Roel Jongeneel

Transcription

1 A Aalysis f the Impact f Alterative EU Dairy Plicies the Size Distributi f Dutch Dairy Farms: a Ifrmati Based Apprach t the N- Statiary Markv Chai Mdel Rel Jgeeel rel.jgeeel@alg.aae.wag-ur.l Paper prepared fr presetati at the X th EAAE Cgress Explrig Diversity i the Eurpea Agri-Fd System, Zaragza (Spai), August 2002 Cpyright 2002 by Rel Jgeeel. All rights reserved. Readers may make verbatim cpies f this dcumet fr -cmmercial purpses by ay meas, prvided that this cpyright tice appears all such cpies.

2 A aalysis f the impact f alterative EU dairy plicies the size distributi f Dutch dairy farms: a ifrmati based apprach t the -statiary Markv chai mdel Rel Jgeeel * Departmet f Scial Scieces Wageige Uiversity PO Bx 8130, 6700 EW Wageige rel.jgeeel@alg.aae.wag-ur.l Draft versi Jauary 2002 Abstract This paper aalyses the impact f the dairy quta scheme the size distributi f the Dutch dairy idustry. A -statiary Markv mdel apprach is used, where the trasiti prbabilities are explaied by a set f exgeus (plicy) variables. Usig a ifrmati theretical apprach, a mdel is estimated fr The Netherlads ad used t simulate the impacts f alterative EU dairy plicies. Several results emerged: a) There is a autmus ver time declie i farm umbers (implyig icrease i farm size). b) The dairy quta regime psitively iflueces 'small' ad 'medium' farm sizes; c) Abliti f the dairy quta will egatively affect the ttal umber f active farms ad favurs further icrease f farm scale. d) Targetig supprt accrdig t eeds icreases the umber f active dairy farms as cmpared with the status qu. Keywrds: Farm size structure, dairy, milk quta, plicy, maximum etrpy * I wish t thak Ams Gla fr his effrts t let us uderstad the ifrmati based apprach durig the Special Mashlt Curse Maximum Etrpy he gave i Wageige i 2001, which icluded a detailed discussi f the matrix balacig-example. I am als idebted t Kstas Karatiiis wh allwed me t lear frm his GAMS prgrams ad t Alis Burrell ad Arie Oskam wh made a umber f helpful cmmets a previus draft. All errrs are my w respsibility.

3 A aalysis f the impact f alterative EU dairy plicies the size distributi f Dutch dairy farms: a ifrmati based apprach t the -statiary Markv chai mdel 1. Itrducti Farm umbers have bee decliig drastically ver the past decades, whereas farm size icreases. Farm size ad structure have lg bee issues csidered by agricultural plicy bth i Eurpe (Keae ad Lucey, 1997) ad the US (Sumer, 1985). Give the mai plicy aim f supprtig farmer's icmes ad the clse relatiship betwee agricultural icme distributi ad farm size, this ccer fr distributial issues is surprise. Give this crrelati it is smewhat surprisig that the agricultural plicies have fte bee lackig effective plicy istrumets fr ifluecig the firm size distributi. Beefits f the cmmdity prgrams, dmiatig traditial agricultural plicies, are kw t be rughly distributed i accrdace with utput ad thus particularly beefit large farms which were less i the eed fr icme supprt. The shift i agricultural plicies frm traditial price supprt t direct paymets, iitiated i the EU with the MacSharry refrm f 1992, icreases the available plicy tls t make farm supprt mre specific with respect t farm size ad distributi. I bth the 1990 ad 1996 US farm bill debates, fr example, several prpsals were develped ad smetimes implemeted that were aimed at directig the bulk f farm prgram paymets twards mid-sized farms, as measured i terms f grss sales (Wlf, 2001, 78). Hwever, the ptetials t pursue a targeted scial agricultural plicy are by far t realized (Pdbury, 2000). The aim f this paper is t aalyse the farm size distributi f the Dutch dairy idustry, with a particular fcus hw the cmm agricultural plicy (CAP) affected this distributi. Mre i particular, this research shuld prvide a framewrk t aalyse the implicatis f chages i the EU dairy plicy (fr example a substatial chage i the dairy quta system r eve its abliti) the dairy farm size distributi. A tl fte used t describe chages i firm size distributis ver time is the Markv prcess. This apprach has the advatage that it relies aggregated data f fiite size categries -- the s-called Markv states-- at give discrete time itervals. Therewith it avids the requiremet lgitudial time rdered micr data describig mvemet f idividuals betwee differet states, data which are ly sparsely available. The mai result f this aalysis is the trasiti prbability matrix, which describes the prbability f a variable i a certai Markv state (fr example a firm size class) t eter ather Markv state. See Lee (1977), Zepeda (1995a,b) ad Karatiiis (2001) fr a list f bth geeral ad agriculture related Markv studies 1. Based Gibrat s Law, which states that firm grwth is idepedet f firm size, firm size was iitially fte mdelled as a purely stchastic Markv prcess, where the trasiti prbability matrix (TPM) is assumed t be cstat ver time (Karatiiis, 2001, 1). Applicatis fllwig this statiary Markv mdel apprach are Adelma (1958), Padberg (1962), Lee et al. (1977), ad Oustapassidis (1986). Hwever, this apprach eglects the impact f the 'evirmet' a idustry's firm structure as well as the behaviral respse f the etrepreeurs t these factrs. 1 Reviewig a umber f studies I have the feelig that Markv appraches ted t uderpredict the umber f small farms beig active i the equilibrium (see als Zepeda, 1995b, 850). 1

