Feed substitution and economies of scale in Irish beef production systems

Transcription

1 Feed substitution and economies of scale in Irish beef production systems Andreas Tsakiridis *a,b, Kevin Hanrahan a, James Breen b, Michael Wallace c, and Cathal O Donoghue a a Rural Economy and Development Programme (REDP), Teagasc, Athenry, Co. Galway, Ireland b School of Agriculture and Food Science, University College Dublin, Belfield, Dublin 4, Ireland c School of Agriculture, Food and Rural Development, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom * andreas.tsakiridis@ucdconnect.ie Paper prepared for presentation at the 149th EAAE Seminar Structural change in agri-food chains: new relations between farm sector, food industry and retail sector Rennes, France, October 27-28, 2016 Copyright 2016 by Tsakiridis, A., Hanrahan, K., Breen, J., Wallace, M., O Donoghue, C. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. 1

2 Abstract We use a short-run translog cost function to model Irish beef production over the period Similar to other countries Irish beef farmers operate in various production systems with many farmers specializing in calf rearing, and other farmers specializing in beef fattening or other production systems. In order to identify potential technological differences and differences in scale economies across beef systems we estimate scale economies, own- and cross-price elasticities, and Morishima elasticities of substitution between purchased cattle, purchased feed, home-grown feed and veterinary services for three beef systems. Results suggest that all inputs are substitutes in the cow-calf, calf-tofinish, and other beef systems (store-to-finish and mixed beef systems) whereas extensive economies of scale exist in the cow-calf and calf-to-finish systems. The same trend is observed for other beef systems until 2005 although post-decoupling these systems operate under decreasing returns to scale. JEL classification: D240 Q120 Keywords: Input demand, Morishima elasticities of substitution, economies of scale, Irish beef systems, unbalanced panel data. 1. Introduction Significant changes have occurred in the Irish beef cattle industry since the 1990s. These changes have been mainly realized through the expansion of the national suckler beef cow herd and the increased importance of European Union s (EU) support payments (Binfield and Hennessy, 2001). The transformation of the Irish beef sector due to policy and economic growth factors was further challenged by the 1996 BSE (bovine spongiform encephalopathy) crisis in the United Kingdom, and the Luxembourg Agreement which initiated the decoupling of all direct payments from agricultural production decisions from 2005 onwards. The recent abolition of the European Union (EU) milk quota system in 2015 is expected to affect Irish beef production through the increase of dairy cow herd and the potential increase in the supply of dairy origin calves available for slaughter (Ashfield et al., 2014). Moreover, beef cattle industries in many countries are challenged from increased competition with other meat industries, continuous trade liberalization, climate change, water pollution, food safety and animal welfare issues. To convert these challenges to opportunities and remain economically viable beef farmers may need to adjust applied technologies as well as the scale of production and their efficiency. Prior knowledge on farm structures may help policy makers predict changes in farm structures while it is crucial for farm managers in determining farm s economic efficiency. Along this line, many earlier empirical studies have analysed the production structures and efficiency of livestock farms and meat processing industries. A widely 2

