Application of Data Envelopment Analysis to dairy farms in the Waikato and Marlborough- Canterbury regions

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1 Application of Data Envelopment Analysis to dairy farms in the Waikato and Marlborough- Canterbury regions Chris Dake 1 Nicola Shadbolt 2 Femi Olubode-Awosola 3 April Agricultural International Ltd 2 Massey University 3 AgResearch Ltd

2 Copyright Copyright in this publication (including text, graphics, logos and icons) is owned by or licensed to DairyNZ Incorporated. No person may in any form or by any means use, adapt, reproduce, store, distribute, print, display, perform, publish or create derivative works from any part of this publication or commercialise any information, products or services obtained from any part of this publication without the written consent of DairyNZ Incorporated. Disclaimer This report was prepared solely for DairyNZ Incorporated with funding from New Zealand dairy farmers through DairyNZ and the Ministry for Primary Industries under the Primary Growth Partnership. The information contained within this report should not be taken to represent the views of DairyNZ or the Ministry for Primary Industries. While all reasonable endeavours have been made to ensure the accuracy of the investigations and the information contained in the report, OneFarm, Centre of Excellence in Farm Business Management expressly disclaims any and all liabilities contingent or otherwise to any party other than DairyNZ Incorporated or DairyNZ Limited that may arise from the use of the information. Date submitted to DairyNZ: April, 2011 This report has been funded by New Zealand dairy farmers through DairyNZ and the Ministry for Primary Industries through the Primary Growth Partnership.

3 Table of Contents Tables... ii Figures... ii 1.0 Introduction Methodology DEA LP model Input price and allocative efficiency ANOVA test of farm systems Results Data used for the study DEA results Waikato region ANOVA results Waikato region Example input-oriented efficient frontier Waikato Region Target input reductions when inefficient farms are made efficient - Waikato Region DEA results Marlborough-Canterbury region ANOVA results Marlborough-Canterbury region Target input reductions when inefficient farms are made efficient - Marlborough-Canterbury region Example variable returns to scale production frontier Marlborough-Canterbury dairy farmers Discussion and Conclusion Inefficient input transformation and technical efficiencies Differences in farm systems Output, input variables and rental price of quasi-fixed inputs i Centre of Excellence in Farm Business Management

4 4.4 Errors of data measurement Including environmental emissions in DEA References Acknowledgements Tables Table 1 Summary of dairy farm survey data from Dairybase... 7 Table 2 Variable returns to scale technical efficiencies of farm systems Table 3 Number of efficient farms (with VRSTE = 1) in each farm system Table 6 ANOVA results (See Appendix 1 for detail results) Table 4 Example production characteristics of Farm Table 5 Input reduction targets Waikato region Table 7 Variable returns to scale technical efficiencies of farm systems Table 8 Number of efficient farms (with VRSTE = 1) in each farm system Table 9 Input reduction targets - Marlborough-Canterbury region Table 10 DEA candidate output and input variables Figures Figure 1 Efficient production frontiers under constant and variable return to scale... 5 Figure 2 Waikato Region: Data summary from Dairybase for the 85 farms in the Waikato region Figure 3 Marlborough-Canterbury Region: Data summary from Dairybase for the 44 farms in the Marlborough-Canterbury Figure 4 Technical efficiencies of dairy farms in the Waikato region Figure 5 Input-oriented production frontier of Waikato dairy farmers under variable returns to scale Figure 6 Technical efficiencies of dairy farms in the Marlborough-Canterbury region Figure 7 Input-oriented production frontier of Marlborough-Canterbury dairy farmers under variable returns to scale ii Centre of Excellence in Farm Business Management