4 N-statiary Markv chai aalysis explicitly allws variables characterisig the idustry's evirmet, amg which plicy variables aimed at ifluecig the sectr, t explai the statiary trasiti prbabilities. Examples f this apprach are Lucas (1978) ad Jvavic (1987). Mst studies usig a -statiary trasiti prbability matrix make very strg parametric distributial assumptis ad ther restrictis. Traditial estimati techiques like OLS fail, r require strg restrictis, because the estimated parameters must satisfy prbability assumptis ( egative prbabilities, addig up). MacRae (1977) suggested a Lgit trasfrmati, which autmatically satisfied the prbabilistic cstraits (see Zepeda 1995a,b fr applicatis). Hwever, there fte is still a degrees f freedm prblem which restricts the researcher t the chice f a limited umber f explaatry variables. Eve if sufficiet degrees f freedm are available there ca be prblems with the cvergece f the estimati algrithms (see Geurts, 1995). I this paper we use the geeralised maximum etrpy (GME) frmalism, which is based Sha s (1948) ifrmati thery ad Jayes (1957a,b) as a estimati prcedure. We emply the geeralised crss etrpy (GCE) frmalism by Gla et al. (1996), ad rely recet Markv mdel applicatis usig this apprach by Gla ad Vgel (2000), Curchae et al., (2000), ad Karatiiis (2001). The GCE frmalism is used t recver cefficiets f the effects f exgeus variables idividual trasiti prbabilities whe a specific (liear) fuctial frm f the relatiship is impsed. This methd allws the use f a extesive set f explaatry variables. The impact f each variable the idividual prbabilities ad size categries is evaluated i the frm f impact elasticities. Prir ifrmati the TPM is itrduced usig the GCE frmalism. I the ext secti (Secti 2) the geeral mdel structure ad the selected explaatry variables are discussed. I Secti 3 the GCE estimatr fr the -statiary Markv mdel is preseted. It als icludes a descripti f the way prir ifrmati is used. Secti 4 discusses the data, describes treds i the Dutch dairy farm size distributi, ad prvides the estimati results. Secti 5 presets the simulati results idicatig the impacts the farm size distributi f fur alterative dairy plicies: status qu, Ageda 2000, quta abliti, ad supprt rebalacig. Fially, Secti 6 clses with sme ccludig ad qualifyig remarks. 2 The Markv mdel Assume the firm size i the dairy idustry is divided it J size categries ad dete by jt the umber f firms i the j-th size categry (j=1,, J). The a Markv chai prcess ca be expressed as where I jt = piji t ; j = 1,..., J i= 1, 1 p ij is the prbability f trasiti frm size i at time t-1 t size (1) j at time t, ad i ad I similar t j ad J. The ttal umber f farms existig at time t, N t, is equal t i = 1 it. I matrix tati equati (1) ca be writte as (t) = P' (t-1) (2) where (t) = ( 1t,..., St )' is a Kx1 clum vectr ad P =(p 1 p 2 p K ) is the trasiti prbability matrix (TPM) with each vectr p i = (p1i, p 2i, K,p Ki ). The prbability matrix is a stchastic matrix satisfyig: I 2

