No evidence of trade-off between farm efficiency and resilience: Dependence of resource-use efficiency on land-use diversity

RESEARCH ARTICLE No Evidence of Trade-Off between Farm Efficiencyand Resilience: Dependenceof Resource-Use Efficiencyon Land-Use Diversity Helena Kahiluoto 1 *, Janne Kaseva 2 1Lappeenranta University of Technology, Saimaankatu 11, 15140 Lahti, Finland, 2Natural Resources Institute Finland, 31600 Jokioinen, Finland *[email protected] Abstract Efficiency in the use of resources stream-lined for expected conditions could lead to reduced system diversity and consequently endanger resilience. We tested the hypothesis of a trade-off between farm resource-use efficiency and land-use diversity. We applied stochastic frontier production models to assess the dependence of resource-use-efficiency on land-use diversity as illustrated by the Shannon-Weaver index. Total revenue in relation to use of capital, land and labour on the farms in Southern Finland with a size exceeding 30 ha was studied. The data were extracted from the Finnish Profitability Bookkeeping data. Our results indicate that there is either no trade-off or a negligible trade-off of no economic importance. The small dependence of resource-use efficiency on land-use diversity can be positive as well as negative. We conclude that diversification as a strategy to enhance farm resilience does not necessarily constrain resource-use efficiency. Introduction Evidence-basedpolicymay be wishful thinkingin times of turbulenceand multi-dimensional epistemic and ontological uncertainty. Robust strategies [1], which work well even if the information is imperfector inputs to the system vary[2], may yield a more favorable cost-benefit ratio for societalinvestments [3]. Enhancement of system resilienceis one such robust strategy [2], and therefore currentlyan important complementation to add to efficiency, for sustainability of farming. Resilienceis the capacity of a system to tolerate disturbanceand reorganizewhileretaining its function,structureand identity [4–6], and to shape change and learn [7–8]. If a social-ecologicalsystem threatens resilienceat larger scales, transformational change is required [9]. In the face of increasedturbulencein the globalclimate and markets, the resiliencediscoursehas emerged in international environmental and economic policy since the start of the current decadeidentity, e.g.,[10–12]. Increasing effort has also beenaddressed to mathematically PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 1 / 16 a11111 OPEN ACCESS Citation: Kahiluoto H, Kaseva J (2016) No Evidence of Trade-Off between Farm Efficiency and Resilience: Dependence of Resource-Use Efficiency on Land-Use Diversity. PLoS ONE 11(9): e0162736. doi:10.1371/journal.pone.0162736 Editor: Gui-Quan Sun, Shanxi University, CHINA Received: February 26, 2016 Accepted: August 26, 2016 Published: September 23, 2016 Copyright: ©2016 Kahiluoto, Kaseva. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The third party to hold the data is Natural Resources Institute Finland, and the person to contact in this matter is Arto Latukka (e-mail [email protected]). Funding: This work was supported by the Finnish Climate Change Adaptation Research Programme (ISTO) and by the Academy of Finland (http://www. aka.fi), grants 140870 and 255954. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. modelvarious aspects of stability of complex systems, e.g.,[13–16]. Diversity generates a variety of possible responses to variability [17–19] and to various threats [20] and material for transformation [21], and as such is a prerequisite for system resilience[20,22–26]. Diversity also implies the generation of ‘perpetualnovelty’ [26], which is critical for reorganizing the system after disturbance[27]. Efficiencyis a key economicconcept and has made a crucialcontribution to sustainability discoursesacross disciplinesand sectors[28]. Eco-efficiency, in terms of the efficientuse of resources (‘more from less’), has long dominated the interpretation of sustainability [29–30] and has substantially influencedsocietaldevelopment strategies.Increasing resource-useefficiency, implying a small ratio of resources to products or revenue, e.g., higheryields per unit area of land or other natural or economicresourcesin agriculturalsystems, is believedto promote economicperformance,foodsecurityand environmental protection [31–32]. Korhonen and Seager[33], Ulanowicz et al. [34] and Goerneret al. [35] argued for the complementarity of the two perspectives,i.e.,efficiencyand resilience,in sustainable development. In stable times, system efficiencyis streamlined for expectedconditions, often creating systems with less diversity, as exemplifiedby the development at variouslevels of agriculturalsystems in