5 1.0 Introduction This study explores the application of advanced modelling techniques for the analysis of the dairy farm business data contained in Dairybase. The study is in two parts. Part 1: the estimation of technical efficiencies of dairy farms in the Waikato and. This is discussed in this report. Part 2: the use of a Markov transition probability model to explain the distribution of dairy herd size over time. This is presented in a separate report. The Dairybase database contains dairy farm business data that can be used to improve the understanding of the relationships between production, profitability and efficiencies of dairy farming. The data has been voluntarily supplied by dairy farmers in New Zealand. Participating farmers, who are either owner-operators or 50:50 share milkers, contribute farm accounts and market values of fixed assets, and physical farm data to the database. Regional and national summary statistics of physical and financial performance of farms derived from the survey are published in annual reports by DairyNZ. Dairybase also provides benchmarks which can be used by farm business as reference for the purposes of monitoring and improving performance. This study reports on the development of a frontier efficiency model in which the relative efficiency of each dairy farm in the production of milk solids is estimated by comparing each farm to the best farms in the data sample. The frontier model is developed such that the best farms lie on the frontier. Two principal approaches can be used to estimate the efficient frontier. The first is a stochastic frontier approach (SFA) where a functional form of the production function is specified and econometric techniques are then used to estimate the model parameters and farm efficiencies (Coeilli, 1996a; Rae et al. 2008; Jiang, 2011). The second approach uses a data envelopment analysis (DEA) where a linear programming model of each farm is specified and used to estimate farm efficiencies (Charnes et al. 1978; Coeilli, 1996b; Rae et al. 2008). DEA is a non-parametric approach which does not require the prior specification of the functional form of the production function. 1 Centre of Excellence in Farm Business Management

6 The application of DEA/SFA in New Agriculture has been examined by Iyer and Rae (2007) and Rae et al. (2008) in their studies of productivity growth in New Zealand Agriculture. Specific applications of efficiency analysis in the New Zealand dairy industry can be found in Jaforullah and Premachandra (2003), Rae et al. (2008), Rouse et al. (2009) and Jiang, In this study the DEA approach is used to estimate dairy farm efficiencies in the production of milk solids in the Waikato and. The production of milk solids specified as a function of four inputs, farm size, peak cows milked, labour and operating farm expenditure is used to develop the efficient frontier. Statistical differences in technical efficiencies and financial performance of the five production systems, defined based on the use of imported feed, is presented in the report. DEAP software (Coelli, 1996b) was used to perform the data envelopment analysis with Win4DEAP (Deslierres, 2006), a MS Windows front end for DEAP, used to facilitate data entry and model execution. An initial objective of this study was to account for environmental inputs in the input-oriented DEA LP model (Reinhard et al., 2000). The plan was to use the OVERSEER nutrient balance model (Wheeler et al., 2003) to estimate environmental variables (GHG emissions, N leached and P loss) for each dairy farm in Dairybase. Unfortunately some of the physical data required for the OVERSEER nutrient balance model was no longer collected for most farms in Dairybase database. A literature review was prepared in anticipation of capturing environmental inputs in the DEA analysis. The literature review is provided in Appendix 2 (Section 8) with the hope that it would form a basis for a future DEA/Stochastic frontier study. The report is organised as follows: Section 2 presents the formulation of the DEA linear programming model that can be used to calculate technical efficiencies of farms and determine input saving targets for inefficient farms. 2 Centre of Excellence in Farm Business Management

7 Section 3 presents the results of the study, focussing on the differences in farm systems with regard to technical efficiencies, production, input and financial performance variables. Conclusions and discussions are presented in Section Methodology 2.1 DEA LP model A key assumption in the application of the DEA approach to dairy farming is that any farm in the data sample being used for the analysis is capable of adopting the output and input mix schedule of any other farm. The production schedule of farm peers can be combined to create a composite farm, called a virtual farm, which may not necessarily exist. An assumption implicit in DEA is that differences in the performance of farms are due to an inefficient transformation of inputs into outputs. A virtual farm corresponding to an existing farm, i, can be created from the following linear programming (LP) model for each farm (Coelli, 1996b). Min θ,λ θ (1) s.t. Y λ y i (2) θx i - X λ 0 (3) y i 0 (4) where θ is the efficiency score of the i-th farm. λ is the N x 1 vector of proportions of other farms used to construct the virtual farm. Y is the matrix of outputs of all farms in the sample and X is the corresponding matrix of inputs. 3 Centre of Excellence in Farm Business Management

