Performance of the Norwegian dairy farms: A dynamic stochastic approach

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Research in Economics

journalhomepage:www.elsevier.com/locate/rie

Research Paper

Performance of the Norwegian dairy farms: A dynamic stochastic approach

Habtamu Alem

Norwegian Institute of Bioeconomy Research (NIBIO), Food production and Society, Raveien 9, 1430, ˚AS, Norway

a r t i c l e i n f o

Article history:

Received 19 June 2020 Accepted 30 July 2020 Available online 7 August 2020 JEL Classiﬁcation:

C23 D22 D25 M21 Keywords:

Dynamic farm management Dairy farm

Performance Adjustment of inputs

a b s t r a c t

Fromatheoreticalperspective,itiswellstatedthatthefarm’sdecisionontheuseofinputsdependsonthefarmer’sabilitytomakeaneﬃcientdecisionovertime.Theexisting literatureinperformanceanalysis ofthe dairyfarms basedonstaticmodelingand thus ignorestheinter-temporalnature ofproductiondecisions.Thispaperaimstoconstructa dynamicstochasticproductionfrontierincorporatingthesluggishadjustmentofinputs,to measuretheperformanceofdairyfarmsinNorway.Theempiricalapplicationfocusedon thefarm-levelanalysisoftheNorwegiandairysectorfor2000-2018.Thedynamicfrontier estimatedusingthesystemGeneralizedMethodofMomentsestimator.Theanalysisshows thatthestaticmodelinthepreviousstudiesunderestimatestheperformanceofthedairy farms.

ThisisanopenaccessarticleundertheCCBYlicense.

(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Thestandard neoclassicalfrontierfunction applied inempiricaleﬃciency modelsentailsan assumption thatall farms arefullyeﬃcient (Alem,2018).Following thepioneeringcontributionsby Aigner etal.(1977) andMeeusenandvanDen Broeck (1977), who independently proposed the stochastic production frontier framework using cross-sectional data, the literaturediverges fromthestandard neoclassicalproductionfunction modelby includingtwo distinct errorcomponents.

Thesetwostudieshavesuggestedthatgiventheinput,therearetwomaincausesforthedeviationoftheactualoutputof agivenfarm fromthemaximumpossibleorthe potentialoutput. Oneofthe deviations(errorcomponents) isattributed tocaptures randomshocks (noise) toa productionsystem thatis beyondthe controlof theproducer andcan affectthe output,forinstance,uncertaintyabouttheweather,disease, andpestinfestation.The second deviationistheinefficiency reflectedinthe shortfallfromthemaximal potential output,whichis individualspecific (farm-effect)interpreted asone- sidedinefficiency(non-negativerandomvariable).Thus,InStochasticFrontierAnalysis(SF)thegapbetweenobservedoutput andthepotentialoutputisexplainedintermsofbothinefficiencyandrandomerrors.

Sincetheintroductionofone-sidedinefficiencywithinthecontextofSFpaneldatamodels,therehasbeenconsiderable researchtoextendandapplythemodeltogenerateconsistentandunbiasedestimates(Alem,2018).Thus,theSFmodelcan becategorisedintwobasedontheassumptionsused.Thefirstcategoryisassumptionsmodelspecificationsuchasonabout thetemporalbehavioroftheinefficiency(e.g.persistentandtransit);distributionoftheerrorterms(exponential,normal, truncated, and gamma distribution); estimation techniques such as Generalized Method of Moments (GMM); Maximum

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likelihood,etc.(seee.g.Greene(2008),andKumbhakaretal.(2015).Thesecondcategoryisassumptionsonthebehaviorof theinputuse(staticanddynamic).Thispapercontributestotheliteraturefocusingonthesecondcategory.

Thereexists astrandofliteraturefocusingonestimatingtheperformance ofthefarmbased onastaticframework as- sumptioninwhichan inputisusedfortheproductionprocess,itimmediatelycontributestoproductionatthemaximum possiblelevelsee(e.g.Alemetal., 2019,Kumbhakaretal.,2014,Sipiläinenetal.,2013).However,oncetheinput isintro- ducedinthe productionprocess,itmight takesome time foradjustingwithin thesystem(MinvielandSipiläinen,2018).