5 K p ij j= 1 p ij 0 ad = 1. (3) Besides the evluti f the size distributi a imprtat ad related issue is the mdellig f etry ad exit frm the idustry. The umber f assumed ptetial etrats t the idustry is kw t have a imprtat effect bth (shrt-ru) prjectis ad equilibrium slutis, eve thugh it will t affect the estimated prprtis f active firms fallig i each size categry (Stat ad Kettue, 1967). By defiig ' prducti' as a additial categry (say crrespdig with state i=0) it allws the mdellig f etry ad exit i the idustry as well as the chage i the size distributi f the 'active' r prducig firms. I a fully cmpetitive evirmet the umber f 'firms i the ' prducti' categry is idetermiate, but might be expected t be large relative t the ttal umber f 'active' farms (Stat ad Kettue, 1967, 639). Hwever, with respect t the dairy idustry, i particular uder the milk quta system, etry cditis seem a limitig factr. Therefre, the ttal umber f dairy farms at the iitial date (1972), will be used as a idicatr f the ttal umber f firms implyig that the umber f firms i state i = 0 at that date is zer. The prbability matrix P is ulikely t be cstat but will rather be depedet the ecmic situati bth iside ad utside the dairy idustry. Fr that purpse it is assumed that p frm (1) is a fucti f a set f explaatry variables, r ij p ij (t)=f ij (z(t-1), β ij ) (4) with f ij (.) detig a geeral fucti f a vectr f N exgeus variables z(t-1) = ( z1, t 1,..., z N, t 1 ) ad β ik a vectr f parameters. This crrespds t P(t) w beig a time depedet r statiary trasiti prbability matrix. Examiig the literature yields a umber f variables likely t affect trasiti prbabilities are relative prices, techlgical chage, ecmies f size, farm debt, suk csts, plicy variables, demgraphic variables, idicatrs related t ff-farm emplymet, etc. (see Gddard et al, 1993 ad Zepeda, 1995b fr a verview) 2. Sice i this paper the specific aim is t aalyse farm size distributi with respect t key plicy the selected explaatry variables (igrig a cstat) are limited t: 1. the level f aggregate milk utput dairy quta; 2. a dummy tred variable idicatig plicy regime (see Secti 4 fr details); 3. the actual farm gate price f milk (based actual fat ad prtei ctet); 4. a techlgy shifter (based estimated autmus milk yield develpmet). Althugh dairy cws play a -egligible rle i EU beef prducti, explicit variable (like fr example the beef price) is take it accut i this case. The Dutch dairy sectr is highly specialized i dairyig ad therefre beef is csidered as a by prduct. 2 Smetimes a disticti betwee the set f variables affectig etry/exit categry ad the set f variables affectig ther categries (examples are Chavas ad Magad, 1988, ad Zepeda, 1995) 3

6 3. The ifrmati apprach t recverig Markv trasiti prbabilities 3.1 The GCE estimatr fr the -statiary Markv Mdel with prir ifrmati The statistical mdel t be estimated csists f (2) ad (4), t each f which a vectr f disturbaces is added (u(t) ad e(t)). x(t) = P' x (t-1) + u(t) (2a) p ij (t)=f ij (z(t-1), β ij ) + e ij (t) (4a) ad x(t) the vectr f prprtis, btaied after rmalizati f the farm umbers i each size class it by the ttal umber f farms i the first perid, N 0. A statiary TPM estimatr usig GCE is develped by Lee ad Judge (1996), ad Gla, et al., (1996). Assume u(t) is a vectr f disturbaces with zer mea buded withi a specified M supprt vectr v. Each elemet f the u T is parameterised as u it = m v mw itm, where w is a M dimesial vectr f weights (i the frm f prbabilities) fr each u it, v is a M dimesial vectr f supprts. With x(t) beig a vectr f prprtis, the supprt vectr ca be set t ( it [0,1] ) r t v = [ 1 / K T, K,0, K, 1/ K T ] (e.g. Gla ad Vgel, 2000 ad Gla et al, 1996, ). By usig GCE, ay prir ifrmati abut P ca be icrprated i the frm f a matrix f prirs Q. Sme research has idicated that farms typically d t decrease i size withut gig ut f busiess, whereas ther studies argue that might scale up r dw i size, but with mre tha e size categry per trasiti (Zepeda, 1995b, 842). The latter assumpti, which seem t be rather plausible whe grwth is csidered as a ctiuus prcess, wuld imply that i geeral x it = pi 1, i, t xi 1, t 1 + pi, i, t xi, t 1 + pi+ 1, i, t xi+ 1, t 1 with all ther elemets i the i-th rw f the prbability matrix expected t be equal t zer. Rather tha impsig this as a restricti which shuld be satisfied, like was de i Zepeda (1995b), here this ifrmati is used as prir ifrmati, which seems likely, but may be verruled by the data. Sice the umber f dairy farms is csistetly dimiishig ver time, Geurts (1995) assumes that the prbabilities f re-etry are equal t zer, r p 0 j = 0 fr all j = 1,..., K with the zer subscript detig the etry-exit categry 3. Ather prir restricti culd be t limit the umber f -mvers t be t lwer that a certai fracti c. The prir ifrmati ca be directly icluded i the Q prir-matrix f the GCE estimatr (see belw). Prir ifrmati abut the disturbace u T, call it w itm, ca be icrprated as well. Sice clearly directed a-priri ifrmati was available, they are assumed t be uifrmly symmetric abut zer. The bjective f the GCE estimatr is t miimize the jit etrpy distace betwee the data ad the prirs. Let H( ) be the measure f crss etrpy, the the GCE is: mi H( P, W,Q, W p, w ) = pij l(p ij / q ij ) + w i j i t m itm l(w itm /w itm ) (5) (6) (7) 3 Ather prir restricti, t further csidered here, culd be t limit the umber f -mvers t be t lwer that a certai fracti. 4