8 The efficiency score is θ 1; if θ = 1 then farm is on the frontier and considered efficient. Constraint Equation (2) ensures the virtual farm produces at the least as many outputs as the farm under study. Constraint Equation (3) determines how much less input the virtual farm requires. If the virtual farm is capable of producing the required output (milk solids) with less input, then the farm under study is considered inefficient. The above formulation is known as input-oriented DEA since it determines how much less input is required to achieve the current production if the farm operated efficiently. An output oriented DEA determines how much extra production can be achieved from the current input use. Equations (1) to (4) yield efficiencies on the assumption that farms are operating at the optimal scale, that is at a constant returns to scale (CRS). The LP equations can be modified to calculate frontiers when variable returns to scale (VRS) are assumed (Coelli, 1996b) to allow the isolation of inefficiencies due to scale. Figure 1 shows an input-oriented DEA with one output and one input. The efficient VRS frontier is marked by farms A, C and E. Farm B is inefficient with the technical efficiency measured as the ratio, VRSTE = 0B v / 0B. The inefficiency due to scale can be calculated as shown in Figure 1. Point B v is the virtual efficient farm corresponding to the inefficient farm B; the virtual farm is created from the peer farms A and C, which are on the efficient frontier. Farm B can reduce input by B v B without reduction in output. 4 Centre of Excellence in Farm Business Management

9 CRS Technical efficiency CRS VRS E CRSTE = 0B c / 0B Output C D VRS Technical efficiency VRSTE = 0B v / 0B 0 Bc B v B Scale efficiency A SE = 0B c / 0B v Input Adapted from Coelli (1996b) and Kirner et al. (2007). CRSTE = VRSTE x SE A, B, C, D, E farms Figure 1 Efficient production frontiers under constant and variable return to scale 2.2 Input price and allocative efficiency The DEA LP model of Equations 1 4 can be used to estimate the technical efficiency of a farm. If price data is available then DEA LP model can be extended to estimate the level of input use that minimises costs (Coelli, 1996b) i.e. cost efficiency. Defining the following variables, * x i is the input use that minimises costs of the i th farm x i is the observed input use the i th farm p i is the vector of input prices of the i th farm then the total cost efficiency (CE) or the economic efficiency of the i th farm can be defined as: * CE = p i x i / p i x i (5) The allocative efficiency (AE) can be determined from the CE and the technical efficiency (TE) AE = CE / TE (6) 5 Centre of Excellence in Farm Business Management

10 The cost and allocative efficiencies are not calculated in this study due to lack of time and resources to calculate input prices; this issue is discussed further in Section ANOVA test of farm systems An analysis of variance (ANOVA) was used to test for differences between the five production systems for the following variables: milk solids, farm size, peak cows milked, labour, operating farm expenses, technical efficiency and total return on equity. A range of statistical tests relevant to DEA applications are presented by Banker and Natarajan (2004). The five production systems defined by DairyNZ are based on the timing and amount of imported feed used in production are described below (Ref): System 1: All grass, self contained 10-15% of owner-operator herds All grass. No supplement feed purchased. No cows grazing off the milking area. System 2: Dry cow feed purchased 35-40% of owner-operator herds Approximately 4-14% of total feed imported and fed to dry cows including dry cows grazing off the milking area. System 3: Feed purchased for dry cows and to extend lactation 30-35% of owner-operator herds Approximately 10-20% of total feed is imported to the milking area to extend lactation (usually autumn feed) and for dry cows. System 4: Feed purchased for dry cows and to extend both ends of lactation 15-20% of owner-operator herds Approximately 20-30% of total feed purchased at both ends of lactation and for dry cows. System 5: Feed purchased for year round feeding less than 5% of owner-operator herds (not reported separately due to low numbers) At least 30% of total feed imported all year round including for dry cows. 6 Centre of Excellence in Farm Business Management

