Disproportional Joint Cost Allocation at the Farm Level by Means of Maximum Entropy

Transcription

1 Federal Department of Economic Affairs FDEA Agroscope Reckenholz-Tänikon Research Station ART Disproportional Joint Cost Allocation at the Farm Level by Means of Maximum Entropy Markus Lips 12 th Meeting of the OECD Network for Farm-Level Analysis, Paris November 13, 2013

2 Overview 1) Motivation 2) Joint cost allocation 3) Two maximum entropy applications and tests 4) Data of arable crop farms 5) Results 6) Conclusions 2

3 Motivation Swiss agriculture needs to reduce costs and improve its competitiveness Goal of agricultural policy Huge interest of farmers to learn more about their full product costs; President of Swiss Farmers Union: Full costing is the most important research project of Agroscope. Agroscope s research agenda includes full costing for all relevant production branches (dairy, arable crops, cattle, pig fattening, fruits and vines) on base of accountancy data Differences between standard costs and actual costing Data base for productivity analyses (homogeneity assumption) 3

4 Literature Swiss farms produce typically several goods (output) and have different production branches (activities) When a farm produces two or more outputs, joint cost items such as labour or machinery have to be allocated to production branches. Joint cost allocation in literature: The estimation of input-output coefficients for group of farms assumes a common production technology. (Cross) Entropy: Léon et al. 1999, Garvey & Britz 2002, Peeters and Surry 2005, Hansen & Surry 2007 Regression analysis: Butault 2011, Kleinhanss et al (FACEPA) At the single farm level: Hard to find references 4

5 Allocation factor Joint cost allocation is usually carried out by means of allocation factors, which builds together the distribution or allocation key. Allocation factors used should reflect the marginal factor costs of the input such as acres, (working) hours, turnover or number of output units (AAEA 2000). We use standard costs (μ) as allocation factors (e.g. machinery costs per hectare of wheat) Factor alpha: I i1 y x i i x = area in hectares y = farmwide costs μ = standard costs i = production branches 5

6 Proportional joint cost allocation Calculation of joint cost items for production branch i (β i ): i i Joint cost allocation is normally done in a proportional way, which signifies a strong assumption: All production branches are treated equally regardless whether the allocation factor is large or small Proportions between production branches remains constant All farms involved face the same treatment; i.e. the proportions between production branches of all farms are constant 6

7 Maximum Entropy Approach to derive β i by means of maximum entropy and standard costs from farm management literature β i machinery costs per ha of wheat p 1 CHF 0.-/ha Farm management literature μ = CHF /ha p 2 CHF /ha Maximum entropy approach provides the p i for all production branches and all joint-cost items comes up with the one and optimal solution for all probabilities p i allows dropping the assumption of a proportional allocation 7

8 CoreModel for one farm and one joint cost item, e.g. machinery, based on Golan, Judge and Miller, 1996 max subject to: i) ii) iii) y H i K k 1 I i1 K I K xi x i k 1 i1 k1 i p i, k p i, k zi, k 1 pi, k ln p i, k indices β = cost per hectare p = probability H = Shannon entropy measure x = area in hectares y = farmwide costs z = support point i = arable crops (prod. branches) k = support points 8

9 Costs per hectare (β i ) 45 Proportional adjustment (α<1) P prop P ME G ME Maximum Entropy adjustment G prop Grassland Potatoes Standard costs (μ i ) 9

10 Disproportional adjustment Maximum Entropy results in a probability distribution in which the adjustment of large standards costs is more likely than the one of small standard costs. The outcome is in line with agricultural practice: There are more possibilities to adjust cost for crops with high standard costs than crops with low standard costs 10

11 Costs per hectare (β i ) 45 Proportional adjustment (α<1) G ME P ME Grassland Potatoes ME adjustment Standard costs (μ i ) ME = Maximum Entropy 11

12 12 Inequality restrictions β Potatoes > β Grassland should be respected β 2 > β 1 can be implemented (Campell and Hill, 2006) β 2 represents the sum of β 1 and the difference between crops 2 and 1. Inequality restrictions are formulated between groups of similar crops rather than single crops. Crops are assigned to groups based on their agronomic qualities. i 2 1 i p. p p. z' z' z' 0. 0 z'. i

13 Upward/downward structure Potatoes Other Crops Grassland Barley Wheat Forest Fallow Land 0 Within groups the rank order may change while the rank order is fix for crops of different groups. 13

14 Three applications 1) Proportional 2) CoreModel 3) CoreModel with Inequality restrictions True joint costs are not available Criteria are needed in order to assess applications 14

15 Two tests Test No. 1; More machinery inputs for potatoes than for grassland Test No. 2; In-between test for all triplets: β i (β 1 < β 2 < β 3 ) β i Grassland Sugar Beet Potatoes Standard costs (μ i ) 15

16 Data from crop farms Swiss Farm Accountancy Data Network (FADN) Only pure arable crops farms (no animal husbandry) 36 farm observations, total 843 hectares (years 2007/08) 12 different production branches Three joint costs items: Labour, measured in normal working days (opportunity costs CHF per day) Machinery costs, farm-owned machines and costs of machinery services Other joint costs, such as insurance premiums, energy, telephone and overheads Standard costs (μ i ) are taken from farm management literature 16

17 Cost categories in Swiss FADN Wheat Potatoes Total Direct costs Land Joint costs Full costs Σ Σ Σ = accountancy data and/or opportunity costs 17

18 Factor alpha Labour Machinery costs Other joint costs Mean value of α Minimum value of α Maximum value of α farm observations 18

19 Test results Test No. 1 (more machinery inputs for potatoes than for grassland) fails in three out of seven farm observations for CoreModel. No failure for Inequality. In-between test (Test No. 2 ) for all 1189 triplets; Number of unsuccessful triplets: Joint cost item CoreModel Applications Inequality Labour 0 0 Machinery Other joint costs

20 Results for labour α Labour = 2.5 Crop No. of cases Labour in NWD per ha Deviation of Inequality from Proportional in % Proportional Core- Inequa- Model lity Wheat Barley Corn Silage Maize Potatoes Sugar Beet Oilseeds Pea Grassland Fallow Land Forest Other Activities

21 Results for machinery costs α Machinery = 0.8 Crop No. of cases Machinery in CHF per ha Deviation of Inequality from Proportional in % Proportional Core- Inequa- Model lity Wheat Barley Corn Silage Maize Potatoes Sugar Beet Oilseeds Pea Grassland Fallow Land Forest Other Activities

22 Conclusions The application CoreModel leads to dissatisfying results while the application Inequality allows using the potential of maximum entropy as a tool for recovering information in favour of joint costs allocation. The suggested approach allows dropping the assumption of a proportional allocation and leads to a disproportional allocation, reflecting a probability distribution in which the adjustment of large standards costs is more likely than the one of small standard costs. Compared to a Proportional allocation the application Inequality reveals deviations in a range between -15% and +18%. Accordingly, it matters whether the joint costs allocation is carried out in a proportional or maximum entropy manner. 22

23 Markus Lips Agroscope Tänikon 8356 Ettenhausen Switzerland agroscope.admin.ch 23