Does Loss of Biodiversity Compromise Productivity in Intensive Agriculture?

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1 Does Loss of odversy Compromse Produvy n Inensve Agrulure?. Pasual, N.P. Russell and A.A Omer Cenre for Agrulural, ood and Resoure Eonoms, Shool of Eonom Sudes, nversy of Manheser, Manheser, M3 9PL, K. e-mal: una.pasual@man.a.uk ASTRACT Ths paper explores he dynam nerrelaon beween bologal dversy, ehnal hange and agrulural produvy. The heoreal nsghs regardng hese lnkages are furhered by dervng he omparave dynam soluons of an opmal onrol model. Ths provdes esable hypoheses ha are nvesgaed usng an oupu-dsane paramer model o a large panel of spealsed ereal farms from he K ( The resuls of hs paper an nform poly makers on he desgn of sound bodversy onservaon poles n sem-naural habas, parularly n he onex of resruurng he CAP. The resuls sugges ha produvy s posvely relaed o ehnal hange and ha he mpa of nreased bodversy on froner oupu s posve wh delnng margnal effes over me. I s hus suggesed ha he objeve of enhanng bodversy levels n sem-naural habas s beng me whou mparng agrulural produvy. urher, would appear ha spealsed produers are onvergng owards a unque bes prae ehnology. KEWORDS: odversy, Opmal Conrol Model, Sohas Produon roner, Tehnal hange We are graeful o he Deparmen of Envronmen, ood and Rural Affars and he Cenre for Eology and Hydrology for permsson o use daa from he arm usness Survey and he Counrysde Survey respevely.

2 .Inroduon The emphass n agrulural prae n ndusralsed ounres has been on reang he opmum envronmen for a sngle arge spees (he rop. Ths has been aheved by adjusng he envronmen so ha growng ondons for he arge spees are opmsed whle hose for ompeng spees ( weeds and pess are delberaely worsened. Ths vew of he agro-eosysem as nvolvng smple ompeve relaonshps beween spees has domnaed agrulural prae; he o-operave or negrave mul-roppng and agroforesry sysems are now mosly found n LDCs where low npu agrulure generally refles lak of apal and spef envronmenal onsrans for nensfaon of produon proesses. In hese ases agrulure provdes a mulfunonal sysem. y onras, he ompeve vson of agrulural produon gnores neraons beween spees and s beng quesoned for no enompassng faors ha may sgnfanly onrbue o shor and long erm agro-eosysem produvy (Mader e al., 22. The new hrus of measurng agrulural susanably s ndave of hs (Krhman and Thorvaldsson, 2. More reenly has been poned ou ha eosysem susanably s more lkely relaed o manenane of spef eosysem funons raher han spees per se. Ths mples ha susanably s less relaed o he dversy of bologal spees han o preservng parular spees ha suppor he neessary eosysem funons (Myers, 996. In he onex of an agro-eosysem, addonal spees mgh redue agrulural produvy hrough ompeon (for nurens, lgh e., or alernavely mgh nrease oupu by supporng eosysem funons ha enhane produvy (e.g. hrough pollnaon, sol nuren enhanemen, negraed pes onrol e.. Thus, here s a balane beng sruk beween dre ompeon beween dfferen spees nludng rop spees, and he suppor provded by non-rop spees for he growng rop hrough he eosysem funons. Ths paper, whh seeks o denfy he effe of bodversy onservaon on agrulural produvy usng a behavoural model and an empral applaon o he K, sars from he noon ha land use hange ranks ahead of all oher physal hanges as a drver of erresral bodversy enhanemen and degradaon (Duhme e al., 997; Swanson, 994. I explores he dynam nerrelaons beween bologal dversy and rop produvy. Theoreal nsghs from an opmal onrol model of bo-eonom neraons n an agro-eologal sysem are used boh o exend our undersandng of he poenal lnkages beween bodversy enhanemen and degradaon, ehnal hange and agrulural adjusmen and o onsru esable hypoheses. In parular he resuls from a omparave dynam analyss provde nsghs abou lkely responses o spef exogenous hanges along he opmal pah of he agro-eologal 2