11 3.0 Results 3.1 Data used for the study Data for the analysis was provided by DairyNZ (Unpublished) from a sample of 296 owner-operated dairy farms for the year: this represents about 4% of the owner-operated dairy farms in New Zealand. This data was voluntarily supplied by dairy farmers who contributed physical farm data, farm accounts and market values of fixed assets to the database. A DEA analysis was undertaken for the Waikato (85 farms) and Marlborough-Canterbury (44 farms) regions (Table 1). All five farm systems are represented in the Waikato region with farm systems 2 and 3 contributing over 71% of farms. 2 is not represented in the sample of farms provided for the Marlborough-Canterbury region and most farms (89%) were farm systems 3 (52%) and 4 (36%). Table 1 Summary of dairy farm survey data from Dairybase Regions Total 1 Northland Waikato Bay of Plenty Taranaki Lower North Island West Coast-Tasman Marlborough-Canterbury Otago-Southland Grand Total Variables used in calculating the technical efficiency of farms were milk solids, farm size, peak cows milked, labour and operating farm expenses (Other outputs and inputs that could have been included in the DEA model are discussed in Rouse et al and Jiang, 2011 and in Section 4.3). The calculated technical efficiencies together with data on total return on equity were used in the ANOVA analysis to test for differences in farm systems. 7 Centre of Excellence in Farm Business Management

12 Total return on equity data was not provided for 2 farms in each region. These farms were excluded from the calculation of summary data and ANOVA involving total equity. All 85 farms in the Waikato and 44 farms in Marlborough- Canterbury regions were used to estimate technical efficiencies. Although there appears to be a number of outliers in the graphs shown in Figure 2, no test was undertaken to identify and eliminate outliers. Figure 2A Figure 2B Milk solids (tonnes) Farm size (ha) Figure 2C Figure 2D Peak cows milked (no) Labour (FTE) Figure 2E Figure 2F 4, % Operating expenses ($000) 3,500 3,000 2,500 2,000 1,500 1, Total return on equity 900% 700% 500% 300% 100% -100% Centre of Excellence in Farm Business Management

13 Figure 2G Technical efficiency Figure 2 Waikato Region: Data summary from Dairybase for the 85 farms in the Waikato region. Two farms were excluded from the total returns on equity graph because of unavailable data. (See Section 4.2 for the technical efficiencies graph) 9 Centre of Excellence in Farm Business Management

14 Figure 3A Figure 3B Milk solids (tonnes) Farm size (ha) Figure 3C Figure 3D Peak cows milked (no) Labour (FTE) Figure 3E Figure 3F Operating expenses ($000) Total return on equity (%) 900% 800% 700% 600% 500% 400% 300% 200% 100% 0% -100% Figure 3G Technical efficiency Centre of Excellence in Farm Business Management

15 Figure 3 Marlborough-Canterbury Region: Data summary from Dairybase for the 44 farms in the Marlborough-Canterbury. Two farms were excluded from the total returns on equity graph because of unavailable data. (See Section 4.2 for the technical efficiencies graph). 3.2 DEA results Waikato region The calculated variable returns to scale technical efficiencies (VRSTE) are shown in Figure 2G and Figure 4. The average VRSTE, 0.85, is high, with a range from 0.62 to 1. The efficient farms (with VRSTE of 1) comprise 16% of farms in the region (Figure 4); and it is also notable that a further 21% of the farms have technical efficiency levels above % Number of farms % 22% 21% 16% < < < < 1 1 Techincal efficiency Figure 4 Technical efficiencies of dairy farms in the Waikato region There appears to be no difference in the five farm systems with regard to VRSTE (Table 2). The ANOVA results presented in Section 4.3 tests for significant differences in the 5 farm systems with regard to the variables shown in Table Centre of Excellence in Farm Business Management

16 Table 2 Variable returns to scale technical efficiencies of farm systems Farm system Count Milk solids (tonnes) Farm size (ha) Peak cows milked (nos) Labour (FTE) Operating expenses ($000) Total ROE (%) Variable returns to scale technical efficiency % % % % % Average % ROE: Total return on equity 1 calculated using 83 farm Efficient farms, with VRSTE = 1, are evenly distributed in each of the farm systems except farm system 1 where none of the farms is significant (Table 3). However one farm in farm system1 has a technical efficiency level of Differences in farm systems with regard to the variables shown in Table 3 when VRSTE level is 1 were not statistically tested because of the small numbers of farms involved. Table 3 Number of efficient farms (with VRSTE = 1) in each farm system Farm systems Count Milk solids (tonnes) Farm size (ha) Peak cows milked (nos) Labour (FTE) Operating expenses ($000) Total ROE (%) Variable returns to scale technical efficiency % , , % % , % 1.00 Average , % 1.00 ROE return on equity 12 Centre of Excellence in Farm Business Management