3 used approach to analyse the production structure of a firm (industry or economic sector) is based on ex-post (positive) methods of analysis and the utilization of Shephard duality theorem. This theorem allows the representation of applied technology by either a production function or a cost function, and the derivation of demand equations which facilitate the econometric estimation of technological parameters (Diewert, 1971). A dual cost function framework has been often employed to analyse the cost structures (as illustrated by e.g. the estimation of input demand and substitution elasticities, economies of size, scale or scope, capacity utilization) of dairy farms (e.g. Moschini, 1988; Wieck and Heckelei, 2007; Mayen et al., 2009; Gullstrand et al., 2014; Casasnovas-Oliva and Aldanondo-Ochoa, 2014; Atsbeha et al., 2015), hog (e.g. Azzam and Skinner, 2007; Duvaleix-Treguer and Gaigne, 2016), fish (e.g. Salvanes, 1989; Kvaloy and Tveteras, 2008), and poultry farms (e.g. Grisley and Gitu, 1985; Bamiro and Shittu, 2009). Other scholars have used various frontier (e.g. Mosheim and Lovell, 2009) and non-frontier approaches (e.g. Pierani and Rizzi, 2003) to estimate economies of scale while accounting for farm inefficiencies. In relation to the beef cattle sector, there exist limited studies on beef farm cost structures. Abdulkadri et al. (2006) analysed the cost structure of mixed wheat-beef cow operations using data at farm level. Abdulkadri et al. (2006) used a dual risk model for multiple outputs to determine economies of scale and scope. Mathews et al. (2008) derived input demand relationships in beef enterprises following the dual approach but used U.S. State-level feedlot monthly data. Employing a generalized McFadden cost function which incorporates seasonal variables, Mathews et al. (2008) estimated ownprice and cross-price elasticities between four weight categories of feeder cattle and two feed components (protein and energy). We aim to fill this gap in the livestock economics literature with an empirical study on the cost structures of Irish beef farms using an unbalanced panel of 1,798 farm households from 2000 to Employing a short-run equilibrium cost model substitution, own- and cross-price elasticities for variable inputs are estimated. Moreover, this study shows how the estimated average short-run economies of scale have been developed from 2000 to 2011 for the whole sample but also across different beef production systems. The next section outlines the theoretical framework, empirical model and estimation method of this study. The third section describes the data set, model variables, beef systems of interest while in the fourth section results are presented. The final section concludes. 2. Theoretical framework and empirical model specification Assuming that farmers have access to the same technology, the applied technology in the short-run is presented by F(Q, X i, L, t, D) = 0 where Q is farm s aggregate output (Q = value of total cattle sales divided by a farm-specific price index for sold cattle), X is a 3

4 vector of quantities of inputs i (i = purchased cattle-c, purchased feed-f, home-grown feed-h, veterinary and breeding services-v), L is an input held fixed or quasi-fixed (land devoted to cattle production), t is a time trend (t = 1,, 12), and D is a categorical variable indicating the beef production system in which a farmer chooses to operate during most of the years of his presence in the data set. Duality theory allows the representation of farm technology with a transformation function or its dual profit, dual cost or dual revenue function (Guyomard, 1988). We assume that Irish beef farmers minimize production costs by choosing a set of unrestricted input factors (C, F, H, V) subject to a quasi-fixed factor (L) and output quantity (Q), rather than maximize profits. The implied dual cost function can be written as: VC = VC * (P c, P F, P H, P V, Q, Z, t, D) (1) and farmer s cost minimizing behavior can be depicted as: VC (P i, Z, Q, t, D) = : F(X i, Q, Z, t, D)} (2) where P i are the prices of variable inputs i. A cost-minimizing behavior is considered as more realistic in the case of Irish beef farmers mainly due to three reasons: (1) as most of the Irish farmers combine two or more farm activities (e.g. a dairy enterprise with a crop and/or beef enterprise), the beef enterprise is the principal farm enterprise in profit terms for only few farmers thus the main source of revenue is a non-beef enterprise; (2) in Ireland, there is a limited transfer of land holdings between farmers, and limited access to rental land (especially for younger farmers), therefore many farmers cannot expand their land, herd and consequently maximize profits; (3) Irish beef production systems are low input systems since cattle s diet mainly consists of grazed and ensiled grass which is the cheapest feed (Crosson et al., 2006). We consider that VC * may be approximated by means of the restricted translog cost function (Christensen et al., 1973) as: ( ) ( ) ( ) (3) 4

