Abstract. The well-known increase in the geographical concentration of hog production suggests the

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1 DOES MANURE MANAGEMENT REGULATION WORK AGAINST AGGLOMERATION ECONOMIES? EVIDENCE FROM FRENCH HOG PRODUCTION Carl Gagné a, Jule Le Gallo b, Solène Larue c and Bertrand Schmtt c a INRA, UMR1302 SMART, F Rennes, France b CRESE, Unversté de Franche-Comté, F Besançon, France c INRA, UMR1041 CESAER, F Djon, France Abstract. The well-known ncrease n the geographcal concentraton of hog producton suggests the presence of agglomeraton economes related to spatal spllovers and nter-dependences among ndustres. In ths paper, we examne whether regulaton of manure management that lmts manure applcaton per acre may weaken productvty gans arsng from the agglomeraton process. We develop a model of producton showng the ambguous spatal effect of envronmental regulaton. Indeed, whle envronmental regulaton trggers dsperson when manure s appled to land as a crop nutrent, t also prompts farmer to adopt manure treatment that favors agglomeraton of hog producton. Estmatons of a reduced form of the spatal model wth a spatal HAC procedure appled to data for French hog producton for 1988 and 2000 confrm the ambguous effect of regulaton of manure management. It does not prevent spatal concentraton of hog producton, and even boosts the role played by spatal spllovers n the agglomeraton process. JEL Classfcaton: Q10, Q53, R12 Key words: Hog producton; Manure management regulaton; Agglomeraton economes; Spatal Econometrcs. Ths research was supported by the French Natonal Agency of Research (ANR) program Systems of Anmal Producton and Sustanable Development (SPADD). The authors thank Lusto Bertnell, Alan Carpenter, Perre Dupraz, Phlppe Legoffe and Mchel Reu for ther helpful comments. We also thank the IFIP (Insttut de la Flère Porcne) for provdng hog-specfc data and Anne-Mare Dussol for preparng agrcultural census data.

2 1. Introducton Emprcal evdence suggests that the spatal concentraton of hog producton has accompaned the rse n hog farm productvty. In the Unted States, Key and McBrde (2007) report that hog producton shfted from the Heartland to the Southeast between 1992 and 1998 and that mean farm output ncreased much more n the Southeast (see also Abdalla et al., 1995). In Europe, smlar changes are observed. For example, n France, Brttany hosts an ncreasng share of hog producton and the productvty of hog producers located n ths regon has mproved (Daucé and Léon, 2003). It appears that n hog producton, agglomeraton can be a source of productvty gans (Roe et al., 2002). However, the spatal concentraton of pg producers s a serous source of pollutants n rvers and streams. Ths s why the European Unon (EU) ntroduced the Ntrates Drectve and the Unted States (US) the Clean Water Act, whose am s to protect water bodes aganst polluton by ntrates from agrcultural sources. In the EU, the applcaton of manure s lmted to a maxmum level of ntrogen per hectare and per year. Ths restrcton on spreadng manure on the land creates dffcultes for regons wth a hgh lvestock densty: there s smply not enough land avalable on whch manure could be appled. Because of the strngency of the EU Ntrate Drectve and non-neglgble costs of complance for hog producers, the latter may respond to exstng or mpendng costs of regulaton by extng the sector or by changng ther scale of producton. The purpose of ths paper s to study the effects of regulaton of manure management on the locaton of hog producton and agglomeraton economes. Because the applcaton of anmal manure on land s restrcted, regulaton of manure management s expected to reduce the spatal concentraton of producton and, n turn, to affect productvty gans related to agglomeraton economes. However, the story s more complex and deserves closer attenton. Indeed, farmers may adopt two types of manure management: () manure spreadng where anmal manure s appled to land as a crop nutrent or/and () manure treatment where the goals are ntrogen reducton, as well as a reducton n odor and n volume. In the frst case, ncreasng hog producton mples that farmers have to spread a larger volume of manure on more and more dstant cropland. Because haulng nutrents to cropland n the form of manure s relatvely expensve, the cost of ths type of manure management not only ncreases wth an ncrease n hog producton but also wth the dstance to the cropland. Ths creates ncentves 2

3 for producers to reduce ther producton. In ths case, manure spreadng trggers the dsperson of hog producton. In the second case, manure treatment technology ams at reducng the volume (so that manure and nutrent transport costs become neglgble) and mprovng market prospects by changng the nutrent composton. However, such a practce s characterzed by substantal fxed costs (IFIP, 2002). Therefore, ths manure management technology may favor the agglomeraton of hog producton. Indeed, because manure treatment technology exhbts economes of scale, ths management system s more proftable wth hgh levels of hog producton. In other words, the use of treatment technology ether at the ndvdual or the collectve level promotes agglomeraton. As a result, envronmental regulaton may trgger ether dsperson or agglomeraton of hog producton dependng on the type of manure management system chosen by the farmers. In ths paper, we determne whether manure management regulaton leads to relocaton of hog producton n areas wth low lvestock densty or whether on the contrary, t strengthens the spatal concentraton of hog producton. To reach our goal, we frst develop a model of locaton and producton n whch farmers can chose dfferent technologes to manage manure and then we test ts man predctons usng French data. We obvously control for the other factors that usually shape the spatal structure of hog producton. More precsely, we dentfy agglomeraton economes by dstngushng market and non-market forces. Cronon (1991) n hs famous book Nature s Metropols provdes a detaled descrpton of the market factors explanng the agglomeraton process of hog producton n Chcago and ts hnterland that occurred n the second half of the 19 th century (see chapter enttled Porkopols). Frst, the proxmty between farmers and slaughterng facltes may be one of the key determnants As mentoned by Cronon (1991), ncentves to slaughter and pack pgs near where farmers rased pgs were strong. Drvng hogs was expensve because of relatvely hgh transport costs and hogs lost weght as they traveled. It was thus unproftable to haul them very far. A second factor explanng the local growth of hog producton s the geographcal proxmty between crop or feed producton and hog producers. As ponted out by Cronon (1991, p. 226): Ther prodgous meat-packng powers meant that once farmers had harvested ther corn crop, pgs (along wth whsky) were generally the most compact and valuable way of brngng t to market. As a result, the proxmty to both crop producton 3