17 3.2.1 ANOVA results Waikato region A one-way ANOVA analysis was undertaken to test whether there were any significance differences between farm systems with regard to VRSTE and the other variables used in the DEA models. In view of the possible outliers noticed in the data (Figure 2), the data was rank transformed before analysis. The rank P values shown in Table 6 (further details in Appendix 1) indicate the null hypothesis of equal means of systems would be rejected at the 5% level for milk solids and operating expenses. The variable VRSTE was not significantly different between farming systems. Table 6 ANOVA results (See Appendix 1 for detail results) rank Milk solids rank Farm Size rank Peak cows milked rank Labour rank Operating expenses rank Total ROE rank Variable returns to scale technical efficiency Treatment P Tukey 5% = 2.79 Mean - Farm system 2 Mean - Farm system Sed t ratio ROE Return on equity Using Tukey s test for 5 treatment levels (farm systems) and 80 residual df, the critical value from the tables is At the 5% level, for milk solids and operating expenses where the overall test was significant, the only significant pairwise difference is between farm systems 2 and Centre of Excellence in Farm Business Management

18 3.2.2 Example input-oriented efficient frontier Waikato Region The estimated production frontier of Waikato dairy farms is shown in Figure 5 as a plot of milk solids vs. peak cows milked. Farms are either on the frontier (the efficient farms) or below the frontier (the inefficient farms). As an input-oriented approach, inefficient farms should be able to reduce the quantity of inputs and still maintain production at the current level. Figure 5 Input-oriented production frontier of Waikato dairy farmers under variable returns to scale Milk solids (tonnes/farm) ,000 1,500 2,000 2,500 3,000 3,500 Peak cows milked (no./farm) Frontier Farms The DEA model provides useful information that can be used to benchmark inefficient farms. Using farm 77 as an example: Farm 77 has a VRSTE of 0.82, and produces 416 t milk solids. Farm 77 is benchmarked against efficient peers which are farms 49, 38 and 85 (Figure 5). The peer weights used are shown in the Table (4): farm 49 has the biggest influence (0.741), followed by farm 85 (0.225) and farm 38 (0.034). 14 Centre of Excellence in Farm Business Management

19 The virtual farm created from the peers and peer weights suggests that the current input used can be reduced without reducing the current milk solid production of 416 t. For example, a target of 34% reduction in farm size can be achieved with a concomitant reduction in other inputs as indicated in Table 4. Farm size, cows milked and labour, may be considered quasi-fixed variables which cannot be altered easily and their effects last for more than 1 year from the time of purchase; this issue and the related concept of rental prices are discussed in Section 4.3) Table 4 Example production characteristics of Farm 77 (shown in Figure 4). Farm 77 Variable returns to scale technical efficiency (VRSTE) Milk solids production (tonnes) 416 Farm peers Peer weights Input use Current Targets % reduction Farm size (ha) % Peak cows milked (nos) 1,240 1,016 18% Labour (FTE) % Operating expenses) 2,462 2,017 18% 15 Centre of Excellence in Farm Business Management

20 3.2.3 Target input reductions when inefficient farms are made efficient - Waikato Region Following the example described in Table 4, the total input reduction that inefficient farms could achieve while maintaining production at current levels is shown in Table 5. The target reductions are farm area (18%), peak cows milked (16%), labour FTE (22%) and operating expenses (14%) while still maintaining milk production of 11,980 t milk solids. Table 5 Input reduction targets Waikato region Target input reduction Row Labels Current milk solid Production (t) Farm size (ha) Peak cows Milked (nos) Labour (FTE) Operating Expenses ($000) , , , , , , , , , Total 11,980 2,044 5, ,374 % Reduction 18% 16% 22% 14% 3.3 DEA results Marlborough-Canterbury region The variable returns to scale technical efficiencies (VRSTE) for Marlborough- Canterbury region are high with an average value of 0.96 (Figure 6 and Table 7), exceeding the average VRSTE of the Waikato region (0.85). The VRSTE of 82% of the farms exceeds 0.9, with 4 farm systems represented in sample exceeding values of 0.94 (Table 7). 16 Centre of Excellence in Farm Business Management