Thus, comparingtheperformance ofthe farmusingtechnicaleﬃciencyscores obtainedbasedonthe staticframeworkis likelytoproducemisleadingresults.Thisismainlybecausethefarm’sdecisionontheuseofinputsdependsonthefarmer’s abilitytomakeaneﬃcientdecisionovertime.ThedynamicSFframeworkrelaxesthestaticassumptionontheuseofinputs.

Intheliterature,wecanfindimportantcontributionstodynamicefficiencymodeling,andthemodeladvanceshavetaken placeintheframeworkofthenonparametricapproachusingdataenvelopmentanalysis(DEA).Anonparametricmeasureof dynamicefficiencyfirstproposed bySilvaandStefanou(2003and2007).Silvaetal.(2015)employedtheadjustmentcost technologyto generalize thestaticconditional inputdistancefunction developedby Chambers etal.(1998)toa dynamic framework.Ahnetal.(2000)examineapotentiallinkbetweentechnicalinnovationandproductiveefficiencylevelusinga parametricdynamicapproach.Recently,wecanfindafew importantcontributionsofadynamicefficiencymodeling from theparametricapproach(e.g.Bhattacharyya,2012;MinvielandSipiläinen,2018;Serraetal.,2011).

Theparametricdynamiceﬃciencymeasuresmainlycarriedout eitherinastructuralorreducedapproach(Minvieland Sipiläinen, 2018). The structural dynamic model approach is mainly based on two methods i.e. shadow cost method (see e.g. Rungsuriyawiboon and Hockmann, 2015) and distance function method (Serra et al., 2011). A shadow cost methodthat relatesactual observedcosts shadoworbehavioralcosts obtainedfromtheoptimizationprograms. However, Serra etal.(2011)arguethat theshadowcostapproachdoesnotspecifytheproductiontechnologydirectly.The dynamic distancefunction approachdeveloped by Serra etal.(2011)isderived fromthe dualitybetweeninputdistance functions andcostfunctionswhichprovideacompletecharacterizationofproductiontechnology.

Thereduceddynamicmodelapproachesmainlytheextension ofthestandard stochasticfrontiermodelthroughanau- toregressiveprocessoforderfortheinefficiencycomponent(seee.g.MinvielandSipiläinen,2018).Thatis,theactualpro- ductiveefficiencyinanyperioddependsontheactualproductinthepreviousperiod.Theproductiveefficiencyinagiven farmis assumedtoberelatedto sluggishadjustments,highadjustmentcosts, oruncertaintyoverfutureproductioncon- ditions. Sluggishadjustments andhighadjustmentcosts of inputsnotonly affecttheadoption oftechnology innovations butcanalsoaffectthewholeproductionprocessbypreventingoutputsfromreaching themaximumpossibleoutputlevel (Ahnetal.,2000;Bhattacharyya,2012).Assuch,inthispaper,wefollowthereduceddynamicmodelapproachthatfollows thesetupusedinAhnetal.(2000)andBhattacharyya(2012).

The empirical application focused on the farm-level analysis of the Norwegian dairy sector. Performance analysis of the dairy sector has received much attention in the literature (see e.g. Alem et al., 2019, Minviel and Sipiläinen, 2018, Sipiläinenetal.,2013). Thisismainlythesector thatishighlyregulated andgetssupportfromthegovernmentwhichin- deedmeasuringproductiveefficiencyhasbecome akeyindicatortocontrolandplantheperformanceofproductionunits forbothpolicy-makersandfarmers.Dairyfarmsfaceacontinuousprocessoftechnologicalandenvironmentalchangesthat requiresthemtomakemanagerialdecisionsinadynamiccontext.Thefarmmakesaproductionplansuchthatanobjective extendingfar intothefuture isoptimized.The vastliterature onNorwegian farmefficiencymeasures haslargely ignored thisissue.Thatis, Thatis,the previous studyestimations werebased on astaticsetting technologyspecificationsee for instanceAlemetal.(2019);Kumbhakaretal.(2008);Lienetal.,2018;Sipiläinenetal.,al.(2013).

The papercontributestotheliterature inseveralways.First,incontrastto Bhattacharyya(2012), weused theﬂexible functionalformforthetechnologyestimationandappliedfortheagriculturalsector.Second,wearefortunatetobeableto usealargefarm-levelpaneldatasetofNorwegiandairyfarmswithobservationsfrom2000to2018.