5 with the symmetry conditions α ij = α ji, and all variables being in logarithmic form except trend (t) and the beef production system dummy (D). In the cost equation (3) an error term (ε it ) is also appended at the end of the formula. The incorporation of the dummy D in equation (3) was motivated due to fact that the variable Q, as defined earlier, captures quality characteristics of the output. Consequently, the operating beef production system which is defined by the types (e.g. calves, weanlings, finished cattle) of purchased and sold cattle is related to output Q, and thus interacts with Q. The variable D could also interact with the prices of purchased cattle however we assume that even if input prices differ from farmer to farmer; still farmers are price takers. Thus, our approach does not account for the possibility when farmers may pay a lower unit price for a variable input due to larger purchased input quantities (cf. Duvaleix-Treguer and Gaigne, 2016). Sufficient conditions for VC function to be homogeneous of degree one in prices P i are: (4) (5) Additionally the cost function should be concave in P i and non-increasing in fixed (or quasi-fixed) inputs (Melfou et al., 2009). The translog cost function is a flexible functional form in the sense that it does not impose any a priori restrictions on the substitution relationships between inputs. As we are interested in estimating input elasticities of substitution, this feature of the translog cost function is important. Moreover, the translog function has enough free parameters to be estimated and provide a second order differential approximation of an arbitrary continuous cost function (Christensen et al., 1973). The cost function (equation 3) contains all the necessary parameters for the calculation of scale economies, input demand and substitution elasticities, and can be estimated economterically in this study by panel data methods (e.g. pooled ordinary least squares, fixed or random effects model). However, simultaneous estimation of eq. (3) with the derived input shares equations and/or revenue (output) share function leads to more efficient estimates. Consequently, invoking Shephard s lemma, the input share equations can be derived from eq. (3): = = (6) where denotes the cost share of variable input i (i = C, F, H, V). Similarly, the output share equation is: = = (7) 5

6 The output share equation imposes optimizing behaviour in the output market (Rodrigues and Arias, 2008). The system of equations (3), (6) and (7) are jointly estimated after imposing parametric restrictions of symmetry and homogeneity of degree one on input prices. The adding-up property (eq. 4) is imposed by dividing variable cost and all input prices by one of the input prices (numéraire) and the share equation of this input is dropped from the estimated system of equations to avoid singularity of the system. The parameters of the dropped input can be recovered by eq. (4) and (5). In this study the dropped variable input was chosen to be the veterinary and breeding expenses. Before taking the logarithms all independent variables were normalized with its mean value in the sample and the time trend variable was normalized to be zero in year This normalization allows the first-order parameters of the logarithmically-transformed variable to be interpreted as cost elasticities at the point of normalization (sample mean in our case). In order to estimate jointly the variable cost function (eq. (3)), with the three share equations for purchased cattle, purchased feed, home-grown feed (as in eq. (6)) and the output share equation for cattle sales (eq. (7)), the three-stage least squares (3SLS) estimation procedure was followed. Nevertheless, the estimates from the 3SLS estimation are sensitive to the choice of excluded input share equation thus the iterated 3SLS (I3SLS) procedure was applied to ensure that the estimated parameters are invariant to the choice of dropped input (Mamatzakis, 2003). Furthermore, we used the withintransformed variables (except the time trend which is exogenous) and the withintransformed cross-products of variables as instruments. Based on the estimated parameters and the cost shares of variable inputs, the constant output own-price ( ) and cross-price elasticities ( ) of variable inputs demand can be calculated as: for all i s for all i,j; i j Different measures of the elasticity of substitution between two inputs have been proposed with the Allen-Uzawa partial elasticity of substitution, being widely presented in literature. This measure of substitution elasticity measures the responsiveness of the demanded quantity of an input to a change in the price of another input, weighted by the cost share of the input for which a price has changed. Hence, the Allen-Uzawa partial elasticity of substitution does not directly measures the change in the relative use of two inputs due to price changes (Magnani and Prentice, 2006). According to Blackorby and Russell (1989), the Morishima elasticity of substitution (MES) is a more insightful measure of input substitution which measures how the ratio of inputs i, j responbds to a change in P j. In other words MES measures relative input adjustment to any single-input 6