industrialcountriesin recent decades[35–42]. Diversity increasesstability of productionin variable agriculturalenvironments [43], and land-use diversity appears to increase farm resilience[44] also in terms of economic returns [45–46]. Consequently, efficiency may run counter to system resilience[33], especiallythrough loss of response diversity [18,20]. On the other hand, basedon ecologicalmodels with economicrelevance, Tilman et al. [47] concluded that diversity should enhance efficiencyin the use of limited resources. The relationship of economic performanceand biodiversity has been assessed [45–46], especiallyfrom the viewpointof ecosystemservices[48–50]. Further, eco-efficiencyin terms of products relative to emissions has been related to diversity in what-if scenarios of social-ecologicalsystems [51]. However, empirical evidencefor the dependencebetweenresource-useor economic efficiencyand productiondiversity is scarce or non-existent. This knowledgegap is also practically important, becausethe current understandingof a trade-offrelation between economic efficiencyand diversity in farming informs agriculturalpolicies. Inspired by the model-basedstudy of Tilman et al. [47], we tested in an empirical case the general beliefthat diversity reduces efficiency, e.g., [44]. The aim of this study thus was to investigate empirically, whetherthere is trade-offbetweendiversity (critical for system resilience) and efficiencyof resource-use (also required for sustainability) on farms, and that way contribute to bridgingthe knowledgegap. We tested the hypothesis that land-use diversity is negatively related to farm efficiencyin terms of revenue per unit of land, labour and capital. We tested this hypothesis in the context of Finnish farms, which during the two last decades increasedrapidly in specializationand size to achieve greater resource-useefficiencythrough economiesof scale[52–53], and for which resilienceis of paramount importance,due to the northernmostlocationin the world and therefore a rapid climate change, as well as tight linkages to volatile globalfoodmarkets. Materials and Methods Farm data The empirical data analysed here originate from the Finnish profitability bookkeepingdata usedto compile the Finnish data for the European Farm Accountancy Data Network (FADN), which is maintained by the European Commission.For comparability and access, variable definitions similar to those in FADN were used for the accounting years of 1998–2008 ([54]; http:// ec.europa.eu/agriculture/rica/definitions_en.cfm).FADN is usedthroughout Europe to evaluate Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 2 / 16 income from agriculturalholdings and the impacts of the CommonAgriculturalPolicy (CAP). Finland has four FADN regions,but the climatic conditions for agriculturein the north clearly differ from those for the south, and most agriculturalproduction,accounting farms and landuse diversity, is concentrated in southern Finland. Other areas were thus excluded from the analysis to remove the bias that could arise through independenteffectsof climate on the revenue and on the diversity of agriculturalland-use.In addition,available agriculturalarea restricts land-use diversity. For smaller farms also other reasons of farming (recreation, maintenance of land value, life style, emotional reasons such as heritageetc.) are in a bigger role which could cause bias into the conclusions if such farms would be included in the analysis of the trade-off betweenresource-useefficiencyand diversity (reflectingthe relation betweeneconomicefficiency and resilience),becausesuch relation has no relevancefor the farmers in those cases. Therefore, the utilisedagriculturalarea (UAA) below 30 hectares(ha) was set as the lower limit for farm size in our analysis. After these restrictionswere applied to remove obvious sources of bias, we were left with the empirical data for 3 268 farms totally over the years (Table 1). Land-use diversity The Shannon-Weaver index [henceforth, the Shannon index] [55], the most commonly used diversity index, was usedto illustrate farm land-use diversity. Specifically, the Shannon index was usedto describethe number and proportional area distribution(richness and evenness)of eightfarm land-use types.A Shannon indexequal to zero indicates that the farm comprises only one land-usetype;the value of the Shannon indexincreasesas the number of different land-use types and/or their evenness increases.The Shannon index gives an equal weight to each observationand is comparable among cases with different compositions [56]. The Shannon index was calculatedaccording to the following eq (1): H¼  XK k¼1 wik Wi lnwik Wi ;for i¼1;...;nfarms ð1Þ where k=1,. . .,Kreferringto the number of land-use types; w ik is the area covered by landuse