The rest of the article is organized as follows. The main theoretical and econometric models are presented in Sections2 and3,respectively.Section 4addressesthe applicationofthe empiricalmodel.Section 5discusses thenature ofNorwegianagriculturefollowedbyadiscussionofthedataanddeﬁnitionsofvariablesusedintheproductionfunction.

Section7coverstheempiricalresultsandﬁnally,Section8presentsconcludingremarks.

2. Theoreticalmodel

Letusconsiderageneralproductionfunction forthe potentialoutput y^∗_it ofa farmithatuses avector ofinputsx_itat timet.

y^∗_it=f

(

^xit;

β )

⁽¹⁾

Wheref(x_it;

β

⁾^is^the^chosen^function^form^(e.g.Cobb–Douglas,Translog);

β

^is^the^vector^of^technology^parameters^to^be

estimated;i=1,…,Ndenotestheproductionunit;andt=1,_…,Tdenotesthetime.

Lety_itbetheactualoutputproducedbyfarmiattimetandlet

θ

^be^the^speedôfâdjustmentôfôutputs.

y_it=

θ

^y^∗it (2)

y^∗_it−yit=y^∗_it

(

¹⁻

θ )

⁽³⁾

(3)

Ifthe speed of adjustment islower than one, then the actual output is will be lower than the potential output. For theﬁrstperiodofproduction,theactual output(y_it) isonly

θ

^fraction^of^the^potential ^output ⁽^y^∗it)^,^however^for^the ^next productionperiodonwards,notonlythe

θ

^fractionôf^the^potentialôutput⁽^y^∗it)^,^butâlso

θ

^fraction^of^the^potential ^output

(y^∗_it)^for^the^previous ^periodôutput îsîmportant.^Therefore,^the ^dynamic^process ôfôutput^generation^can^be represented by:

yit+1=

θ

^y^∗it+

θ

^y^∗it

(

¹⁻

θ )

^or^y^it+1=

θ

^y^∗it+

(

¹⁻

θ )

^y^it ⁽⁴⁾

yit =

θ

^y^∗it+

(

¹−

θ )

^yit−1 (5)

SubstitutingEq.(1)to(5),

yit =

θ

^f

(

^x^it^;

β )

⁺

θ (

¹⁻

θ )

^f

(

^x^it−1;

β )

⁽⁶⁾

Eq.(6)demonstratesthatthecurrentoutputdependsonthecurrentandpastinputs.

3. Empiricalmodel

Wechooseatranslog(TL) specificationforourempiricalanalysisbecauseofits flexibilityandEq.(1)specifiedasaTL productionfunctioninlogformas:

lny^∗_it=

β

⁰⁺⁴

j=1

β

^j^ln^x^jit⁺ ¹2

4 j=1

β

^{j j}

lnxjit

2

+⁴

j=1

4

l=2

β

jllnxjitlnx_lit+

β

^t^D^t

+ ¹₂

β

tt+⁴

j=1

β

jtlnxjitDt

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where y^∗_it is a vector of potential outputs, x_jit is a vector of inputs (^j=1,· · ·,J) ^by ^farms (ⁱ=1,· · ·,N) ând ^time (^t=1,· · ·,T)^,âll^Greek^lettersâre^parameters^to^beêstimated, ând^D^t îs^the^dummy^variable^for^time^to^capture^the^tech- nologicalchange.

Thedynamicstochasticproductionfrontierthatincorporatesthesluggishadjustmentofinputsandtheerrortermscan bewrittenas:

lny_it=

(

¹−

θ )

^ln^yit−1+

θ ( β

0+⁴

j=1

β

jlnx_jit+ ¹₂⁴

j=1

β

j j

lnx_jit

2

+ ⁴

j=1

4

l=2

β

jllnx_jitlnx_lit+

β

^t^D^t⁺ ¹2

β

^tt ⁺⁴

j=1

β

jtlnx_jitDt

)

+

(8)

Theerror-termsɛit splitsintotwocomponents,i.e.

ε

it≡

v

it−u_it.Thecomponent(u_it) capturestransient(time-varying) andproducer speciﬁc ineﬃciency with u_it∼N⁺(

μ

,

σ

u²). v_it is the idiosyncratic errorterm capturing random shocks and assumedv_itissymmetricandtosatisfytheclassicalassumptionsi.e.,

v

_it^iid_∼N(⁰,

σ

v²). .AllGreeklettersareparametersto beestimated.Thetrendvariable,t,isintroducedtocapturetheeffectoftechnologicalchangeandstartswitht=1for2000 andincreasesbyoneannually.