4 (or feed supplers) and slaughterng facltes tended to result n large productvty gans. Both these factors combned wth nnovatons n meat transportaton to serve fnal consumers and wth ncreasng productvty of pork packers (due to hgher dvson of labor) enabled Chcago and ts surroundng area to produce and pack a very large quantty of hogs (more than a mllon hogs were slaughtered annually n Chcago n the 1870s). Although Cronon s explanatons are related to the relatve transport costs and scale economes observed around Chcago n the second half of 19 th century, these arguments should hold today to explan the agglomeraton of hog producers n a few locatons. Indeed, the rato of transport costs to output or nput prces n the pork sector s far from neglgble. New economc geography now provdes rgorous frameworks to explan the role of ncreasng returns and trade costs n agglomeraton processes (Fujta and Thsse, 2002). The lterature teaches us that producers can also beneft from the geographcal proxmty of other producers n the same sector: the non-market nteractons or the so-called Marshallan externaltes act as a shft factor that modfes the relatonshp between cost and output. Geographcal proxmty nduces more contacts and, n turn, facltates the transmsson of nformaton regardng changes n output and nput markets as well as the development of techncal or organzatonal nnovatons or new nputs (Duranton and Puga, 2004), the so-called nformaton spllovers. Frequent contacts also allow purchasers or supplers to buld the trust requred to wrte ncomplete contracts as shown by Leamer and Storper (2001). In other words, the productve effcency of farmers should ncrease wth the number of farms that set up n the same area and decrease wth an ncrease n the dstance between them. Our study dffers sharply from recent emprcal studes examnng the role of tradtonal locaton factors as well as envronmental regulaton nvolved n the locaton of anmal producton. Frst, whle much attenton has been devoted to the mpact of the strngency of envronmental regulaton on the locaton of anmal producton, lttle attenton has been pad to the mpact of manure management systems on the process of agglomeraton. For example, Isk (2004) and Roe et al. (2002) studed how dfferences n the strngency of envronmental regulatons among US States affect the locaton of anmal producton. However, these authors dd not test the mpact of manure management on the agglomeraton of hog producton. Second, we buld a theoretcal model to enable us to dentfy 4

5 the relatonshp between locaton and hog producton when farmers can choose dfferent technologes to manage manure. The combned effects of spatal spllovers, access to supplers or purchasers, envronmental regulaton and negatve externaltes on local producton are not a pror obvous and can lead to serous problems n dentfyng and evaluatng the respectve roles of these dfferent factors. Last, we mplement recent developments n spatal econometrcs to take nto account some crucal bases that have been gnored. The approach used by Roe et al. (2002) does not control for the endogenety of the locaton of slaughterng facltes and of nput supplers, whereas hog producton and the producton of other lvestock by hog producers are determned smultaneously n dfferent areas. In addton, unlke Isk (2004), who uses two-stage least squares, we perform a generalzed spatal two-stage least squares estmaton (GS2SLS), as suggested by Kelejan and Prucha (1998), combned wth a heteroskedastc and autocorrelaton consstent non-parametrc estmaton of the varance-covarance matrx (Kelejan and Prucha, 2007) to control for unmodeled factors n the resdual terms. Our theoretcal model shows that regulaton of manure management has an ambguous effect on the spatal dstrbuton of hog producton. By favorng the use of a manure treatment system, strcter regulaton of the manure applcaton rate or a decrease n avalable land for manure applcaton may trgger the spatal concentraton of hog manure. Furthermore, we show from our framework that a larger share of manure managed by treatment technology strengthens the role of agglomeraton economes n productvty gans. Our emprcal tests of these predctons confrm the ambguous effect of the rato of manure producton to avalable land on hog producton. In accordance wth our theoretcal model, an ncreasng rato of local manure producton to land avalablty ncreases the densty of hog producton whle a rse n ths rato for the surroundng countes trggers dsperson. The total effect s more lkely to be negatve but not sgnfcant. In other words, regulaton of manure management does not work aganst the spatal concentraton of hog producton. In addton, we show that the regulaton of manure management has boosted the role played by non-market spatal externaltes n the agglomeraton process. The rest of the paper s organzed as follows. In the followng secton, we develop the theoretcal model whle the emprcal model and econometrcs ssues are descrbed n Secton 3. Data 5

6 are presented n Secton 4 and our results are reported and analyzed n Secton 5. The last secton concludes the paper. 2. Theory In ths secton we develop a spatal model of hog producton by takng nto account spllovers, lnkages wth the feed supplers and wth the slaughterng facltes/processors, and manure management. The objectve of the model s to clarfy the mpact of envronmental regulaton on the hog producer s choce accordng to her/hs locaton. General framework Consder an economy wth R regons, labeled r = 1,..., R separated by a gven physcal dstance and wth three types of producers (hog producers, slaughterng facltes and feed producers). Each regon s formally descrbed by a one-dmensonal space y. Each regon hosts one slaughterng faclty (n short SF) located at the orgn y = 0, I farms located at y wth = 1,..., I (or at dstance y from the SF) and K feed producers located at y wth k = 1,..., K. The dstance between farmer and feed k producer k s gven by u k y k y when they are located n the same part of the regon or by uk yk + y when they are not located n the same part of the regon. We focus on the behavor of a farmer producng n locaton and belongng to regon r. Because n our framework there are no nteractons between hog or nput producers located n dfferent regons, we can drop n our notatons for the ndex (r) dentfyng the regon where the farmer produces (we only consder the mpact of the locaton of the fnal consumers on producton). We assume that the proft functon of a hog producer s gven by: ( ) π = ( z τ y ) h C. g(.) (1) r where z r s the unt prce of pork prevalng n regon r (each farmer s a prce taker), τ s the unt transport costs of pork between farms and the slaughterng faclty, h s the producton level of farm, C(.) s the cost functon n producng output and g (.) s the cost functon n manure management. 6

