Are larger farms more effcent? A farm level study of the relatonshps between effcency and sze on specalzed dary farms n Sweden Helena Hansson Swedsh Unversty of Agrcultural Scences, Department of Economcs, PO Box 7013, SE-750 07 Uppsala, Sweden, emal: helena.hansson@ekon.slu.se The study explored how economc, techncal and allocatve nput effcences n specalzed Swedsh dary farms are affected by dfferences n farm sze. The effcency analyss showed that costs could decrease by 30% f all farms were as effcent as the best farms n the sample. The effect of farm sze was analysed n second-stage regressons. Two measures of farm sze were consdered: ncome from dary and the number of hectares, together wth squared measures of both sze measures and varables to control for geographc locaton. The results showed that the relatonshps between farm sze and effcency can be descrbed as non-lnear, where effcency frst tends to decrease wth sze and then ncrease. The average scale effcency was 94.7%, suggestng that, on average, the farms are close to ther optmal scale. The paper concludes by suggestng that farm effcency can be ncreased both by focusng on ncreasng the knowledge about how nputs can be more optmally combned and by growth of the farms. However, the latter suggeston requres farm growth amng at the larger farm segments. Key-words: Dary farms, data envelopment analyss, effcency, farm sze, Sweden, tobt regresson Introducton Durng the last decades, Swedsh dary producton has undergone extensve structural changes at the farm level. From 1990 to 2006, the number of dary farms decreased by about 69%, meanwhle the amount of mlk produced only decreased by 9% (Statstcs Sweden 2007). Durng the same tme perod, the mean herd sze more than doubled, from 22 to 48 cows (Statstcs Sweden 2007). Ths mples that small farms change to other producton lnes, go out of busness or merge wth other farms. The trend s not unque for Sweden; decreases n the Agrcultural and Food Scence Manuscrpt receved August 2007 325
Hansson, H. Are larger farms more effcent? number of dary farms are also reported n other North European countres, meanwhle the sze of the dary herds grows at a rapd speed (Statstcs Sweden 2002, 2006). For example, from 1997 to 2003, the number of Fnnsh dary farms decreased by 35.5% (Statstcs Sweden 2002, 2006). At the same tme the average Fnnsh dary herd grew 35% to 17.5 cows (Statstcs Sweden 2002, 2006). In Denmark, the number of dary farms decreased by 39% from 1997 to 2003, whle ther average herd sze grew by 44% to 75 cows (Statstcs Sweden 2002, 2006). Smlar trends,.e. fewer and larger dary farms, are also reported for the U.S (Tauer and Mshra 2006, MacDonald et al. 2007). A clear reason underlyng the descrbed structural changes s the desre ether to ncrease productvty and farm return by realzng returns to scale or to ncrease farm return by larger producton volumes. Farm growth was stressed as crucal by Newman and Mattews (2006) who found a productvty growth rate of Irsh dary farms of 2% annually. They suggested that larger scale of dary farms s necessary because the 2% are not suffcent to cover both nflaton and possble declnes n nomnal mlk prces. A revew of the lterature on farm level effcency n dary and related farms shows that these farms have a large potental for ncreased returns f all farms were as effcent as the best farms. For example Oude Lansnk et al. (2002) studed techncal effcency of Fnnsh farms, usng the data envelopment analyss (DEA), and they found that the conventonal lvestock farms had techncal effcency scores of 69%. Consequently, these farms should be able to reduce ther costs by 31% f the average farms were as techncally effcent as the best farms n the sample. Renhard et al. (2000) studed a sample of Dutch dary farms, usng both the stochastc fronter approach (SFA) and DEA. They found an average techncal effcency score of 89% n the SFA case and 78% n the DEA case. The dfference between the SFA and the DEA results s lkely to depend on the determnstc nature of DEA, where all devatons from the effcent fronter are consdered as neffcency. Heshmat and Kumbhakar (1994) examned the techncal effcency n four panels of Swedsh dary farms, durng 1976 to 1988, excludng 1985, usng the SFA. They found that the average techncal effcency scores were located between 81% and 83% for all four panels. Gven the results n the revewed lterature, one urgent queston s how the dary farms can become more effcent. An approach observed emprcally, n the structural changes n progress, s to enlarge farm sze to realze cost advantages of larger scales, so-called economes of scale. In Sweden, ths approach s also drven by polcy makers such as dary farm advsors, who encourage dary farms to become larger. Furthermore, the observed approach s drven by technology developments whch buld on large loose housng systems. Nevertheless, the effect of farm sze on dary farm effcency s not clear, and consequently t s unsure whether the outcome of a farm enlargement wll be a more effcent farm. Penrose (1959) argues that frm nputs are ndvsble, and that the desre to fully use all nputs trggers frm growth. However, growth then mples that some other nput s not fully used, whch arguably leads to neffcency and neffcency n producton s consequently lkely to reman. Some authors have