3 sysem. Hypoheses ha we onsru around hese nsghs are esed by applyng an oupubased dsane funon model o a large panel of spealsed ereal produers n he K. The key relaonshps beween agrulural avy and bodversy are based on measures of spees dversy from he Counrysde Surveys (Hanes-oung e al., 2 and ndes of npu use and onservaon avy on panel farms derved from he arm usness Survey. Parameers of hs relaonshp, nally esmaed for he panel as a whole, are appled o he farm level daa se o generae a farm level bodversy ndex for all 466 farms over he sample perod. The prnpal fous n hs paper s on he poenal mpa of hanges n bodversy on agrulural produvy. Seon 2 desrbes an opmal onrol model ha ses ou a smplfed framework n whh hese relaonshps an be explored from a heoreal perspeve. Seon 3 nvesgaes he dynams of he relaonshp beween bodversy ehnal hange and agrulural oupu n more deal, and seon 4 desrbes he farm panel daa and he onsruon of he bodversy ndex. Seon 5 hen oulnes he spefaon and esng of alernave versons of he sohas froner model and he key resuls relaed o ehnal hange and oupu. nally some onludng ommens are n seon A model of bodversy and arfal npu alloaon The presen model s based on he maxmsaon of he dsouned presen value of soey s uly flows o perpeuy. The dre uly funon s spefed as [(,(], where ( represens he flow aual agrulural oupu a me, and ( sands for bodversy loss arbuable o nensve use arfal npus, (, and buffered by envronmenal onservaon expendures, R(. The problem s o fnd he opmal rade-off n he alloaon of uly yeldng serves: agrulural food supply, (, and he bodversy sok, (. 2, assumng ha he margnal ules are as follows <, <, for a srly onave and lnearly separable uly funon., <,, and > As agrulural oupu reles on he negry of he agro-eosysem for s produvy and susanably, he modellng of agrulural developmen over me should onsder he relaonshp beween agrulural produvy and bodversy. Reen eologal sudes sugges ha he relaonshp s posve (ullok e al. 2; Rhards, 2. Hene, he sok of bodversy, (, eners no he produon funon alongsde (,.e. [(,(] represens poenal agrulural oupu and s assumed srly onave wh, < > and, <, alongsde weak essenaly: (. > 2 Noe ha ( refers o he level (sok of bodversy n me, whle ( refers o bodversy loss (a flow varable. 3

4 In he presen model, bodversy onveys a somewha general noon a any of hree levels (spees, gene and eosysem dversy wh eah level havng a se of subomponens and hene a dfferen neraon wh he produon proess. Ths mples ha he effe of a hange n (, on he margnal produ of (, s lkely o be dfferen a eah level or sublevel of (. or nsane, an nrease n nse or mro-organsm dversy would nrease he margnal produ of ferlser sne enhanes he sol produvy (. Alernavely, an nrease n naural vegeaon dversy would derease he margnal produ of ferlser as nreases he ompeon agans he ulvaed rops (. Smlar examples ould be saed for oher omponens of bodversy. or smply, [(, (], s assumed o be lnearly separable n ( and (..e.. In order o nlude he effe of ehnologal progress, a dynam produon funon s proposed n he form of [(, (, A(], where A( represens he sae of ar, or an exogenous represenaon of he produon possbly froner. The bodversy mpa (or loss funon, [(, (], s assumed o depend on he level of agrulural nensfaon hrough use of (, and on he exsng sae of bodversy, (. The laer effe s nluded o refle he noon ha he level of bodversy makes a posve onrbuon o eosysem reslene, n he sense ha bodversy an enhane he ably of he agro-eosysem o olerae and overome he adverse effe of agrulural aves (u and Mage, 2; Trenbah, 999; Swanson, 997. I s furher assumed ha, a he margn, bodversy loss,, nreases (dereases a an nreasng (dereasng rae due o nreases n npu nensfaon (bodversy sok.e., >, and, >, and ha he bodversy mpa funon s > < lnearly separable n and,.e.. The problem s o hoose he opmal me pahs of he onrol varables (( and R(, (, aounng for he evoluon of (. In general hs evoluon ough o refle (a he naural growh funon of, (b he onservaon aves underaken, R, and ( he nensfaon of arfal npu use: G[ (, (, R( ] ( sng an exended logs funon: α( / K R (a where α > refles he naural rae of growh of and K sands for he agro-eosysem s bodversy arryng apay. On nensfed agrulural sysems s ypal o fnd relavely low levels of relave o he poenal arryng apay. Hene, sne he erm /K s possbly neglgble, equaon (a smplfed o yeld: α R (b 4

5 where α, and are all onsan parameers. Aordng o Eq. (b, s enhaned proporonally o nvesmen n onservaon, R, beng he rae of ndued growh 3, and s proporonally redued due o arfal npu applaon. I s worh nong ha whls bodversy s onsdered o be naural apa, s assumed ha no depleon n bodversy ours as a resul of s suppor o he produon proess. Sne he opmsaon problem s spefed wh an nfne me horzon, o allow for ner-emporal neraons beween agrulure and s mpa on bodversy, we show ha he soluon of he frs order ondons would lead o a seady sae marked as (,,, ϕ and s reahable from he nal sae ondon (. Tha s, here s an mpl ermnal sae Lm ( ( φ where φ s a veor of exogenous parameers and varables nludng he dsoun rae, ρ, and ehnologal progress, A. The aggregae objeve funon s defned as follows: ρ MaxW ( (, ( e u ( (, ( d,, R (2 where ρ > s he dsoun rae; subje o ( he equaon of moon for (, ( he non-negavy onsrans,.e. and, ( he nal ondon (, (v he mpa funon (., (v he envronmenal onservaon nvesmen funon (3: R ( ( (, ( ( (3 The urren-value Hamlonan s n urn: H C (, ϕ( α (. (4 where ϕ s he urren shadow value of bodversy or osae varable. Applyng he Maxmum Prnple for an opmal neror soluon shows ha: 4 H C α [ (. ] (5a ϕ H C ϕ (5b 3 The parameer also an be nerpreed as he margnal degradaon n ( aused by nrease n (.e. he opporuny os of R(. 4 See Omer e al. (23 o verfy ha he urren value Hamlonan s maxmsed. 5