7 subject t three sets f cstraits: (a) The K T data csistecy cstraits (Equatis (2)); (b) The rmalizati cstraits fr bth the trasiti prbabilities (K cstraits) ad the errr weights (K T cstraits): K j pij = 1, M m w itm = 1 (prper distributis); ad (c) the K 2 egativity cstraits fr P ad the K T M cstraits fr w: P 0, ad w 0. H(.) ca be iterpreted as a dual-lss fucti, which gives equal weights t predicti ad precisi. The sluti t the abve system f equatis is derived Gla, et. al., (1996, Chapter 6). 3.2 A Markv mdel with a liear explaati fucti I this secti it is assumed that the trasiti prbabilities ca be explaied by a liear fucti f exgeus variables. Allwig fr -statiarity f the TPM (i.e. substitutig 4a it 2a), the Markv prcess ca w be expressed as: x(t) = P (t) x(t-1) = [β z(t) + e(t)]' x(t-1) + u(t); t=1,,t (8) MacRae (1977) pits ut that i mst estimati methds, each rw f trasiti prbabilities must be frmulated t deped the exact same set f exgeus variables. Furthermre, Lee, et al. (1977) ad MacRae, (1977) develp the statistical prperties f the disturbace terms e ad u i (4). The GCE frmalism allws the disturbaces e ad u t be recvered separately. Let each β ij ad each e ijt be parameterized ver a discrete fiite supprt space: S H β ij = s d ijsθ s, ad e ijt = h g ijth φ h, where φ, θ are supprt vectrs f size S ad H respectively, ad d ad g are the crrespdig prbabilities t be recvered. The Markv prcess i (8) w becmes: x jt = K i x i,t-1 N ij d ijsθ s z,t-1 + g ijth φ h + η s H h m v m w jtm ; j=1,,k, t=1,, T (9) where N ij is the umber f cvariates i the (ij)th cell. Applyig GCE β, e, ad u ca be determied thrugh the recvered values f d, g, ad w respectively. The bjective fucti crrespdig t this mdel, which has t be miimized t btai the GCE estimates, is H( D,G, W;D,G, W ) = i + j i t m s d w ijs itm l(d l(w ijs itm / d /w ijs itm ) ) + where zer-superscripts dete prir values f matrices r parameters. As ca be see the prbabilities are lger direct elemets i the bjective fucti. As a csequece stchastic prir ifrmati the prbability structure P ca lger directly be icluded, as was the case i (7). The liear mdel (9) des t autmatically satisfy the stadard rmalisati ad egativity cstraits trasiti prbabilities (see equati 3). Therefre a umber f additial restrictis are impsed. Firstly, -egativity cstraits are impsed the parameters, i.e d 0, g 0, ad w 0. Secdly, the parameter ad errr weights are restricted d ijs = 1 i j t h g ijth S s l(g ijth / g ijth ) (10), g ijth = 1 ad M m w itm = 1 t guaratee them t reflect prper distributis. Hwever, this still t guaratees H h, 5

8 that the prbabilities f the trasiti matrix will satisfy the rmal regularity cditis. I rder t guaratee -egativity f the prbabilities ad guarateeig the sum f the prbabilities beig equal t 1 therefre ad N ij d ijsθ s z,t-1 0, i,j = 1,, K ; t= 1,,T (11a) s N ij K j shuld hld. s d ijs θs z,t-1 = 1 i = 1,, K; t= 1,,T (11b) The prir ifrmati regardig the structure f the trasiti prbability matrix (see equatis 5 ad 6) ca als be frmulated i terms f additial cstraits. T exclude firms t mve mre tha 1 stage upwards r dwwards i the farm size distributi the fllwig cstraits satisfy N ij d ijs θs z,t-1 = 0, i,j = 1,, K j i + 2 ; t= 1,,T (12a) s N ij d ijs θs z,t-1 = 0, i,j = 1,, K ; j i 2 ; t= 1,,T (12b) s The restricti excludig re-etry is 4 N ij d ijs θs z,t-1 = 0, i=0, j = 1,, K ; t= 1,,T (13) s Sice the errr vectr e is t ecessarily zer fr each bservati, the prir restrictis upward ad dwward mvemet ad re-etry d t imply ay prbabilities t be strictly restricted t zer. The restrictis specified s far guaratee that the -statiary Markv chai mdel satisfies all the regularity prperties the trasiti prbabilities ad the prir ideas, with respect t the sample ifrmati. Whe the estimated mdel is used t simulate ut f the sample evirmet, say fr z values ut f the rage implied by z(t), there is guaratee that the prbabilities will satisfy the regularity prperties 5. The impsed restrictis ly guarateed the regularity cditis t lcally (ly fr the csidered sample) hld. A way t make it mre likely that the mdel will be well-behaved whe it is used i ut f sample simulatis, is t create a RxK vectr f 'extreme' explaatry variables, say z, ad add the fllwig additial restrictis t the ptimisati prblem: ad N ij d ijsθ s z 0, i,j = 1,, K ; t= 1,,T (14a),t-1 s 4 Nte that fr j 2 the re-etry restrictis are already implicit i (12a). 5 This might be i particular a prblem whe the mdel is used t explai a highly disaggregated farm size distributi patter. 6

9 N ij K dijs θs z,t-1 = 1 i = 1,, K; t= 1,,T (14b) j s The vectr z ca be iterpreted as a vectr spaig up the discreti space f the exgeus plicy (ad -plicy) variables. If the z values used fr the ut f sample simulati remai withi this space, the mdel will t becme subject t theretical icsistecies Impact measures, diagstics ad iferece The direct effects f X ad Z the TPM are captured thrugh the margial effects ~ pij / x ad j ~ pijt / z, with t p~ the estimated trasiti prbability (at time t), ad x ijt j ad z detig the mea values (ver t=1,..., T). These margial effects evaluate the impact f each farm class j r explaatry variable the -statiary TPM. The first e ca best be iterpreted i terms f the reallcati f the firm size distributi ver time. The secd e gives the margial effect f a chage i the explaatry variables the TPM. A mre cveiet frm is the prbability elasticity (Zepeda, 1995b): E P ijt ~ p = z ijt t z ~ p t ijt = β z ijt t z t z ~ p t ijt = β ijt z t β z P Where E ijt measures the percetage chage f the th (exgeus) variable the trasiti prbability betwee states i ad j at time t. The "impact elasticity" measures the (idirect) effect f the -th exgeus variable the umber f farms i the j-th categry (evaluated at sample average): E x z p x(t) j, t t-1, ij t-1, j = = x i,t 1 = z t-1, x j,t i zt 1, x j,t i z ijt t j,t (15) z t-1, β ijt xi,t-1 (16) x Theil's iequality measure will be used as a gdess f fit idicatr. This statistic, calculated fr each size class, ca be iterpreted as a gdess f fit idicatr. 4. Data ad estimati results The data represet the Dutch dairy farms size distributi frm ad cmprise 7 size classes. A graphical illustrati f the evluti f the dairy farm size distributi i the Netherlads is give i Figure 1. The smaller size classes shw a strg declie ver time. The tw largest size classes (70-99 ad 100- ), i the fllwig labelled as the 'large' farms, shw a icrease ver the pre-quta perid, a declie i the first 5 years after the itrducti f the quta, ad mre r less stabilise thereafter. Class shws a similar patter, but is still gig t slightly decrease frm 1989 a ward. The mid-size class (30-49) shws a cyclical behaviur, with, hwever, a clear dwward tred. I the fllwig the size classes ad are labelled as the categry medium-sized farms. The 'small farms', csistig f size classes (1-29), 6 Alteratively, e ca assume a multimial Lgit trasfrmati, which satisfies bth the rmalisati ad the egativity cstraits glbally (MacRae, 1977; Gla et al., 1997). 7