21 Number of farms % 39% 16% 2% 0.7 < < < 1 1 Technical efficiency Figure 6 Technical efficiencies of dairy farms in the Marlborough-Canterbury region Table 7 Variable returns to scale technical efficiencies of farm systems Farm system Count Milk solids (tonnes) Farm size (ha) Peak cows milked (nos) Labour (FTE) Operating expenses ($000) Total return on equity (%) Variable returns to scale technical efficiency % % % % 0.98 Average % 0.96 The proportion of farms that are technically efficient in the Marlborough- Canterbury region is 39% compared to 16% in the Waikato region (Table 3 and Table 8). 17 Centre of Excellence in Farm Business Management

22 Table 8 Number of efficient farms (with VRSTE = 1) in each farm system Farm system Count Milk solids (tonnes) Farm size (ha) Peak cows milked (nos) Labour (FTE) Operating expenses ($000) Total ROE (%) Variable returns to scale technical efficiency % % % 1 Average % 1 ROE return on equity ANOVA results Marlborough-Canterbury region An ANOVA analysis undertaken using ranked values of farm size, peak cows milked, labour, operating expenses, total return on equity and VRSTE did not show significant differences between farm systems. The estimated p-values range from (labour) to (VRSTE). The complete ANOVA results are shown in Appendix 8.2. In contrast, in the Waikato region differences between 2 and 4 were detected for milk solids production and operating expenses at the 5% level (Section 3.2.1) Target input reductions when inefficient farms are made efficient - Marlborough-Canterbury region Since VSTE of over 82% of farms in the Marlborough-Canterbury region exceed 0.9, the target input-use reductions required to maintain milk solid production at 15, 245 t from inefficient farms are low, ranging from 5% (operating expenses) to 12% (labour) (Table 9). The required input use reductions for the inefficient farms in the Waikato region range from 14% to 22%. 18 Centre of Excellence in Farm Business Management

23 Table 9 Input reduction targets - Marlborough-Canterbury region Milk solids (tonnes) Farm size (ha) Peak cows milked (nos) Labour (FTE) Operating expenses ($000) , , , , % Reduction 7% 6% 12% 5% Example variable returns to scale production frontier Marlborough-Canterbury dairy farmers The efficient frontier of dairy farms in the Marlborough-Canterbury region is shown in Figure 8 for milk solids versus peak cows milked. Efficient farms lie on the solid line while inefficient farms fall below the solid line in an input-oriented orientation. Inefficient farms are able to reduce input use and still maintain production at current levels as shown in Table 9. 1,200 1, Milk solids (tonnes/farm) Frontier Farms ,000 1,500 2,000 2,500 Peak cows milked (no./farm) Figure 7 Input-oriented production frontier of Marlborough-Canterbury dairy farmers under variable returns to scale 19 Centre of Excellence in Farm Business Management

24 4.0 Discussion and Conclusion The focus of this study has been the estimation of variable returns to scale technical efficiencies (VRSTE) of dairy farms in the Waikato and for the production of a single output (milk solids) and the use of 4 inputs (farm size, peak cows milked, labour and operating farm expenses). Dairybase data of was used for the analyses. A key objective of the study was to test the difference between DairyNZ defined farm systems for the estimated VRSTE, output and input variables and a financial performance measure (total return on equity). The data envelopment analysis (DEA) model of Coelli (1996b) was used to develop a linear programming (LP) model for each dairy farm. The LP models, when solved, determine the frontier on which the efficient farms occurred and the level of inefficiencies of farms that are below the frontier. Input reduction targets of the inefficient farms were estimated and the DEA LP model also identified specific efficient farms against which each inefficient farm should be benchmarked. 4.1 Inefficient input transformation and technical efficiencies A key assumption of the input-oriented DEA models of dairy farms is that technical inefficiency of a farm derives from the inefficient transformation of inputs (farm size, peak cows milked, labour and operating farm expenses) to output (milk solids). The estimated average technical efficiency under the assumption that dairy farms exhibit variable returns to scale are large at 0.85 and 0.96 for the Waikato and, respectively, for the Dairybase data provided for this study (Tables 2 and 7). The distribution of technical efficiencies (Figures 3 and 7), however, indicate there is scope for some farms to reduce input use without reducing milk solids production. The input target reductions are higher for farms in the Waikato region than for farms in the (Tables 5 and 9). 20 Centre of Excellence in Farm Business Management