6 [ ] ϕ C H (5 ρϕ ϕ H C [ ρ α ϕ ] (5d Equaon (5a resaes he sae equaon, (5b esablshes ha he urren shadow value of bodversy (ϕ s posve, whle (5 saes ha should be alloaed suh ha he margnal uly and dsuly of arfal npu use are balaned. or an neror soluon, he brakeed erm ( s posve as ϕ s posve and he frs erm s unambguously posve. rom (5b-5 an be defned as an mpl funon of and wh and,.e. (, s he level of ha solves he OCs. > < 3. The effe on agrulural oupu of ehnologal hange and bodversy Ths seon looks a he effe of ehnologal hange (A on (a he seady sae equlbrum levels for and (sa omparave analyss, and (b he opmal me pahs o suh an equlbrum (dynam omparave analyss. The seady sae soluon of hs agro-sysem s 5 [ ] J g f S ρ α (α (6a [ ] J g f S ρ α (α (6b To nvesgae he effe of an exogenous hange n A on he seady sae, we dfferenae Eq. (6 wh respe o A: > S A J f A (7a > S A J f A (7b Aordng o he model, an nrease n ehnologal progress, leads o hgher seady sae value of boh and. The omparave dynams analyss shows how he sae and onrol varables hange along her opmal me pahs n response o hanges n ehnologal progress (A. The me pahs, defned by he defne soluon of he dynam sysem of he model, are gven as: [ ] r e k, ; (, ; ( φ φ (8 5 The dervaon of he omparave sa soluons are shown n he appendx. 6

7 where k s defned as follows: ( r k (8a r To derve he loal omparave dynams, he me pahs gven by (8 are dfferenaed wh respe o A o show boh he shor-run and long run effe: 6 r ( e > ( ;, φ A A (9a ( ;, φ r A Ake A > (9b Eq (9b saes ha opmal levels of ( nrease wh an nrease n ehnologal progress, bu he rae of nrease delnes as he erm r ke approahes zero as me approahes nfny, gven k < and r <. Tha s, he effe of mprovng ehnology n rop produon shfs he seady sae of o a hgher level. gure deps he effe n a (A, spae. The lef hand sde of (9b s he slope of he solne, whh equals and A A A a, and r begns o delne as nreases sne he negave erm ke beomes smaller as k < r <. A posve hange from A o A, (hrough me s assoaed wh a hgher seady sae for, loaed on a new flaer solne (gure. The nrease n rop oupu due o ehnal hange s a key predon whh omes as a esable hypohess n he nex seon. Smlarly he model also preds ha bodversy nreases due o ehnologal progress bu whle he rae of nrease s nally below ha a he seady sae, nreases over me as r e goes o zero (as me approahes nfny. 6 The dervaon of he omparave dynams are shown n he appendx. 7

8 ' b a A A A gure : Dynam omparave analyss of a hange n A on long run level of The mpa of bodversy on oupu an also be nvesgaed hrough omparave dynam analyss. ( ;, φ r ke > (9 Equaon (9 saes ha he along he opmal pah nreases over me when bodversy nreases. I an be noed ha as me nreases, he opmal rae of hange n dereases unl he new seady sae s reahed. The hange owards he new seady sae value for s deped graphally n gure 2. eause he and solnes are upward slopng (Omer e al, 23, any hange n wll nrease he seady sae level of (fgure 2. Ths hypohess s also esed n he empral model. ( ' ' b a ( gure 2: Dynam omparave analyss of a hange n on long run level of 8

9 The empral analyss wll herefore fous on wo key predons ha relae o he dynam behavour of agrulural produvy: a Agrulural produvy along he opmal pah s posvely relaed o ehnal hange b The mpa of hanges n bodversy on froner oupu s posve and delnng over me 4. The Daa Empral analyss n hs sudy s foused on esng he wo key predons of he heoreal model as ndaed above. Ths s arred ou usng a daa se onsrued from he K arm usness Survey (S 7 reords of a panel of approxmaely 23 speals ereal produers (from 989 o 997. In addon bodversy measures aken from plo-level observaons n he K Counrysde Survey have been used o onsru a farm level bodversy ndex. Ths daase (desrbed n more deal below s used o esmae he parameers of a dynam produon froner. I s assumed ha hs froner models he opmal pah of aual agrulural oupu orrespondng o n he heoreal model. 8 The varables nluded n he analyss are: ( value of rop oupu per heare ( K, he man rop enerprse oupu exludng se-asde paymens, ( oal labour os per ha, nludng mpued os of famly and hred labour, ( os of mahnery use per ha, (v os of ferlser use per ha, and (v os of pesde use per ha. The daa on oss and revenues have been deflaed by he relevan Agrulural Pre Index (API, base year In addon, a bodversy ndex measure s nluded n he analyss (he followng seon explans he daa and onsruon of hs ndex. Summary sass for hese varables are shown n able. Table : Summary sass for seleed varables on ereal farms n he Eas of England Varable Mean S.Dev Mnmum Maxmum Oupu odversy (ndex erlser Labour Mahnery Pesde use The K S s an annual survey underaken by he Deparmen of Envronmen, ood and Rural Affars (DERA. 8 Noe ha he model n seon 2 assumes ha farmers are fully effen, and hus, hey an be sad o operae on he produon froner. 9 The pre ndes whh are aken from DERA s webse, 9