10 shw a sharp declie up till 1984, which is ctiued after the itrducti f the milk quta, but at a lwer rate f declie. Because the milk quta regime itrduces a chage i treds rather tha a shift-effect, a dummy tred 7 variable was used capture the dairy quta effect. Ispecti f Figure 1 suggests that the itrducti f the milk quta system slwed dw farm size adjustmet i the Dutch dairy sectr. Hwever, the sectral adjustmet prcess did t cme t a stadstill but ctiued als after Over the csidered perid the ttal umber f active farms declies by 72,235 farms r abut 70% '1-9 '10-19 '20-29 '30-49 '50-69 '70-99 ' Figure 1 Dairy farm size evluti (abslute umber f farms) 8 I the estimated mdel the farm size distributi is aggregated it three classes (small, medium, ad large) f active farms (see discussi abve) ad e class f iactive farms 9. The GCE ptimisati prblem was prgrammed ad slved i GAMS (see Brke et al,1992 fr a further descripti f this algebraic mdellig package). The estimated TPM is give i Table 1 (average evaluated ) 10. As the diagal elemets f the matrix shw farms are very likely t stay i their curret farm size class frm e year t the ext. Hwever, i particular withi the medium ad large size classes the situati is far frm stable, but large prprtis are mvig i ad ut. 7 I ctrast with Geurts (1995) wh uses a shift-factr. The dummy tred variable is zer i the case f quta, 1 i 1984, 2 i 1985 ad s. 8 The figure is similar t the figure which e wuld get whe the prprtis (expressed i terms f the ttal umber f active ad iactive farms f the iitial perid 1972/73) wuld have bee calculated. S Figure 1 gives the patter f prprtis the mdel has t explai. 9 Aggregati (which implies a lss f ifrmati) is de as a first step i the aalysis, i the fial research paper the aim is t prvide a mre disaggregated aalysis. Prelimiary effrts shw that it is techically pssible t estimate such a disaggregated mdel (8 size classes (icludig iactive) with 7 explaatry variables). 10 Nte that sice the TPM is t evaluated at the sample average sme residuals i e(t) might be -zer causig sme slightly egative prbability values r slight deviatis frm the addig up cditi. 8

11 Table 1 Trasiti prbability matrix iactive small medium large iactive small medium large The impact f the exgeus variables the umber f farms i each class size are give by the impact-elasticities (Table 2) 11. As the Table shws the impact f the techlgy shift is i favur f a icreasig farm scale. I ctrast, the milk quta dummy i particular favurs the smaller farms. Table 2 Impact-elasticities f exgeus variables iactive small medium large milk utput dummy tred milk price tred A icrease i the ttal milk utput has a egative impact the umber f iactive farms, viz. prfitability helps farms i survivig. The itrducti f the milk quta regime leads t a declie i the umber f iactive farms ad large farms ceteris paribus. I ctrast the quta regime favurs the umber f farms i the 'small ad 'medium' size classes. A icrease i the milk price shws a similar impact tha the quta itrducti. This implies that a milk price declie leads t a icrease f the umber f iactive farms as well as the umber f 'large' farms. It is strage that the verall impact f the grwth treds wrks i favur f the umber f 'small' farms ad egatively iflueces the umber f 'large' farms. This bservati is i ctrast with a lt f evidece ad eeds further study. The value f the Theil iequality cefficiet fr classes 'iactive', 'small', 'medium' ad 'large' is , , 0.008, ad respectively. Sice the values are clse t zer, the mdel des a acceptable jb i explaiig the evluti f farm size distributi i the past fr all classes. Rughly sevety percet f the estimated parameters were sigificat. 5. Simulated Structural Chages i the Dutch dairy idustry The mdel is used t ivestigate hw the Dutch dairy farm size distributi may chage i the future, depedig alterative plicy scearis. Fr the perid the fllwig EU dairy plicy scearis are csidered: 1) Status qu ( plicy chage) (SQ). Ageda 2000 is t implemeted. Milk prices ad milk quta remai at their year 2000 values, ly tred variable chages. 11 The estimated impact f the explaatry variables the prbability matrix are t preseted here t save space, but are available up request ad will be icluded whe fial results are btaied. 9

12 2) Ageda 2000 (AG). Startig i 2004/05, the milk price is reduced by 15% i 3 steps as cmpared with 2000/01 ad kept stable frm 2007/08 ad wards. I cjucti milk quta are icreased 1.5% ad als kept cstat frm 2007/08 ad wards. A decupled milk premium is itrduced, which icreases frm 8.3 Eur/t i 2004/05 t 25.0 Eur/t i 2006/ ) Abliti f milk qutas (QA). Milk qutas are ablished i 2004/05. The milk price is assumed t immediately drp by 30% ad t further declie by 1% per year afterwards 13. Milk utput is assumed t icrease with 1% per year 14. 4) Rebalacig f supprt (RS). Similar t Ageda 2000, but with a adjusted cmpesatry paymets regime. The itrduced milk premium is differetiated betwee farm size classes (ad lger csidered t be decupled) 15. Small farms ad medium farms get a effective milk price f 120% ad 110% f the actual milk price respectively. Large farms get price premium supprt. The simulati results are cmpared t the referece sceari Status qu (idicated as sceari SQ) ad summarized i Figure 2 ad Table 3. Figure 2 gives the evluti f the ttal umber f active dairy farms uder the alterative scearis. As the Figure shws, the declie i the ttal umber f farms will ctiue i the future, irrespective f the plicies pursued. I SQ the ttal farm umber declies frm i 2000/01 (see Table 3) t i 2014/15 (-21%). This implies a aual reducti i ttal dairy farm umbers f 2%, which is t urealistic, althugh lwer tha i the last decade. The quta abliti sceari QA leads t a ttal farm umber declie f 26% i 2014/15, which is 5 percetage pits mre tha SQ. I ctrast, fr the same year the supprt rebalacig sceari SR has a ttal farm umber which is mre tha 6% abve the SQ. The ttal differece betwee SR ad SQ is 2800 farms (which is rughly 10 percet f the ttal farm ppulati i 2014/15). Table 3 Summary f results plicy scearis #-SQ 00/01 #-SQ 14/15 dev-ag dev-qa dev-sr small medium big ttal Sice the milk premium is csidered t be decupled its impact is t take it accut i the simulati. 13 The estimated milk price declie with quta abliti is based Kleihass et al (2001) ad Bejami et al (1999) wh calculate r use milk price reductis varyig frm -18% t -53%. 14 Estimate based assumed average milk shadw price f 70% f actual milk price, a milk supply elasticity f 0.5, a autmus yield icrease f abut 1% per year, ad a ttal herd size expasi f 0.5% per year. 15 I this sese the supprt rebalacig (SR) sceari has similar characteristics as a egative icme tax system. 10

13 RS SQ AG QA /01 02/03 04/05 06/07 08/09 10/11 12/13 14/15 Figure 2 The evluti f ttal dairy farm umbers Table 3 shws the impacts f the distributi f dairy farms. As cmparig the first tw clums shw the ttal umber f 'small' farms icreases frm 25% i 2000/01 t abut 50% i 2014/15. This is ulikely whe thikig frm the curret cditis, where there is relatively little part-time farmig. At the same time the shares f medium sized farms declies frm 54% t 38% ad f large sized farms frm 21% t 12%. As already ted i the ed f the previus secti this is still a puzzlig utcme which eeds further studyig. As cmpared with SQ the abliti f the milk quta regime leads t lwer umber f 'small' ad 'medium' farms ad a icrease f 'large' farms. This seems plausible, althugh i rder fr the milk balace t be hld, the average herd umber i the varius classes has t chage. Frm the disaggregated data we see this is happeig. The supprt rebalacig sceari has a psitive impact all (active) size classes, but i particular favurs 'small' farms. The icrease i the umber f farms i all categries, with still the quta i place, seems ulikely, eve with a sigificat icrease i part-time farmig. 6 Ccludig remarks Sice this paper reflects wrk i prgress these results have a prelimiary character. Althugh the predicted adjustmet i the aggregate umber f dairy farms was t i ctrast with expectatis, as ted befre, sme puzzlig fidigs abut the tred patter i the farm size distributi were fud. The geeral result that keepig the milk quta system i place slws dw the adjustmet i the farm size evluti ad therewith has a psitive impact the ttal umber f active farms is hwever a plausible result which is als cfirmed by Geurts (1995). Abliti f quta will icrease the dyamics ad is likely t imprve the chages fr the 'large' farms. Sice 'large' farms due t their scale have a lwer cst price f milk, this favurs efficiecy i prducti. If the mai aim is t pursue a scial plicy supprtig small ad medium sized family farms, ur first results suggest that the targetig f supprt makes it pssible t d a much better jb tha is realised with the curret plicies. Future research will fcus disaggragati f the aalysis, a further refiemet i the 11

14 explaatry variables (fr example the iclusi f a reveue variable, which will allw t study the cupledess f direct paymets). With respect t the estimati prcedure a -zer cvariace structure f the errr terms acrss size categries will be take it accut (alg lies suggested i Gla, 1996, 186). Als a multimial lgit specificati, which autmatically satisfies the theretical requiremets, will be aalysed, althugh ur first results with this specificati idicate that the multimial lgit is mre sesitive with respect t cvergece f the ptimal sluti as the liear specificati chse here. Mrever, we will elabrate the use f prir ifrmati. Althugh fr example the milk utput cditi (r quta cstrait) is autmatically satisfied by the sample data, it might still be pssible t use prducti balace cditis t impse further cstraits parameters 16. Fially, the etry/exit decisi will be re-examied. Refereces Chavas, J-P ad G. Magad (1988) "A Dyamic Aalysis f the Size Distributi f Firms: The Case f the US Dairy Idustry". Agribusiess 4(4), Bejami, C. A. Ghi ad H. Guymard (1999) "The future f Eurpea dairy plicy". Caadia Jural f Agricultural Ecmics 47, Brke, A., D. Kedrick ad A. Meeraus (1992) GAMS User's guide; release Sa Fracisc: The Scietific Press. Curchae, M., A. Gla, ad D. Nickers (2000) "Estimati ad evaluati f la discrimiati A ifrmati apprach." Jural f Husig Research, 11 Geurts, J.A.M.M., (1995) Techical & structural chages i Dutch dairy farms (Msc-thesis). Wageige: Wageige Uiversity. Gddard, E., A. Weersik, K. Che (1993) "Ecmics f Structural Chage i Agriculture". Caadia Jural f Agricultural Ecmics 41, Gla, A., ad S.J. Vgel, (2000) "Estimati f statiary scial accutig matrix cefficiets with supply side ifrmati." Ecmic Systems Research, 12. Gla, A., G. Judge, ad D. Miller (1996) Maximum etrpy ecmetrics. Chichester: Jh Willey ad Ss. Heessy, Th. (2001) "Mdellig Farmer Respse t Plicy Refrm: A Irish Example". Rural Ecmy Research Cetre, Teagasc, Dubli, mime. Jayes, E.T., (1957a) "Ifrmati thery ad statistical mechaics". Physics Review 106, Jayes, E.T., (1957b) "Ifrmati thery ad statistical mechaics II." Physics Review 108, Jvavic, B., (1982) "Selecti ad the evluti f idustry." Ecmetrica, 50(3), Karatiiis, K. (2001) Ifrmati Based Estimatrs fr the N-statiary Trasiti Prbability Matrix: A Applicati t the Daish Prk Idustry. Cpehage: Departmet f Ecmics ad Natural Resurces, Ryal Agricultural Uiversity f Cpehage. Keae, M. ad D. Lucey (1997) "The CAP ad the Farmer" i: C. Rits ad D.R. Harvey eds. The Cmm Agricultural Plicy (2 d editi) Walligfrd: CAB Iteratial, J = 16 x( t) q Fr example, takig it accut (15) ad give fixed ttal milk utput, it ca be shw that E 0 1, j = j j s, q where s j represets the share f the j-th size categry i ttal milk utput, which impses a restricti the parameters. 12

15 Kleihass, W, D. Maegld, M. Bertelsmeier, E. Deeke, E. Giffhr, P. Jägersberg, F. Offerma, B. Osterburg ad P. Salam (2001) "Mögliche Auswirkuge eise Ausstiegs aus der Milchquteregelug für die deutsche Ladwirtschaft". Arbeitsbericht 5/2001 (Arbeitsgruppe "Mdellgestützte Plitikflgeabschätzug" der FAL, Brauschweig). Lee, T.C. ad G. Judge (1996) "Etrpy ad Crss Etrpy Prcedures fr Estimatig Trasiti Prbabilities frm Aggregate Data." I Berry, D.A., C.M. Chaler, ad J.K. Geweke, eds, Bayesia Aalysis i Statistics ad Ecmetrics, Chichester: Jh Wiley ad Ss, Lucas, R.E.Jr., (1978) "O the size distributi f firms." Bell Jural f Ecmics 9: MacRae, E.C., (1977) "Estimati f time varyig Markv prcesses with aggregate data." Ecmetrica 45, Mittelhammer, R.C, G.G. Judge ad D.J. Miller (2000) Ecmetric Fudatis. Cambridge: Cambridge Uiversity Press. Oustapassidis, K. (1986) "Greek Agricultural Cperatives: radical chage f tred recgiti?" Oxfrd Agraria Studies XV, I, Padberg, D.I. (1962) "The use f Markv prcesses i measurig chages i market structure." America Jural f Agricultural Ecmics, Pdbury (2000) "US ad EU agricultural supprt; Wh des beefit?" Curret issues 2000(2), ABARE (prject 1633). Sumer, D. A. (1985) "Farm Prgrams ad Structural Issues". I: B. Garder, ed., U.S. Agricultural Plicy: The 1985 Farm Legislati. AEI Sympsia series, N. 85c, Washigt DC. Sha, C.E., (1948) "A mathematical thery f cmmuicati." Bell System Techical Jural, Stat, B.F. ad L. Kettue (1967) "Ptetial Etrats ad Prjectis i Markv Prcess Aalysis". Jural f Farm Ecmics, 49, Wlf, C.A. ad D.A. Sumer (2001) "Are Farm Size Distributis Bimdal? Evidece frm Kerel Desity Estimates f Dairy Farm Size Distributis". America Jural f Agricultural Ecmics 83(1): Zepeda, L., (1995a) "Asymmetry ad statiarity i the farm size distributi f Wiscsi milk prducers: A aggregate aalysis." America Jural f Agricultural Ecmics, 77: Zepeda, L., (1995b) "Techical chage ad the structure f prducti: A statiary Markv aalysis." Eurpea Review f Agricultural Ecmics, 22: