## ABSTRACT

## Key words

**INTERPRETIVE SUMMARY**: This study provides insights on the design of effective payments for environmental services conditioned to enteric methane emissions reduction. Two indicators of enteric emissions were compared, and the extra production costs for adding more grass in fodder systems as an emission reduction lever were computed for representative French medium and large dairy farms. Results show that an emission indicator accounting for diet effects is crucial to accurately monitor farmers' effort. Moreover, farms face heterogeneous extra-costs for changing cows' feed ration, and it should be taken into account in the definition of the payment amount to ensure a large-scale adoption.

## INTRODUCTION

- Myhre G.
- Shindell D.
- Bréon F.-M.
- Collins W.
- Fuglestvedt J.
- Huang J.
- Koch D.
- Lamarque J.-F.
- Lee D.
- Mendoza B.
- Nakajima T.
- Robock A.
- Stephens G.
- Takemura T.
- Zhang H.

- Gavrilova O.
- Leip A.
- Dong H.
- Macdonald J.D.
- Gomez Bravo C.A.
- Amon B.
- Barahona Rosales R.
- Agustin del Prado A.
- Aparecida de Lima M.
- Oyhantcabal W.
- van der Weerden T.J.
- Widiawati Y.

- Martin C.
- Promiès D.
- Ferlay A.
- Rochette Y.
- Martin B.
- Chilliard Y.
- Morgavi D.
- Doreau M.

_{2}in Sweden and 45€/teqCO

_{2}in France, while the EU ETS (European Trading System) market price was 44€/teqCO

_{2}(

- The World Bank

### BACKGROUND ON ENTERIC METHANE EMISSION INDICATORS

- Negussie E.
- de Haas Y.
- Dehareng F.
- Dewhurst R.J.
- Dijkstra J.
- Gengler N.
- Morgavi D.P.
- Soyeurt H.
- van Gastelen S.
- Yan T.
- Biscarini F.

- Allen B.
- Hart K.
- Radley G.
- Tucker G.
- Keenleyside C.
- Oppermann R.
- Underwood E.
- Menadue H.
- Poux X.
- Beaufoy G.
- Herzon I.
- Povellato A.
- Vanni F.
- Prazan J.
- Hudson T.
- Yellachich N.

- Gavrilova O.
- Leip A.
- Dong H.
- Macdonald J.D.
- Gomez Bravo C.A.
- Amon B.
- Barahona Rosales R.
- Agustin del Prado A.
- Aparecida de Lima M.
- Oyhantcabal W.
- van der Weerden T.J.
- Widiawati Y.

### A TIER 3 INDICATOR APPLIED IN THE FRENCH ECO-METHANE RESULT-BASED SCHEME

- Martin C.
- Promiès D.
- Ferlay A.
- Rochette Y.
- Martin B.
- Chilliard Y.
- Morgavi D.
- Doreau M.

_{4}/L (

*Methane*) can be calculated from milk productivity in kg/cow/year (

*Productivity*) and the ratio of the sum of fatty acids with 16 carbon atoms or less (FA ≤ C16) to the total amount of fatty acids (

*TotalFA*) in the milk they produce (1). This ratio has a strong biological causal relationship with methanogenesis in the rumen and is significantly reduced by more sources of omega-3 in cows' diet.

This formula was coinvented by teams from the animal feed manufacturing company Valorex (P. Weill and G. Chesneau) and the French National Institute for Agricultural Research (INRA) (Y. Chilliard, M. Doreau and C. Martin), and received a patent under the title “Method for evaluating the quantity of methane produced by a dairy ruminant and method for decreasing and controlling such quantity” (WO2009156453A1) (

_{2}eq, making the scheme a result-based PES. The reduction is calculated relative to baseline monthly emission levels attributed to the farm that are representative of its type of fodder system. Through the definition of different baseline scenarios, the PES design partially considers the variability in the potentiality of environmental services provision according to the production basin and the fodder system. Hence, rather than rewarding farms that produce the least emissions per unit of product (which would tend to favor the most productive farms), Eco-Methane supports all emission reduction efforts.

- Bleu-Blanc-Coeur

_{2}eq with a financial envelope made of donations from private actors (15€/tCO

_{2}eq on average in 2017). The main strengths of the scheme lie in the strong scientific foundations of the method for quantifying emissions and the easy participation procedure for dairy farmers. Each contract signatory commits to provide a monthly milk analysis to the association and to include feed with a high content of sources of omega-3 in dairy cow rations (alfalfa, extruded linseed, grass). This data is used to estimate enteric methane emissions using (1). Eco-Methane is recognized by the United Nations as a GHG emission reduction project eligible for issuing carbon credits (

## MATERIALS AND METHODS

### Data

Variable | 1st quartile | Median | Mean | 3rd quartile |
---|---|---|---|---|

Utilized Agricultural Area (ha) | 50.0 | 80.0 | 87.4 | 110.0 |

Fodder area (ha) | 40.0 | 60.0 | 67.4 | 80.0 |

Corn silage area (ha) | 1.0 | 10.0 | 14.1 | 20.0 |

Pasture area (permanent and temporary) (ha) | 26.0 | 40.0 | 50.3 | 61.0 |

Productivity (L/cow) | 5,593.4 | 6,676.4 | 6,707.9 | 7,851.1 |

Number of dairy cows | 35 | 55 | 58 | 70 |

Agricultural Work Unit | 1.0 | 2.0 | 1.8 | 2.1 |

Purchase of cattle feed concentrates (€) | 14,326.0 | 24,996.5 | 32,853.2 | 43,645.0 |

### Attribution of enteric methane emissions

The emission factor

*EF*(kgCH

_{4}/cow/year) can be easily calculated for each farm of the FADN from the milk production (kg/year) of the herd (

*Milk production*) and the number of dairy cows (

*Ncows*). We then derive an emission indicator (

*TIER2)*per liter of milk (gCH

_{4}/L), capturing variability according to milk productivity (L/cow/year) (3).