studed how dary farm producton s affected by farm sze and suggest that techncal effcency s postvely affected by farm sze (Bravo-Ureta and Reger 1991, Alvarez and Aras 2004, Barnes 2006, Hadley 2006) but that economc and allocatve effcences are negatvely affected by farm level sze (Bravo-Ureta and Reger 1991). These fndngs thus suggest that larger farms are better at usng ther nputs n a techncally effcent way, but worse at combnng ther nputs n a optmal way takng prces nto consderaton. The applcatons n these three studes were made to New England (Bravo-Ureta and Reger 1991), Span (Alvares and Aras 2004), Ireland (Barnes 2006) and England and Wales (Hadley 2006). Karaganns et al. (2002) found evdence of decreasng returns to scale n UK dary farms, whch suggests that n these farms, unt producton cost wll ncrease when the farms become larger. On the other hand MacDonald et al. (2007) found ncreasng returns to scale n U.S. dary farms, suggestng cost advantages at larger farms. Outsde the dary sector, Helfand and Levne (2004) found a non-ln- 326
ear relatonshp between the sze of farms n Brazl and techncal effcency, where techncal effcency frst decreased and then ncreased wth sze. Irázoz et al. (2003) found no conclusve results on the relatonshp between techncal effcency and sze, measured n terms of the total producton, n hortcultural producton n Span. Sharma et al. (1999) found a postve relatonshp between economc, techncal and allocatve effcency and sze, defned as the number of sows, n swne farms n Hawa. If we are to understand f and how the observed structural changes wth fewer and larger dary farms n the North European countres, are to lead to more effcent farms, further studes that analyse how farm sze affects farm effcency are needed. Unless ncreasng returns to scale,.e. cost advantages of larger farms, are present, returns ncrease because producton s scaled up. In ths stuaton the neffcent producton remans. Not only does the fact that prevous lterature show no clear, unambguous relaton between farm sze and effcency justfy further studes, but more mportantly: prevous lterature s not possble to generalze easly to e.g. north European countres because of dfferences n farmng systems, clmate and culture. Ths study amed to nvestgate how economc, techncal and allocatve nput-orented effcences were affected by dfferences n farm sze n dary farms n Sweden. Moreover, the study amed to nvestgate the farm scale effcences and effects 1 to further study the potental mprovements n effcency due to larger farms. The results showed that there s room for mprovements n farm effcency f all farms were as effcent as the best ones. Further, the results showed that the relatonshp between farm effcency and sze can be descrbed as non-lnear, where effcency s frst decreasng wth farm sze and then ncreasng. 1 Note that scale effcences and effects are not the same thng. See below. 327 Method The study was conducted n three steps. Frst, farm economc, techncal and allocatve nput-orented effcences were estmated. The effcency scores were based on the framework developed by Farrell (1957). Second, the nfluence of farm sze on effcency was determned. Thrd, farm level scale effcences and effects were assessed. The analyss bulds on comparsons between farms wth dfferent levels of effcency and sze at a gven pont n tme. Ths means that the dynamc aspect of farm growth s not ncorporated n ths study. A descrpton of effcency In effcency studes, the nput-orented effcency scores consder the cost sde of a frm, by answerng the queston of how much costs can decrease through more effcent use and more optmal combnaton of nputs, whle a gven level of outputs s produced. Techncal effcency measures the extent to whch the frm uses ts nputs as ntensely as possble. Allocatve effcency measures the extent to whch the frm combnes ts nputs n the optmal combnaton, takng nput prces nto consderaton. Economc effcency s a combned measure of both techncal and allocatve effcences and thus measures the overall effcency. If sngle output and two nputs are assumed, the three nput-orented effcency scores can be shown graphcally as n Fgure 1. The soquant represented by YY shows the techncally effcent way of producng the gven output Y. A farm stuated somewhere along ths soquant s therefore techncally effcent. The economcally effcent pont s at the tangency pont between the soquant and the socost lne PP. At ths pont, the techncal rate of substtuton equals the economc rate of substtuton. Assume a frm, whch produces Y wth the nputs x1 and x2, stuated at the pont R. Its economc nput-orented effcency s measured as the dstance 0R dvded by the dstance 0R. The techncal effcency of ths frm s measured as the dstance 0Q dvded by the