4. Application

The dynamic stochastic production frontier model in Eq.(8) includes the dependant variable and one period lagged dependantvariable(lny_itandlny_it₋₁)^which^bothâre^the^functionôf^theêrror^term⁽ɛit).Thelaggeddependentvariableisan endogenousregressorbyconstructioninEq.(8).Thus,theconventionalfixedeffectestimatorisbiasedandinconsistent.To dealwiththisproblem,theGeneralizedMethodofMoments(GMM)estimatorinthespiritofArellanoandBond(1991)and Blundelland Bond (1998) are predominantlyapplied inpractice forthat consistently estimatesEq. (8).GMM uses a set ofmomentconditionsrelatingto thefirst differencedregressionequation,andanother setofmomentconditions forthe regressionequationinlevels(SeeforexampleBhattacharyya,2012).

Arellano and Bond (1991) argue that additional instruments can be obtained in a dynamic panel data model ifone utilizestheorthogonalityconditionsthatexistbetweenlaggedvaluesoflny_it₋₁andthedisturbanceserrorterm(ɛit).Letus illustratethiswiththesimpleautoregressivemodel:

lnyit=

α

^ln^y^it−1+

β

^j^ln^x^jit ⁺

ε

^it ⁱ⁼¹^,^{· · ·}^,^N^and^t⁼¹^,^{· · ·}^,^T ⁽⁹⁾

BludellandBond(1998)andBhattacharyya(2012)suggestedthattheﬁrstdifferencesofthetwoormore-periodlagged dependentvariablesarevalidinstrumentsfortheequationinlevels,andtwoormoreperiodlaggeddependentvariablesin levelsarerelevantinstrumentsfortheequationinﬁrstdifferences.Togetaconsistentestimateof

δ

âs^N→∞withTfixed, wefirstdifference(9)toeliminatetheindividualeffectsis

lny_it−lnyit−1 =

α (

^lⁿ^y^it−1−lnyit−2

)

⁺

β

j

lnx_jit−lnx_jit₋₁

+

ε

^it⁻

ε

^it−1 (10)

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andnotethat(

ε

it−

ε

it−1)isMA(1)withaunitroot.Fort=3,theﬁrstperiodweobservethisrelationship,wehave lny_it₋₃−lny_it−2 =

α (

^lⁿ^yit−4−lny_it−3

)

⁺

β

j

lnx_jit₋₃−lnx_jit₋₂

+

ε

it−2−

ε

it−3 (11) In this case, lny_it−1 and lnx_jit₋₂ are a valid instrument, since they are highly correlated with (lny_it−4−lny_it−3) and (^ln^xjit−3−lnx_jit₋₂) respectively, butnot correlated with(

ε

it−2−

ε

it−3) aslong as the ɛit are not serially correlated. One can continueinthis fashion,adding an extravalid instrumentwitheach forwardperiod, sothat for periodT,the set of validinstrumentsbecomes(lny_it−1,…,lny_it−T,T−2)and(lnx_jit₋₁,…,lnx_jit_−T,T−2).

WeestimateEq.(8)usingaone-stepGMMestimatorfollowingtheaboveprocedure.TheArellanoandBond(1991)testis appliedtotheresidualsindifferencestotestforsecond-orderautocorrelation.Moreover,Sargan’sJtestisusedtodetermine thevalidityoftheoveridentifyingrestrictions.

AllvariablesexpressedinEq.(8),eachvariableisdividedbyitsgeometricmeanwhichallowsforapossibilityoftheTL first-orderparametersdirectlyinterpreted aspartialproductionelasticitiesatthegeometric meanofthedata(Coellietal., 2005).Thetrendvariableisnormalizedtobezerointheyear2018.Variousspecificationtestsofhypothesesaboutthepa- rametersinthefrontierandtheinefficiencymodelwereperformedusingthegeneralizedlikelihoodratio(LR)teststatistic.

Sinceonlythesumoftwoerrorterms(

ε

it=

v

it−u_it)^can^beôbservedⁱⁿÊq.⁽⁸⁾^,^the^farm’s^technicalêfficiencyîndex^can be estimatedusingtheconditional meanoftheefficiencyterm, proposedby BatteseandCoelli(1988),i.e.E(êxp(−u_it

ε

it). Thestaticmodelwithtime-varianttechnicalefficiencyasgiveninEq.(8)isestimatedasafixed-effectsmodelandaccord- ingly,the technicalefficiencyis estimatedusing Batteseand Coelli(1988).For empiricalapplication, we used Norwegian dairyfarmdata.