7 price changes. Two inputs are considered as substitutes (complements) if an increase (decrease) in the price of an input results in increased (reduced) demanded quantity of the other input relative to the quantity of the input whose price has changed (Angulo, 2013). The formula for the computed Morishima elasticities of substitution is: A measure of short-run scale economies (SCE SR ) has been defined by Christensen and Greene (1976) as one minus the proportional increase in cost resulting from a proportional increase in output: ( ) If SCE SR is positive (negative), there exist short-run increasing (decreasing) returns to scale. 3. Data An unbalanced panel of Irish farmers has been constructed for the years from 2000 to 2011 inclusive. Since 1972 Teagasc National Farm Survey data are annually collected as part of a requirement to provide farm level data to the EU Farm Accountancy Data Network (FADN). Each farm is assigned with a weighting factor for more accurate representation of the national farm population (Teagasc, 2014). Farms comprise either specialized or mixed enterprises, such as dairy, beef, sheep, and/or tillage enterprises, with many beef enterprises being combined with other farm enterprises or off-farm employment. The gathered data include detailed information on the financial structure of the farm household and enterprise-specific level, such as direct and overall cost of production, market returns, subsidies and other grants. There are also data on quantities of inputs, yield, sales volume, inventories, livestock numbers, age of animals, technical and physical farm infrastructure, as well as farm household socio-demographic information. Irish beef farmers source calves from their own beef and dairy breeding herd, with a smaller proportion of calves being purchased from other sucker beef cow farms. The traditional calving season is spring, and suckler beef cows rear their own calves until weaning at the end of the first grazing season (O Donovan et al., 2011). While some of the weaned female calves will be kept as replacement breeding stock, a large proportion of weaned calves will be sold in livestock marts or other farms (backgrounding operations or cattle finishers). Other farmers will decide to keep the weanlings during the winter (indoors feeding) and place them on pasture next spring. At the age of approximately 12 months or more, the majority of these weaned calves will be sold as stores (also referred as post-weanlings or feeder cattle) which will eventually enter the 7

8 finishing phase and being fed with high-energy diets. A smaller proportion of suckler cow farmers will retain most of the calves from birth to slaughter. In this study, farmers are grouped in three distinct production systems; namely (1) the cow-calf system (C-C) where more than 50 per cent of the cattle enter the beef enterprise as calves (purchased calves plus calves from beef cow and/or dairy herd) and more than 50 per cent of the cattle exit as sold weanlings or stores; (2) the calf-to-finish system (C- F) which differs from the previous system only because the majority of cattle exiting the enterprise are sold as finished animals; (3) the other systems (O-S) category refers to farmers who mainly buy cattle as weanlings and/or stores and finish them (cattle finishers); but also famers with diverse beef herds without any animal class being dominant when cattle are purchased or sold (mixed system). A very small proportion of beef farms in the sample could not be classified in any of the above mentioned systems. Our initial data set refers to 13,885 observations from more than 2,000 different farms. Prior to the econometric estimation, data cleaning involved the identification of inconsistent and missing records, the exclusion of extreme observations (outliers) and farms with less than ten grazing cattle livestock units (LU). This process reduced our observations to 8,662 referring to 1,798 farms. For the purpose of estimating the cost function, the production of beef enterprises is aggregated into a single output; the total sales revenue from sold calves, weanlings, stores, finished cattle, cattle for breeding and other cattle. The implicit volume of composite output is obtained by dividing revenue from cattle sales by farm-specific Laspeyres price indices for cattle sales. The hectares of land (area for hay and silage plus the fodder and non-fodder crops area) devoted for the cattle enterprise are considered as a quasi-fixed factor of production. The four inputs (X i ) in eq. (2) are (1) purchased cattle (heads), (2) purchased tonnes of concentrate feed and milk substitutes, (3) total tonnes of hay, silage, fodder and non-fodder fed to cattle, and (4) cost for veterinary and cattle breeding services. The price index (Laspeyres index) for veterinary and breeding services was obtained from the Irish Central Statistics Office (CSO) with base year 2000, while farm-specific Laspeyres price indices (base year 2000) were constructed for the remaining inputs. The mean values of these price indices and some other variables are given in Table 1. Table 1. Summary statistics of selected variables Variable Unit Cow-calf system (n=4,342) Calf-tofinish system (n=2,077) Other systems (n=1,562) All beef farms (n=8,662) Mean (Standard deviation) Purchased cattle Base year 2000 (=100) (32.650) (29.232) (31.482) (31.896) 8