Due to the absence of data on dairy cows' diet, a Tier 3 method cannot be applied to evaluate individual emissions of FADN farms and capture both productivity and diet effects. In particular, data are too limited to estimate individual enteric methane emissions of French farms using (1). They are, however, sufficient to identify their Eco-Methane scenario and therefore the baseline emissions corresponding to their fodder system. Baseline emissions from the 11 scenarios are available per month and were obtained from BBC. We calculate the annual average to define the Eco-Methane baseline emissions indicator (

*Eco-Methane baseline*) (Table 2).

Scenario | Corn in the fodder area | Production basin | Eco-Methane baseline (gCH_{4}/L) |
---|---|---|---|

1 | More than 30% | Plains outside the western region | 15.75 |

2 | Plains of the western region | 15.92 | |

3 | Between 10 and 30% | Plains outside the western region | 15.83 |

4 | Plains of the western region | 16.43 | |

5 | Less than 10% | Plains outside the western region | 16.56 |

6 | Plains of the western region | 17.38 | |

7 | More than 10% | Mountains | 15.96 |

8 | Less than 10% | Mountains of the Massif Central | 17.13 |

9 | Mountains of the Northern Alps | 17.83 | |

10 | Mountains of Franche-Comté | 16.22 | |

11 | Other mountains | 17.20 |

### Estimation of the extra-cost of milk production with more grass in the fodder system

_{2}eq in 2017 and increased to 40€/tCO

_{2}eq in 2018 and 2019. Farmers participating in Eco-Methane received an average of 15€/tCO

_{2}eq in 2017, suggesting that the payment of the scheme is suboptimal and provides little incentive to participate (

- Bleu-Blanc-Coeur

*x*with exogenous input prices

*w*that minimize variable costs given the production level

*y*targeted by the farmer and available quasifixed inputs

*z*such as land, labor and equipment that are assumed to be predetermined in the short term. The cost minimization approach is motivated by the fact that French dairy farmers are constrained in the quantity of milk they produce in the terms of their contract with dairy plants (

It must be concave, nondecreasing and homogeneous of degree 1 in variable input prices, decreasing with (binding) fixed factors of production, and monotonic according to output levels.

*VC*correspond to intermediate consumption and the variable input cost share functions (6) and (7), derived from Shephard's lemma. The translog functional form is commonly used in the literature on the cost structure and efficiency of dairy farms because of its flexibility and the possibility of imposing homogeneity of degree 1 (

*i*and

*t*are indices for individuals and years, respectively. We assume that dairy farms produce one output, the quantity

*Y1*of the milk of cows produced per year (

*milk production*). Considering the joint production of milk and a bad output (enteric methane emissions) would be of main interest. This is the approach used in (

*X1*and cattle feeding stuffs

*X2*, for which the expenses represent a high share of intermediate consumption. The choice of including fuel is motivated by the possibility of calculating farm-level fuel prices and therefore capturing more heterogeneity. The price of fuel

*W1*(

*fuel price*) is calculated from the nonroad gas oil expenses and volumes. As individual cattle feeding stuff prices are not available in the data,

*W2*(

*feed price*) is measured by the index of purchase prices of the means of agricultural production (IPAMPA) for adult cattle feeding stuffs of year

*t-1*, available for each French current administrative region. While in practice, a bargaining effect may create endogeneity between milk production and feed prices, we assume it is sufficiently low not to overestimate too much milk marginal production costs (

*Z1*(

*grassland*) includes permanent and temporary pastures, alfalfa for dehydration and other artificial fodders. We add 2 other quasifixed factors of production: machinery and constructions fixed assets

*Z2*(

*capital*) and annual work units

*Z3*(

*labor*). Since sample farms are all specialized in dairy milk production, we do not consider them as multi-output farms. We verify the production of crops and other livestock products represents a much lower share of total gross products (see Table A2 in the Appendix). Yet, we add the aggregated volume

*Y2*of the other products of the farm (

*other productions*) as a control variable to capture heterogeneity linked to diversification.

*Y2*is calculated as the total gross product of the year (crop products, livestock products and other products) net of animal purchases and milk production of the cows, deflated by the French agricultural producer price index (API) of year

*t*. We further control for the farm total utilized agricultural area

*Q1*(

*utilized agricultural area*), 20 regional dummies

*Dri*approximating the pedoclimatic conditions, and time fixed effects with 2 yearly dummies

*Tt*. The coefficients α,

*β*,

*δ*,

*ν*,

*ρ*,

*ζ*,

*θ*,

*γ*, and

*µ*are the parameters to be estimated and describe the effects of the covariates on the independent variables.