Hansson, H. Are larger farms more effcent? x2 P 0 Y R' Q R Q' Fg. 1. Economc, techncal and allocatve nput-orented effcency. Economc effcency s measured as 0R /0R. Techncal effcency s measured as 0Q/0R. Allocatve effcency s measured as 0R /0Q. dstance 0R. Allocatve effcency, fnally, s measured as the dstance 0R dvded by the dstance 0Q. Economc effcency can then be recognzed as the product of techncal and allocatve effcences. All effcences are measured n the nterval 0-1, where 1 ndcates full effcency. For a revew of effcency measures see e.g. Coell et al. (2005) Y' P' x1 devatons from the effcent fronter as neffcency, whereas SFA reports some as stochastc varaton. Both DEA and SFA are emprcal methods, whch mples that they construct effcent fronters based on the most effcent frms n the sample at hand. The remanng frms get effcency scores n relaton to the effcent fronter. Ths means that the effcency of one frm s measured n relaton to the other frms n the sample. DEA was appled n ths paper because we experenced advantages of t such as t does not requre specfcaton of functonal form and that t allows easly for the decomposton of the economc effcency score nto ts techncal and allocatve parts. Before estmatng the farm level effcences, an assumpton about the scale at whch the farm s operated s needed. Varous constrants at the farm, such as fnancng and goals of the farmer can cause the farm to operate at a scale that s not long-run optmal from an economc pont of vew. Prevous lterature has found that at farms, other goals than proft maxmzatons nfluence the actons (e.g. Gasson et al. 1973, Lunneryd 2003). To account for ths, varable returns to scale (VRS), whch allows operaton at all scales, was assumed when assessng the economc, techncal and allocatve nput effcences. Step 1: estmaton of farm effcency Data envelopment analyss, DEA (Charnes et al. 1978) was used to estmate the farm effcency. DEA s a determnstc approach that uses lnear programmng to calculate the farm effcency score. An alternatve way of estmatng effcency scores s the stochastc fronter approach, SFA (Agner et al. 1977, Meeusen and van den Broeck 1977) whch makes use of econometrc methods. DEA and SFA have been compared n several emprcal settngs, wth the common result that they assess relatve effcency to the same frms and that the average effcency scores are ether equal or lower n DEA (Balcombe et al. 2006, Cullnane et al. 2006, Irázoz et al. 2003, Coell and Perelman 1999, Sharma et al. 1999, Rest 1997). Lower average effcency scores n DEA are expected because DEA reports all 328 DEA equatons to calculate economc, allocatve and techncal effcency Assume n farms, whch use the nput matrx X, to produce the output matrx Y. The nput and output matrces of each ndvdual farm,, are x and y respectvely. Further, assume that each farm faces a cost-mnmzng nput bundle, x and an nput prce vector w. In ths settng, the DEA economc nput effcency scores were obtaned by frst solvng the followng lnear programme: Subject to mn y λ, x N1' λ = 1 λ 0 ' w x, + Yλ 0, x Xλ 0 (1)
where w x, would be the mnmum cost of farm f t was as effcent as the most effcent farm n the sample. The economc effcency score of each farm was obtaned by comparng the mnmum cost of the farm to ts actual cost: w (2) ' x EE = w ' x Techncal effcency scores were obtaned by solvng the followng programme: Subject to mn θ, θ y + Yλ 0, N1' λ = 1, λ 0, θ (0,1] θ x Xλ 0, λ (3) where N1 λ=1, s a constrant to ensure the assumpton of VRS. Fnally, the allocatve effcency scores were obtaned by dvdng the economc effcency score wth the techncal effcency score: EE AE = θ (4) Each DEA equaton,.e. equaton 1 and 3, was solved once for each farm n the sample. Further, the calculatons n equaton 2 and 4 were done once for each farm. where ε~n(0,σ 2 ) and the are the parameters for the explanatory varables. (For a revew of tobt regresson, see for example Hayash 2000). The combnaton of DEA effcency scores and tobt regresson s common n the lterature, where examples nclude Sharma et al. (1999), Galanpoulos et al. (2006), Haj and Andersson (2006) and Barnes (2006). However, the approach was crtczed by Smar and Wlson (2007) because the explanatory varables used n the second stage regresson are lkely to be correlated to the nputs and outputs used to estmate the frst stage DEA effcency scores, and because DEA scores can be based n small samples. Instead, Smar and Wlson (2007) suggested two bootstrap algorthms to overcome these problems. Afonso and St Aubyn (2006) compared n an emprcal settng the results from the bootstrap algorthms and the tradtonal twostage approach and found that both the estmated coeffcents and the sgnfcance levels were very smlar n all three cases. Ths questons the value of the extra computatonal burden caused by the bootstrap algorthms. Furthermore, Hoff (2007) compared emprcally the DEA-tobt model wth more complcated regresson models and concluded that the tobt model s often suffcent to assess the second stage effects of DEA models. Step 3: scale effcences and effects Step 2: regressons analyss To assess the effect of dfferences n farm sze, the effcency scores were regressed on varables measurng farm sze. Because effcency scores cannot be larger than one, the censored, or tobt, model was used. The tobt model can be wrtten as follows: y =Σ y = 1 f y = y β x + ε, = 1,2,... n, f y y 1 < 1 (5) 329 DEA scale effcences,.e. the extent to whch the farm s operatng at ts economcally optmal scale, were calculated by solvng equaton 3 agan. However, ths tme the constrant N1'λ=1 was deleted to obtan a measure of techncal effcency under the assumpton of constant returns to scale (CRS). The scale effcency (SE ) of each farm was then calculated as follows: TE SE = TE CRS VRS (6) where TE CRS s the techncal effcency of farm under the assumpton of CRS, and s the techncal effcency of farm under the assumpton of VRS.