10 Area (ha Values per heare unless oherwse spefed. The odversy Index: The bodversy ndex used n hs sudy s based on measures of plan dversy from he major Counrysde Surveys underaken n 978, 99 and 998. Daa was avalable for ndvdual survey plos loaed n sx Envronmenal ones (Es aross England. Ths sudy fouses on daa for Envronmenal one sne he boundares of hs zone orrespond mos losely o hose of he area spanned by he panel of farms. Measures of spees rhness were suppled for egh Aggregae Vegeaon Classes (AVCs and a number of road Habas n hs one. A sngle bodversy ndex has been onsrued from hs daa, followng he aggregaon approah used by he Cenre of Agrulure and Envronmen of he Neherlands (Wenum e al Sne farms may over more han one haba ype, haba dversy has been aouned for. urher, he ndex s also orreed o aoun for he fa ha farms ofen presen dfferen landsape feaures, e.g. hedges, walls and feld margns, whh ypally hos dverse vegeaon lasses. The bodversy ndex, s gven by: a k n S ( j kj kj kj where, S kj s he mean spees rhness of AVC n road Haba j n E k ; n kj s a measure of AVC domnane n road Haba j (he proporon of he number of plos of AVC n H j o he oal number of plos of all AVCs n H j, and, a kj s he salar assoaed wh road Haba domnane n E k ( he proporon of he area of H j n E k o he oal area of all H n E k. 2 esdes he 978, 99 and 998 perods for whh he daa from he major surveys s avalable 3 wo addonal observaons, for 997 and 999, have been onsrued from he naonal esmaes on eah AVC publshed as par of CS2 resuls adjused for E. Ths bodversy ndex ogeher wh he measures on bodversy onservaon R and agrulural npu use are used o esmae by OLS he parameers (Table 2 of a dsree-me aggregae verson of he sae equaon of bodversy: α ln ln R, ( A measure of spees rhness per plo, based on ounng only nave and onssenly denfed spees, s used n CS as a smple measure of plan dversy. The Counrysde Vegeaon Sysem (CVS desrbes egh aggregae vegeaon ypes 2 Daa on area of broad habas s aken from he CS2 webse, 3 The daa for 978 s no presened by H, so he H breakdown from 99 s used as a proxy for 978 by mergng he wo daa ses by plo d, n SAS, and hen usng only hose plos for 978 whh are repeaed n 99 o onsru he 978 ndex.

11 A dummy varable s spefed for R based on he nroduon of Agr-envronmenal shemes followng he reforms of he CAP 4 n 992, whle he naonal average of pesde use s used as a proxy measure for. The albraed parameers (sandard devaons n brakes are: α.32 (.8, 2.24 (.88,.3 (.4. sng hese values, n he sae equaon allows esmaon of he value of (usng an erave approah a any parular year ( for any of he surveyed farms gven farm observed values for R and and a sarng value for : Average farm spef bodversy ndexes for he perod are shown n gure 3. gure 3. odversy Index, odversy Index year The omplee per heare daa se n ndex form (99, nludng he bodversy ndex, s presened n gure 4. Ths shows ha bodversy remans approxmaely onsan over he daa perod as a whole, rsng slghly o 99, hen delnng sgnfanly o 995, reoverng n he laer years of he daa perod. erlzer follows a smlar paern wh a more subsanal delne o 995 and a more vgorous reovery owards he end of he perod. Labour, mahnery and pesde use delne nally, reoverng o a peak n 993 afer whh labour onnues o delne whle mahnery and pesdes reman a approxmaely 99 levels. Value of oupu per heare nreases subsanally over he perod, wh a sgnfan dp below rend n 995 and a subsanal reovery owards he end of he perod. There are learly wo denfable dynam paerns. On he one hand labour, mahnery and pesde use follows a paern of nal delne wh reovery o peak n 993 followed by onsan or slgh delne. On he oher hand he behavour of bodversy 4 The dummy values are zero for perods before 993 and one for and afer 993.