*eit*,

*u1it*and

*u2it*are the error terms assumed to follow a normal distribution.

To account for the correlations between the error terms of the different equations, we use a 3-stage least squares regression analysis. The system of equations (5) + (6) + (7) is estimated for all the farms of the sample and then for the 3 major production basins and groups of Eco-Methane scenarios defined in Table 2 to identify potential differences in extra costs according to the type of dairy system. The different steps to derive the specification of the system are described in the Appendix. Descriptive statistics of the model variables of the sample and subsamples are presented in Table 3.

Variable | France n = 2,205 | Western plains n = 645 | Plains outside the western region n = 965 | Mountains n = 585 | Plains, > 30% of corn in the fodder area n = 767 | Plains, 10-30% of corn in the fodder area n = 574 | Plains, <10% of corn in the fodder area n = 279 |
---|---|---|---|---|---|---|---|

Scenarios | 1–11 | 2, 4, 6 | 1, 3, 5 | 7–11 | 1–2 | 3–4 | 5–6 |

Variable Costs (€/year) | 128,073.5 | 139,405.3 | 136,399.4 | 96,533.0 | 170,654.1 | 124,656.0 | 90,248.5 |

(105,612.7) | (107,167.1) | (112,800.6) | (80,772.0) | (124,937.8) | (71,877.3) | (57,036.7) | |

Milk production (L/year) | 398,594.1 | 446,128.0 | 402,355.2 | 306,703.0 | 526,707.0 | 396,281.9 | 156,204.9 |

(297,513.2) | (328,781.5) | (296,923.0) | (226,416.1) | (333,580.8) | (213,270.9) | (266,216.2) | |

Other productions (€/base 100/year) | 498.6 | 581.3 | 554.6 | 274.4 | 750.2 | 488.6 | 317.0 |

(671.5) | (642.3) | (770.2) | (413.0) | (871.1) | (432.8) | (349.0) | |

Fuel price (€/L) | 0.60 | 0.59 | 0.59 | 0.61 | 0.59 | 0.59 | 0.60 |

(0.10) | (0.10) | (0.11) | (0.10) | (0.10) | (0.10) | (0.10) | |

Feed price (base 100) | 96.6 | 96.5 | 96.6 | 96.8 | 96.6 | 96.5 | 96.6 |

(2.4) | (2.4) | (2.4) | (2.3) | (2.4) | (2.4) | (2.4) | |

Grassland (ha) | 51.1 | 42.1 | 52.7 | 65.5 | 34.2 | 50.6 | 66.1 |

(41.0) | (31.5) | (38.6) | (47.8) | (25.8) | (32.5) | (36.1) | |

Capital (1000€) | 171.0 | 160.5 | 179.4 | 179.5 | 189.1 | 144.8 | 163.4 |

(155.9) | (146.8) | (163.7) | (160.8) | (161.8) | (141.1) | (153.5) | |

Labor (AWU) | 1.8 | 1.9 | 1.9 | 1.7 | 2.0 | 1.7 | 1.7 |

(1.0) | (1.0) | (1.0) | (1.0) | (1.1) | (0.8) | (0.9) | |

UAA (ha) | 87.4 | 84.3 | 92.6 | 86.3 | 93.3 | 85.5 | 79.3 |

(58.1) | (55.3) | (60.0) | (57.8) | (60.6) | (48.2) | (42.1) |

## RESULTS AND DISCUSSION

### Allocation of Eco-Methane scenarios and distinction of 3 milk production basins

### Enteric emissions: relation to productivity and fodder system

_{4}/L, while it is 16.3 gCH

_{4}/L for the Eco-Methane baseline indicator, suggesting that considering the fodder cropping system in the calculation revises enteric emissions downwards. Both indicators show a decrease in emissions per liter of milk as productivity increases (Table 4). Dairy systems with lower enteric emissions per liter of milk are productive systems with more than 30% of corn silage in the fodder crop rotation, while grass-based systems have the highest emissions. The comparison of the 2 indicators allows to nuance the performance of the different systems in terms of diet and productivity effects.

Scenarios | Plains outside the western region | Western plains | Mountains | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

1, 3, 5 | 1 | 3 | 5 | 2, 4, 6 | 2 | 4 | 6 | 7–11 | 7 | 8 to 11 | |

% corn in fodder area | >30 | 30–10 | <10 | >30 | 30–10 | <10 | ≥10 | <10 | |||

Sample share (%) | 31.4 | 10.0 | 9.9 | 11.5 | 44.3 | 23.7 | 16.8 | 3.8 | 24.3 | 6.5 | 17.8 |

Productivity (1,000L/cow) | 6.72 | 7.65 | 6.94 | 5.72 | 6.98 | 7.33 | 6.79 | 5.59 | 6.20 | 6.91 | 5.94 |

TIER2 (gCH_{4}/L) | 18.55^{d} | 17.46^{l} | 18.22^{fhj} | 19.78^{a} | 18.23^{ehi} | 17.80^{k} | 18.38^{defg} | 20.22^{a} | 19.07^{c} | 18.19^{gij} | 19.40^{b} |

Eco-Methane baseline (gCH_{4}/L) | 16.07^{q} | 15.75^{u} | 15.83^{t} | 16.56^{n} | 16.24^{p} | 15.92^{s} | 16.43° | 17.38^{l} | 16.55^{n} | 15.96^{r} | 16.76^{m} |

- Negussie E.
- de Haas Y.
- Dehareng F.
- Dewhurst R.J.
- Dijkstra J.
- Gengler N.
- Morgavi D.P.
- Soyeurt H.
- van Gastelen S.
- Yan T.
- Biscarini F.