Hansson, H. Are larger farms more effcent? To dentfy the scale type 2 at whch the frm s operatng, equaton 3 was solved once more, but ths tme the constrant N1 λ = 1 was changed to N1'λ 1, to mpose non-ncreasng returns to scale. If the new techncal effcency score obtaned s equal to the one obtaned by mposng varable returns to scale, the frm s operatng at decreasng returns to scale (DRS); otherwse t s operatng at ncreasng returns to scale (IRS). A frm operatng at ts optmal scale,.e. at CRS was dentfed by nvestgatng whether TE CRS = TE VRS, where equalty means that the farm s operatng under CRS. (See for example Coell et al. 2005). As was stressed n Forsund and Hjalmarsson (2004), DEA scale effcency scores may depend on the orentaton (nput or output) n the analyss. As a consequence the procedure followed n ths paper should be nterpreted n lght of the nput-orented DEA analyss. Data and descrpton of the studed farms Farm level accountng data from Statstcs Sweden were used n ths study. Statstcs Sweden collects detaled nformaton about the farms ndvdual balance sheets and ncome statements. The dataset s an unbalanced panel and stratfed accordng to farm sze and geographcal locaton. Regonal prce data from a database 3 consstng of gross margn 2 A frm can be operatng under ether constant, ncreasng or decreasng returns to scale. Constant returns to scale refers to a stuaton where the percentage ncrease n total costs s equal to the percentage change n output when the frm ncreases ts output. Increasng returns to scale refers to a stuaton where the percentage ncrease n total cost s less than the percentage change n output, when the frm ncreases ts output. Decreasng returns to scale refers to a stuaton where the percentage ncrease n total cost s larger than the percentage change n total output, when the frm ncreases ts output. 3 Agrwse, publshed by the department of economcs, SLU, Sweden. 330 budgets for dfferent agrcultural producton lnes and regons n Sweden were used when t was not possble to calculate the prces drectly from the accountng data. Ths means a use of standard prces, whch do not take nto account the possblty of negotatng prces. Therefore, the actual nputs of farms that can negotate prces may be underestmated, and as a result ther effcency scores overestmated. Only specalzed dary farms, defned as farms where the ncome from mlk s at least 75% of the total ncome, were studed. Furthermore, farms wth a mlk producton of less than 160,000 ltres per year,.e. a herd sze of approxmately 20 cows were deleted from the dataset, to get a dataset wth an average herd sze that reflects the real average herd sze n Sweden accordng to the latest offcal statstcs. Ths also avods nfluence from farms that are lkely to have qutted dary producton snce the data were collected. In total, 209 farms were studed. The dataset s an unbalanced data panel startng n 1998 and endng n 2002. To take stochastc varaton n the data, to whch DEA s senstve, nto consderaton each farm was represented by ts own average of nputs, outputs and prces. Each farm was thus represented by ts own average sze over the years t partcpated n the dataset. The number of dary cows was not explctly ncluded n the dataset. However because the dstrbuton of the number of cows n the sample s relevant background nformaton to the study, the number of dary cows was approxmated by assumng that each cow on average yelded 8000 ltres of mlk per year. In Fgure 2, the dstrbuton of the number of cows n the sample s shown. The fgure shows that there s a large varaton n the number of cows n the sample. Varables used n the effcency estmatons Inputs were aggregated nto sx varables: fodder, labour, captal, energy, seed and fertlzer, whch are consdered as the man purchased nputs of a dary farm. The fodder varable conssted manly of