7 Implementaton of envronmental regulatons mples complance costs for producers thereby reducng profts. We assume that the cost functon s addtvely separable nto output and manure management. The technology of producton s gven by h = A f( xk, l) where x k s the quantty of nputs used by farms wth f x > 0 and f xx < 0 1 and l s the labor force dedcated to hog producton wth f l > 0 and f ll < 0 so that the margnal productvty of each producton factor decreases. Note that A = a where j a j represents nformaton spllovers receved by a farmer located at y from a farmer located at j y j. Hence, A represents the nformaton feld, whch s a spatal externalty. The amount of nformaton receved by a farm depends on the sze of the other farms and on ts locaton relatve to the others. We consder: δ a = ρ y y h (2) j j j where ρ > 0 and δ > 0 are two postve constants, δ measurng the ntensty of the dstance-decay effect and ρ s a scale parameter. Ths type of expresson s extensvely used n spatal models of nteracton. Gven the technology of producton, the cost functon C(.) depends postvely on h and negatvely on A wth C C/ h > 0, h C C/ h > 0and hh 2 2 C C/( h A) < 0 as well 2 ha as on the wage rate (denoted w l ) and the cost of feed (or crop when the feed s produced by the hog farmer) ncurred by the farmer (denoted w k ). We assume that wk wk ξkuk = + where ξ k s the unt transport cost of feed between farms and feed producers (u k s the dstance between the two) and w s the feed producer s prce. Thus, we consder that the farmer ncurs transport costs for each type of feed (or crop) nput. Next, we take nto account the fact that manure management s regulated. Envronmental regulaton not only mples complance costs for producers but also that the manure applcaton rate k 1 f x denotes the frst dervatve of f (.) wth respect to each component. The second dervatve s subsequently denoted by f xx. 7

8 cannot exceed a threshold value. Hence, we consder that one unt of avalable cropland cannot exceed m unts of manure and that s unts of cropland are avalable at each locaton. Let θ be the quantty of manure for each unt of output so that θ h s the quantty of manure that farmer has to manage. Farmer may use two types of manure management technology: spreadng or/and treatment. Farmer allocates a fracton µ of manure to spreadng. 2 Each farmer can also use a manure treatment faclty wth a capacty v = (1 µ ) θh and a cost functon c 1 ( v ) characterzed by ' c / > 0 1 c1 v and c / < 0 1 c1 v. What matters for our study s the fact that '' 2 2 treatment technology s characterzed by scale economes (IFIP, 2002) and that the cost of transportng treated manure s not sgnfcant. When the farmers choose to spread manure, ths ncurs costs of applcaton that are gven by c 2 ( µ θh ) wth ' c / > 0 2 c2 h and c / 0 2 h. Wthout loss of 2 2 = generalty, we assume the technology for applyng manure yelds constant economes of scale. Hence, the costs assocated wth manure management ncludng the costs of treatment, manure applcaton and j m manure transport are gven by g(.) c1( v) + c2( µθ h) + τm y yj mjs where τ m s the unt transport cost (ncludng travel tme) between where the manure s stored and the feld 3, and m j s the mass of manure appled n locaton j by farmer. Gven our assumptons, each farmer apples the same quantty of manure at each locaton ( mj = y m m y j m). 4 Each farmer has n locatons where the manure can be appled wth n = θh / ms. In addton, we assume that c '' s not too hgh so that there are no ncreasng returns to scale n overall producton ( C + g < 0 ). Hence, the functon cost of manure management can be rewrtten as follows: hh µθ h g(.) = c1( v) + c2( µθ h) + τm (3) 2ms hh 1 2 Innes (2000) provdes a detaled analyss of the mpact of envronmental regulaton on lvestock producton wth respect to the locaton of producers. However, ths author does not analyze restrctons on manure applcaton per unt of land and consders hog producton as gven. 3 Transportng manure s tme consumng (and ncreases wth the dstance travelled). 4 Except for the more dstant locaton where 0 mj the same quantty of manure at each locaton. m. For the sake of smplcty, we assume farmers spread 8

9 Hence, manure spreadng yelds decreasng economes of scale because of manure transport costs. In addton, trval calculatons reveal that the margnal cost of manure management ( g g/ h ) s gven by: ' ' 2 2 gh = c1+ c2 + τ mµ θ h / ms > 0 (4) h The margnal cost ncreases wth the quantty of manure per unt of output θ, more restrcted applcaton rates (lower m ), cost of transport between the farm and the manured feld τ m and the share of manure whch s spread snce we have: g µθ h = > 0 µ 2 h '' cθh τm ms whle the margnal cost vares wth hog producton as follows: g = c + τ µ θ ms (5) '' 2 2 hh 1 m / whch can be postve or negatve. Envronmental regulaton, locaton and producton The equlbrum output ( h ) for each farm s mplctly defned n the followng equalty: π = = h ( zr τ y ) Ch( wk, wl, A, h ) gh( θ, µ, m, s, τm, h ) 0 (6) We frst analyze the drect effects of the envronmental regulaton on producton. Some trval calculatons reveal that: h gh / ( ms) τ mµ θ h /( ms) = = > 0 ( ms) C + g C + g hh hh hh hh (7) Remember that C + g < 0 and C < 0. It appears that strcter regulaton of manure applcaton hh hh hh rates (low m ) or lower avalablty of surroundng cropland (low s) works aganst agglomeraton of hog producton because of the ncreasng cost of spreadng manure. Ths effect s weakened when the share of manure that s managed by treatment reaches hgh values (lower µ ). However, n (7), we assume that µ s exogenous and does not react to a change n the applcaton rate ( m ) or n land avalablty (s). When µ s endogenous, the effect s ambguous. 9

10 Indeed, when n order to mnmze the cost of manure management (3) each farmer sets µ at a gven rate of hog producton, the equlbrum share of manure managed by spreadng µ s mplctly gven by g (.) / µ = 0 or, equvalently, by: µ θh c + c + τ = ms ' ' 1 2 m 0 (8) In addton, some standard calculatons show that: 2 g '' m = µ c ms (.) τ θh, 2 2 g(.) '' 2µτ mθ h = c1 + > 0 µ h ms and 2 g(.) µτ mθh = < 0 2 µ ( ms) ( ms) '' Hence, µ s an nteror soluton when c1 + τ / ms > 0 and t s easy to check that m µ < and d /dh 0 µ >. In other words, manure treatment technology s more lkely to be used when hog d /d( ms) 0 producton s relatvely hgh and when the manure applcaton rate s strctly lmted. Hence, when µ s endogenous, equaton (7) becomes: h 1 gh gh dµ = + (9) ( ms) Chh + g hh ( ms) µ d( ms) + where we have now: g hh gh gh dµ = + h µ dh As a result, strcter manure management regulaton or decreasng land avalablty has an ambguous effect on hog producton. Even though the drect effect works aganst agglomeraton of hog producton (because of the costs assocated wth manure spreadng), the ndrect effect favors hog producton because the use of treatment technology ncreases. Hence ncreasng the capacty to treat manure may enable economes of scale n manure management that off-set addtonal costs of complance. We now study the mpact of locaton on hog producton for a farmer located at. By usng (5), we can also study how a shock at locaton j s transmtted to locaton. Frst, t s easy to check that (10) h C h C + g ha = ρ y j hh hh y j δ (11) whch s postve and related to postve spatal nformaton spllovers. Hence, ncreasng hog producton n the farms located around farm ncreases hog producton on ths farm. We expect that 10

11 the magntude of the effect ncreases when the avalablty of the surroundng cropland (s) s very low (remember that g decreases wth s). More nterestng, agglomeraton s favored ( h hh / h s hgh) j when the farmers manage more and more manure usng the treatment system (lower µ ). Indeed, ghh ncreases wth µ. In addton, at a gven dstance to the slaughterng faclty, the mpact of the dstance to a feed producer on hog producton s as follows: h Ch / wk = ξk < 0 u C + g k hh hh (12) As expected, the mpact of the dstance to an nput suppler reduces hog producton. It also appears that the magntude of ths effect ncreases when the farmers favor the manure treatment system (low µ ) and decreases when manure applcaton s strctly lmted (hgh m ). Hence, envronmental regulaton favorng the adopton of manure treatment technology nduces more hog producton around nput producers, whle strcter lmts on manure spreadng dscourage co-agglomeraton of farmers and nput producers. Further, t appears that the magntude of the dstance effect to a feed producer on hog producton ncreases wth the weght of ths nput n the producton process (because C / w ncreases) and transport costs of feed unt ( ξ k ). Hence, we expect that the locaton of hog producton s strongly affected by access to feed supplers because the ntermedate consumpton of feed represents more than 50 percent of producton costs for hog producers. Concernng the mpact of the dstance to the slaughterng faclty on farm s producton, the relatonshp s more complex. Indeed, at a gven dstance to the nput supplers, we have: h k h τ ChA A = + < 0 y C + g C + g y hh hh hh hh (13) The frst term of the RHS n (13) concerns unt transport costs of the hogs between the farm and the SF whle the second term of the RHS captures the nfluence of a change n locaton on the ntensty of spllovers. Wthout nformaton spllovers, hog producton decreases wth respect to the dstance to the 11

12 SF. The slope ncreases wth the cost of transportng hog unts (τ ) and wth the share of manure managed by a treatment system ( g hh decreases). When nformaton spllovers occur, we have A / y < 0 so that the decrease n hog producton wth the dstance to the SF s hgher when technologcal externaltes occur. As mentoned above, an ncreasng share of manure managed by a treatment system makes the slope stronger. We now turn to the mpact of a consumpton shock on hog producton. More precsely, we study the mpact of a shock n the demand prevalng n regon r. We know that the regonal prce of pork depends postvely on the demand for pork and thus on the spatal dstrbuton of consumers because transport costs ncrease consumer prces. We denote the demand for pork by consumers located n regon r to producers located n regon r by Drr ' ( trr ', I r' ) where t rr ' s the transport cost, ncreasng the dstance between the regon where the pork s produced and the regon where the pork s consumed whereas I r ' s the ncome n regon r. Because zr( I r' ) and Dr r' Dr' r =Σ (the total demand addressed to producers n regon r), some standard calculatons reveal that: h dt ( ) z I C + g D r', r r = > r' hh hh r 0 (14) dt ( ) = D / R. Hence, the mpact of a change n the wealth prevalng n a regon depends wth r', r r' r' both on the transport costs of the processed product and on the relatonshp between the regonal pork prce and regonal demand. To sum up, our model shows that regulaton of manure management has an ambguous effect on the spatal dstrbuton of hog producton. On the one sde, manure management regulaton trggers dsperson when manure s appled to land as a crop nutrent. On the other sde, by favorng the use of treatment systems, strcter regulaton of the manure applcaton rate or a decrease n avalable land for manure spreadng trggers spatal concentraton of hog manure. Furthermore, the characterstcs of manure management technology affect the magntude of agglomeraton economes related to nformaton spllovers and access to slaughterng facltes and to nput supplers. More precsely, a hgher share of manure managed by treatment technology strengthens agglomeraton economes. 12