### Impact of increasing the grassland area on the marginal cost of milk production

^{2}). Consistent with the hypothesis of cost minimization, imposing restrictions on the parameters across equations also improved the variable cost estimation quality. Therefore, we present the results of the constrained system estimation.

The results presented in the following paragraphs are calculated from the regression results detailed in the Appendix (Tables A4-A10).

France | Plains of the western region | Plains outside the western region | Mountains | Plains with more than 30% of corn silage in the fodder area | Plains with 10 to 30% of corn silage in the fodder area | Plains with less than 10% of corn silage in the fodder area | |
---|---|---|---|---|---|---|---|

Marginal cost (€/1000L) | 241.5 | 230.5 | 251.0 | 261.1 | 225.7 | 225.1 | 262.0 |

Extra-cost (€/1000L/ha) | −0.02 | −0.48 | 0.58^{+} | −0.41 | −1.38^{+} | 0.28 | −1.82*** |

Variable cost regression R^{2} | 0.91 | 0.91 | 0.91 | 0.91 | 0.90 | 0.91 | 0.89 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

## CONCLUSIONS

## ACKNOWLEDGMENTS

## APPENDIX

Steps to impose homogeneity of degree 1 in input prices:

Parameter constraints to impose to our system:

Homogeneous function to estimate:

**Input demand functions:**applying Shephard' lemma:

Administrative Region | Department | Scenarios | Production share (volume) | Attributed scenarios |
---|---|---|---|---|

Ile de France | 1, 3 or 5 | 1, 3 or 5 | ||

Champagne Ardennes | 1, 3 or 5 | 1, 3 or 5 | ||

Picardie | 1, 3 or 5 | 1, 3 or 5 | ||

Haute Normandie | 1, 3 or 5 | 1, 3 or 5 | ||

Centre | 1, 3 or 5 | 1, 3 or 5 | ||

Basse Normandie | 2, 4, 6 | 2, 4 or 6 | ||

Bourgogne | 1, 3 or 5 | 1, 3 or 5 | ||

Nord Pas De Calais | 1, 3 or 5 | 1, 3 or 5 | ||

Lorraine | 54 | 1, 3 or 5 | 59% | 1, 3 or 5 |

55 | 1, 3 or 5 | |||

57 | 1, 3 or 5 | |||

88 | 7 or 11 | 41% | ||

Alsace | 1, 3 or 5 | 1, 3 or 5 | ||

Franche-Comté | 25 | 7 or 10 | 76% | 7 or 10 |

39 | 7 or 10 | |||

70 | 1, 3 or 5 | 24% | ||

Pays de la Loire | 2, 4 or 6 | 2, 4 or 6 | ||

Bretagne | 1, 3 or 5 | 1, 3 or 5 | ||

Poitou-Charentes | 1, 3 or 5 | 1, 3 or 5 | ||

Aquitaine | 1, 3 or 5 | 1, 3 or 5 | ||

Midi-Pyrénées | 46 | 7 or 8 | 60% | 7 or 8 |

12 | 7 or 8 | |||

9 | 1, 3 or 5 | 40% | ||

31 | 1, 3 or 5 | |||

32 | 1, 3 or 5 | |||

65 | 1, 3 or 5 | |||

81 | 1, 3 or 5 | |||

82 | 1, 3 or 5 | |||

Limousin | 1, 3 or 5 | 1, 3 or 5 | ||

Rhône Alpes | 1 | 1, 3 or 5 | 75% | 1, 3 or 5 |

7 | 1, 3 or 5 | |||

26 | 1, 3 or 5 | |||

38 | 1, 3 or 5 | |||

42 | 1, 3 or 5 | |||

69 | 1, 3 or 5 | |||

73 | 7 or 8 | 25% | ||

74 | ||||

Auvergne | 7 or 8 | 7 or 8 | ||

Languedoc-Roussillon | 11 | 1, 3 or 5 | 10% | 7 or 8 |

30 | 1, 3 or 5 | |||

34 | 1, 3 or 5 | |||

66 | 1, 3 or 5 | |||

48 | 7 or 8 | 90% | ||

Provence Alpes Côte d'Azur | 5 | 7 or 11 | 87% | 7 or 11 |

4 | 1, 3 or 5 | 13% | ||

6 | 1, 3 or 5 | |||

13 | 1, 3 or 5 | |||

83 | 1, 3 or 5 | |||

84 | 1, 3 or 5 |

Q1 | Q2 | Mean | Q3 | |
---|---|---|---|---|

% variation of milk production volume relative to the farm mean over 2016–2018 | 1.64 | 3.49 | 4.85 | 6.63 |

Share of milk production in the total gross product | 69.19 | 77.74 | 76.57 | 85.15 |

Share of crop production in the total gross product | 0.20 | 3.99 | 6.34 | 10.98 |

Share of other livestock products in the total gross product | 0.00 | 0.00 | 0.87 | 0.00 |