Number of farms 120 80 40 0 < 40 cows 40< cows <60 60< cows <80 80< cows <100 Fg. 2. The dstrbuton of cows n the sample. >100 cows concentrate and mneral fodder. Labour represented the total labour need at the farm and conssted of both famly labour and hred labour. Captal was a measure, n SEK, of producton rghts, fxed equpments and buldngs. Energy was a measure of the amount of ol and electrcty used. Seed and fertlzer measured how many klograms of each were used. Because ncluson n the sample was based on the farms degree of specalzaton n mlk producton, outputs conssted manly of mlk. However, the farms also used ther nputs to produce other outputs than mlk, such as lvestock, crop and forage. Total outputs were therefore aggregated nto a sngle measure of farm output: total revenue. Two dfferent measures of sze were consdered: ncome from mlk and number of hectares. Income from mlk measured the sze of the dary producton and the number of hectares measured the physcal sze of the farm. It would have been more preferable to measure the sze of dary producton n the number of cows at the farm; however, ths measure was not avalable for all farms n our dataset. To account for the possblty of non-lnear effects, squared measures of the sze varables were also ncluded n the regressons. Summary statstcs of the data are contaned n Table 1. To account for dfferences n effcency due to dfferences n geographcal locaton, dummy varables representng dfferent geographcal locatons were used. In offcal statstcs, Sweden s normally dvded nto eght producton areas, accordng to Fgure 3. These producton areas were used as ndcators of geographc locaton. To avod perfect multcollnearty, the dummy varables for locaton n area 8, Nö, northern Sweden, were not ncluded n the regressons. Ths mples that the coeffcents of the geography dummes should be nterpreted as the relatve effect compared to beng located n northern Sweden. Table 1. Summary statstcs of the varables n the study. Fgures based on 209 specalzed dary farms Mean Standard devaton Fodder (klograms) 230961 205626 Labour (hours) 5042 1935 Captal (SEK) 1038829 1133996 Energy (unts) 127660 94242 Seed (klograms) 6110 5806 Fertlzer (klograms) 5159 4466 Total ncome (100000 SEK) 14.01 10.28 Prces (SEK per klogram unless otherwse stated) Prce of fodder 1.52 0.25 Prce of labour (SEK/hour) 95.83 4.26 Interest rate 0.065 0.011 Prce of energy (SEK/unts) 0.61 0.19 Prce of seed 2.76 0.14 Prce of fertlzer 7.65 0.66 Measures of sze Income from mlk (100000 SEK) 11.53 8.62 Number of hectares 68 43 To avod bases due to nflaton, the monetary values were deflated to the prce level of the frst year n the panel,.e. 1998. In 1998, 1 USD was equal to approxmately 8 SEK. 331
Hansson, H. Are larger farms more effcent? 1 3 5 6 7 2 8 4 Results Area 1: Gss Area 2: Gmb Area 3: Gns Area 4: Ss Area 5: Gsk Area 6: Ssk Area 7: Nn Area 8: Nö Fg. 3. Producton areas n Sweden. Source: Statstcs Sweden pers. comm. 2006 Descrptve statstcs of the effcency results Farm level economc, techncal and allocatve nputorented effcences were calculated accordng the method outlned above. The results are shown n Table 2. The results reported n Table 2 show that effcency could ncrease f all farms were as effcent as the most effcent farms n the sample. The man cause of low economc effcency s the low allocatve effcency,.e. nsuffcent cost mnmzaton. The dstrbutons of both the techncal and allocatve effcences are skewed towards full effcency; Table 2. Mean, mnmum (mn), standard devaton (std) and dstrbuton of the economc, techncal and allocatve nput effcences. Economc effcency Techncal effcency however the dstrbutons of economc effcences are skewed towards lower effcency. Ths mples that a larger part of the farms have a hgh techncal and allocatve effcency, whereas a larger part of the farms have low economc effcency. The farms were sorted accordng to ther economc effcency results, a measure whch shows the overall effcency of the farms, and grouped nto four groups each contanng 25% of the farms. Average economc effcency, ncome from dary and number of hectares were then calculated for each group. The results are contaned n Table 3. The results n Table 3 show that the 25% most effcent farms, on average, s also the group wth the largest average dary producton. Ths was also confrmed n a sgnfcant t-test. However, ths group seems to be smaller n terms of the number of hectares. It s nterestng to note that the farms n the second hghest effcency quartle are, on average, the smallest farms n both sze classes. The fact that the farms n the second most effcent quartle are the smallest farms was also confrmed by sgnfcant t-tests. Tobt regresson results Allocatve effcency Mean 0.696 0.877 0.795 Mn 0.357 0.495 0.395 Std 0.136 0.123 0.106 Number of fully effcent farms 5 60 5 Skewness 0.107-0.829-0.550 Kurtoss -0.190-0.053 0.992 The nfluence on farm level effcency of dfferences n farm sze was also assessed by tobt regresson, accordng to the method outlned above. Because 332
