Estimation of Costs of Production at Farm Level

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1 Estimation of Costs of Production at Farm Level Estimation of flexible cost functions using the EU-FADN database Bruno Henry de Frahan and Rembert De Blander Université catholique de Louvain EAAE Congress, Zurich, August 30, 2011

2 Overview Cost function specification and estimation FADN data Generation of indicators Estimates for selected dairy EU regions Conclusions

3 Cost function: Augmented SGM Symmetric generalized McFadden cost function Cubic output terms (bold) Accommodate decreasing marginal costs (caused by quota) TC = + ( θ W ) a' Yt + ( φ' Y ) b' Wt + Y ' CW + Z' DW ( φ' Y ) ( θ W ) Z' FZ( φ' Y ) + Y ' GY + Z' HY + y ( Y'Q Y) m m W ' EW + 2 ( ) ( φ' Y ) θ W m W: input price vector Y: output quantity vector Z: fixed input quantity vector t: time θ W and φ Y: fixed-weight indices for first-order homogeneity in input prices and TC(Y=0, W,Z)=0

4 Derived input demand equations to estimate x i = θ + + ia' Yt + ( φ' Y ) bit + Y ' Ci + Z' Di( φ' Y ) ( φ' Y ) θi W Ei W EW ( θ W ) ' ' 2( θ W ) θi ( φ' Y ) Z' FZ + Y ' GY + Z' HY + y ( Y'Q Y) + i Imposed theoretical restrictions: Symmetry restrictions on elements of E, F, G and every Q m Adding up constraints for row elements of E Concavity of TC in input prices Convexity of TC in fixed inputs Convexity of TC in output quantities for the standard SGM Convexity of every MC m in output quantities for the augmented SGM Monotonicity conditions in output quantities but not in input prices and fixed input quantities m m m ε

5 Estimation procedure Non-linear seemingly unrelated regression of full system of I derived input demand equations Fixed-effect panel estimation: within-transformed system of equations period-specific error component is accounted for by using cluster-corrected standard errors

6 FADN data 3 panels for each member state or Nuts1 region: dairy, livestock and crop farms based on TF classification Outputs and inputs aggregated into a limited number of categories Törnqvist price indices for each category Prices: farmgate prices regional average Eurostat prices

7 Generation of indicators Marginal and average costs: MC AVC = TC = y 0 MC / y y Elasticities of input demands and marginal costs and / y MCp and = MC AVCp / = p AVC / p Elasticities of cost with respect to output (cost flexibilities) Economies of scale and scope: ORTS PSRTS ESCP ft ft = TC = = / [ TC ( Y, W, Z, t) TC ( Y, W, Z, t) ] M [ TC ft ( Ym, W, Z, t) ]/[ TC ft ( Y, W, Z, t) ] m= 1 ft m= 1 ft M y MC ft m / y MC

8 Specifications and econometrics results for dairy farms in selected EU regions Member country Region Cost function specification Uncentered R² Range Minimum Maximum Significant coefficients (%) Belgium - Augmented SGM Germany Bavaria Standard SGM Germany Lower Saxony Standard SGM Italy Veneto, Lombardy & Piedmont Augmented SGM France Brittany Augmented SGM France Pays de la Loire Standard SGM France Basse-Normandie Standard SGM Netherlands - Standard SGM Austria - Standard SGM

9 Input demand elasticities for Belgian dairy farms Own input demand elasticity of: Minimum Maximum Median Animal-specific inputs Crop-specific inputs, inc. land Cow inputs Intermediate inputs Purchased feeds

10 Marginal cost elasticities for Belgian dairy farms Elasticity of marginal cost of: with respect to: Minimum Maximum Median Milk milk output 1.5 e Milk other outputs 3.8 e Other outputs milk output 3.6 e Other outputs other outputs

11 Marginal and average costs of milk in selected EU dairy regions (means) Marginal cost Average cost Member Region (% of farm (% of farm country ( /ton) ( /ton) gate price) gate price) Belgium Germany Bavaria Germany Lower Saxony taly Veneto, Lombardy & Piedmont France Brittany France Pays de la Loire France Basse-Normandie Netherlands Austria

12 Marginal costs of milk for dairy farms in French and German regions ( /ton) Bavaria (DEU) Lower Saxony (DEU) Brittany (FRA) Pays de la Loire (FRA) Basse-Normandie (FRA)

13 Marginal costs of milk for dairy farms in other EU member countries ( /ton) /ton Belgium Italy The Netherlands Austria

14 Scale economies of dairy farms in selected EU dairy regions Country Region ORTS St.Dev PSRTS St.Dev Belgium e e-5 Germany Bavaria Germany Lower Saxony Italy Veneto, Lombardy e e-04 & Piedmont France Brittany France Pays de la Loire France Basse- Normandie Netherlands Austria

15 Scope economies of dairy farms in selected EU dairy regions Country Region ESCP St.Dev Belgium e-5 Germany Bavaria Germany Lower Saxony Italy Veneto, Lombardy & Piedmont e-06 France Brittany France Pays de la Loire France Basse-Normandie Netherlands Austria

16 Conclusions Possible to estimate rigourisely a cost function from FADN and, hence, marginal and average cost and other indicators Less successful for livestock and crop farms Monotonicty in some input prices is not always met Large variations in results across farms Barely any scale economies except in Brittany and NL, and some scope economies in AU and Bavaria Suitable for ex-post and ex-ante evaluations Documentation and Stata codes are available!

17 Thank you!

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