Share of fuel expenses in intermediate consumption | 3.60 | 4.60 | 4.88 | 6.00 |

Share of cattle feed expenses in intermediate consumption | 19.10 | 25.20 | 24.63 | 31.00 |

Share of fertilizer expenses in intermediate consumption | 3.29 | 5.29 | 5.78 | 7.76 |

France | Plains of the western region | Plains outside the western region | Mountains | Plains with more than 30% of corn silage in the fodder area | Plains with 10 to 30% of corn silage in the fodder area | Plains with less than 10% of corn silage in the fodder area | |
---|---|---|---|---|---|---|---|

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{Y}_{1}<0}\mathrm{\partial}{Y}_{1}<0$ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{Z}_{1}<0}\mathrm{\partial}{Z}_{1}<0$ | 0.2 | 2.3 | 4.2 | 26.3 | 21.5 | 51.0 | 24.4 |

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{Z}_{2}<0}\mathrm{\partial}{Z}_{2}<0$ | 86.0 | 19.7 | 86.5 | 68.7 | 45.0 | 59.9 | 64.5 |

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{Z}_{3}<0}\mathrm{\partial}{Z}_{3}<0$ | 38.3 | 41.4 | 29.2 | 16.9 | 39.2 | 21.3 | 71.8 |

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{W}_{1}>0}\mathrm{\partial}{W}_{1}>0$ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

$\mathrm{\partial}VC/\phantom{\mathrm{\partial}VC\mathrm{\partial}{W}_{2}>0}\mathrm{\partial}{W}_{2}>0$ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

${\mathrm{\partial}}^{2}VC/\phantom{{\mathrm{\partial}}^{2}VC\mathrm{\partial}{{W}_{1}}^{2}<0}\mathrm{\partial}{{W}_{1}}^{2}<0$ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

${\mathrm{\partial}}^{2}VC/\phantom{{\mathrm{\partial}}^{2}VC\mathrm{\partial}{{W}_{2}}^{2}<0}\mathrm{\partial}{{W}_{2}}^{2}<0$ | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 3.398*** (0.658) | Constant | ||

${\beta}_{1}$ | 1.156*** (0.202) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.457*** (0.029) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | 0.007 (0.108) | Ln (grassland) | ||

${\delta}_{2}$ | 0.086 (0.065) | Ln (capital) | ||

${\delta}_{3}$ | 0.739*** (0.214) | Ln (labor) | ||

${\beta}_{11}$ | −0.054 (0.042) | 0.5 *Ln (milk production)^{2} | ||

${\rho}_{11}$ | −0.002 (0.020) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | −0.026^{+} (0.015) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.151*** (0.040) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.024*** (0.003) | Ln (milk production) *Ln (feed price/fuel price) | -Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | 0.002 (0.002) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | 0.004* (0.002) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.003** (0.001) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | −0.009** (0.003) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.014 (0.013) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | 0.001 (0.009) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | −0.014 (0.023) | Ln (grassland) *Ln (labor) | ||

${\delta}_{22}$ | 0.014* (0.007) | 0.5 *Ln (capital)^{2} | ||

${\delta}_{23}$ | 0.035* (0.016) | Ln (capital) *Ln (labor) | ||

${\delta}_{33}$ | 0.091 (0.061) | 0.5 *Ln (labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.002*** (0.000) | utilized agricultural area | ||

${\gamma}_{1}$ | −0.199 (0.326) | Champagne-Ardennes | ||

${\gamma}_{2}$ | −0.146 (0.325) | Picardie | ||

${\gamma}_{3}$ | −0.121 (0.325) | Haute Normandie | ||

${\gamma}_{4}$ | −0.086 (0.326) | Centre | ||

${\gamma}_{5}$ | −0.119 (0.325) | Basse Normandie | ||

${\gamma}_{6}$ | −0.107 (0.329) | Bourgogne | ||

${\gamma}_{7}$ | −0.107 (0.325) | Nord-Pas-De-Calais | ||

${\gamma}_{8}$ | −0.119 (0.325) | Lorraine | ||

${\gamma}_{9}$ | −0.094 (0.327) | Alsace | ||

${\gamma}_{10}$ | −0.123 (0.325) | Franche-Comté | ||

${\gamma}_{11}$ | −0.156 (0.325) | Pays de la Loire | ||

${\gamma}_{12}$ | −0.207 (0.324) | Bretagne | ||

${\gamma}_{13}$ | −0.111 (0.326) | Poitou-Charentes | ||

${\gamma}_{14}$ | −0.080 (0.326) | Aquitaine | ||

${\gamma}_{15}$ | −0.257 (0.325) | Midi-Pyrénées | ||

${\gamma}_{16}$ | −0.200 (0.327) | Limousin | ||

${\gamma}_{17}$ | −0.104 (0.325) | Rhône-Alpes | ||

${\gamma}_{18}$ | −0.247 (0.325) | Auvergne | ||

${\gamma}_{19}$ | −0.233 (0.327) | Languedoc-Roussillon | ||

${\gamma}_{20}$ | −0.281 (0.332) | Provence-Alpes-Côte d'Azur | ||

Baseline: Ile-de-France | ||||

${\mu}_{16}$ | 0.024* (0.011) | Year 2016 | ||

${\mu}_{17}$ | 0.003 (0.010) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.912 | −306.535 | −14.425 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 5.422*** (1.075) | Constant | ||

