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

4.3  The gap in the growth of labour productivity

An alternative approach is to assess the contribution of the capital-labour ratio to the differences in the growth rate of labour productivity. Following Jorgenson, Gollop and Fraumeni (1987) we can express the growth in labour productivity as a function of the growth in multi-factor productivity and the growth of capital intensity as follows:

(4)      ΔIn(Y/L)t = ΔInMFPt + αΔIn(K/L)t

where the term on the LHS of the equation is the change from year t-1 to year t of the log of labour productivity; the first term on the RHS is the change in the log of multifactor productivity (from t-1 to t); and ΔIn(K/L)t is the change in the log of the capital-labour ratio from t-1 to t. The parameter α is the average income share of capital in years t-1 and t.

Although this Solow-type growth accounting framework has its limitations,[2] this methodology remains an important tool in productivity analysis, as it permits disentangling the relative contribution to output from the accumulation of factors of production and the efficiency in their utilisation (MFP).

Using equation (4),[3] we analyse the contribution of capital accumulation to labour productivity growth in New Zealand and Australia (see Table 4).

Table 4: Contributions to Labour Productivity Growth
  New Zealand Australia Australia minus New Zealand
  1987-1994 1995-2002 1987-1994 1995-2002 1987-1994 1995-2002
Growth in Labour Productivity 1.7% 1.4% 1.2% 2.4% -0.5% 1.0%

Made up of:

           
MFP 1.1% 0.8% 0.7% 1.1% -0.4% 0.3%
Capital intensity 0.6% 0.6% 0.5% 1.3% -0.1% 0.7%

Table 4 shows that 70% of the difference in labour productivity growth between New Zealand and Australia is due to the capital-labour ratio rather than MFP.[4] This is consistent with the finding by the IMF (2002) that around three-quarters of the gap in labour productivity is accounted for by the relatively lower capital intensity in New Zealand. From these findings, a case can be made that understanding why New Zealand’s labour productivity lags that of Australia depends critically on further insights as to why the capital intensity is lower. We explore this issue in Sections 5 and 6 of this paper.

4.4  The gap in the level of labour productivity

Using the growth accounting framework, we can also estimate the contribution of the capital intensity level gap to the New Zealand-Australia labour productivity level gap.

Table 5 gives this decomposition of levels based on the following relationship[5]:

(5)     

where is the average labour income share of both New Zealand and Australia, and the MFP gap is calculated as the residual.

Table 5: Contributions to the gap in the level of labour productivity between New Zealand and Australia in 2002
2002
Relative labour productivity in New Zealand (Australia=100) 77
Relative MFP in New Zealand (Australia=100) 83
Relative capital intensity in New Zealand (Australia=100) 72
New Zealand-Australia Gap in Labour Productivitya -0.26

Made up of (%)

MFP 42
Capital Intensity 58

a: This value is the logarithm of labour productivity (Y/L) for New Zealand ratio minus the logarithm of labour productivity in Australia, both measured for 2002. The negative sign reflects the fact that Australian labour productivity was some 25% higher than that in New Zealand in that year.

Table 5 shows that New Zealand’s labour productivity level was only 77 percent of Australia’s labour productivity level in 2002. From equation (5) above, this equates to a labour productivity gap of 26%. Of this, 58% can be explained by the lower capital intensity in New Zealand relative to Australia. The same decomposition was applied to all years from 1987 to 2002 and the results are plotted in Figure 10.

These results rely on our measurement of the capital stock which, as we discuss earlier, is sensitive to the initial value and depreciation rate used. However, not only does the IMF (2002) report similar results, when we calculate equation (5) using a series obtained from the OECD (discussed in more detail in section 6.6), we find that an even larger percentage of the labour productivity gap in 2002 can be explained by the lower capital intensity in New Zealand (73%).

Figure 10: Contributions to the labour productivity gap between New Zealand and Australia: 1987- 2002
Contributions to the labour productivity gap between New Zealand and Australia: 1987- 2002
Source: OECD and Statistics New Zealand.

4.5 Decomposing the output gap

An alternative approach is to decompose the output gap between New Zealand and Australia. In this way we can isolate the contributions from both capital and labour (as opposed to the capital-labour ratio). To do this, we re-write equation (5) as:

(6)     

Table 6 shows the percentage contributions to the output gap from capital, labour and MFP based on equation (6) from 1987 to 2002.

Table 6: Percentage contributions to the output gap between New Zealand and Australia: 1987-2002
Year Contribution from K Contribution from L Contribution from MFP
1987 39 53 8
1988 38 55 7
1989 39 56 5
1990 41 54 5
1991 42 52 5
1992 42 51 7
1993 44 50 6
1994 45 50 5
1995 46 49 5
1996 46 48 6
1997 45 48 7
1998 45 47 8
1999 45 47 8
2000 46 47 6
2001 47 46 7
2002 48 46 6

Note: These results were calculated using equation 6. Figures may not add up to 100 due to rounding.

While from 1987 until 2000 the contribution to the output gap between New Zealand and Australia from labour has outweighed the contribution from capital, the contribution from labour has been decreasing since 1990. Thus in 2001 and 2002 the difference in capital stocks between New Zealand and Australia accounted for more (marginally) of the difference in the relative outputs.

Notes

  • [2]The growth accounting framework is not a theory of growth in that it does not tell us what drives productivity growth, or input accumulation, or if there is any interaction between input accumulation and productivity growth; but it can help identify broad areas for focus.
  • [3]With MFP calculated as the residual.
  • [4]Care should be exercised in interpreting the residual (MFP) as a measure of the technological endowment of a country. Other factors are also included, such as changes in managerial practices, model misspecification and measurement problems
  • [5]See Nishimizu and Jorgenson (1995).
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