5. ThenatureofNorwegianagriculture

The primary objectivesofNorwegian agriculturalandfoodpolicies, assetout inWhite Paperno.11(2016–2017), are long-term foodsecurity; agricultural production in all parts of thecountry; creating more added value;and sustainable productionwithreducedgreenhousegasemissions.Consumersare tobeprovidedwithwholesome, high-qualityproducts and the productionprocess should be mindful ofaspects relatedto the environment, public health, andanimal welfare (OECD,2017).Dueconsiderationisgiventotheideathat farmers,asself-employedindividuals,shouldhaveopportunities forthesameincomedevelopmentasothersinsociety.Toachieve theseobjectives,thegovernmentsupports thefarmers.

Asinmostdevelopedcountries,farminghasbecomehighlymechanizedandthenumberoffarmshasbeendeclining,with productionbecomingconcentratedonfewerfarms.Accordingtoa2017StatisticsNorwayreport,in1991,therewere96000 farms;thisdeclinedto42000in2015.Moreover,2.3%fewerfarmswereregisteredin2016comparedto2015.Thenumber offarmsgrowingonlycropsdecreasedby29%duringtheperiod2006–2016.Moreover,theaveragefarmsizeincreasedfrom 14.7hain1999to23.9hain2016(StatisticsNorway,2017).In1991,thenumberofdairycowsstoodat342000,compared to224000in2015,whilethenumberofdairyfarmsdecreasedfrom27625to8860overthesameperiod.

Livestock dominates Norwegian agriculture inall regions andabout30% of thefarmers inNorway specializein dairy farming(Alemetal.,2019).Overthepastthreedecades,various regulatoryschemeshavebeenestablishedtoalignaggre- gatemilkproductionwithdomesticdemand(JervellandBorgen, 2000).From 1977to1983,dairy farmerswhovoluntarily stabilized orreducedtheir supplyofmilk relativeto abase yearobtainedabonus. However, over theseyears,aggregate milksupplyincreased.Toavoidtheoverproductionofmilkforthedomesticmarket,thegovernmentintroducedatwo-price scheme in1983. The quotas limited theamount of milkfarmers could sell atfull price. Until 1990, investments forthe developmentandentryofnewgenerations offarmingfamiliesentitledsome farmerstoobtain anadditional(free)quota.

Manyfarmersexpandedtobeefproduction(bypurchasingcalvesorsucklercows)touseidleresources(suchasland,buildings,andlabor)thathadpreviouslybeenusedfordairycows.In1996,thegovernmentimplementedasystemforrestricted redistribution of milk quotas usingregionally based, regulated quota sales.Initially, the governmentmanaged the quota transfer;however,from2002,aportionofthequotacouldbesoldandboughtbetweenfarmers.Leasingofmilkquotashas beenallowed since2009.Thereisan upperlimit onthemilkquotaperfarm,though thislimit hasbeenchanged several times.Norwegianagricultureissoheavilysubsidizedthat,withoutsupport,itwouldnotbecompetitivewithimports.There isathreatthatNorwaymaybeobligedbyinternationalpressurestocutbackonborderprotectionandoutput-relatedsub- sidies.Thiswouldforce adramaticandpainfulshifttowardsmorecompetitiveagriculture.Therefore,thereisacasetobe madetourgentlytakestepstoimprovetheproductivityandmanagementoffarming.

6. Data

ThedatasourceistheNorwegianFarmAccountancySurveycollectedbytheNorwegianInstituteofBioeconomyResearch (NIBIO).Itincludesfarmproductionandeconomicdatacollectedannuallyfromabout1000farms.¹Thereisnolimitonthe numberofyears afarm maybeincluded inthesurvey.However, forvariousreasons,approximately10% ofthe surveyed farmsarereplacedperyear.

1The number of participants varies from year to year. For example, in 1991 data were collected from 1049 farms but in 2013 the number of farms was 924.

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Table 1

Descriptive statistics (mean values per farm) for dairy farms (20 0 0–2018).

Mean Standard deviations Output variable

Total revenue in NOK ^∗ 1,567,332 1,021,241 Input variables

land in hectare 34.4 20.4

labor in hours 3534 940

Materials in NOK 502,254 322,294 Capital in NOK 484,443 267,996

Observation 5327

∗ NOK = Norwegian kroner, 2015 values.

Fig. 1. The median, ﬁrst and third quantile values (middle, bottom, and top lines) of outputs and inputs.

Thedatasetusedisanunbalancedpanelof5323observationson663Norwegiandairyfarmsinvolvedintheproduction ofdairy outputfortheyear2000–2018.Toensurethatmilkoutputisthemainfarmoutput,weselectthosefarmswhose milksalesrepresentatleast80% oftotalfarmincome.The variablesselectedforthisanalysiscontainone outputvariable andfourinput variables. Output(y) includes dairy production,which representstotal farm revenuefrom milkanddairy products,exclusive ofdirect governmentsupport.The output isvaluedin Norwegiankroner(NOK) andadjusted to2015 valuesusingtheconsumerpriceindex (CPI).The TLproductionfunction intheempirical model(8)isspecified withthe followingfourinputvariables.Farmland(x₁),definedasproductiveland(bothownedandrented)inhectaresandlabor(x₂), measuredasthetotallabor hoursused onthefarm,includinghiredlabor, owners’ labor,andfamilylabor.Materials(x₃), includingfertilizers,feed,oilandfuelproducts,electricity,expenses forcropandanimalprotection,constructionmaterials andothercosts;andfixedcost(x₄),includingfixedcostitemsplusmaintenancecostson-farmcapitaltiedupinmachinery, buildings,andlivestock.AllcostsaremeasuredinNOKadjustedto2015values.Maintenanceandcostsassociatedwiththe hiringofmachinesareregisteredannually.

Toaccommodatepanel featureswithfarminformationoverseveralyearsintheestimation,onlythosefarmsforwhich atleastthreeyearsofdatawere available wereincludedin theanalysis.Asummaryofthe outputandinputvariables is showninTable1.Fig.1showstheinputandoutputfortheyear2000–2018.Allinputs, investment,andoutputs increase forthestudyperiod.

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Table 2

Estimated parameters for the dynamic model and its Static counterpart.

Dynamic model Static model

Estimated value Robust Std. error Estimated value Robust Std. error Elasticities

y t-1(lagged output) 0.488 ^∗∗∗ 0.011

x 1(Land) 0.140 ^∗∗∗ 0.009 0.256 ^∗∗∗ 0.009

x 1(Labour) 0.034 ^∗∗∗ 0.008 0.056 ^∗∗∗ 0.008

x 3(Materials) 0.233 ^∗∗∗ 0.006 0.420 ^∗∗∗ 0.007

x 4(capital) 0.105 ^∗∗∗ 0.006 0.268 ^∗∗∗ 0.007

t (Time-trend) 0.013 ^∗∗∗ 0.001 0.034 ^∗∗∗ 0.000

AR (1) −2.849 ^∗∗∗

AR (2) 0.244

Sargan test 22.730 Nr. of instruments 20

Technical eﬃciency 0.970 0.022 0.919 0.073

Number observation 5327 5327

∗p < 0.10, ^∗∗p < 0.05, and ^∗∗∗p < 0.01 .

∗The second-order parameters in the TL are dropped, to save space, but is available from the authors.

7. Resultsanddiscussion 7.1. Modelspeciﬁcationtests

ParameterestimatesforthedynamicmodelarereportedinTable2.Asabaselineforcomparisons,Table2alsoreports parameterestimatesforthestaticcounterpartofthedynamicmodel.Thedynamicmodeldiffersfromthestaticonemainly in thefact that it accountsfor laggeddecisions andthat it doesinclude laggeddependant variable andestimatedusing GMM.

Variousspecificationtestswere conductedto obtainthe bestmodelandfunctional formforthedata underanalysis.² First,wetestedthenullhypothesisthattherearenotechnicalefficiencyeffectsinthemodelsforthefiveregionsandthe pooleddata.Thenullhypothesiswasrejected.Thattestconfirmedthattechnicalinefficiencyconstitutesthelargestshareof totalerrorvariance.Second,LRtestsforallSFmodelsforeachregionandthepooleddatarevealedthatasimplificationof thetranslog(TL)toCobb-Douglasfunctionalformwasrejected.Thus,theTLfunctionalformwasretained.

The AR (2)test statistic(p-value =0.81),asreported incolumn(1) ofTable 2corresponds to thetest of thenullhy- pothesisthat theresiduals inthefirst-differencedregressionexhibitnosecond-order serialcorrelation.Following thetest procedureproposedbyArellanoandBond(1991),anegativefirst-orderserialcorrelationintheequationinfirstdifferences isexpected andtheAR (1)test statisticsupports that.Thus, therandom shocksto thesectors arenot seriallycorrelated andtheestimationresultsareconsistent.The Sargan(1958)andHansen(1982)J-statisticwhichisusedtodeterminethe validity oftheoveridentifying restrictionsandstatisticfortestingexogeneityoftheinstrumental variables,asreportedin column(1)ofTable2,supportsthevalidityoftheinstruments(p-value= 0.302).TheGMMsystemestimationusesinter- nal instrumentsfor estimation,andthus, therecan be severalvalid instrumental variables.Thus, the setof instrumental variablesforwhichtheSargantestofexogeneitywasthemostpowerful.

7.2. Elasticities

Table 2shows theparameters of dynamicandstaticmodel estimates.Bothmodels exhibited positiveand highlysig- nificantfirst-orderparameters,fulfillingthemonotonicityconditionforawell-behavedproductionfunction.Theestimated elasticity ofdairy output to land input (x₁) issignificant withvaluesof 0.140and 0.256 fordynamic andstaticmodels, respectively.Iftheland inputincreaseby 1%inthedynamicmodel,thedairyoutput willincreaseby anestimated0.14%, ceteris paribus.Theestimatedelasticities ofdairyoutput tolabor input(x₂) were 0.034and0.056 fordynamicandstatic models,respectively.Theestimatedelasticitiesofdairyoutputtomaterialinput(x₃)were0.233and0.420fordynamicand staticmodels,respectively.Thecoefficientsofthematerials(x₃)arethe largestamongother partialproductionelasticities statisticallysignificant(p<0.001)inbothmodels.Theseresultsimplythatthepercentagechangeinmaterialshasalarger influenceondairyproductioncomparedtootherfarminputs.Thestaticmodelresultisconsistentwithresultsintheliter- ature,forinstance,Alemetal.(2019).Thepartialelasticityofcapitalcost(x₄)waspositiveandstaticallysignificantavalue of0.105and0.268fordynamicandstaticmodels,respectively.

TheresultinTable2alsoshowsthattheoneperiodlaggedoutputhasasigniﬁcantpositiveeffectonthecurrentoutput, where output is measured in logarithm. Using the estimated value of (¹−

θ

) = 0.488, the actual change in the output of a sector in any period is 52% of the change in output that is needed to catch up with the potential output in that

2Tests are not reported here due to space but are available upon request from the principal author.

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Table 3

Distribution of technical eﬃciency scores.

Percentile Dynamic model Static model Difference

1% 0.901 0.647 0.254

5% 0.947 0.764 0.183

10% 0.958 0.818 0.140

25% 0.968 0.895 0.073

Mean 0.970 0.919 0.051

75% 0.978 0.968 0.010

90% 0.981 0.978 0.003

95% 0.983 0.982 0.001

99% 0.997 0.990 0.007

Std.devation 0.017 0.073

Observations 5327 5327

Welch test comparing mean TE 49.85 ^∗∗∗

Fig. 2. Yearly average technical eﬃciencies for dynamic and static models.

period.Further, an estimate of (¹−

θ

) îs statistically significant atthe 1% level indicating that the speed of adjustment issignificantly differentfromunity. Assuming similarspeeds ofadjustmentforinputs acrosssectors, thisresultsupports the partial adjustment schemefor output and suggeststhat the static model is a misspecified one for thissample. The coefficientsforthetimetrend(0.013)impliesthattheproductivityofdairyfarmsresourceuseincreasedonaverageby1.3%

overtheperiod2000−2018.

7.3.Technicaleﬃciency

Theestimatedtechnicalefficiency(TE)scoresarereportedinTable3.TheaverageTEscoreof0.97whilethestaticoneis 0.92.TheWelchtest,reportedinTable3,indicatesthedynamicandthestaticefficiencyscoresaresignificantlydifferent.As thedynamicefficiencyscoresarehigher,thissuggeststhat,inoursample,thestaticmodelunderestimatetheperformance of the dairy farms. Considering the dynamic TE score which implies that these dairy farms producing only 97% of the maximumpossible(frontier)output,giventheinputused.Thatisanaveragedairyfarmcanincreaseitsoutputbyaround3 ifitbecomestechnicallyefficient.Inthestaticcase,theestimatedscoressuggestthatfarmerscouldimprovetheirtechnical efficiencylevelby8percentonaveragewithoutincreasingtheirinputuse.Table3alsoshowsthedistributionofthefarms inthesampleaccordingto theirtechnicalefficiency.Thus, forinstance,1%ofthefarms areonly 90%and0.65%technical efficientfordynamicandstaticmodelsrespectively.While10%ofthesamplefarmsare95%and0.82%technicalefficient.

Fig.2showsthattheyearlyaverageofTEscoresinwhichthedynamicmodelscoresarehigherthanthosefromthestatic model.AsimilarresultalsoreportedinSimilarresultshavebeenreportedforinstanceseeMinvielandSipiläinen(2018).

TheTEscoreforNorwegianregionsandfarmsizereportedinTables4and5,respectively.Theresultsshowthatthereis nosigniﬁcantdifferenceinregionsandfarmsizesforthetwodifferentmodels.AsimilarresultreportedAlemetal.(2019)

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Table 4

Technical eﬃciency scores by region.

Regions Dynamic model Static model Number of Observations

Eastern Norway Lowlands 0.968 0.928 442

(0.019) (0.058)

Eastern Norway other parts 0.971 0.913 865

(0.015) (0.070)

Agder and Rogaland -Jæren 0.974 0.951 304

(0.001) (0.054)

Agder and Rogaland -other parts 0.967 0.888 539 (0.021) (0.096)

Western Norway 0.971 0.913 1132

(0.018) (0.082)

Trøndeland -Lowlands 0.973 0.937 388

(0.013) (0.051)

Trøndeland -other parts 0.972 0.928 676

(0.016) (0.058)

Northern Norway 0.969 0.920 981

(0.017) (0.071)

All regions 0.970 0.919 5327

(0.017) (0.073) Standard errors in parentheses.

Table 5

Technical eﬃciency scores by Farm size.

Regions Dynamic model Static model Number of Observations

< 10 hectar of land 0.964 0.786 125

(0.024) (0.113)

10- 20 hectar of land 0.971 0.900 1091 (0.019) (0.080)

20- 30 hectar of land 0.972 0.921 1514 (0.012) (0.062)

30- 50 hectar of land 0.970 0.928 1725 (0.015) (0.062)

> 50 hectar of land 0.968 0.941 872

(0.023) (0.071)

All farm size 0.970 0.919 5337

(0.017) (0.073) Standard errors in parentheses.

8. Conclusion

The existingliterature inperformanceanalysisbased onstaticmodelingandthusignores theinter-temporalnatureof productiondecisions.Thisstudydeparts fromstaticmodelingbydevelopingadynamicstochasticframeworktoinvestigate theperformance offarms focusingonNorwegiandairy farms.Thisformworkallows accountingforthedynamicnatureof theenvironmentinwhichdairy farmsoperate.Theempiricalapplicationfocusedonthefarm-levelanalysisoftheNorwe- giandairysectorusingpaneldatafortheyear2000–2018.Theresultshowsthatthedynamicproductionmodelprovidesa morerealistic approachtomeasuretheperformance oftheNorwegiandairy farm,wheresluggish adjustmentofinputsis avery crediblephenomenon. Theaveragetechnicalefficiencyscoreof0.97forthedynamicmodelwhilethestaticoneis 0.92.TheWelchtest,reportedinTable3,indicatesthedynamicandthestaticefficiencyscoresaresignificantlydifferent.As thedynamicefficiencyscoresarehigher,thissuggeststhat,inoursample,thestaticmodelunderestimatetheperformance ofthedairyfarms.ConsideringthedynamicTEscorewhichimpliesthatthesedairyfarmsproducingonly97%ofthemax- imumpossible(frontier)output,giventheinputused.Thatisanaveragedairyfarmcanincreaseitsoutputbyaround3if itbecomestechnicallyefficient.Inthestaticcase,theestimatedscoressuggest thatfarmerscouldimprovetheirtechnical efficiencylevelby8percentonaveragewithoutincreasingtheirinputuse

Supplementarymaterials

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