12 pesde and oupu s more volale. All hree daa seres show a sgnfan reduon o a rough n 995. Ths would pon o bodversy and ferlzer use as he key deermnans n oupu and also o he weak relaonshp beween labour use and oupu. gure 4: Average values for all npus, odversy erlser Labour Mahnery Pesde eld Noe: The baselne daa values for 99 are as follows: odversy 3.53 (ndex; erlzer 88/ha; Labour 69/ha; Mahnery 23/ha; Pesde 89/ha; Oupu 737/ha. 5. The Sohas roner Model: A Cobb-Douglas sohas froner produon model s defned for arable rop produon on ereal farms n he Eas of England 5 β β V (2 k k k where s he log of rop oupu of he h farm a me perod (hundreds pounds per ha; s he log of bodversy; 2 s he log of ferlser use (hundreds pounds per ha; 3 s he log of labour use (hundreds pounds per ha; 4 s he log of mahnery use (hundreds pounds per ha; 5 s he log of pesde use(hundreds pounds per ha; 6 s he year of observaon where 6, 2,,9; 5 A ranslog was also red bu he neraon erms reaed sgnfan mulolneary. 2

13 The V s are assumed o be ndependenly and denally N(,σ 2 v dsrbued random errors ha are ndependen of he s. The s are non-negave random varables assoaed wh ehnal neffeny of produon. Three dfferen froner models are onsdered based on dfferen spefaons for he s. The Cobb-Douglas sohas froner produon funon (2 s esmaed 6, gven hree dfferen spefaons of he ehnal neffeny effes defned by equaons (2a, (2b and (2. Several versons of eah of hese hree models were esmaed o es varous hypoheses usng he generalzed lkelhood rao sass (Table 3. Model s a me-varyng neffeny model, as desrbed by aese and Coell (992, n whh he neffeny effes are defned as: { [ ( T } exp η ] (2a where η s an unknown parameer o be esmaed, and are ndependen and denally dsrbued random varables obaned by he runaon a zero of a he N(,σ 2 u dsrbuon. The parameer esmaes for model are gven n able 4. Model 2 s a neural sohas froner model, based on aese and Coell (995, n whh he neffeny effes are defned as W (2b j j j where s farmer s age (years, 2 represens envronmenal paymens, 3 s a dummy varable defned for parpaon n agr-envronmenal shemes, 4 s a hred labour ndex, 5 s a dummy varable defned for hrng labour, 6 s he year of observaon, and W s are unobservable random varables ha are ndependen and denally dsrbued, obaned by he runaon a zero of a he N(,σ 2 u dsrbuon, suh ha W are non-negave. Model 3 s a non-neural sohas froner model, based on Huang and Lu (994, n whh he neffeny effes are defned as j j j j k W (2 jk k j Ths model s an exended verson of model 2, n whh here are neraons beween farmspef varables (s and he npu varables (s n he sohas froner. However, should be noed ha model 2 and 3 are no a generalzaon of model, and hus anno be esed agans model Table 2 shows he resuls of esng some neresng null hypoheses for he spefaon of he above models. 6 Maxmum lkelhood esmaes of he parameers of hese models were obaned usng he ompuer program, RONTIER verson 4. (Coell,

14 Table 2: Generalzed Lkelhood-Rao Tess for Parameers of he Sohas roner Produon Models for Cereal armers n Eas of England Null Hypohess log lkelhood LR CV (% C V(5% Model H : µ η * H : β 6 H η H µ Model *Ths CV (ral value s obaned from Kodde and Palm ( H : j * H β 6 H :... 6 Model H : j jk * H : β 6 H : jk, k, j,...6 H : 6k k 6, k,...,6 H : 3k 4k, k,..., Gven model spefaon, he null hypohess ha ehnal neffeny s no presen,.e. H : µ η, s rejeed by he daa. The null hypohess of no ehnal hange, H : β 6, s also rejeed and he hypohess ha he ehnal neffeny effes are me nvaran, H : η, s rejeed as well. urher, he half-normal dsrbuon seems an adequae represenaon for he dsrbuon of he farm ehnal neffeny effes,.e. H : µ, s no rejeed a he 5% level of sgnfane. These hypoheses ess sugges ha he preferred model s Model, wh a half normal dsrbuon and me-varyng farm neffeny effes or hs model, an be noed ha η >, mplyng ha ehnal neffeny derease over me. Gven model 2, he null hypohess ha neffeny s no presen, H : j jk, s srongly rejeed, and he null hypohess of no ehnal hange, H : β 6, an be also rejeed. The hypohess ha he neural model (Model 2 s an adequae represenaon of he daa, H : jk, s also rejeed by he daa, smlarly o he null for no year neraon wh he explanaory varables n he neffeny sub-model, H : 6k. Lasly, he null of 4

15 no neraon beween he dummy varables n he neffeny sub-model and he npu varables, H : 3k 4k, s also rejeed. These ess ndae ha Model 3 s preferred o Model 2. The parameer esmaes are gven n able 3. Table 3: MLE parameer esmaes of he generalzed Cobb-Douglas sohas froner produon models and 3 Model Model 3 Varable Parameer Coeffen T-rao Coeffen T-rao Consan β odversy β erlzer β Labour β Mahnery β Pesdes β Tme β Ineffeny model Consan Age Envronmenal pay D Hred labour Index D Tme odversy-age.3 4. odversy-env. Pay odversy-d odversy-hred lab odversy-d odversy-tme erlzer-age erlzer-env. Pay erlzer-d erlzer-hred lab erlzer-d erlzer-tme Labour-Age Labour-Env. Pay Labour-D Labour-Hred lab Labour-D Labour-Tme Mahnery-Age Mahnery-Env. Pay Mahnery-D Mahnery-Hred lab Mahnery-D Mahnery-Tme Pesdes-Age Pesdes-Env. Pay