${\beta}_{1}$ | 0.413 (0.419) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.423*** (0.048) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | 0.423* (0.210) | Ln (grassland) | ||

${\delta}_{2}$ | −0.078 (0.146) | Ln (capital) | ||

${\delta}_{3}$ | 0.744^{+} (0.400) | Ln (labor) | ||

${\beta}_{11}$ | 0.015 (0.100) | 0.5 *Ln (milk production)^{2} | ||

${\rho}_{11}$ | −0.046 (0.043) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | 0.044 (0.038) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.100 (0.085) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.041*** (0.005) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | 0.001 (0.004) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | −0.018*** (0.003) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.005* (0.002) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | 0.003 (0.005) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.047 (0.042) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | 0.004 (0.021) | Ln(grassland)*Ln(capital) | ||

${\delta}_{13}$ | 0.030 (0.051) | Ln(grassland)*Ln(labor) | ||

${\delta}_{22}$ | −0.031^{+} (0.018) | 0.5*Ln(capital)^{2} | ||

${\delta}_{23}$ | −0.063* (0.032) | Ln(capital)*Ln(labor) | ||

${\delta}_{33}$ | 0.143 (0.106) | 0.5*Ln(labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.002*** (0.000) | utilized agricultural area | ||

${\gamma}_{11}$ | −0.043* (0.019) | Pays de la Loire | ||

${\gamma}_{12}$ | −0.099*** (0.019) | Bretagne | ||

Baseline: Basse Normandie | ||||

${\mu}_{16}$ | 0.003 (0.019) | Year 2016 | ||

${\mu}_{17}$ | −0.018 (0.017) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.915 | −362.617 | −18.850 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 5.254*** (0.929) | Constant | ||

${\beta}_{1}$ | 0.668* (0.293) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.404*** (0.043) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | −0.310* (0.156) | Ln (grassland) | ||

${\delta}_{2}$ | 0.101 (0.087) | Ln (capital) | ||

${\delta}_{3}$ | 1.558*** (0.321) | Ln (labor) | ||

${\beta}_{11}$ | 0.012 (0.057) | 0.5*Ln (milk production)^{2} | ||

${\rho}_{11}$ | 0.047^{+} (0.027) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | −0.038* (0.019) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.297*** (0.056) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.033*** (0.004) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | 0.001 (0.004) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | 0.009*** (0.002) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.001 (0.002) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | −0.032*** (0.005) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.006 (0.016) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | −0.001 (0.012) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | −0.040 (0.031) | Ln (grassland) *Ln (labor) | ||

${\delta}_{22}$ | 0.024* (0.009) | 0.5 *Ln (capital)^{2} | ||

${\delta}_{23}$ | 0.087*** (0.022) | Ln (capital) *Ln (labor) | ||

${\delta}_{33}$ | 0.022 (0.089) | 0.5 *Ln (labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.001*** (0.000) | utilized agricultural area | ||

${\gamma}_{1}$ | −0.175 (0.283) | Champagne-Ardennes | ||

${\gamma}_{2}$ | −0.100 (0.282) | Picardie | ||

${\gamma}_{3}$ | −0.078 (0.282) | Haute Normandie | ||

${\gamma}_{4}$ | −0.010 (0.283) | Centre | ||

${\gamma}_{6}$ | −0.067 (0.285) | Bourgogne | ||

${\gamma}_{7}$ | −0.079 (0.282) | Nord-Pas-De-Calais | ||

${\gamma}_{8}$. | −0.078 (0.282) | Lorraine | ||

${\gamma}_{9}$ | −0.059 (0.283) | Alsace | ||

${\gamma}_{13}$ | −0.052 (0.283) | Poitou-Charentes | ||

${\gamma}_{14}$ | −0.063 (0.283) | Aquitaine | ||

${\gamma}_{16}$ | −0.163 (0.285) | Limousin | ||

${\gamma}_{17}$ | −0.093 (0.282) | Rhône-Alpes | ||

Baseline: Ile-de-France | ||||

${\mu}_{16}$ | 0.057** (0.017) | Year 2016 | ||

${\mu}_{17}$ | 0.017 (0.016) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.911 | −276.665 | −12.377 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 1.397 (1.152) | Constant | ||

${\beta}_{1}$ | 1.285** (0.427) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.408*** (0.058) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | 514* (0.257) | Ln (grassland) | ||

${\delta}_{2}$ | 0.270* (0.136) | Ln (capital) | ||

${\delta}_{3}$ | −0.193 (0.437) | Ln (labor) | ||

${\beta}_{11}$ | 0.001 (0.094) | 0.5 *Ln (milk production)^{2} | ||

${\rho}_{11}$ | −0.060 (0.047) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | −0.055^{+} (0.032) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.093 (0.083) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.025*** (0.006) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | 0.006 (0.005) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | 0.019*** (0.004) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.013*** (0.003) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | −0.016* (0.006) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.062 (0.049) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | −0.014 (0.020) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | 0.081 (0.055) | Ln (grassland) *Ln (labor) | ||

${\delta}_{22}$ | 0.025* (0.012) | 0.5* Ln (capital)^{2} | ||

${\delta}_{23}$ | 0.078* (0.039) | Ln (capital)* Ln (labor) | ||

${\delta}_{33}$ | −0.074 (0.145) | 0.5 *Ln (labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.002*** (0.000) | utilized agricultural area | ||

