The New Zealand North and South Island dairy farms differ in terms of climate, soil type and farming history. Using stochastic frontier models, an unbalanced panel of 1,294 dairy farms for the period between 1998/99 and 2006/07 is employed to test the hypothesis that the two regions share the same technology (The New Zealand dairy season runs from 1 June to 31 May each year). Results indicate heterogeneity in production technology across farms located in different islands. A meta-frontier model proposed by Battese et al. (J Product Anal 21:91–103, 2004) and O’Donnell et al. (Empir Econ 34:231–255, 2008) is therefore used to calculate the technological gap and compare on-farm technical efficiency.
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Given this assumption, the simultaneous-equation bias often associated single-equation production models is avoided (Zellner et al. 1966).
O’Donnell et al. (2008) pointed increases in the (technology gap) ratio imply decreases in the gap between the regional frontier and the meta-frontier, the use of MTR instead of TGR helps avoid the confusion.
Capital stock itself is distinct from the flow of capital services obtained from it, and it is the later that should represent ‘capital’ in production functions. But data dictate what we can do; there is no detailed information to reflect capital stock durability and composition. The use of the capital stock concept instead of the service flow concept may bias the estimation results if the capital service flow is a function of capital vintage as shown by Yotopoulos (1967). This is especially a concern with the expansion that has occurred in the South Island, as the use of capital stock places more weight on the more durable asset, such as irrigation and new land purchased. It would be particularly useful if more information on capital is collected in future surveys.
This was a reasonable assumption to make in the NZ dairy inputs market.
Four farms in the sample have zero value observations for electricity expenses, 2 farms have zero observations for feed expenses, and 33 have zero observations for fertilizer expenditure. Given that the “zero cases” are not a significant proportion in the sample, and they are perceived to be useful in the estimation of parameters which are common to all farmers, we adopted the approach of including "zero cases" by using the value of one. See Battese (1997) for a more detailed discussion on handling a significant proportion of "zero observations" when estimating agricultural production functions.
This is similar to Mbaga et al. (2003), Saha and Jain (2004), and Hailu et al. (2005). The production unit is the 'cow' rather than the 'farm'. This specification implicitly assumes that the per-cow technology is invariant with respect to cows. It is also equivalent to impose CRTS on a production function with the 'farm' as the production unit and the 'cow' as an input on the right hand side. We acknowledge that for those who prefer to have the latter, the returns to scale (RTS) in this per-cow specification is not RTS in the usual sense, they might characterize changes in inputs per cow as changes in inputs mix. Therefore a researcher might want to consult on the production unit in practice before the specification of a production function.
Irrigation data was not collected for season 2001/02 so the variable cannot be used in constructing the frontier.
The average dairy land price went up by 91 % over this sample period.
The correlation coefficients of TE estimates obtained between CD and TL frontiers were in the range of 0.98 and 0.88 for this study.
Both the two-sample t test and the Wilcoxon rank-sum test reject the equality of mean TE scores between North Island and South Island at better than a 1 % significance level.
A New Zealand dairying regional map is attached in Appendix.
Waikato also has the largest number of observations.
The average TE is 92.3 % in 2006/07 for South Island as shown by Fig. 3, and the most efficient farm was estimated to have a TE score of 98.4 %.
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The authors would like to thank the editors and the two anonymous referees for their constructive suggestions and comments that led to significant improvement of the paper. The authors are grateful to Matthew Newman from DairyNZ for making the data available.
Appendix A: NZ dairying regional map
Appendix A: NZ dairying regional map
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Jiang, N., Sharp, B. Technical efficiency and technological gap of New Zealand dairy farms: a stochastic meta-frontier model. J Prod Anal 44, 39–49 (2015). https://doi.org/10.1007/s11123-015-0429-z
- Meta-frontier model
- Stochastic production frontier
- NZ dairy farming