16 Pesdes-D Pesdes-Hred Lab Pesdes-D Pesdes-Tme Tme-Age Tme-Env. Pay Tme-D Tme-Hred Lab Tme-D Tme-Tme σ η Log-lkelhood D: Dummy varable for envronmenal paymens reeved ( f reeved, oherwse; D2 dummy varable for hred labour (, f posve expendures n hred labour, oherwse Elases of mean produon for ereal produers: The elasy of mean produon wh respe o k h npu varable for a non-neural sohas froner produon funon s ln E ( β µ C (3 k k k where µ (3a j j j j k jk k j C µ µ φ( σ φ( σ σ σ µ µ ϕ( σ ϕ( σ σ (3b and φ and ϕ represen he densy and dsrbuon funons of he sandard normal random varable, respevely. The elasy of mean oupu wh respe o k h npu varable n (4 has wo omponens. The frs one s he radonal elasy of he oupu wh respe o he k h β npu,, whh s referred o as he elasy of froner oupu. or he Cobb-Douglas k non-neural sohas froner produon funon, he oeffens of he logarhm of he npus, β k s, are he elases of he froner rop oupu wh respe o he orrespondng npu. The esmaed froner elases. are shown n able 4. 6

17 The seond omponen of he elasy of mean oupu, C µ, s he k ehnal effeny elasy wh respe o he k h npu. Aordng o he non-neural SP model (Model 3, he froner, effeny and mean oupu elases for eah of he npus are presened n able 4. Mean oupu elases by npu, for eah year, are presened n able 5 and llusraed n fgure 5. Table 4: Elases of rop oupu wh respe o all he npus Varable roner oupu Tehnal effeny Mean oupu odversy erlzer Labour Mahnery Pesdes...2 Tme.5.6. Reurn o Sale.67 Table 5: The elases of mean rop oupu wh respe o he dfferen npus for eah year ( ear odversy erlzer Labour Mahnery Pesdes Tehnal hange Avg

18 gure 5: Change n elasy of rop oupu wh respe o odversy elasy roner elasy w.r. Tehnal effeny elasy w.r.. Mean oupu elasy w.r year The resuls deped n gure 5 are onssen wh he predon generaed n (9: he mpa of bodversy on froner oupu s posve and delnng. Ths mples ha, for froner oupu among he sampled farms, reurns o nreases n bodversy are delnng. In addon, as also shown n fgure 5, nreased bodversy has been assoaed wh nreased ehnal effeny afer 992, when broad based envronmenal paymens were nrodued. Thus, up o 992 hgher bodversy was assoaed wh produers ha were furhes below he produon froner, whle afer hs me, nreased levels of bodversy seem o have nreased effeny levels. Ths also mples ha he ne mpa of bodversy on mean oupu has been posve over mos of he daa perod. Tehnal progress and produvy hange: The SP model 3 also allows o nvesgae produvy growh by obanng esmaes of he me dervave of he mean rop oupu. The esmaed me oeffen s sgnfanly dfferen from zero, and beng posve ( ˆ6 β.6, ndaes here s posve annual ehnal progress n mean froner rop oupu of abou 6%. Ths suppors he posve preded by he heoreal model, equaon (9b. As wh he mpa of bodversy he mpa of exogenous ehnal progress (he rae of he produvy growh over me s deomposed no wo omponens assoaed wh ehnal hange and effeny hange (aese e al. 2. Ths deomposon of he rae of hange of mean rop oupu wh respe o me s gven by ln E ( β µ C (4 8

19 β where represens he mpa of exogenous ehnal hange and C µ shows he mpa of hs hange n effeny levels. gure 6 llusraes hese values for he urren analyss. gure 6: The rae of hange of mean rop produon wh respe o me.2.5 Tehnal hange Tehnal effeny hange produvy growh elasy year Tehnal Effeny and Convergene o bes prae: I has been emphassed here ha whle he heoreal model assumes ha all farmers are fully effen (.e. hey operae on he froner usng bes prae ehnology, he empral model allows ha some farmers may be more suessful han ohers a ahevng bes prae. The sysema par of devaons n oupu and npu use from froner levels are represened by he measures of ehnal effeny ha are provded by hs model. Though no enompassed by he heoreal framework adoped here, we beleve ha addonal analyss of hese measures an provde useful nsghs for he problems beng nvesgaed. In parular, hese measures and how hey hange over me an llusrae onvergene (or nononvergene o bes prae among our sample of farms. Gven he spefaon of he sohas froner produon funon defned by equaon 2, he ehnal effeny of a gven farm a a gven me perod s alulaed as (aese and Coell 992: TE exp( (5 The mean ehnal effeny of ereal farms n he Eas of England does no dffer sgnfanly for he seleed models. I s.86 for he non-neural model (model 3 whle s.84 for he neural model. However, an be observed ha whls ehnal effeny 9