${\gamma}_{10}$ | 0.109*** (0.030) | Franche-Comté | ||

${\gamma}_{18}$ | 0.006 (0.025) | Auvergne | ||

${\gamma}_{19}$ | 0.032 (0.050) | Languedoc-Roussillon | ||

${\gamma}_{20}$ | 0.017 (0.079) | Provence-Alpes-Côte d'Azur | ||

Baseline: Midi-Pyrénées | ||||

${\mu}_{16}$ | 0.032 (0.023) | Year 2016 | ||

${\mu}_{17}$ | 0.030 (0.020) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.910 | −289.950 | −12.903 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 6.811*** (1.111) | Constant | ||

${\beta}_{1}$ | −0.265 (0.449) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.388*** (0.046) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | 0.283 (0.233) | Ln (grassland) | ||

${\delta}_{2}$ | 0.320* (0.140) | Ln (capital) | ||

${\delta}_{3}$ | 1.445** (0.437) | Ln (labor) | ||

${\beta}_{11}$ | 0.262* (0.105) | 0.5 *Ln (milk production)^{2} | ||

${\rho}_{11}$ | −0.092^{+} (0.049) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | −0.078* (0.037) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.235* (0.096) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.046*** (0.006) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | 0.002 (0.004) | 0.5*Ln(feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | −0.013*** (0.003) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.007** (0.002) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | −0.008 (0.005) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.001 (0.019) | 0.5* Ln (grassland)^{2} | ||

${\delta}_{12}$ | 0.063** (0.019) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | −0.061 (0.040) | Ln(grassland)*Ln(labor) | ||

${\delta}_{22}$ | −0.005 (0.016) | 0.5*Ln(capital)^{2} | ||

${\delta}_{23}$ | 0.018 (0.031) | Ln(capital)*Ln(labor) | ||

${\delta}_{33}$ | 0.237* (0.102) | 0.5*Ln(labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.002*** (0.000) | utilized agricultural area | ||

${\gamma}_{1}$ | −0.194 (0.300) | Champagne-Ardenne | ||

${\gamma}_{2}$ | −0.241 (0.285) | Picardie | ||

${\gamma}_{3}$ | −0.236 (0.285) | Haute Normandie | ||

${\gamma}_{4}$ | −0.178 (0.286) | Centre | ||

${\gamma}_{5}$ | −0.214 (0.284) | Basse Normandie | ||

${\gamma}_{6}$ | −0.163 (0.293) | Bourgogne | ||

${\gamma}_{7}$ | −0.185 (0.284) | Nord-Pas-De-Calais | ||

${\gamma}_{8}$ | −0.199 (0.287) | Lorraine | ||

${\gamma}_{9}$ | −0.217 (0.289) | Alsace | ||

${\gamma}_{11}$ | −0.228 (0.284) | Pays de la Loire | ||

${\gamma}_{12}$ | −0.273 (0.284) | Bretagne | ||

${\gamma}_{13}$ | −0.240 (0.287) | Poitou-Charentes | ||

${\gamma}_{14}$ | −0.178 (0.286) | Aquitaine | ||

${\gamma}_{16}$ | −0.236 (0.308) | Limousin | ||

${\gamma}_{17}$ | −0.120 (0.290) | Rhône-Alpes | ||

Baseline: Ile-de-France | ||||

${\mu}_{16}$ | 0.034^{+} (0.017) | Year 2016 | ||

${\mu}_{17}$ | 0.004 (0.016) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.902 | −320.701 | −17.652 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | 6.926*** (1.244) | Constant | ||

${\beta}_{1}$ | −0.008 (0.460) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.426*** (0.051) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | −0.071 (0.289) | Ln (grassland) | ||

${\delta}_{2}$ | 0.100 (0.147) | Ln (capital) | ||

${\delta}_{3}$ | 0.992* (0.445) | Ln (labor) | ||

${\beta}_{11}$ | 0.083 (0.105) | 0.5 *Ln (milk production)^{2} | ||

${\rho}_{11}$ | 0.031 (0.063) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | 0.003 (0.035) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | −0.190* (0.088) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.035*** (0.006) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | −0.001 (0.004) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | −0.004 (0.004) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.003 (0.002) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | 0.009 (0.006) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | 0.009 (0.060) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | −0.023 (0.022) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | −0.008 (0.063) | Ln (grassland) *Ln (labor) | ||

${\delta}_{22}$ | −0.002 (0.017) | 0.5 *Ln (capital)^{2} | ||

${\delta}_{23}$ | 0.008 (0.035) | Ln (capital) *Ln (labor) | ||

${\delta}_{33}$ | 0.076 (0.119) | 0.5 *Ln (labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.001* (0.000) | utilized agricultural area | ||