25 4.2 Differences in farm systems DairyNZ has defined five production systems based on the timing and amount of imported feed used in production. An objective of this study was to determine if technical efficiencies differ between farm systems. An ANOVA analysis using ranked VRSTE indicated no differences between systems in both the Waikato and. With the exception of milk solids production and operating expenses in the Waikato region, there were no significance differences between farm systems with regard to output and inputs. In the Waikato, the only significant difference was farm system 2 was different from system 4 for milk solid production and operating expenses. There was also no differences between farm systems with regard to total return on equity which was the financial performance variable used in this study. A similar result was obtained in the study by Shadbolt (unpublished) on the Competitive strategy analysis of NZ pastoral dairy farming systems. 4.3 Output, input variables and rental price of quasi-fixed inputs The DEAP software used is capable of handling multiple outputs as well as multiple inputs. Table 10 (and also Rouse (2009) and Jiang (2011) show outputs and inputs that could have been included in the DEA model. However, because of time constraints, the production function chosen for this study was a single output (milk solids) as a function of the first 4 inputs (farm size, peak cows milked, labour and operating farm expenses. However, the contribution of some of the excluded input variables would have been captured by the operating farm expenses variable used in the DEA model. 21 Centre of Excellence in Farm Business Management

26 Table 10 DEA candidate output and input variables Candidate outputs Milk solids Non-Dairy Cash Income Total Gross Farm Revenue A financial performance measure (such as total return on equity) Candidate inputs Farm size Peak cows milked Labour Operating farm expenses Total Stock Expenses Supplements purchased, made and cropped Nitrogen applied Pasture and Crop eaten Total Farm electricity Environmental inputs (GHG emissions, N leached, P loss) Allocative efficiencies were not calculated in this study. To do so would have required input prices to be calculated. Where the inputs are true variable inputs, i.e. their effect is realised completely in the year they were purchased (e.g. nitrogen fertiliser), the price of the input is equal to the unit purchase price of the input. The inputs used in the DEA model, farm size, cows milked and labour, may be considered quasi-fixed variables since their effects last for more than 1 year from the time of purchase. For example, the productivity of cows extends over several years depending on their service life which can be up to 5 years, after which the cow is usually been removed from the herd. As such, the annual price of a cow can be set as an annual implicit rental price such that the present value of rents generated over the (service) life time of the cow is equal to its purchase price. The implicit rental price (also known as the user cost of capital) represents the cost that a farmer may charge himself/herself or others for the use of capital livestock for one accounting period (OECD, 2009; Statistics New Zealand, 2009). The user cost of such quasi-fixed inputs could therefore be used together with variable inputs price (such as nitrogen fertiliser price) in future DEA analysis. 22 Centre of Excellence in Farm Business Management

27 4.4 Errors of data measurement A limitation of the DEA LP model used in the study is the assumption that the data is measured without error. Where errors occur, calculated technical efficiencies would be incorrect for a DEA LP model. The alternative approach for estimating technical efficiencies that includes errors in the data is the use of the stochastic frontier approach (SFA). The SFA is an econometric model where the error of the equation is decomposed into a (a) random variable which accounts for random errors and (b) a non-random variable which accounts for technical inefficiencies. (Coelli, 1996b). However the development of a successful SFA depends on the correct specification of the functional form of the production function and the error generating functions. Attempts have been made to make the DEA LP stochastic through the use of the standard LP chance-constraint formulation (Kasman and Turgutlu, 2007). This is done by converting Equation (2) to a chance-constraint as shown in Equation (8) Prob(Y λ y i ) α (8) This limits the probability of farms producing an output that exceeds the best-practice levels (on the frontier) to α or less. In chance-constraint DEA, most of the inefficient farms would still be expected to fall below the frontier. As noted by Kasman and Turgutlu (2007) the chance constraint does not eliminate the fundamental differences between the SFA and DEA formulations. 4.5 Including environmental emissions in DEA An initial objective of this study was to account for environmental inputs in the input-oriented DEA LP model (Reinhard et al., 2000). The plan was to use the OVERSEER nutrient balance model (Wheeler et al., 2003) to estimate environmental variables (GHG emissions, N leached and P loss) for each dairy farm in Dairybase. This approach was used in a previous internal study at AgResearch to estimate environmental variables for farms in the Dexcel database for the Waikato region in the 2004 season; the Dexcel database is the predecessor of the current Dairybase. However, when the Dairybase data was 23 Centre of Excellence in Farm Business Management

28 obtained for this study it became apparent that some of the physical data required for the OVERSEER nutrient balance model was no longer collected for most farms in Dairybase database. Future studies should attempt to include on-farm environmental emissions in a DEA/Stochastic frontier study. 5.0 References Banker, R.D., Natarajan, R. (2004). Statistical tests based on DEA efficiency scores. Chapter 11 in Handbook on Data Envelopment Analysis, W.W. Cooper, L. Seiford and J. Zhu (Eds.), Kluwer Academic Publishers, Norwell, MA, (2004), pp Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measuring the efficiency of decision units. European Journal of Operational Research, 2, Coelli. T, A. (1996a). Guide to FRONTIER Version 4.1:A computer program for stochastic production and cost function estimation. Centre for Efficiency and Productivity Analysis. Coelli. T, A. (1996b). Guide to DEAP Version 2.1: A data envelopment computer program. Centre for Efficiency and Productivity Analysis. DairyNZ (Unpublished) Dairybase Economic Survey, Deslierres, M. (2006). Win4DEAP, Version 1.1.2, Iyer, K.G; Rae, A.(2007). Benchmarking MAF Policy s Sector Productivity Measures. Amended Final Report for MAF. September Centre for Applied Economics and Policy Studies. Massey University, Palmerston North. Jaforullah, M. and Premachandra, E. (2003). Sensitivity of technical efficiency estimates to estimation approaches: an investigation using New Zealand dairy industry data. Economics Discussion Papers No. 306, The University of Otago, Dunedin. 24 Centre of Excellence in Farm Business Management

29 Jiang, N. (2011). Efficiency analysis of NZ dairy farming and the issue of climate change policy. A Stochastic Frontier Analysis. A thesis submitted for the degree of Doctor of Philosophy at the University of Auckland, Auckland, New Zealand. pdf?sequence=2 Kasman, A., Turgutlu, E. (2007). A Comparison of Chance-constrained DEA and Stochastic Frontier Analysis: An Application to the Turkish Life Insurance Industry. Kirner, L.; Ortner K. M.; Hambrusch, J. (2007). Using technical efficiency to classify Austrian dairy farms. OECD (2009). Measuring Capital, OECD MANUAL. (2009). Second Edition, 1_1_1,00.html Rae, A; Iyer, K.G.; Su J-J. (2008). Total Factor Productivity Growth Determinants in New Zealand Agriculture. Report Submitted to the Ministry of Agriculture and Forestry. October Centre for Applied Economics and Policy Studies. Massey University. Palmerston North. New Zealand. Rouse, P; Chen, L.; Harrison, J.A. (2009). Benchmarking the performance of dairy farms using data envelopment analysis. The University of Auckland, New Zealand. Shadbolt, N. (unpublished). Competitive strategy analysis of NZ pastoral dairy farming systems et al, year, data). Statistics New Zealand (2009). Productivity Statistics, Sources and Methods (Revised March 2009). 25 Centre of Excellence in Farm Business Management

30 Wheeler, D.M.; Ledgard, S.F.; de Klein, C.A.M.; Monaghan, R.M.; Carey, P.L.; Dowell R.W.; Johns, K.L. (2003). OVERSEER moving towards on-farm resource accounting, New Zealand Grasslands Association Proceedings 65, Acknowledgements We are grateful to Dr. Neil Cox of AgResearch for supplying the ANOVA program and assisting with the ANOVA analysis. 26 Centre of Excellence in Farm Business Management