20 appears o nrease onssenly over me aordng o he resuls from model, model 3 shows a yle paern n effeny, even hough he rend on average s nreasng. gure 7 shows how he mean ehnal effeny of ereal farms n he Eas of England vares over me for boh hese models. Table 6 repors he sample desrpve sass of effeny sores (from model 3 for he nne-year perod. I an be noed ha he sandard devaon of sores s beng redued onssenly from..2 n durng o he measured lowes n 997 (.4. Ths mples ha besdes an nreasng rend n mean effeny levels, he dsperson s also beng redued over me. Noe also ha he mnmum effeny levels have been onssenly rsng. Table 6 also repors he resuls of a z es for he equaly of means of effeny sores for subsequen perods. The ess sugges ha only beween and , he average effeny sores an be onsdered o be equal. Hsograms of he ehnal effeny sores aross farms for he me perod are presened n gure 8. gure 7: Change n Mean Tehnal Effeny over me (gven Models and 3 Avg. Tehnal Effeny Model Model year Table 6 Sample desrpve sass of ehnal effeny sores gven Model 3 T sa N of ear Mean Sd Dev Mnmum Maxmum Dff. farms means Sg level Dff means

21 Coun Coun Coun Coun Coun Coun Coun Coun Coun Coun gure 8: Effeny sore hsograms, e89 e94 e9 e e92 e93 e e95 e96 e97 6. Conlusons Ths paper has explored he dynam neronneedness beween bologal dversy ehnologal hange and rop produvy n he onex of spealsed nensve agrulure. A heoreal opmal onrol model has provded wo hypoheses ha have been esed usng an eonomer model appled o a panel of spealsed ereal farms n he Eas of England for he perod The esable hypoheses are ha (a produvy along he opmal pah s posvely relaed o ehnal hange and ha (b he mpa of hanges n bodversy on froner oupu s posve and delnng over me. 2

22 As regards he frs hypohess, has no been rejeed by he daa. urhermore, deparng from he noon ha farmers operae on he froner, ehnal neffenes have been measured. A remarkable fndng s ha whle boh ehnal effeny and produvy are nreasng, he dsperson of effeny levels aross farms s beng sysemaally redued. Ths mples ha spealsed produers are onvergng owards a unque bes prae ehnology, used by fewer farms a he begnnng of he 99s. Smlarly, he daa has been unable o reje he seond null hypohess of he posve effe of bodversy on produvy. Ths has mporan mplaons for envronmenal poly. I suggess ha he nroduon of CAP based bodversy onservaon poles n sem-naural habas, represens a wn-wn senaro. Tha s, he poles are onssen wh her envronmenal objeve o enhane bodversy levels whou mparng agrulural produvy. The laer effe has been found o arse hrough he posve effe of bodversy on boh froner oupu and also on resoure use effeny levels. 22

23 Appendx: To run he omparave analyss we need o fnd he seady sae soluon and he me pahs of and. ( ( rs, we need o denfy he seady sae soluon a. A equlbrum, he dynam sysem s (., ( g α (A ] [, ( f ρ α (A2 The Jaoban marx evaluaed a he seady sae, ( s: S f f g g J (A3 where: ( g α > (A3a [ ] g < (A3b ( 2 ] [ ] [ f < (A3 [ ] ( 2 ] [ f > (A3d Hene: S f g f g J < > (A4 As s esablshed ha S J s negave for he seady sae o be a saddle pon (Omer e al, 23, he followng seady sae values of and are derved from he lnearsed sysem of equaons (A and (A2 usng Cramer s rule. [ ] J g f S ρ α (α (A5a [ ] J g f S ρ α (α (A5b Seondly he me pahs of and were denfed by solvng he model sysem usng he lnearsed sysem of he model: ( ( 23

24 J d (A6 where ] [ α > [ ] < ( 2 ] [ ] [ < [ ] ( 2 ] [ > o fnd he general soluon, whh s gven as ( ( (A7 represens he seady sae equlbrum, and represens he omplemenary funons based on he redued equaons of he model sysem,, whh are found by usng ral soluon, suh as ha and,n urn mplyng ha and, where m and n are arbrary onsans and r s he haraers roo. r me ( r ne ( r rme r rne y subsung he ral soluon no he redued equaons and mulplyng by he salar e : r n m r r (A8 24

25 To fnd nonrval soluon of m and n, he haraers equaon of he sysem ha gves he haraers roos r of he sysem. an be solved: r r (A9 Eah roo wll draw ou from (A8 a parular se of nfne number of soluon values of m and n ha ed o ogeher by where s a onsan, whh s defned from (A8 as follows: r m k n k ( r r k (A Then we an defne and where s an arbrary onsan, whh would be deermned from he nal ondon. Then subsung hese expressons of and n along wh he values of no he ral soluon gves he omplemenary funons,, and hene he opmal pahs as: m r k n k r m r r r e e e n m e r r e k e k 2, ; (, ; ( 2 φ φ (A or a dynamally sable equlbrum, he omplemenary funon should onverge.e. as. Sne a saddle pon has one negave roo and one posve (say and r hen he onvergene of he omplemenary funons requres.e. he posve roo should drop ou leavng only he negave roo o make he equlbrum sable. < 2 r > 2 sng he nal ondon o defnse from (A: A, (, ( e e r (, and (. Therefore, he defne soluon of he dynam sysem of he model, s gven as: [ ] r e k, ; (, ; ( φ φ (A2 25

