Nitrogen Fertilizer Demand from Danish Crop Farms - Regulatory Implications of Farm Heterogeneity

Transcription

1 MPRA Much Persoal RePEc Archve Ntroge Fertlzer Demad from Dash Crop Farms - Regulatory Implcatos of Farm Heterogeety Lars Går Hase AKF 2004 Ole at MPRA Paper No , posted 16. July :06 UTC

2 Regulatory Implcatos of Heterogeety - the Case of Ntroge Fertlzer Demad from Dash Crop Farms Lars Går Hase AKF (Isttute of Local Govermet Studes - Demark September 2001 Please address all correspodece to Lars Går Hase, AKF, Nyropsgade 37 DK-1602 Copehage V, Demark (phoe: , fax: , E-mal: LGH@AKF.DK. The research leadg to ths paper was fuded by The Dash Evrometal Research Programme. I thak Has Aderso, Boe Frederkse, Bert Hasler, Eskl Heese, ad Jørge Dejgård Jese for may helpful commets ad Ladbrugets Rådgvgsceter (The Dash Agrcultural Advsory Cetre for provdg access to ther data. 1

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4 Abstract I ths paper we estmate troge fertlzer demad elastctes for Dash crop farms usg the dual proft fucto approach o mcro pael data. The model cludes several farm specfc parameters allowg us to estmate the mea demad elastcty ad test for homogeety of elastctes across pael farms. We fd a mea ow prce elastcty for troge of ad a sgfcat stadard devato from ths mea for dvdual farms of Heterogeety of demad elastctes mples that regulatg fertlzer applcato through madated uform percet reductos, as s curretly used Dash troge regulato, creases abatemet costs whe compared to tax regulato. Somewhat surprsgly, ths oly causes the abatemet costs of quota regulato to be 8% larger tha wth tax regulato. Smulato results dcate that the prmary threat to the effcecy of uform reducto schemes comes from accurate estmato of baseles rather tha from heterogeety of elastctes. 3

5 1. Itroducto Ntrate leachg s cosdered to be a serous evrometal problem Demark, ad agrcultural applcato of troge fertlzer has bee regulated for a umber of years. As a umber of other coutres, Dash regulato of fertlzer applcato s essetally based o stadards ad orms. Uder the preset regulatos, crop farms are requred to reduce troge fertlzer applcato to 90% of the proft maxmzg level, wth each farm s basele beg calculated so as to take accout of lad qualty, lad allocato to each crop ad crop rotato etc. o the dvdual farm. Nocomplat farmers are fed wth a fee calculated as a progressve fucto of the magtude of ocomplace. Depedg o poltcal prortes, f the reducto farm profts ad lad values caused by such a system are substatally smaller tha for tax regulato, (as s cofrmed ths study, quotas may be vewed as havg a dstrbutoal advatage over taxes. O the other had, proportoal reducto quotas are less effcet tha e.g. a fertlzer tax, f fertlzer prce elastctes vary across farms ad/or baseles are accurately estmated. Furthermore, the quota system requres motorg of detaled farm level data for calculato of baseles ad for deterrg llct ter-farm fertlzer tradg. I ths paper we quatfy the abatemet costs ad dstrbutoal effects of reducg troge fertlzer applcato o Dash crop farms through proportoal reducto quotas, grad fathered tradable quotas ad a fertlzer tax. Ths s doe by estmatg troge fertlzer demad for Dash crop farms usg the dual proft fucto approach o mcro pael data. The model cludes several farm specfc parameters so that heterogeety of elastctes amog pael farms s allowed ad ca be tested agast a hypothess of homogeeous elastctes. We reject the homogeeous elastcty hypothess ad fd a szable varato farm elastctes (wth a stadard devato for dvdual farm elastctes of over 50% of the pael mea. Somewhat surprsgly, ths oly causes the abatemet costs of quota regulato to be 8% larger tha wth tax regulato. Smulato results dcate that the prmary threat to the effcecy of uform reducto schemes comes from accurate estmato of baseles rather tha from heterogeety of elastctes. Sce regulato of agrcultural troge fertlzer applcato s also udertake a umber of other coutres, these fdgs may be of more geeral terest. Our aalyss may also be of methodologcal terest sce we explot the possbltes of our pael data by specfyg a varat of the tras-log proft fucto that allows heterogeety of elastctes ad makes testg agast a hypothess of homogeeous elastctes possble. Although a umber of recet papers have estmated the fertlzer demad of dustralsed farmers, (e.g. Burrell ( cludg a good revew of older studes, Debaly ad Vroome (1993, Rayer ad Cooper (1994, Garca ad Radall (1994, Mergos ad Stoforos (1997, heterogeety of elastctes ad ts regulatory mplcatos has receved lttle atteto. I secto 2 we preset the ecoomc model ad fuctoal specfcato to be estmated. The data are descrbed secto 3, ad model estmato s preseted secto 4. Secto 5 summarses the results, ad coclusos are draw secto The Model I the followg we assume that crop farm producto s descrbed by a well-behaved 4