type kof farm i;W i represents the total area of farm i; and w ik /w i is the proportion of area covered by land-use type k. The Shannon index is expressed in logarithmic form, and to describethe true diversity (‘land-use diversity’), it needsto be converted (exp(H)). Agriculturalspecialisationis a categorical variable in the Finnish profitability bookkeeping data (as in FADN); it consists of categories that are both exhaustive and mutually exclusive such that each observationis assigned to one and no more than one category. The following six agriculturalland-use types were usedas independentclasses for calculatingthe Shannon index: cereals (correspondingto FADN variable SE035), other field crops (SE041), vegetables,berries, flowers and ornamental plants (SE046-SE046), perennialcrops (SE054-55), foddercrops and fallow (SE071-73), and other. Only on 69 farms the class ‘other’ represented more than 10% of the agriculturalland area, while89% from the total 3 268 farm observationsover years did not have the class ‘other’ at all. This indicates that no bias in the analysis was caused by the lacking information of the diversity within the class ‘other’. We then calculatedPearson’s correlation coefficientsfor the Shannon index and farm input/output variables, such as UAA, labour, farm capital and total revenue. Resource-use efficiency Resource-useefficiencywas measured as a relation betweenthe use of the major farm resources land, labour and capital, and farm revenue, using Cobb-Douglasregression model. In addition, ‘technical efficiency’was measured with stochastic frontier models as the ratio betweenthe Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 3 / 16 Table 1. Farm inputs (labour, capital and land), total revenue and land-use diversity per production line. Variable Mean St. Dev. Min Max All farms (3268) Labour, h 3 347 2 144 159 16 608 Farm capital, €277 055 237 930 19 724 2 288 832 UAA, ha 71 40 30 655 Total revenue, €90 391 98 649 125 1 222 089 Shannon index 0.686 0.241 0 1.316 Cereals,oilseeds and protein crops (1140) Labour, h 1 686 972 191 8 570 Farm capital, €180 394 137 295 19 724 2 288 832 UAA, ha 79 52 30 655 Total revenue, €38 702 34 329 125 419 030 Shannon index 0.675 0.244 0 1.316 Field crops (453) Labour, h 2 811 1 858 159 12 989 Farm capital, €227 728 164 551 34 528 983 156 UAA, ha 73 38 31 315 Total revenue, €75 594 66 440 2 112 454 462 Shannon index 0.869 0.177 0 1.256 Specialist dairying (692) Labour, h 5 623 2 037 1 982 16 608 Farm capital, €348 065 301 236 70 732 1788 464 UAA, ha 60 26 30 200 Total revenue, €123 574 67 223 29 736 393 392 Shannon index 0.648 0.174 0 1.076 Specialist granivores (284) Labour, h 4 349 1 674 668 14 140 Farm capital, €482 851 354 022 65 385 2 069 981 UAA, ha 60 27 30 181 Total revenue, €215 821 161 085 48 569 669 621 Shannon index 0.502 0.252 0 1.054 Field crops and grazing livestock (283) Labour, h 4 336 1 572 246 10 434 Farm capital, €255 716 152 461 50 305 924 458 UAA, ha 76 39 30 226 Total revenue, €64 566 42 936 13 624 173 232 Shannon index 0.781 0.214 0 1.207 Various crops and livestock (416) Labour, h 3 342 1 208 980 8 091 Farm capital, €351 556 201 211 74 132 1 161 327 UAA, ha 70 27 30 201 Total revenue, €127 904 101 417 13 123 927 783 Shannon index 0.641 0.253 0 1.299 UAA = utilised agricultural area; Shannon index = Shannon index for land-use diversity; sample size in parentheses. doi:10.1371/journal.pone.0162736.t001 Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 4 / 16 observedoutput (here total revenue) to the maximum output under the assumption of fixed inputs [57], i.e.,the resource-useefficiencyof individualfarms relative to the maximum resource-useefficiencyof the farms. Use of the major farm resourcesland, labourand capital was illustrated by the following input resources: the total UAA of holding (ha; SE025), total labourinput on holding in hours (h; SE011), and farm capital as the sum of the average of the working capital of livestock, permanent crops, land improvements, buildings,machinery and equipment, and circulatingcapital (€; SE510). The total revenue was calculatedas output from crops and crop products, livestockand livestockproducts and other output (correspondingto FADN variable SE131), in €. For detailed definitions of the variables, see [54]. The Cobb-Douglas regression model The Cobb-Douglasproductionfunctionsee [58] is widely usedin econometricsto represent the relation betweenseveralinputs and production[59]. It allows the quantity of one input to affect the productivityof another input. We included the Shannon index in the model,in analogyto inputs [60]. The Cobb-Douglasmodel includedthree inputs (land, capital and labour), the Shannon index, and a single output, total revenue. The model can be expressed as yj¼A xb1 1jxb2 2jxb3 