26 Referenes aese, G. E. and Coell, T. J. (992 roner produon funons, ehnal effeny and panel daa: wh applaon o paddy farmers n Inda, Journal of Produvy Analyss, 3:53-69 aese, G.E. and Coell, T.J. (995 A model for ehnal neffeny effes n a sohas froner produon funon for panel daa, Empral Eonoms, 2: ullok, J.M., Pywell, R.., urke, M.J.W., and Walker, K.J. (2 Resoraon of bodversy enhanes agrulural produon, Eology Leers, 4(:85-89 Coell (996 A Gude o RONTIER Verson 4.: A Compuer Program for Sohas roner Produon and Cos unon Esmaon. Workng paper No. 7/96. Cenre for Effeny and Produvy Analyss. Deparmen of Eonomers. nversy of New England, Ausrala. DERA (22, Workng wh he Gran of Naure: a bodversy sraegy for England, Deparmen for Envronmen, ood and Rural Affars (K. Duhme, Paule S, aer H (997 Quanfyng arges for naure onservaon n fuure European landsapes, Landsape And rban Plannng, 37 (-2: Ehrlh, P.R. (995, The sale of human enerprse and bodversy loss. In: Exnon Raes (edors, Lawon, J.H. and May, R.M. Cambrdge nversy Press, Cambrdge, K, pp ry, G.L.A. (989, Conservaon n Agrulural Sysems. In: The Senf Managemen of Temperae Communes for Conservaon (edors, Speellerberg, I.., Goldsmh,.., and Morrs, M.G. lakwell Senf Publshers, Oxford, K, pp Gller, K.E., eare, M.H., Lavelle, P., Iza, A.-M.N. and Swf, M.J., 997 Agrulural nensfaon, sol bodversy and agroeosysem funon. Appled Sol Eology 6(: 3-6. Grossman, G. and Krueger, A. (995, The nvered-: Wha does mean? Envronmen and Developmen Eonoms. ( Hanes-oung, R.H., arr, C.J., lak, H.I.J., rggs, D.J., une, R.G.H., Cooper,.H., Dawson, L.G., rbank, L.G., uller, R.M., urse, M.T., Gllespe, M.K., Hornung, D.C., Howard, D.C., MCann, T., Morerof, M.D., Pe, S., Ser, A.R.J., Smh, S., So, A.P., Suar, R.C., and Wakns, J.W. (2, Aounng for naure habas n he K ounrysde, DETR, London Huang, C.J. and Lu, J.T. (994: Esmaon of a Non-Neural Sohas roner Produon unon. Journal of Produvy Analyss, 5: 7 8. Krhmann H, Thorvaldsson G (2, Challengng arges for fuure agrulure European Journal Of Agronomy, 2 (3-4: Kodde, D.A. and Palm, A.C. (986, Wald Crera for Jonly Tesng Equaly and Inequaly Resrons. Eonomera, 54: Mader P, lessbah A, Dubos D, Guns L, red P, Nggl (22 Sol ferly and bodversy n organ farmng, Sene, 296 (5573:

27 Myers, N. (996 Envronmenal Serves of odversy, Proeedngs of he Naonal Aademy of Senes of he ned Saes of Amera, 93(7, Omer, A., Pasual,. and Russell, N. (23 Agrulural Inensfaon and odversy Loss: Is There an Agr-EKC?, Shool of Eonom Sudes, nversy of Manheser, K, Workng Paper WP-37 Rhards, A.J. (2 Does low bodversy resulng from modern agrulural praes affe rop pollnaon and yeld?, Annals of oany, 88(: Swanson T. (994 The Eonoms Of Exnon Revsed And Revsed - A Generalzed ramework or The Analyss Of The Problems Of Endangered Spees And odversy Losses, Oxford Eon Pap 46: 8-82 Suppl. S Swanson, T. (997 Wha s he publ neres n he onservaon of bodversy for agrulure? Oulook on Agrulure, 26(:7-2 Trenbah,.R. (999 Mulspees roppng sysems n Inda Predons of her produvy, sably, reslene and eologal susanably Agroforesry Sysems, 45(- 3:8-7 Wenum, J., uys, J. and Wossnk, A. (999 Naure Qualy Indaors n Agrulure. In rouwer,. and Crabree,. (999 Envronmenal Indaors and Agrulural Poly, CAI, Wallngford, K. u, W and Mage, J.A. (2 A revew of oneps and rera for assessng agroeosysem healh nludng a prelmnary ase sudy of souhern Onaro, Agrulural Eosysems and Envronmen 83(3: