall index of total inputs. The main reason for land’s relatively small user cost was due to the fact that they did not include a depreciation component – they assumed that maintenance activities picked up elsewhere lead to the quality of land being held constant through time. However, they also made this assumption in their 2000 paper for Canada.

The difference in the findings comes down to the different user cost assumptions. They state that depending on what methodology is used to measure user costs, including land can potentially have a significant impact on measured TFP. The effect of including land (whose quantity remains constant over time and therefore provides an offset against other inputs whose quantities are usually increasing through time) is reinforced in their 2000 paper by the user cost approach as rapidly increasing land prices give progressively more weight to the constant quantity of land. In their 1999 paper for New Zealand they use a more “sophisticated” ex post user cost method which largely negates this effect, as the asset specific capital gains term offsets and in some cases exceeds the interest rate term leading to a small user cost value.

The capital stock calculated for this paper excludes both inventories and land. However, as a preliminary investigation, we added the Business and Agricultural Land data from Diewert and Lawrence (1999) to our capital stock data for New Zealand, and data on Rural and Commercial Land for Australia from the Australian Bureau of Statistics (2005). Figure 3 shows the result of doing this for the years for which data were available. When land is added to the capital stock, New Zealand appears to have a similar level to that in Australia (at least up to 1998), although the general downward trend is preserved if moderated. This suggests that the omission of land from the capital stock data may play a large role in concluding that New Zealand is capital-shallow compared with Australia. However, the indicator presented in Figure 3 is a very crude approximation; this warrants further investigation which we plan to undertake in future.

### Human Capital

Another important aspect of the total capital stock of an economy which is often ignored in capital stock measures is the stock of human capital. It is not yet standard practice for official statistical agencies to include human capital in their capital stock measures, although Jorgenson and Fraumeni, as early as 1989, proposed a new system of national accounts for the US in which human capital was included in an extended notion of the total capital stock.

Le, Gibson and Oxley (2002) (using a lifetime labour income method outlined by Jorgenson and Fraumeni, 1989, 1992a, 1992b) made some preliminary comparisons between the physical capital stock within New Zealand and the human capital stock. They found that the value of the human capital stock was approximately twice that of the physical capital stock within New Zealand, and this ratio had been rising from 1986 to 2001. In contrast, using Wei’s (2001) estimates, the Australian ratio of human to physical capital appeared to be falling, and was lower than New Zealand’s ratio in 1996. This suggests that New Zealand may not be capital-shallow compared to Australia if we were to adopt an extended notion of the capital stock. However, we do not include human capital in our measure of the capital stock in this paper.

#### Notes

• [1]See Appendix A for a description of the data.
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