Table 3. Average sze of farms n dfferent economc effcency quartle classes. Average economc effcency Mean Standard devaton Average ncome from dary (100 000 SEK) Mean Standard devaton Mean Average number of hectares Standard devaton The hghest quartle 0.873 0.067 13.54 13.18 72.45 56.13 The second hghest quartle 0.737 0.030 9.61 5.81 55.60 32.68 The thrd hghest quartle 0.647 0.025 11.53 8.01 64.44 35.20 The lowest quartle 0.530 0.065 11.45 4.82 77.43 42.02 the sze measures are lkely to be correlated, three models were estmated, once for each effcency measure. In the frst model, the sze of the dary producton was ncluded. In the second model, the effect of the physcal sze n terms of the number of hectares was consdered. In the thrd model, fnally, all three sze measures were ncluded. In all three regresson models, the effect of geographc locaton was controlled for. The regresson results are presented n Table 4. Both the sze of the dary producton and the physcal sze of the farm sgnfcantly affect economc and techncal effcency; however only the sze of the dary producton sgnfcantly affects allocatve effcency. In all cases where the lnear effects are sgnfcant, so are also the squared effects, suggestng that farm sze affects effcency n a non-lnear way. Further, all sgnfcant squared effects are postve whch ndcate that effcency s frst decreasng wth farm sze and then ncreasng. Geographc locaton nfluence especally techncal effcency, ndcatng that the techncal effcency of the farms dffer dependng on what regon the farm s stuated n. The results also show that allocatve effcency s not affected by geographc locaton and that economc effcency s affected only on a few occasons by geographc locaton. Ths suggests that the possbltes of the farmers to combne nputs n the optmal way are not affected by geographc locaton. Farm level scale effcency and effects Scale effcences and effects were calculated accordng to the method outlned above. The results are contaned n Table 5. The average level of scale effcency was 94.7%. Ths means that the farms operate close to ther long-run optmal scale. The dstrbuton of scale effcency s skewed towards full scale effcency whch also ndcates that the farms are close to ther optmal scales. However, the results also show that several farms operate under ncreasng returns to scale and should thus be able to ncrease ther effcency by growng. On the other hand, a closer look at these partcular farms reveals that the average scale effcences of the IRS farms are hgh, 92.5% whch means that they are close to ther optmal scale, even though operatng under IRS. Dscusson Ths study amed to nvestgate how farm economc, techncal and allocatve nput effcences of specalzed dary farms n Sweden were affected by dfferences n farm sze. The study was motvated by the changng dary farm structure that s occurrng n Sweden and other North European countres, where the number of dary farms decreases rapdly, meanwhle the remanng farms get larger. In ths 333
Hansson, H. Are larger farms more effcent? Table 4. Results from the regressons of sze and geographc locaton on economc, techncal and allocatve effcency. P-values n parenthess. Economc effcency Techncal effcency Allocatve effcency Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Intercept 0.743 0.738 0.772 0.890 0.957 0.990 0.895 0.834 0.866 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Income from dary -0.016-0.013-0.018-0.001-0.012-0.017 (0.000) (0.005) (0.002) (0.873) (0.000) (0.000) (Income from dary)^2 0.000 0.000 0.001 0.000 0.000 0.000 (0.000) (0.000) (0.001) (0.106) (0.000) (0.000) Hectares -0.026-0.011-0.044-0.045-0.008 0.012 (0.001) (0.205) (0.000) (0.000) (0.236) (0.105) Hectares^2 0.001 0.000 0.002 0.002 0.000-0.000 (0.001) (0.298) (0.000) (0.004) (0.165) (0.400) Gss 0.007-0.012-0.005 0.036 0.035-0.016 0.032-0.017 0.028 (0.904) (0.836) (0.928) (0.585) (0.600) (0.801) (0.943) (0.719) (0.541) Gmb 0.045 0.053 0.037 0.076 0.099 0.040-0.006-0.008 0.013 (0.291) (0.228) (0.398) (0.135) (0.050) (0.426) (0.865) (0.817) (0.719) Gns 0.143 0.130 0.135 0.160 0.167 0.124 0.044 0.025 0.059 (0.001) (0.005) (0.003) (0.003) (0.002) (0.018) (0.220) (0.499) (0.107) Ss 0.065 0.063 0.057 0.110 0.107 0.078-0.009-0.009 0.004 (0.169) (0.201) (0.230) (0.054) (0.062) (0.161) (0.813) (0.822) (0.908) Gsk 