9 (Laspeyres price index) Purchased feed (Laspeyres price index) Base year 2000 (=100) (20.718) (22.292) (20.353) (21.031) Home-grown feed (Laspeyres price index) Base year 2000 (=100) (11.590) (12.702) (12.435) (11.964) Veterinary and breeding services (Laspeyres price index) Base year 2000 (=100) ( ( ( (10.060) Land devoted for cattle production Hectare (19.394) (26.103) (21.484) (22.091) Herd size (total cattle LU) NFS-grazing livestock units (dairy cow equivalent ) (21.223) (35.518) (29.936) (27.905) Farmer s age Years (12.158) (13.040) (33.130) (19.225) Percentage of purchased cattle in variable costs (%) (25.256) (25.534) (28.195) (33.632) Percentage of purchased feed in variable costs (%) (21.662) (22.067) (17.369) (23.382) Percentage of home-grown feed in variable costs (%) (14.621) (12.867) (7.657) (13.434) Percentage of veterinary and breeding services in variable costs (%) (16.727) (14.314) (13.080) (17.128) 9

10 Variable costs (per cattle LU) Deflated variable costs with CSO Total Input Price Index (base year 2000) ( ) ( ) ( ) ( ) Source: Authors calculations based on data from the sample under study. Figures account for farm sampling weights (each farm variable is multiplied by its associated Teagasc NFS weighting in order to get a more accurate representation of the farm at national level. Prices for feed (purchases and home-grown) are not too different across beef systems and the overall sample mean, whereas the price of purchased cattle is not surprisingly higher for farmers in other systems as many of them are cattle finishers who buy older animals (weanlings or stores) which typically cost more than calves. Farmers in the calf-to-finish system have larger cattle herd and devote more land for beef production. On average, C-F farmers use more purchased feed (about 47 per cent of total variable cost is for purchased feed), while O-S farmers spend more on buying cattle and C-C farmers on veterinary and breeding services. According to the figures in Table 1 the most cost ineffective (per LU) beef system is O-S (625 per LU). 4. Results Following the procedure described in section 2, the system of variable cost function, three input demand equations and output share equation was estimated (parameter estimates are provided in Table A1 of the Appendix and refer to the sample mean i.e. the average beef farm of the sample). Most of the coefficients are significantly different from zero at 10 per cent critical level. Regarding the two principal regularity conditions, the estimated input price coefficients α i should be non-negative to ensure concavity in prices (a sufficient condition for concavity) at the mean of the sample, and the fitted (predicted) cost shares should be all strictly positive (Berechman, 1983). As shown in Table A1 all α i s are positive and the fitted input shares were found to be strictly positive (at the mean of the sample) indicating that the employed cost function was well-behaved in this respect. Table 2 presents the estimated own- and cross-price elasticities across all beef farms. As expected all own-price elasticities are negative with home-grown feed being the most responsive to price changes (its estimated own-price elasticity is %). If the price of home-grown feed increases by 1%, its demand will decrease by 0.896%. Nevertheless, the demand for all inputs appears inelastic as all the estimated own- and cross-price elasticities have (absolute) value less than unity. 10

11 Table 2. Own and cross-price elasticities of demand evaluated at the sample average shares (standard errors in parentheses) Purchased cattle (C) Purchased feed (F) Home-grown feed (H) Veterinary and breeding services (V) *** (0.020) *** (0.015) *** (0.031) *** (0.016) *** (0.017) *** (0.043) *** (0.104) *** (0.053) *** (0.010) *** (0.033) *** (0.171) *** (0.076) *** (0.010) *** (0.031) *** (0.142) *** (0.083) Source: Authors calculations. The estimates account for farm sampling weights. The significance thresholds are respectively 1% ( *** ), 5% ( ** ), and 10% ( * ). Positive but not strong cross-price elasticities suggest that for the average Irish beef farm, all inputs are substitutes. The demand for purchased cattle seems to be affected by increases the price of feed concentrates (the opposite holds as well) while home-grown feed demand is more responsive to changes in veterinary and breeding services cost. Table 3. Morishima elasticity of substitution evaluated at the sample average shares (standard errors in parentheses) Purchased cattle (C) Purchased feed (F) Home-grown feed (H) Veterinary and breeding services (V) *** (0.051) *** (0.033) *** (0.043) *** (0.031) *** (0.174) *** (0.190) *** (0.136) *** (0.087) *** (0.083) *** (0.100) *** (0.212) *** (0.235) Source: Authors calculations. The estimates account for farm sampling weights. The significance thresholds are respectively 1% ( *** ), 5% ( ** ), and 10% ( * ). 11