3jeoHjþεj;j¼1;. . . ;nð2Þ where y j is the output of farm jand x 1 ,x 2 and x 3 are the area (ha), labour (h) and farm capital (€) of farm j. The parameter H j is the Shannon index of farm j, and ε j is the error term, which was assumed to be independent and normally distributed.The remaining parameters (A,β 1 , β 2 ,β 3 and ω) were unknownand had to be estimated. The equation was modifiedfor estimating the coefficientsof the parameters.Taking the natural logarithmof both sidesof the equation leads to ln yj¼ln A þb1ln x1jþb2ln x2jþb3ln x3jþoHjþεj;j¼1;. . . ;nð3Þ By choosingY = ln(y j ),X = ln(x ij )and H = H j , we obtained a linear regression equation Y¼b0þb1X1þb2X2þb3X3þoHþεð4Þ where the unknown parameters could be estimated. Becausethe productionlines differedin terms of diversity and revenue,we includedthe productionlines in the modelas dummy variables.Dummy variables are a seriesof binary variables that identifywhetheror not each observationis a memberof a specificcategory. The years with a statisticallysignificant(α= 0.1) interaction of Shannon index and productionline were not includedin furtheranalyses due to technical and interpretational complexities. The stochastic frontier production models The Cobb-Douglasregression models used in the analyses above assume that all farms represent equal technicalefficiency. Becausethis assumption may not be valid, we also applied a stochastic frontier production function,which adds to the model a new term, technical inefficiencythat after a mathematical transformation represents the technicalefficiencyof each farm. We used two most common stochastic productionfunctions:the Cobb-Douglasand the translog productionfunction.The translog productionfunctionis more flexible,becauseall secondorder cross-terms of inputs and the Shannon index are includedin the model, unlike the Cobb-Douglasproduction functionthat assumes all cross-terms to be zero. The stochastic frontier productionmodelincludedthree inputs (land, capital and labour),the Shannon index Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 5 / 16 and a single output, i.e.,total revenue.We also investigated whetherthe associationof the total revenue and the Shannon index dependson productionline (Table 1) by including a separate intercept term for them. Thus, the Cobb-Douglasproduction functioncan be expressed as lny ¼b0þXn i¼1bilnxiþεð5Þ and the translog productionfunctionas lny ¼b0þXn i¼1bilnxiþ1 2Xn i¼1Xn j¼1bij lnxilnxjþεð6Þ where yis the output of farms and nis the number of inputs added with the Shannon index (x). The parameters β 0 ,β i and β ij are the unknownparameters to be estimated. The ε= v-u, where v is the systematic error component, which is assumed to be independentlyand identically distributed, random error having normal distributionwith mean being zero and variance beingσ v2 .u is a non-negative random variable, whichis assumed to account for technicalinefficiencyin production,having normal distribution with mean being zero and variance beingσ u2 (Fig 1). Fig 1. The stochastic production frontier [61–62]. Observed productions and frontier productions are indicated with xand o, respectively. The frontier production (FP), consisted of observed production, inefficiency effect and random noise, can lie above or below the frontier prodution function (PF), depending on the noise effect. doi:10.1371/journal.pone.0162736.g001 Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 6 / 16 Model comparisons We determinedwhetherthe technicalinefficiencyterm needs to be added,relative to the Cobb-Douglasregression models, i.e., whether stochastic frontier models (Cobb-Douglasor translog stochastic frontier models) would be required instead of Cobb-Douglasregression models (see above). The key parameter to test the need of the technical inefficiencyterm is γ= σ u2 /(σ u2 +σ v2 ), which tells the proportionof variance of the efficiencyterm from the overall variance. If hypothesis H 0 :γ= 0 holds, there is no need for an efficiencyterm in the model. Since γ[0,1] and the hypothesis is one-sided,we usedcritical values from Kodde and Palm (1986) for a likelihoodratio test. The distributions of a technical inefficiencyterm were compared based on the information criteria (AIC, Bayesian information criterion (BIC)). The likelihoodratio test and BIC were usedto determinewhether the translog production functionwould be more appropriate than the Cobb-Douglasproductionfunctionin the stochastic frontier models.The likelihoodratio test statistic can be definedby D¼  2fln½LðH0Þ ln½LðH1Þg ð7Þ where L(H 0 )and L(H 1 )are the values of the likelihoodfunctionof the null hypothesis (H 0 :β ij = 0) and the alternative hypothesis. Test statistic Dis distributed chi-squared with degrees of freedom equal to the number of parameters that