6 producto fucto f(x,,z where x s a aggregate crop output (postvely sged, s troge fertlzer put (egatvely sged ad z s put of cultvated lad whch s cosdered fxed for the scope ad tme horzo of the aalyss. The producto of the termedate fxed cultvated lad put s specfed as follows: z = z(captal, labour, materals, ucultvated lad so that the specfed prmary puts ca be dropped from the model sce the termedate put s observed the data. We assume that cultvated lad s produced usg lad, tractor ad harvestg equpmet, ad fuel ad labour as puts (.e. the cost of cultvatg a hectare of lad s assumed to be depedet of the amout of fertlzer appled ad the crop yeld harvested. The remag o-utret croppg put (dryg costs, sowg seed ad pestcde costs s assumed to be proportoal to crop producto (.e. a lmtato producto relatoshp. Proportoalty to crop output s also assumed for phosphorous ad potash fertlzer sce, uder Dash farmg codtos they are usually appled to sure a ample stock of these utrets for growg crops (.e. the utret restrctg crop producto s ormally troge. Thus, oly troge fertlzer put ad lad eter to a complex producto relatoshp wth crop output. Whle retag flexble estmato of behavour wth respect to key troge flows, ths smple specfcato makes t possble to estmate farm specfc fertlzer demad elastctes ad test for homogeety. We deote the dual proft fucto B(p x,p,z,2 where p x s a prce dex of aggregate crop output, p s the prce of troge fertlzer ad 2 s a vector of parameters. For farmer, the complete system of proft ad derved demad ad supply fuctos becomes: B B(p x,p,z,2 x *B (p x *p,p,z,2 x *B *p (p x,p,z,2 (1 The shadow values or ret of the fxed cultvated lad puts r, ca be derved from the proft fucto as: r *B *z (p x,p,z,2 (2 Regulatory effcecy After estmatg 2, the effect o farm of troducg a troge tax t ca be smulated by sertg p + t to (1. We deote tal farm proft ad troge fertlzer applcato B I B(p x,p,z,2 5

7 ad I *B (p x *p,p,z,2 B T B(p x,p %t,z,2 ad respectvely ad after tax proft ad fertlzer applcato are deoted T *B *p (p x,p %t,z,2 respectvely. Thus the chage abatemet costs (.e. proft reducto less tax paymet c T ad the chage troge applcato T o farm that s duced by a fertlzer tax become: c T B I & B T & t( T (3 T I & T (4 Explotg the proft/producto fucto dualty vrtual prce result of Neary ad Roberts (1980, the correspodg effect of a troge quota Q, ca be smulated by sertg a farm specfc fertlzer tax q, whch exactly esures that troge demad equals the quota (.e. that Q *B (p x whle refudg tax reveue. Rememberg that fertlzer put ad quotas *p,p %q,z,2 are egatvely sged, farm proft uder the quota becomes: B Q B(p x,p %q,z,2 & q (Q (5 ad the correspodg abatemet cost ad troge applcato chage o farm become: c Q B I & B Q (6 Q I & Q (7 For a regulator wshg to mplemet a aggregate reducto goal N, t s well kow that a fertlzer tax wll esure the dstrbuto of reductos amog farmers that mmzes aggregate abatemet costs: j c T # j c Q (8 whe j T j Q N. 1 The curret Dash fertlzer quota system ams to reduce fertlzer applcato to 90% of 1 We use fertlzer applcato as a dcator of troge loss/leachg the followg. Ths s clearly ot a reasoable effect dcator for lvestock farms where maure applcato s mportat, but for crop farms wthout maure applcato t may be acceptable. Furthermore, the aggregato level of the model estmated here mples that the two measures, by defto, are proportoal, makg dstcto redudat for the followg aalyss. 6