0.068 0.058 0.057 0.135 0.117 0.091-0.019-0.020-0.002 (0.056) (0.122) (0.118) (0.001) (0.007) (0.030) (0.510) (0.520) (0.950) Ssk 0.030 0.041 0.029 0.134 0.169 0.136-0.055-0.050-0.054 (0.566) (0.452) (0.568) (0.036) (0.009) (0.027) (0.191) (0.257) (0.196) Nn 0.021 0.033 0.023 0.106 0.122 0.115-0.053-0.045-0.053 (0.626) (0.472) (0.594) (0.043) (0.022) (0.027) (0.139) (0.225) (0.131) Log lkelhood 129.408 119.664 130.244 24.635 23.428 33.505 171.819 162.569 174.292 Income from dary was measured n hundreds of thousands. The number of hectares was measured n tens of hectares. Gss, Gmb, Gns, Ss, Gsk, Ssk and Nn refer to geographc locatons accordng to Fgure 3. 334
Table 5. Mean, mnmum, standard devaton and dstrbuton of the scale effcency results. Mean 0.947 Standard devaton 0.065 Mnmum 0.654 Skewness -1.576 Kurtoss 2.358 Number of farms operatng under CRS 1 42 Number of farms operatng under IRS 2 133 Number of farms operatng under DRS 3 34 1 Constant returns to scale 2 Increasng returns to scale 3 Decreasng returns to scale settng t s mportant to understand f and how farm effcency, and n the contnuaton, farm profts, are affected by farm sze. The results n ths study are mportant because they show n several dmensons how effcency s affected by farm sze. The effects of farm sze are evaluated for all major nput-orented effcency scores. Further, both the lnear and squared effects of farm sze are consdered. Prevous lterature does not gve suffcent advce on how dary farms n North European countres are affected by the structural change, because t does not show a clear, unambguous relaton between effcency and sze. Further prevous lterature does not easly apply to north European countres because of dfferences n e.g. farmng systems, clmate and culture. The effcency results reported n ths paper show that especally the average techncal effcency score s the hgher score. Further, the average allocatve effcency scores are lower than the average techncal effcency scores. Ths mples that the man reason for economc neffcency s low allocatve effcency. Ths study shows, lke other lterature (e.g. Oude Lansnk et al. 2002, Renhard et al. 2000, Heshmat and Kumbhakar 1994) that effcency could ncrease f all farms were as effcent as the most effcent farms. The average techncal effcency scores found n ths paper are generally hgher than those found n the studes referred to above. However, based on comparsons between our study and other effcency studes, t s not possble to argue how much more or less effcent Swedsh dary farms are compared to other farms n other countres because effcency s a relatve concept based on the sample and because of dfferences n the methodology choce or n the varable specfcaton (see for example Coell et al. 2005). Consderng two measures of sze n the second-stage regressons; the sze of the dary producton (ncome from dary) and the physcal sze of the farm (the number of hectares) and controllng for dfferences n geographcal regons, farm sze was found to typcally nfluence effcency n a non-lnear way. In partcular, the results suggest that both economc and techncal effcences are frst negatvely nfluenced by both concepts of farm sze and then postvely nfluenced by farm sze. Allocatve effcency, on the other hand, s not affected by the physcal sze of the farm, but by the sze of the dary producton. Also n ths case, effcency s typcally frst decreasng wth farm sze and then ncreasng. A plausble reason for the observed non-lnear relatonshps between farm sze and effcency s that to effcently use technology assocated wth larger scale farmng, a reasonably large farm s requred. Therefore, modest growth among the smallest farms may not lead to more effcent farms, ndeed t may decrease effcency. Our results are somewhat dfferent from prevous lterature studyng the relatonshps between farm effcency and the sze of the dary producton. For example, based on a dvson of ther sample nto three groups, Bravo-Ureta and Reger (1991) found negatve relatonshps between the sze of the dary herd and economc as well as allocatve effcences, but a postve relatonshp between techncal effcency and farm sze. Further, Alvarez and Aras (2004), Barnes (2006) and Hadley (2006) found that techncal effcency n dary farms was postvely affected by farm sze, as measured by the sze of the dary producton. Nether of the two referred studes ncluded squared measures of farm sze. Compared to results from outsde the dary sector, the results reported here are smlar to results reported by Helfand and Levne (2004) who found that techncal effcency was frst decreasng and 335
Hansson, H. Are larger farms more effcent? then ncreasng wth farm sze. Our results dffer from those of Sharma et al. (1999) who found postve lnear relatonshps between all major effcency scores,.e. economc, techncal and allocatve effcency and farm sze. The average scale effcency was 94.7%. Ths result suggests that, on average, the studed farms are operatng close to ther optmal scales. Ths n turn suggests that the farmers would not gan much n terms of effcency by beng at a more optmal scale. Lookng at the scale effects, several farms are characterzed by ncreasng returns to scale and thus should be able to ncrease ther earnngs by enlargng ther sze: however, the average scale effcency s hgh also n ths group wth an average score of 92.5%. The results mply that there s a potental effcency gan from ncreasng farm sze to operate at a more optmal scale, but that ts magntude may not be very large. Conclusons and suggestons The results on especally economc and allocatve effcency scores show that the farms can become more effcent f they became better at combnng ther nputs n the cost mnmzng way, whle remanng at the same farm sze. Furthermore, the regresson results suggest effcency s typcally frst decreasng and then ncreasng wth farm sze. Therefore, ths paper suggests two ways to ncrease effcency among dary farms. Frst, ncreased effcency can be acheved by focusng on ncreasng the knowledge about how nputs can be combned more optmally. Ths suggeston s supported by Rodgers (1994) who argued that the farm market or the farm technology s not the cause of the low farm earnngs. Rather, Rodgers (1994) stressed the mportance of mprovng the human captal and concluded that the man tool to ncrease farm earnngs was to ncrease the human captal. If the farmers were better at combnng ther nputs optmally accordng to nput prces, ther overall economc effcency would ncrease because ther allocatve effcency would ncrease. A concrete way to acheve ths would be to develop tools to assst the farmers n valung ther nputs. Second, ncreased effcency can be acheved by focusng on farm growth. However, because effcency s typcally frst decreasng and then ncreasng wth farm sze, ths strategy requres that the farmers am for farm szes n the larger sze segments f the strategy s to lead to more effcent farms. Acknowledgements: I am grateful to Prof. Bo Öhlmér and Prof. Hans Andersson for valuable comments on earler drafts. The paper has also benefted from comments from the Edtor and from two anonymous Referees. The study was fnanced by the Swedsh Farmers Foundaton for Agrcultural Research (SLF), Sweden, to whom I also express my grattude. References Afonso, A. & St. Aubyn, M. 2006. Cross-country effcency of secondary educaton provson: A sem-parametrc analyss wth on-dscretonary nputs. Economc Modellng 23: 476 491. Agner, D., Lovell, C.A.X & Schmdt, P. 1977. Formulaton and Estmaton of Stochastc Fronter Producton Functon Models. Journal of Econometrcs 6: 21 37. Alvarez, A. & Aras, C. 2004. Techncal effcency and farm sze: a condtonal analyss. Agrcultural Economcs 30: 241 250. Balcombe, K., Fraser, I. & Km, J.H. 2006. Estmatng techncal effcency of Australan dary farms usng alternatve fronter methodologes. Appled Economcs 38. 221 2236. Barnes, A.P. 2006. Does mult-functonalty affect techncal effcency? A non-parametrc analyss of the Scottsh dary ndustry. Journal of Envronmental Management. 80: 287 294. Bravo-Ureta, B.E. & Reger, L. 1991. Dary Farm Effcency Measurement Usng Stochastc Fronters and Neoclasscal Dualty. Amercan Journal of Agrcultural Economcs 73: 421 428. Charnes, A., Cooper, W. W., & Rhodes, E. 1978. Measurng the Effcency of Decson Makng Unts. European Journal of Operatonal Research 2: 429 444. Coell, T. & Perelman, S. 1999. A comparson of parametrc and non-parametrc dstance functons: Wth applcaton to European ralways. European Journal of Operatonal Research 117: 326 339. Coell, T., Rao, P. D. S., O Donnell, C. J., & Battese, G. E. 2005. An Introducton to Effcency and Productvty Analyss. Sprnger Scence+Busness Meda Inc. New York. 336
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