${\gamma}_{1}$ | −0.021 (0.053) | Champagne-Ardenne | ||

${\gamma}_{2}$ | 0.024 (0.071) | Picardie | ||

${\gamma}_{3}$ | −0.039 (0.047) | Haute Normandie | ||

${\gamma}_{4}$ | 0.130 (0.119) | Centre | ||

${\gamma}_{5}$ | −0.055^{+} (0.029) | Basse Normandie | ||

${\gamma}_{6}$ | −0.036 (0.066) | Bourgogne | ||

${\gamma}_{7}$ | −0.011 (0.045) | Nord-Pas-De-Calais | ||

${\gamma}_{8}$ | −0.020 (0.039) | Lorraine | ||

${\gamma}_{9}$ | 0.004 (0.059) | Alsace | ||

${\gamma}_{11}$ | −0.063* (0.029) | Pays de la Loire | ||

${\gamma}_{12}$ | −0.163*** (0.029) | Bretagne | ||

${\gamma}_{13}$ | 0.029 (0.053) | Poitou-Charentes | ||

${\gamma}_{14}$ | −0.038 (0.053) | Aquitaine | ||

${\gamma}_{16}$ | −0.037 (0.062) | Limousin | ||

Baseline: Ile-de-France | ||||

${\mu}_{16}$ | 0.006 (0.019) | Year 2016 | ||

${\mu}_{17}$ | −0.027 (0.018) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.908 | −341.414 | −18.898 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

Coefficient | Estimate | Variable cost equation | Fuel cost share function | Feed cost share function |
---|---|---|---|---|

${\alpha}_{0}$ | −5.524* (2.228) | Constant | ||

${\beta}_{1}$ | 2.652*** (0.786) | Ln (milk production) | ||

${\alpha}_{2}$ | 0.441*** (0.096) | Ln (feed price/fuel price) | 1- constant | constant |

${\delta}_{1}$ | 2.645*** (0.552) | Ln (grassland) | ||

${\delta}_{2}$ | 0.086 (0.210) | Ln (capital) | ||

${\delta}_{3}$ | −1.532* (0.731) | Ln (labor) | ||

${\beta}_{11}$ | −0.190 (0.172) | 0.5*Ln (milk production)^{2} | ||

${\rho}_{11}$ | −0.269*** (0.080) | Ln (milk production) *Ln (grassland) | ||

${\rho}_{12}$ | −0.008 (0.054) | Ln (milk production) *Ln (capital) | ||

${\rho}_{13}$ | 0.163 (0.157) | Ln (milk production) *Ln (labor) | ||

${\zeta}_{12}$ | 0.039*** (0.010) | Ln (milk production) *Ln (feed price/fuel price) | - Ln (milk production) | Ln (milk production) |

${\alpha}_{22}$ | −0.001 (0.009) | 0.5 *Ln (feed price/fuel price)^{2} | -Ln (feed price/fuel price) | Ln (feed price/fuel price) |

${\nu}_{21}$ | −0.002 (0.008) | Ln (feed price/fuel price) *Ln (grassland) | -Ln (grassland) | Ln (grassland) |

${\nu}_{22}$ | −0.002 (0.003) | Ln (feed price/fuel price) *Ln (capital) | -Ln (capital) | Ln (capital) |

${\nu}_{23}$ | −0.039*** (0.011) | Ln (feed price/fuel price) *Ln (labor) | -Ln (labor) | Ln (labor) |

${\delta}_{11}$ | −0.260* (0.118) | 0.5 *Ln (grassland)^{2} | ||

${\delta}_{12}$ | −0.055 (0.047) | Ln (grassland) *Ln (capital) | ||

${\delta}_{13}$ | 0.280** (0.105) | Ln (grassland) *Ln (labor) | ||

${\delta}_{22}$ | 0.037^{+} (0.019) | 0.5 *Ln (capital)^{2} | ||

${\delta}_{23}$ | 0.004 (0.057) | Ln (capital) *Ln (labor) | ||

${\delta}_{33}$ | −0.492*** (0.182) | 0.5 *Ln (labor)^{2} | ||

${\beta}_{2}$ | 0.000*** (0.000) | other productions | ||

${\theta}_{1}$ | 0.002^{+} (0.001) | utilized agricultural area | ||

${\gamma}_{1}$ | −0.184** (0.060) | Champagne-Ardennes | ||

${\gamma}_{2}$ | −0.131^{+} (0.076) | Picardie | ||

${\gamma}_{3}$ | −0.084 (0.086) | Haute Normandie | ||

${\gamma}_{4}$ | −0.108 (0.156) | Centre | ||

${\gamma}_{5}$ | 0.028 (0.052) | Basse Normandie | ||

${\gamma}_{7}$ | −0.249** (0.086) | Nord-Pas-De-Calais | ||

${\gamma}_{8}$ | −0.088 (0.054) | Lorraine | ||

${\gamma}_{9}$ | 0.368^{+} (0.208) | Alsace | ||

${\gamma}_{11}$ | −0.164*** (0.047) | Pays de la Loire | ||

${\gamma}_{12}$ | −0.060 (0.069) | Bretagne | ||

${\gamma}_{14}$ | −0.012 (0.191) | Aquitaine | ||

${\gamma}_{16}$ | −0.436** (0.158) | Limousin | ||

Baseline: Ile-de-France | ||||

${\mu}_{16}$ | 0.006 (0.034) | Year 2016 | ||

${\mu}_{17}$ | 0.004 (0.030) | Year 2017 | ||

Baseline: 2018 | ||||

R^{2} | 0.894 | −282.326 | −9.027 |

^{+}

*P*< 0.10, *

*P*< 0.05, **

*P*< 0.01, ***

*P*< 0.001.

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