12 The estimated Morishima elasticities of substitution (Table 3) confirm that all inputs are substitutes and they reveal much stronger substitution relationships compared to the cross-price elasticities. Home-grown feed is a strong substitute for all other inputs; a 1 per cent increase in the price of home-grown feed causes the purchased cattle-homegrown feed ratio to increase by per cent. This confirms the key role of home-grown feed in Irish production systems. The estimated annual short-run scale economies for all beef farms and across the three systems of interest from 2000 to 2011 are given in Table 4. Farmers in the C-C system exhibit positive scale economies every year with significant increase from 2000 to Post-decoupling scale economies continued to increase but in a more moderate manner. Positive scale economies suggest that unit beef production cost declines as the size of beef enterprise increases. The same holds for C-F farms and when scale economies are estimated for the entire sample. Contrary to the suckler cow systems, O-S farmers exhibit economies of scale until 2004 while from 2005 onwards realize diseconomies of scale. Nevertheless, the estimated average scale economies of O-S farmers for the 12 year period under study indicate that they have operated closer to the optimal point where scale economies equal zero. Table 4. Average economies of scale over time Cow-calf system Calf-to-finish system Other systems All beef farms

13 Average Observations ( ) R 2 (cost function) Note: The estimates account for farm sampling weights. 5. Conclusions Our analysis focuses on the period , a period of important policy changes, increased competition between meat industries, and international trade liberalization. Although C-C farmers are generally vulnerable to market changes due to their inability to operate exclusively on cattle margins as do beef cattle finishers (Schroeder and Featherstone, 1990), we found extensive economies for Irish C-C. Farmers operating in C-F system also exhibit scale economies while farmers in mixed systems of operating exclusively in the cattle fattening phase experienced diseconomies of scale from 2005 until Increased scale economies was found for the wider beef farming industry suggesting that significant cost reductions could be achieved with increased output level. Consequently an increased supply of dairy origin calves might lever this output shift. The estimation of input elasticities of substitution does not imply significant technological differences across the beef systems under study. Existing information asymmetries between upstream (e.g. C-C systems) and downstream segments (e.g. O-S) of the beef industry may explain differences in their estimated scale economies. References Abdulkadri, A.O., Langemeier, M.R., and Featherstone, A.M. (2006). Estimating economies of scope and scale under price risk and risk aversion. Applied Economics, 38(2): Angulo, L.P. (2013). Labour inputs substitution during corporate restructuring: a translog model approach for US freight railroads. Applied Economics, 45: Atsbeha, D.M., Kristofersson, D., and Rickertsen, K. (2015). Broad breeding goals and production costs in dairy farming. Journal of Productivity Analysis, 43:

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16 Teagasc (2014). Teagasc National Farm Survey Results 2013: Appendix. Retrieved September 2016 from Wieck, C. and Heckelei, T. (2007). Determinants, differentiation, and development of short-term marginal costs in dairy production: an empirical analysis for selected regions of the EU. Agricultural Economics, 36: Appendix Table A1. Parameter estimates-all beef farms (n = 8,457) Symbol Estimate Standard error Symbol Estimate Standard error *** * *** *** ** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** * *** ***

17 0.680 *** *** * *** ** *** (constant) *** (x 10-4 ) Note: Results from I3SLS. The estimates account for farm sampling weights. R 2 (cost function) = The significance thresholds are respectively 1% ( *** ), 5% ( ** ), and 10% ( * ). 17