8 the proft maxmzg level o crop farms (for farms wth amal husbadry, the ambto s to crease maure utlzato as well. Ths s doe by calculatg a proft maxmzg basele for each farm usg self reported crop rotato ad lad allocato ad madatg a fertlzer quota of 90% of ths basele. Quotas are cotrolled by radom checks of farm accouts etc. If the regulator s able to geerate exact estmates of each farm's basele fertlzer applcato, ad f fertlzer demad elastctes are homogeeous across farms, the such a quota system wll duce abatemet costs equal to those duced by a fertlzer tax (.e. t q 1... q... q m. If, o the other had, these assumptos do ot apply, proportoal reducto quotas wll be less effcet ad may mply substatally hgher abatemet costs. Dstrbutoal effects Dstrbutoal effects may be a mportat dmeso of strumet choce geeral, ad perhaps especally so whe farmers are regulated. Ths s because regulato ot oly affects curret farm profts, but we would also expect future proft losses to be captalsed lad values so that addto curret owers may suffer substatal captal losses. Cosder frst the dstrbutoal effects of a fertlzer tax. The core effect s the reducto of aual farm profts B T.e: B T B I & B T (9 Sce lad s a mmoble factor of producto, a reducto farm proft wll probably affect the value of farmlad. If farms are typcally sold as oe ut (a gog cocer, a smplstc dcator of the effect o farm values s the captalzed value of the aual proft reducto L T.e.: L T B T / (10 where s the terest rate. At preset, however, the Dash agrcultural sector s udergog substatal cocetrato ad farmers expadg lad holdgs have for some tme bee domat o the demad sde of the lad market. If exstg farmers egagg margal adjustmets of lad holdgs domate the market, a more relevat dcator of the effect o lad values wll be the effect o margal lad ret, sce ths dcates the effect of regulato o what exstg farmers are wllg to pay for addtoal lad. We deote the tal ret of the margal hectare of cultvated lad r I *B (p x *z,p,z,2 the after tax ret r T. Sce captal ad labour put to cultvated lad are *B (p x *z,p %t,z,2 moble factors of producto, t seems reasoable to assume that the etre ret chage accrues to the mmoble factor lad. A smplstc dcator of the effect o lad values ths case s the captalzed value of the chage margal lad ret L T.e.: ad L T (r I & r T z / (11 7

9 Though both dcators are crude, the lad value effects they spa may dcate the magtude of the lad value effects of regulato. Now we cosder the dstrbutoal effects of a quota. The core proft effect ad captalzed value hereof are: ad B Q B I & B Q (12 L Q B Q / (13 Margal lad ret uder a quota s the margal effect o proft (defed (5 of creasg cultvated lad put.e.: r Q dbq *B Q % *B Q *q & *q *Q Q dz *z *p *z *z & q (14 *z By sertg the defto Q *B (p x the equato s reduced to: *p,p %q,z,2 r Q *BQ *z & q *Q *z (15 Thus the captalzed value of ths effect becomes : L Q (r I & r Q z / (16 3. The Data Estmatos are based o a pael data set provded by Ladbrugets Rådgvgsceter (The Dash Agrcultural Advsory Cetre. The pael cotas aual data, ad s ubalaced coverg te growg seasos (1982 to 1991 wth, o average, 1350 farms represeted each year wth each farm partcpatg 3.9 years o average. Data are sampled from detaled gross marg accouts through a volutary programme where oly a small part of the more busess oreted farmers partcpate. O the oe had, volutary partcpato s a advatage that partcpatg farmers a pror are motvated ad have a cetve to provde data of hgh qualty. O the other had, the sample of farmers the data set s ot represetatve of the populato of Dash farmers. For ths aalyss a group of specalsed crop farms were selected. The crtera for selectg was that the farmer had o amal husbadry (cattle, pgs, chckes etc. Specalsed crop farms comprse about 15% of all farms the data set. I the estmato we further restrct the sample to farms that have partcpated the pael for more tha three seasos. 8

10 For each farm the data clude detaled aual accouts of varable costs alog wth correspodg accouts of quattatve flows of most troge relevat puts ad outputs (.e. fertlzer ad crop yeld. Ths allows a aalyss of producto ad calculato of output ad put prces at the farm level. Coeffcets dcatg average troge cotet of crop outputs have bee added eablg us to calculate aual farm level mass balaces for troge ad resdual troge loss (see Hase ad Jese (1998 for detals. Mea values of the prce dex for each are reported table 1. Table 1 Meas of farm specfc prce dexes for specalzed crop farms Year Crops N-fertlzer Prces of troge put were calculated drectly for each farmer as cost dvded by volume. Usg a commo base observato (cotag all crop types, Fsher prce dexes for crops were costructed based o the dvdual farmer's prce. These were calculated as come (et of proportoal put costs.e. costs of dryg, sowg seed, pestcdes ad phosphorous ad potash fertlzer dvded by volume. Thus prces for troge put ad crop output vary across farms as well as over tme. Both dexes exhbt substatal varato over the data perod though o tred s apparet. Mea values for key producto varables ad evrometal dcators are show table 2. As oted above appled troge fertlzer volume s regstered farm accouts whle troge loss s calculated usg regstered volumes ad stadard (average troge coeffcets (aga see Hase ad Jese 1998 for detals. Proft shares are defed as shares of gross profts before deducto of fxed costs ad costs of cultvato. Thus ths proft cocept equals come from crop sales et of proportoal put costs mus the cost of troge fertlzer, so that the sum of the two proft shares (the put share beg egatvely sged by defto equals oe for each observato. 9

11 Table 2. Meas of producto ad emsso varables for specalzed crop farms Proft share - Crops Proft share - N-fertlzer Cultvated area hectares Appled troge fertlzer kg/hectare Ntroge loss 62.6 kg/hectare Number of farms 194 Number of observatos 967 The partcpatg crop farms are substatally larger tha s typcal for Dash crop farms, whle fertlzer applcato ad troge loss per hectare correspod to that of typcal Dash crop farms (see e.g. Brouwer et al. (1995 for troge balaces ad a useful cross coutry comparso. 4. Estmato The proft fucto (1 s assumed to have the tras-log fuctoal form wth the followg estmable specfcato: l(b,t a %b x l(p x,t % b l(p,t % b z l(z,t % ½[l(p x,t l(p,t l(z,t ] c x,x c,x c x, c, c x,z c,z l(p x,t l(p,t (17 c z,x c z, c z,z l(z,t yeldg derved proft share equatos of the followg form: s x,t b x s,t b % c x,x l(p x,t % c x, % c,x l(p x,t % c, l(p,t % c x,z l(z,t (18 l(p,t % c,z l(z,t (19 where s a farm dex, t dcates the tme perod ad s x,t p x,t x,t ad s,t p,t,t are the proft shares of crop output ad troge fertlzer put. Note that a, b x, ad b are farm specfc parameters allowg fxed effects each budget share equato as well as the proft equato. B,t B,t 10

12 x,x x,,,,,x Furthermore c x, c, c ad c are permtted to vary across farms a structured way (specfed below that allows for homogeety as well as varyg degrees of heterogeeous prce elastctes across farms. The complete system s estmated two steps. Frst, the system of derved proft share equatos (wthout the proft fucto s estmated usg maxmum lkelhood estmato. Restrctg the parameters to esure symmetry ad homogeety prces (but ot the fxed lad put (.e. b x % b 1, c x,z &c,z ad c, &c,x &c x, c x,x for all we elmate the crop s x equato (,t to avod sgularty (the maxmum lkelhood procedure esures that estmates are varat as to whch equato s elmated. Techcally, the c parameters (19 are estmated usg wth farm trasformed varables, elmatg tme varat farm specfc costat b ad the homogeety/symmetry restrctos,.e.: s,t c, (lñ(p,t & lñ(p x,t % c,z lñ(z,t (20 where. dcates wth trasformed varables. The fxed effects b are the estmated as ˆb s,t & ĉ, (l (p,t & l (p x,t & ĉ,z l (z,t for each wth. dcatg the mea value of the varable take over the tme perods that farm partcpates the pael. The degrees of freedom allowed by the data makes estmato of urestrcted farm specfc c, coeffcets feasble. Istead we geeralze the stadard tras-log model by lettg deped o farm specfc mea put prces usg the followg quadratc specfcato: c, c, " 1 % " 2 s % " 3 ( s 2 (21 The quadratc fuctoal form s a flexble geeralsato of the usual uform coeffcet assumpto, whch s attractve for our purposes sce, whe serted to the tras-log ow prce elastcty formula e s % c, s & 1 the mea prce elastcty becomes: e s % (" 1 % " 2 s s % " 3 ( s 2 & 1 s % " 1 s % " 2 % " 3 s & 1 (22 Ths s ce because, f " 1 = 0 ad " 3 = -1 the e becomes costat (homogeeous across farms 11

13 whch makes t possble to test the hypotheses of elastcty homogeety. We ca also test for applcablty of the usual smple tras-log specfcato (.e. restrctos " 2 = 0 ad " 3 = 0. After sertg (21 to (20 ad regroupg we have the followg equato to be estmated: s,t " 1 ([lñ(p,t & lñ(p x,t ] % " 2 ([ s (lñ(p,t & lñ(p x,t ] % " 3 [( s 2 (lñ(p,t & lñ(p x,t ] % c (23,z [lñ(z,t ] % u,t where square paretheses dcate the depedet varables used estmato ad u,t s a error term. The error term s assumed to be ormally dstrbuted ad equato (23 was estmated wth SAS PROC MODEL usg full formato maxmum lkelhood. Results of ths estmato are reported table 3 (parameters for the crop equato were calculated resdually. Table 3 Commo parameters estmated the frst step Estmated geeral model Test of restrctos (lkelhood rato Parameter Estmate Approx Std Err Approx Prob Homogeeous Elastctes Stadard Tras-Log " 1 " 2 " 3 c,z DF Model sg. R P 2 (4= ( P 2 (2=17.81 ( P 2 (2= 4.96 ( Table 4 cotas the mea, meda ad stadard devato of the dstrbuto of resdually calculated farm specfc fxed effects. Table 4 Farm specfc fxed effects estmated the frst step Parameter mea of estmates meda of estmates std. dev. of estmates b b x *

14 I the secod step the remag parameters of the proft fucto were estmated treatg fxed effects ad parameters estmated the derved system as kow,.e. : l(b,t & b x l(p x,t & b l(p,t & l(p x,t z,x c l(z,t & l(p z,,t c l(z,t ½[l(p x,t c x,x l(p,t ] c,x c x, c, l(p x,t l(p,t (24 a % b z l(z,t % l(z,t c z,z l(z,t If the parameters estmated the frst step are ubased, ths wll also be the case for parameters estmated the secod step. However, the procedure may geerate heteroscedastcty ad valdate the usual ferece statstcs. Results of the secod step (also estmated wth SAS PROC MODEL usg full formato maxmum lkelhood are preseted table 5. Table 5 Parameters estmated the secod step Parameter Estmate Approx Std Err* Approx Prob* b z c z,z mea of Estmates meda of Estmates std. dev. of Estmates a DF Model sg. R P 2 (2= ( Note: * ferece statstcs are codtoal o kow frst step parameters,.e. a lower boud for true stadard errors. The frst step estmato s hghly sgfcat though most dvdual parameters are ot. Estmated share equatos are cosstet wth mootocty ad covexty. Ispecto of error correlato matrces dd ot reveal serous seral correlato. Statstcal tests showed that the error dstrbuto s sgfcatly dfferet from the ormal dstrbuto though resdual plots dcated that devato s ot substatal. Resdual plots showed clear sgs of heteroscedastc error terms. Though o-ormalty ad heteroscedastcty may valdate ferece tests, parameter estmates are stll ubased. The secod step estmato s also hghly sgfcat ad error correlato matrces ad resdual plots dd 13

15 ot dcate serous seral correlato or heteroscedastcty, but sgfcat o-ormalty was detected. Estmated prce elastctes (see appedx have the expected sgs over 95% of all sgle observatos. All sgle observatos of rets of cultvated lad have the expected sg. I cocluso the estmated model performs well statstcally ad geerates plausble behavoural fereces. Acceptg the geeral model the restrcto tests reported table 3 ca be terpreted. Though qualfed by o-ormalty ad heteroscedastcty the clear rejecto of the homogeety hypothess dcates that troge demad elastctes are heterogeeous across pael farms. Ths s cofrmed by the bootstrap cofdece terval aroud the calculated stadard devato of farm elastctes from the pael mea that s reported below. The restrcto resultg the smple stadard tras-log specfcato ca, o the other had, oly be rejected at the 10% level. I cocluso elastctes are heterogeeous across the pael, but the geeral model specfcato oly results a slghtly better descrpto of ths heterogeety tha the stadard tras-log specfcato. I the followg secto we base results o the geeral model specfcato. 5. Results I table 6 we report mea elastctes ad stadard devatos of dvdual farm elastctes from these meas (as a measure of the heterogeety of elastctes the sample usg the parameters reported the prevous secto. Mea ad stadard devatos of farm elastctes are calculated usg oe observato for each farm evaluated at mea farm prces. 2 Table 6 Ow prce elastcty of troge fertlzer val* Pot estmate 90% cofdece ter- Mea of pael farm elastctes [-0.58 : -0.31] Stadard devato of farm elastctes from pael mea 0.24 [ 0.01 : 0.41] Note: Oe elastcty observato per farm evaluated at mea farm prces. * Calculated by bootstrappg based o 1250 data re-samplgs. The mea ow prce elastcty for troge fertlzer of reported here has a short ru Marshala terpretato. Gve ths, t s le wth or somewhat larger umercally tha the elastctes foud several recet studes (all based o aggregate tme seres coverg all or most of the 2 Note that the reported measures are almost detcal to the correspodg measures after prce deflato to the mea pael prce level (see appedx. Deflato gves cosstet estmates of aggregate behavour, however, deflato may wde cofdece tervals aroud the calculated dvdual farm elastctes. I our case the dscusso turs out to be academc sce the resultg elastctes are almost detcal. 14

16 agrcultural sector, e.g. Burrel (1989 fds a short ru elastcty of betwee -0.4 ad -0.6, ad Rayer ad Cooper (1994 fd a elastcty of betwee -0.1 (short ru ad (log ru, for the UK, whle Debaly ad Vroome (1993 report betwee -0.2 (short ru ad -0.4 (log ru for the USA, all wth Marshala terpretatos as ours. Three studes of fertlzer demad by Dash agrculture are of specal terest. I a older study usg aggregate tme seres coverg the etre Dash agrcultural sector, Dubgaard (1987 estmates a Marshala troge fertlzer ow prce elastcty of Jese (1996, usg a estmated aggregate model of Dash agrculture, fds a Marshala log ru elastcty for composte NPK-fertlzer of -1.8 ad Krstese ad Jese (1999, usg cost fuctos estmated o pael data, fd a short ru Hcksa elastcty for composte NPK-fertlzer of for Dash crop farms. Our fdg s somewhat larger umercally tha Dubgaard's result but smaller tha the comparable elastctes mpled by the two more recet studes. 3 The ma cotrbuto of ths paper s the quatfcato of the heterogeety of elastctes across farms. As a measure of ths, the stadard devato of dvdual farm elastctes from the mea of pael elastctes s foud to be 0.24 as dcated table 6. The bootstrap cofdece terval dcates that ths s sgfcatly dfferet from zero at the 5% level, supportg the clear rejecto of the homogeeous elastcty hypotheses the prevous secto. Thus, the stadard devato s sgfcat ad szable: wth 50% of the pael farms havg elastctes outsde the to rage aroud the mea elastcty. If all farms had had the same fertlzer demad elastcty quotas, requrg uform percetage reductos fertlzer applcato would result a optmal allocato of cutbacks across farms. Whe elastctes are heterogeeous, however, uform percetage reductos become effcet, ducg aggregate abatemet costs that are larger tha the mmum level that would be esured by tax regulato. Ths s the classcal effcecy argumet for preferrg ecoomc cetve regulato to stadards ad orms. I practcal applcatos, a regulator usg uform percetage reducto quotas also faces the problem of estmatg fertlzer applcato baseles for each farm. Ths s ot a trval task sce basele applcatos deped o a umber of farm specfc factors whch are ot observed perfectly by the regulator (farm lad qualty, local weather codtos, capacty ad qualty of fxed captal puts, etrepreeural talet etc.. Thus baseles wll geerally be estmated wth some degree of error, mplyg that the appled dvdual farm quotas wll devate some radom way from the uform percetage reducto goal. I addto, f the farm specfc formato used for calculatg baseles depeds o farm producto decsos, cetves that dstort these decsos may be geerated. Usg our model of pael farms we are able to quatfy the abatemet cost crease of reducto quotas caused by elastcty heterogeety ad the addtoal abatemet cost crease that would result from varous magtudes of radom errors basele measuremet. Because of the 3 Whe cosstetly estmated results for both composte fertlzer ad troge are reported (see Burrel, 1989 ad some of the older studes summarsed Burrel s paper the troge elastcty teds to be the same sze or umercally larger. Thus the Hcksa short ru composte elastcty reported by Krstese ad Jese (1999 dcates a short ru Marshala troge elastcty umercally larger tha whle the composte Marshala log ru elastcty reported by Jese (1996 probably mples a comparable elastcty substatally larger tha the oe foud here. 15

17 aggregato level of the estmated model, the effect of dstortg cetves geerated by the basele calculato system caot be evaluated. Results are preseted the frst row of table 7 where abatemet costs (DKK/klo reducto troge applcato are dcated for a 10% reducto applcatos. The fertlzer tax rate t s foud by terato ad abatemet costs calculated usg equato (3 parametersed wth the estmated model. For the quota system the basele for each farm s calculated as the farm's optmal uregulated fertlzer applcato plus a radom error term draw from a ormal dstrbuto wth zero mea ad a stadard devato of the dcated percetage of the farm's optmal applcato level. Thus the abatemet cost dfferece betwee the tax ad the quota wth 0% measuremet error ca be terpreted as the solated cost effect of the estmated pael elastcty heterogeety, whereas dffereces to the remag colums clude the added cost effect of the dcated basele measuremet error. 4 I the fal colum the abatemet cost of a correspodg tradable quota system s preseted. These are calculated uder the assumpto that the quota market s perfect (.e. resultg a post tradg allocato of quotas equal to the applcatos duced by a fertlzer tax, so that abatemet costs are depedet of the tal quota dstrbuto. By desg, the fertlzer tax geerates cetves that mmze abatemet costs. We see that the abatemet cost crease uder the o-tradable quota scheme duced by the szable elastcty heterogeety estmated here s relatvely small, amoutg to a cost crease of less tha 8%. Ths s about the magtude of the abatemet cost crease caused by a 2.5% basele measuremet error, whereas larger measuremet errors cause substatally larger cost creases. Note that the table does ot clude dstortg effects or admstratve costs of the o-tradable quota systems basele estmato procedure. If these are mportat, the effcecy advatage of usg taxes wll be greater tha dcated the table. Lkewse the table does ot clude added admstratve costs or cetve dstortos of the tradable quota systems grad fatherg procedure, whch may cause such a system to be less effcet tha tax regulato. 4 Specfcally farm quotas Q are set to a uform percetage of each farm's estmated basele applcato (cludg measuremet error. The farm specfc tax rates q whch mplemet these are foud by terato for each farm after whch abatemet costs are calculated usg equato (6. The uform percetage of baseles used to calculate farm specfc quotas that esure a aggregate 10% applcato reducto are foud by terato a outer loop. Wthout measuremet error, a uform percetage of 90 esures a 10% reducto. Wth a ormally dstrbuted measuremet error, some 90% quotas may exceed actual optmal farm applcato so that the uform percetage must be creased order to avod exceedg the 10% reducto goal. 16

18 Table 7 Abatemet costs ad agrcultural come effects whe aggregate N-fertlzer applcato s reduced by 10% (DKK per klo N-fertlzer reducto Tax No-tradable Quotas* proportoal percet reducto applcato wth basele measuremet error of 0 % 2½ % 5 % 7½ % 10 % Gradfathered Tradable quotas* Average abatemet costs Average farm proft Average farm captal loss Note: Measuremet errors are ormally dstrbuted wth stadard devato of the dcated per cet of basele. Calculatos are at 1989 fertlzer ad crop prces. The fertlzer tax rate s DKK/klo N-fertlzer. The appled quota percetages of basele applcato are 90.0% for tradable quotas ad o-tradable quotas wth a 0% error, 90.2% for a 2½% error, 90.5% for a 5% error, 90.9% for a 7½% error, ad 91.5% for a 10% error. The terest rate used the calculato of captal loss s 10%. * Excludg the possbly dstortg effect o farm producto decsos of the basele estmato procedure/tal quota dstrbuto procedure. I rows two ad three the polcy effect o aual farm proft ad lad values are preseted (per klo fertlzer reducto for cross row comparablty. The effect o aual proft s calculated usg equatos (9 ad (12 respectvely. The lower boud o the lad value effects s calculated usg equatos (10 ad (13, ad equatos (11 ad (16 are used to fd the upper boud (the traslog specfcato of (10,(11 ad (13 s straght forward, see appedx for specfcato of (16. Closely matchg the reveue rased by a fertlzer tax, the reducto t causes farm come s betwee 11 ad 18 tmes the come reducto caused by a quota system. The correspodg lad value reductos are betwee 11 ad 19 tmes as large. The substatal dffereces dstrbutoal effects are ot surprsg gve the elastcty of troge demad ad the relatvely small abatemet cost advatage of the fertlzer tax. The dstrbutoal effects of the tradable quota system are smaller tha for the o-tradable system, reflectg the effcecy advatage. 5 Aga table 7 assumes that the basele estmato procedure/quota dstrbuto procedure has eglgble dstortoery effects. 6. Coclusos Usg farm level pael data ad a geeralzed tras-log proft fucto specfcato wth a umber of farm specfc parameters we fd a short ru Marshala prce elastcty for troge fertlzer demad by Dash crop farms of Ths s wth the spa of elastctes foud teratoally ad other 5 Sce basele measuremet error oly affects the tal dstrbuto of quotas the tradable quota system, ths does ot affect the effcecy or aggregate farm come preseted here. However measuremet error may cause substatal come redstrbuto amog dvdual farmers. 17

19 Dash studes. The ma cotrbuto of ths paper s the quatfcato of the heterogeety of elastctes across farms. As a measure of ths, the stadard devato of dvdual farm elastctes from the mea of pael farm elastctes s foud to be Ths dcates szable heterogeety wth 50% of the pael farms havg elastctes outsde the to rage aroud the mea elastcty. The classcal ecoomc argumet for cetve regulato s that heterogeety of elastctes causes abatemet costs of uform percetage reducto quotas to crease above the mmum level esured by tax regulato. However, the abatemet cost crease duced by the (szable estmated heterogeety amouts to less tha 8% of the abatemet cost mmum that s esured f reductos are duced by a fertlzer tax. Ths result s somewhat surprsg, suggestg that the classcal argumet for cetve regulato may be relatvely weak eve regulatory stuatos wth substatal polluter heterogeety. Our smulato results dcate that accurate estmato of baseles may be a more mportat threat to the effcecy of uform reducto schemes tha heterogeety of elastctes. The substatal agrcultural come ad lad value reductos assocated wth a fertlzer tax ca be avoded wthout effcecy loss through a system of grad fathered tradable quotas (assumg that a o-dstortg quota dstrbuto procedure s utlzed. If polcymakers, for ethcal or other reasos, forbd tradg, our results dcate that the effcecy loss due to heterogeety s lmted. There may stll, however, be a substatal effcecy loss due to basele measuremet error ad to dstortg cetves geerated by the basele estmato procedure. At ay rate, our results dcate that careful desgg of basele estmato procedures should be gve a hgh prorty wheever uform percetage reducto schemes are used. It s mportat to stress that the specfc mplcatos regardg the Dash troge quota system draw here oly cover ts applcato to crop farms. Iterpretato as a evaluato of the system geeral would be msleadg sce relatve performace of dfferet regulatory strumets o farms wth lvestock may be very dfferet. Frst of all, because behavoural relatos for pg ad dary farms may dffer substatally ad secod, because the Dash quota system has specal rules for lvestock farms reducg quotas by the calculated fertlzer value of maure. 18

20 Appedx Prce elastctes derved from the geeral model Ow ad cross prce elastctes ad lad ret are calculated for expected put/output proft shares for each data observato ad for each farm at mea farm prces both for o-deflated prces ad after deflatg to the mea pael prce level. The mea, meda ad stadard devato of the dstrbuto of dvdual observato ad farm elastctes/rets ad the proporto of postve elastctes/rets are reported for all put/output prce combatos. Iput/ output Idvdual observatos o-deflated prces (967 observatos o-deflated mea farm prc- es Farm observatos (194 observatos Prces Prces x Mea meda Std Dev %>0 p x p % 5% p x p % 3% Mea meda Std Dev. %> % 5% % 3% Lad ret DKK/hectare Mea Meda Std Dev Lad ret DKK/hectare Mea Meda Std Dev %>0 100% %>0 100% 19

21 Iput/ output x Mea meda Std Dev %>0 Idvdual observatos deflated prces (967 observatos p x Prces p % 4% Farm observatos deflated mea farm prces (194 observatos p x Prces p % 3% Mea meda Std Dev. %> % 4% % 3% Lad ret DKK/hectare Mea Meda Std Dev %>0 100% Lad ret DKK/hectare Mea Meda Std Dev %>0 100% 20

22 Dervato of the quota effect o margal lad ret The geeral specfcato of margal lad ret uder quotas from equato (15 s: r Q *BQ *z & q *Q *z (a.1 Q *B Q where the tras-log specfcato of B b z % c z,x l(p x,t s *z % c z, l(p,t % c z,z l(z,t z straghtforward. The tras-log specfcato of Q (.e. the fertlzer demad duced by the tax adjusted prce (p %q s Q BQ s so that: (p %q *Q *z *B Q s *z *B Q s *z % B Q *B Q s *z % B Q *s *l(z % BQ c,z z *s *z /(p %q *l(z *z /(p %q /(p %q whch, after sertg to (a.1, gves the followg tras-log specfcato of margal lad ret: r Q BQ z b z % c z,x l(p x,t % c z, l(p,t % c z,z l(z,t & q p %q *B Q s *z % BQ c,z z (a.2 21

23 Refereces Brouwer, F.M., F.E.Godeschalk, P.J.G.J.Hellegers ad H.J. Kelholt (1995, Meral Balaces at Farm Level the Europea Uo', Report, The Hague, Agrcultural Ecoomcs Research Isttute. Burrell, A.,(1989, ' The Demad for Fertlser the Uted Kgdom', Joural of Agrcultural Ecoomcs vol. 40, pp1-20. Debaly, M. ad H. Vroome, (1993, 'Dyamc Fertlzer Nutret Demads for Cor: A Cotegrated ad Error-Correctg System', Amerca Joural of Agrcultural Ecoomcs vol. 75, pp Dubgaard, A., (1987, 'Recoclato of Agrcultural Polcy ad Evrometal Iterests Demark (Regardg cotrols o troge fertlzer', Multpurpose Agrculture ad Forestry, Proceedgs of 11th Semar of the Europea Assocato of Agrcultural Ecoomsts, 28 Aprl - 3.May, 1986 (eds. M. Merlo et al.. Garca, R.J. ad A. Radall, (1994, 'A Cost Fucto Aalyss to Estmate the Effects of Fertlzer Polcy o the Supply of Wheat ad Cor', Revew of Agrcultural Ecoomcs vol. 16, pp Hase, L.G. ad H. S. Jese (1998, 'Model for desg ad Evaluato of evrometal Regulato Dash agrculture. Mdway report', SØM-publcato No. 24. AKF-Forlaget, Copehage. Jese, J.D., (1996, 'A Appled Ecoometrc Sector Model for Dash Agrculture (ESMARALDA', SJFI-report o. 90, SJFI, Copehage. Krstese, K. ad J.D. Jese (1999, 'Dash Farmers' Adjustmet Capabltes: The Case of Fertlzer Regulato', SJFI-workg paper o. 2/1999, SJFI, Copehage. Mergos,G.J. ad Ch.E. Stoforos, (1997, 'Fertlzer Demad Greece', Agrcultural Ecoomcs vol. 16, pp Neary J.P. ad K.W.S. Roberts (1980, 'The Theory of Household Behavour uder Ratog', Europea Ecoomc Revew, vol. 13, p Rayer, A.J. ad D.N. Cooper, (1994, 'Co-tegrato Aalyss ad the UK Demad for Ntroge Fertlzer', Appled Ecoomcs vol. 26, pp