are constrained.BIC can be defined by BIC ¼  2fln½LðHiÞþkln½Ng ;i¼0;1ð8Þ where kis the number of free parameters and Nis the sample size. To facilitate theinterpretation of the translogproductionmodels,all the variableswere dividedby their sample means before estimation. Consequently, the first-ordercoefficientscan be interpreted as elasticitiesof the sample means [63]. The interaction terms show how the estimated elasticities vary with a movement away from the sample means. The statistical analyses were performedusing SAS software (SAS Institute, Inc., Cary, NC, USA)and the REG, GLM, MIXEDand QLIM procedures.The R 3.1.1 package ‘frontier’ (version 1.1–0) was also used to test more complex models that could not be applied using SAS (R Development Core Team). Results Land-use diversity in relation to farm inputs and total revenue The Shannon index varied by farm productionline (Table 1); the highestdiversity indiceswere found for farms with fieldcrops as the productionline, followed by farms with fieldcrops and grazinglivestock.The lowest Shannon index was measuredfor specialistgranivore farms.Only five farms had five different land-use types; the greatest proportion of the farms (55%) had three different land-use types, and forty farms had only a single land-use type. The Shannon index for farm land-use diversity was weakly negatively correlated with total revenue, while it was weaklypositively correlated with UAA (Table 2). However, in production-line-specific analyses, the Shannon index was correlated with UAA only, i.e., weakly positively correlated with UAA for cereals,oilseedsand protein crops (r = 0.27, P<0.001) and fieldcrops (r = 0.28, P<0.001) farms. Land-use diversity in relation to farm resource-use efficiency Cobb-Douglasregressionmodel. When using the traditionalCobb-Douglasregression models,we found no statistical support for the negative dependenceof resource-useefficiency on land-use diversity. There was no statistically significant differencein the dependenceof Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 7 / 16 resource-useefficiencyon land-use diversity among the production lines; p-values of the Shannon index varied from 0.48 to 0.83 over years. In the fittest modelwhichincludedthe three inputs (land, labourand capital), the Shannon index and the productionlines, the estimate of the Shannon index varied from -0.085 to 0.028 with the confidenceinterval from [-0.323, 0.153] to [-0.206, 0.263], respectively. The models explained 80–86% of the total variance, while the proportionof land-use diversity was less than one percent. In the year 2000, the traditional Cobb-Douglasregression model where the differenceamong farms in resource-useefficiency is included in the experimental error term, was shown to be adequate, but in other years stochastic frontier productionmodels were preferred (Table 3). Stochastic frontier Cobb-Douglasproduction model. In the stochasticfrontier production models,where a new term,the technical inefficiencyof farms was included,the null hypothesis, H 0 :γ= 0 (the technical inefficiencyeffectin the model is zero), was rejected (P<0.002) for all the years (apart from 2000) (Table 3). Therefore, we concluded that there was a technical inefficiencyeffectin the modelfor all the years (apart from 2000), i.e.,the farms differed from each other in terms of resource-useefficiency, and therefore the stochastic frontier modelsfitted to the data betterthan the regressionmodels.The exponential distributionfor the technical inefficiencyterm was found to be more appropriate than the half-normal and truncatednormal distributions, based on the information criteria.However, the differences among the selecteddistributionand the other ones consideredwere minor. According to the BIC criterion,the Cobb-Douglasstochastic frontier model was adequate for everyyear. Similarly to the regression model, the fittest stochastic frontier production model showed no statistical support for the negative dependenceof resource-use efficiencyon diversity:p-values of the Shannon index varied from 0.58 to 0.99 over years (Table 4). The mean technical efficiencyscore of farms, 0.8, indicated that the average resource-use efficiency of the farms was 80%. Stochastic frontier translogproduction model. Based on the alternative comparison method,likelihoodratio test, the Cobb-Douglasstochastic frontier production modelwas an adequate functionalform for the years 2004 and 2006 (Table 3). For the years 2001, 2002 and 2005, the more flexibletranslog production model was more appropriate. In the years 2001, 2002 and 2005, a small positive, statistically non-significant,dependenceof resource-useefficiencyon land-usediversity was indicated p = 0.406,p = 0.663 and p = 0.560,respectively) (Table 5). According to the translog productionmodel,the coefficientsof the interactionsof land-use diversity with UUA and capital indicatedthat as land-use diversity of a farm increases,the resource-useefficiencyof UUA use tendsto decreaseand the resource-useefficiencyof capital use to increase,in terms of revenue [63]. There was no statistically significantinteraction of land-use diversity and resource-useefficiencyin labour use (Table 5). The elasticitiesof inputs Table 2. Pearson correlation matrix of land-use diversity, total revenue and inputs (labour, farm capital and land). Shannon index Total revenue UAA Labour Farm capital Shannon index 1 Total revenue -0.102*1 UAA 0.201*0.276*1 Labour -0.029 0.532*0.162*1 Farm capital -0.104*0.835*0.482*0.561*1 Shannon index = Shannon index for land-use diversity; UAA = utilised agricultural area; n = 3268. Statistically significant correlations (P<0.05) are marked with asterisks. doi:10.1371/journal.pone.0162736.t002 Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 8 / 16 of both Cobb-Douglasand translog models could be interpreted similarly, becauseall the variables were dividedby their sample means before estimation. The elasticitiesillustrate the dependenceof resource-useefficiencyon land-use diversity and inputs. The small negative elasticitiesof land-use diversity in 2004 and 2006 indicatedthat a 10% increase in land-use diversity would result in approximately half a percentagedecreasein total revenue. The positive elasticities indicated increase in total revenue by increasinginputs (Fig 2). The confidence intervalsindicate that total revenue could at maximum increase by 3% (year 2001) or decline by 3% (year 2004) associatedto 10% increaseinland-usediversity (Fig 2). The lack of statistical significancein the dependenceof resource-useefficiencyon land-use diversity, togetherwith the near-zero value of the coefficientfor the land-usediversity, indicate that there is either no dependenceof resource-useefficiencyon land-use diversity or the dependence is very small. Table 3. Comparison of the Cobb-Douglas regression (H 0 ) and stochastic frontier Cobb-Douglas (H 1 ) and translog (H 2 ) production models. Log-likelihood values of the models Comparison of the models Year H 0 : Cobb-Douglas, λ= 0 a H 1 : Cobb-Douglas b H 2 : translog c H 0 vs H 1 :w2 1 d H 1 vs H 2 :w2 10 e H 1 vs H 2 :ΔBIC f 2000 -123.7 -122.5 -107.1 2.4 30.8*27* 2001 -147.2 -130.2 -102.1 34.0*56.2*1 2002 -128.1 -119.7 -93.6 16.8*52.2*4 2004 -159.1 -154.9 -148.6 8.4*12.6 44* 2005 -172.4 -154.8 -135.5 35.2*38.6*18* 2006 -189.1 -140.8 -134.1 96.6*13.4 43* Likelihood ratio test (H 0 vs H 1; H 1 vs H 2 ) and Bayesian information criterion (H 1 vs H 2: ΔBIC) were used in statistical inference to select the adequate model for each year. Based on the likelihood ratio test, the Cobb-Douglas regression model is adequate in 2000 and the stochastic frontier Cobb-Douglas production model in 2004 and 2006. Based on the Bayesian information criterion, the stochastic frontier Cobb-Douglas production model is adequate for every year. a The log-likelihood value of the Cobb-Douglas regression model without the inefficiency effect (λ). b The log-likelihood value of the stochastic frontier Cobb-Douglas production model with the inefficiency effect. c The log-likelihood value of the stochastic frontier translog production model with the inefficiency effect. d Likelihood ratio test for H 0 : The technical inefficiency effect is absent. The significance level α= 0.05 (*). e Likelihood ratio test for H 1 : ‘The Cobb-Douglas model is an appropriate functional form ‘. The significance level α= 0.05 (*). f The difference of Bayesian information criterion (BIC) values of the stochastic frontier Cobb-Douglas and translog production models. Positive values favor Cobb-Douglas in every case; values over ten indicate a very strong evidence against translog (*). doi:10.1371/journal.pone.0162736.t003 Table 4. Maximum-likelihood estimates of the land-use diversity of the stochastic frontier Cobb-Douglas production models. Year Coefficient of Shannon index Standard Error of Shannon index P value of Shannon index 2000 0.018 0.113 0.873 2001 0.018 0.101 0.860 2002 0.002 0.111 0.990 2004 -0.063 0.115 0.582 2005 0.055 0.102 0.592 2006 -0.037 0.097 0.701 The small coefficient of the Shannon index with no statistical significance indicates no or a minor dependence of resource-use efficiency on land-use diversity. Shannon index = Shannon index for land-use diversity. doi:10.1371/journal.pone.0162736.t004 Farm Resource-Use Efficiency and Land-Use Diversity PLOS ONE | DOI:10.1371/journal.pone.0162736 September 23, 2016 9 / 16 56. Jost L. Partitioning diversity into independent alpha and beta components. Ecol. 2007; 88: 2427– 2439. 57. 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