13 3. The emprcal model and econometrc ssues Gven the dscusson n the foregong secton, our am s to evaluate the mpact of land avalablty for manure spreadng on the spatal re-allocaton of hog producton and, n turn, what extent manure management regulaton affect agglomeraton economes. To test our theoretcal predctons, we consder the followng emprcal model: H= ρw H+ γ X+ γ E+ γ Z+ ε (15) h X E Z where H s a n 1 vector of the dependent varable n each of the n countes for a gven perod, ρ s the scalar spatal autoregressve parameter, W s an ( n n) spatal weghts matrx, X, E and Z are h n k 1, n k2 and n k3 matrces of k = k1+ k2 + k3explanatory varables related to access to purchasers and supplers (X), envronmental constrants (E) and farm structures (Z), whereas ε s a n 1 vector of error terms, the propertes of whch are detaled below. Fnally, γ X, γ E and γ Z are the k 1 1, k 2 1 and k 3 1 parameter vectors to be estmated. The spatal lag of the dependent varable s ntroduced n order to capture the role of spatal nformaton spllovers n hog producton. The spatal weght matrx Wh contans elements ϕ that can j be nterpreted as the decreasng role of dstance n the ntensty of postve nteractons between farmers located n county) and those located n j (respectvely, n the row, column, of the matrx). We use a dstance squared decay functon as, ϕ = d (where d j s the physcal dstance n klometers j 1 j between the captal of county and j) f the dstance s less than 200 km, otherwse ϕ j s set to 0. The cut-off value of 200 km was chosen because t appears that cooperatves (producer organzatons va whch nformaton spreads) have a regonal feld of acton. The elements along the man dagonal are ϕ j = 0. The weghts have been standardzed so that the elements n each row sum to s 1: ϕ = ϕ ϕ. j j j j Concernng access to slaughterng facltes, local consumers and nput supplers (vector X ), we consder the three followng varables: 13

14 () Access to the slaughterng faclty from locaton : S ( Ws I) S = + where S s a vector contanng the sze of the slaughterng facltes, dentty matrx. Therefore, lne of W s s a spatal weght matrx related to S and I the S contans the sze of the slaughterng faclty located n county plus a dstance-weghted average of 's neghborng facltes. The ntroducton of the (W s + I) matrx ams to capture the role of transportaton costs of lve pgs between farms and nearby slaughterhouses. We use an nverse dstance matrx. For the cut-off, we consder the mnmum dstance ensurng that each observaton has at least one neghbor. Thus, for W s, the cut-off s around 34 klometers. () Access to fnal consumers from locaton : Pop WR Pop = where Pop s a vector contanng the populaton of the county and capture the transport cost of hog meat to end markets. set to the same dstance as that to the slaughterhouses. W R s the spatal weght matrx related to Pop, n order to W R s an nverse dstance matrx wth a cut-off () Two measures of access to the nput supplers at locaton : frst, X = ( W + I) X wth 1 x 1 X 1, a vector contanng the avalable quantty of crops and W x, the spatal weght matrx related to X 1. We expect a postve mpact of the access to purchasers or supplers on pork producton. Wx s an nverse dstance matrx wth a cut-off set to 100 klometers, n order to take nto account the transport cost of cereals. Second, we ntroduce the regonal mxed feed producton (specfc for hogs) as vector X 2. 5 To capture envronmental constrants (vector E ), we frst buld a varable related to the EU regulaton concernng manure spreadng. We use the rato of the potental quantty of ntrogen produced by all lvestock located n regon (N) to the supply of land avalable for manure spreadng (L) n order to capture the mpact of ms. We also ntroduce a spatal dmenson of ths varable by usng the rato (N/L) n county and n neghborng places,.e. the rato of neghborng places weghted by dstance. ( W (N/L)) N. In ths way, we consder that land avalablty for spreadng hog 5 As can be seen below, we were unable to collect precse data on the locaton and producton quanttes of each frm producng ndustral mxed feed. The only avalable data concern regonal producton of feed. Ths s why the form of ths varable dffers from the others. 14

15 manure decreases wth lvestock producton and wth the dstance between the locaton of farms and the locaton of the cropland. Second, we consder the mpact of populaton locaton on the locaton or the growth of the producton facltes. Indeed, hog producton causes local external costs related to odors and other ambent effects that the hog producer must reduce because of local envronmental regulatons. Ths constrant (for the producer) creates some addtonal costs by shrnkng the expanson of hog producton. We assume that these emsson abatement costs ncrease wth an ncrease n the sze of the local populaton (Pop). The effort to reduce emssons ncreases wth an ncrease n the number of resdents). To estmate model (15), called a spatal lag or spatal autoregressve model, we use spatal econometrc technques (Anseln, 2006; LeSage and Pace, 2008). The maxmum lkelhood (ML) estmaton method s by far the most common methodologcal framework appled n spatal econometrcs n ths case snce t allows the endogenety of the spatally lagged varable WH h to be controlled for (Anseln, 2006). Such an approach was used by Roe et al. (2002) to reveal agglomeraton economes n hog producton. However, as we argue below, other varables are determned at the same tme as the dependent varable, such as the locaton of slaughterng facltes or nput supplers. The locaton of processors or supplers s also determned by the spatal dstrbuton of hog producers due to market mechansms or vertcal coordnaton prevalng n the hog sector. Furthermore, our envronmental constrants (N/L and W N.N/L) nclude hogs among the local lvestock and mght be also endogenous. Although the endogenety ssue could be source of econometrc bases, ths problem has been dsregarded so far. It causes addtonal econometrc complextes, snce, as ponted out by Fngleton and Le Gallo (2008), the estmaton of such a model wth a spatal autoregressve process and endogenous varables s not possble wth the usual maxmum lkelhood (ML) approach. Other approaches have to be used. The strategy that we follow conssts n performng a generalzed spatal two-stage least squares estmaton, suggested by Kelejan and Prucha (1998). Ths approach uses the lower orders of the spatal lags of the exogenous varables as nstruments for the endogenous spatal lag W H h, together wth other nstruments for the other endogenous varables. 15

16 These are detaled below. Moreover, n order to control for unmodeled factors n equaton (15), two strateges may be adopted, one of whch s used n ths paper. The frst s to specfy a parametrc error process, such as a frst spatal autoregressve error process or spatal correlaton process n the errors: ε= ηw ε+ ν (16) ε where η s a scalar spatal autoregressve parameter; W ε s a frst-order contguty matrx and ν s a n 1 vector such as ν ~ 2 d(0, σ I n ). The method of estmaton of a general model wth an endogenous spatal lag, addtonal endogenous varables and a spatal autoregressve error term was suggested by Fngleton and Le Gallo (2008). However, whle specfyng the error process could result n gans n effcency f properly specfed, there s also a rsk of msspecfcaton f the error terms are also heteroskedastc or f they are not dstrbuted accordng to a frst-order spatal autoregressve model. Therefore, n ths paper we use Kelejan and Prucha s (2007) non-parametrc heteroskedastcty and autocorrelaton consstent (HAC) estmator of the varance-covarance matrx n a spatal context,.e. a SHAC procedure. In partcular, these authors assume that the ( N 1) dsturbance vectors ε of model (15) s generated as follows: ε = Rξ, where R s an ( N N) non-stochastc matrx whose elements are not known. Ths dsturbance process allows for general patterns of correlaton and heteroscedastcty. The asymptotc dstrbuton of the correspondng OLS or IV estmators mples the varance-covarance matrx 1 Ψ= n Z' Σ Z, where ( σ j ) Σ= denotes the varance-covarance matrx of ε. Kelejan and Prucha (2007) show that the SHAC estmator for ts (r, s) th element s: n n ˆ 1 ˆˆ rs n xr xjsεε jk( dj / dn ) = 1 j= 1 Ψ = (17) where x r s the th element of the r th explanatory varable; ˆ ε s the th element of the OLS or IV resdual vector; d j s the dstance between unt and unt j; d n s the bandwth and K(.) s the Kernel functon wth the usual propertes. Here, we use the Parzen kernel wth bandwdth set to the frst 16

17 decle, the frst quantle and the medan of the dstance dstrbuton. The results obtaned are qute robust wth respect to the choce of bandwdth and we report those obtaned wth the medan. 4. Data. The majorty of data used n ths paper come from agrcultural censuses (1988 and 2000). Varables relatve to slaughterhouses and to the mxed feed sector as well as data on the structures of farms were suppled by the French Pork Sector Insttute (IFIP). Data concernng populatons (and the labor market among the nstruments) come from populaton censuses (1990 and 1999). Fnally, to buld nstrument varables, we used clmate varables provded by Météo France, whereas data on land qualty come from the INDIQUASOL database (from Servce Unt INFOSOL, INRA, Orléans). The spatal unt used n ths paper s the French canton (an admnstratve delneaton smlar to a county). Ths s a qute fne spatal dsaggregaton for analyss. However, some of these unts changed durng our study perod because of admnstratve changes (merged or splt) so we performed the analyss on 3,589 unts for 1988 and 3,572 unts for Dependent varable Consderng the heterogenety n the sze of the county and workng on the mpact of envronmental regulatons on the agglomeraton of hog producton, we use the densty of pgs n the county as dependent varable,.e. the number of hogs nventory per hectare at the county level expressed n large stock unts. Fgure 1 shows the spatal dstrbuton of the dependent varable for Hog producton s qute unevenly dstrbuted across French countes, wth a strong geographcal concentraton n some areas of France, notably n Brttany n the West. [Fgure 1 about here] Explanatory varables Varables used to estmate equaton (15) are descrbed n Table 1. As explanatory varables, we nclude access to agrcultural land used for corn (( W I) Corn) cereals (( W I) Cereal) x ( X1 ( Wx I) X1) x + and other + as a proxy for access to local producton of hog feed = +. Moreover, gven that the proten-rch feed used to feed hogs s mported, we 17

18 use the regonal quantty of ndustral hog feed ( X Mxed Feed ) 2 =. As data on supples of hog feed at the county level were not avalable we use data avalable at the regonal level. In contrast to access to corn and other cereals, access to ndustral feed s assumed to be exogenous. [Table 1 about here] The potental demand for pork s represented by access to slaughterhouses ( S = ( Ws + I) S) and by the spatal lag of the populaton ( Pop W R Pop) =. We assume the frst varable s endogenous, because of the locaton of slaughterhouses and the locaton of pg farms are endogenously determned, whle the second s consdered to be exogenous. The rato of the quantty of ntrogen to land potentally avalable for manure spreadng at the level of the county ( N/L) and ts spatal lag ( (N/L)) W are bult as follows. The quantty of ntrogen at county level ( N ) s calculated for all lvestock located n the county usng coeffcents from the French agrcultural census. The land potentally avalable for manure spreadng ( L ) represents 70% of the total cultvated area. If the rato at county level s hgher than a maxmum threshold, farmers could try to spread ther manure n neghborng countes or/and treat hog manure. Thus, we also take nto account the spatal lag of the rato (wth a dstance matrx adjusted because of hgh transport costs of manure). Ths envronmental rato and ts spatal lag are consdered to be endogenous because they nclude manure produced by hog producton at county level. Hog producers can be separated nto three man orentatons, due to a dfference n ther producton technologes: breedng only, breedng-and-fattenng, and after-weanng-and-fattenng. Famers who only breed manage sows to produce small weanlng hogs, farmers who wean and fatten rase weanlngs to fatten them, and farmers who breed and fatten do both. The majorty of French hog producers breed and fatten, so we use the densty of the other two orentatons as control varables n our model ( B densty for breedng only and F densty for after-weanng-and-fattenng). These varables control for the effect of producton orentaton on the agglomeraton of producton. Fnally, we nclude a varable descrbng the local densty of non hog farms n the county (NHF densty) n order to test whether nter-sector externaltes exst between the dfferent types of anmal producton, as suggested by Roe et al. (2002). N 18

19 Instrumental varables. Followng Kelejan and Prucha (1998), we should use a lnearly ndependent subset of the exogenous varables and ther low order spatal lags to account for W H.H and other endogenous varables: ( Wx + I) Corn; ( Wx + I) Cereal ; ( Ws + I) S ; (N / L) ; and, W N (N/L). Other nstruments should also be ncluded to account for the other endogenous varables. We use accessblty of crops (when ths s not ncluded as an explanatory varable) and the densty of hog smallholders. 6 We also use the share of unemployed workforce and the rato of non-sklled workers to all workers as nstruments for the slaughterhouse. Snce slaughterhouse labor s manly not specalzed, unemployed and unsklled workers can relatvely easly get a job n ths sector. Hog producton has an mpact on the land use as well as on the total amount of manure to be spread, mplyng that our envronmental rato s endogenous. As an nstrumental varable, we use sol qualty (as a proxy for the proporton of clay n sols) whch s assumed to be exogenous. In addton, we use clmate varables such as mean sunshne, mean ranfall and mean temperature. We chose these nstruments usng a step by step procedure based on the Sargan test. If the Sargan test shows that the set of nstruments s not vald 7, the resduals are regressed on all nstrumental varables. Ths regresson helps dentfy whch nstruments are sgnfcantly correlated wth the resduals and are thus not vald. 5. Results. In ths secton, we present the results of our dfferent estmatons. We frst estmate equaton (15) for the year 2000 wth several specfcatons to examne the robustness of the man results. Then, we estmate the same specfcaton usng data for 1988 and 2000 to compare the change n results over tme. From an econometrc pont of vew, regardless of regressons, the Hausman test s always sgnfcant at 5%, meanng that, dependng on the nstruments we specfed, the varables that we suspected to be smultaneously determned wth the dependent varable are ndeed endogenous. In 6 We used a French typology takng nto account four knds of farm s orentatons: hogs and cereals, hogs and mlk, smallholders, and hog specalsaton. 7 So that the set of nstruments s vald, the probablty assocated wth the test must be above

20 addton, we can never reject the null hypothess of exogenous nstruments, accordng to Sargan s test. Fnally, the qualty of adjustment ranges from 40% to 50%. Locaton of hog producton: agglomeraton economes vs. envronmental regulatons. When we focus on the results of models 1, 2, 3 and 4 presented n Table 2, t frst appears that the explanatons for the ncrease n hog producton around Chcago n the second half of 19 th century gven by Cronon (1991) s stll vald n 2000 to explan the agglomeraton of hog producers n a few locatons n France. Indeed, proxmty to slaughterng facltes (( W I) S) s + and to ndustral feed producers (Mxed Feed) plays a sgnfcant and postve role n the locaton of hog producton, whatever the specfcaton. However, proxmty to fnal consumers ( Pop) W appears to have no effect on the spatal locaton of hog producton and the relatonshp wth the slaughterhouses s the only forward lnkage at work. Smlarly, whle hgher regonal producton of ndustral feed tends to R ncrease local hog producton, access to cereals or to land under corn ( W + I) Corn and x ( W + I) Cereal ) has no nfluence on the locaton of hog producton, n contrast to the results of Roe x et al. (2002). Ths pont s mportant because, unlke Roe et al. (2002), we control for the endogenety of access to corn and cereal producton as well as of access to slaughterng facltes and to mxed feed. When we do not control for ths endogenety (see Table A.1 n the Appendx), we obtan the same results reported n Roe et al. (2002). [Table 2 about here]. Lke n Roe et al. (2002), our results show that the spatal lag of the dependant varable (W H.H) amng at capturng nformaton spllovers plays a postve and sgnfcant role n the densty of hog producton. Hence, agglomeraton economes arsng from spatal non-market nteractons between farmers are at work n the French hog sector. We now turn to the role of envronmental regulaton. The estmate of local populaton (Pop) exhbts the expected sgn. Local populaton sze has a negatve and sgnfcant effect on the agglomeraton of hog producton, regardless of estmatons. Analyss of the role of regulaton of manure management s more complex. Indeed, n model 1, we buld a global rato of ntrogen 20

21 producton by anmals to avalable land at the county level and at the level of the surroundng countes: ( W + I) (N/L)). Ths varable has no sgnfcant effect so that there s no global effect of N the avalablty of land for manure spreadng on the locaton of hog producton. In the followng models, we separate the ratos of ntrogen producton to avalable land at the county level and at the level of the surroundng places. In ths case, the estmatons reveal a sgnfcant and postve effect of the rato when t s calculated at the county level and an opposte sgn (.e. sgnfcantly negatve) for ts spatal lag. Thus, ncreasng the local producton of manure relatve to the land avalable rases the densty of hog producton whle a rse n ths rato for the surroundng countes trggers spatal dsperson of hog producton. The latter effect s expected when manure spreadng s the manure management technology used by farmers, whle the former effect suggests that farmers may also use manure treatment technology to reduce manure spreadng. Hence, ths suggests that both types of technology for managng manure are used at county levels. In other words, hgher transport costs arsng from manure spreadng or lower land avalablty n surroundng places reduce hog producton, ceters parbus, as shown by the negatve sgn of the spatal lag, but favor the spatal concentraton of hog producton because the use of the manure treatment system leads to economes of scale. Note that ths result s qute robust. It stll holds when we ntroduce the varables measurng access to crops (models 3 and 4). Indeed, even f there may be some lnkages between the actvtes of manure spreadng and the presence of crops, the ntroducton of these varables does not dsturb the sgn or the magntude of the coeffcents assocated wth manure management varables. Explorng the role of costs related to manure management. The role played by regulaton of manure management deserves more attenton. We checked the robustness of the effects of regulaton of manure management on local hog producton densty by addng two types of control varables. Frst, the specalzaton of farmers may nfluence our results. Indeed, whether the local farms are specalzed ether n pglet producton or n pork producton, may modfy the parameter results. In model 5, we ntroduce the type of specalzaton prevalng n each county. Whle the densty of breedng farms plays a role n the locaton of hog producton, the densty of feedng farms has a sgnfcant and postve effect. However, t does not change the estmates of all the other varables but only slghtly reduces the sgnfcance of the postve N/Leffect. 21

22 Second, the quantty of manure resultng from all anmal producton can capture agglomeraton economes related to the sharng of the same ndvsble nfrastructure by the dfferent types of anmal producers ( nter-sector scale economes ). Hence, the local rato of manure producton by anmals to land avalable for spreadng may capture nter-sector scale economes, explanng the postve sgn of ths effect. In order to control for ths, n our model, we also ntegrate the densty of non-hog farms n the county (NHF densty n model 6),.e. the other lvestock rasers. We expect a postve sgn for the latter varable. The results show that the densty of lvestock farms wth no hog producton postvely nfluences the agglomeraton of hog producers revealng the postve role of spatal spllovers between dfferent types of lvestock farms. However, the ntroducton of ths type of urbanzaton economy does not change the parameter values assocated wth amount of land potentally avalable for manure spreadng. These values keep the same sgn and reman sgnfcant even f the magntude of the coeffcent decreases slghtly. Hence, the role of regulaton of manure management has an ambguous mpact on agglomeraton. The local level of land avalable for manure spreadng favors agglomeraton whle the level reached n the surroundng locaton favors dsperson of hog producton. However we can use the elastctes evaluated at the mean values from the parameter values of model 6 (see Table 3 obtaned wth the means lsted n Table 1) to analyze the global mpact of EU regulatons concernng manure spreadng. The same change n the rato of manure producton to avalable land n all countes leads to the followng global mpact of the regulaton of manure management on hog producton: h / (N/L) ϕ = where j s j s ϕ j are the standardzed weghts n the spatal matrx wth s ϕ j j=1 (see secton 3). The global effect s thus more lkely to be negatve. However, the total effect s not sgnfcant. Consequently, regulaton of manure management does not work aganst the spatal concentraton of hog producton. Another strategy to check the robustness of our results conssts n estmatng model 6 from data for 1988 (data concernng the last agrcultural campagn before 2000). Because the EU ntrate drectve was ntroduced n 1991, we would not expect the effects of the varables assocated wth regulaton of manure management to be sgnfcant n In order to dscuss the changes n the 22

23 magntude of coeffcents between 1988 and 2000, we report the elastctes evaluated at the mean values for 1988 and 2000 for each varable n model 6 (see Table 3). As expected, our results show that the potental for manure spreadng at county level or at the level of the surroundng countes had no sgnfcant mpact n Ths confrms that the regulaton of manure management has a sgnfcant effect on the locaton of hog producton. [Table 3 about here]. The mpact of manure management regulaton on agglomeraton economes The results presented n Table 3 also show that the sgnfcance and the sgn for the other varables do not change over tme, except for the densty of lvestock farms wthout hogs, whch was not sgnfcant n Ths result confrms the postve role of access to nputs/ouputs and spatal spllovers and the negatve role of urbanzaton n hog producton. However, whle the magntudes of the elastctes assocated wth the spatal lag and wth the proxmty to slaughterng facltes and access to mxed feed reached comparable levels n 1988 (elastctes between 0.33 and 0.35), a herarchy emerges among those three varables durng the perod Indeed, n 2000, the elastcty to the spatal lag of hog producton densty becomes much hgher the elastctes related to both access varables (0.61 for the former versus 0.24 and 0.27 for access varables). Thus, whle all the three varables appear to act wth the same strength, the role of spatal nteracton between hog producers (.e. spatal lag) s clearly strengthened n We can nterpret these changes by the followng phenomena. Frst, the lmted declne n elastcty to access to slaughterng facltes and feed producers may be due to the fall n transport costs over ths perod. Second, the ntroducton of the EU ntrate drectve also boosted agglomeraton economes by strengthenng spatal nteractons between farmers. Ths may be due to the need to nvest n shared nputs to change manure management (such as a collectve treatment faclty) and to the ncreasng role of producers organzaton n the French hog sector. 6. Summary and concludng remarks In ths paper, we have developed a theoretcal analyss to explan how regulaton of manure management affects the locaton of hog producton wthn a spatal model that also takes nto account tradtonal spatal spllovers and access to nput supplers and to demand. Our theoretcal model 23

24 ncludes a choce between two technologes for manure management and results show that dsperson s favored when manure s spread on land as a crop nutrent, whle agglomeraton s strengthened when farmers choose manure treatment. We showed how the adopton of a manure treatment system s favored by ncreasngly strct regulaton of manure spreadng. Then, we conducted an econometrc study takng nto account dfferent bases that are gnored n the lterature. Our estmatons usng 1988 and 2000 French hog producton data confrm the mportant role played by local nteractons between hog producers (spatal spllovers) and by ther backward and forwards relatonshps (nput/output market accessblty). Emprcal results also suggest that the regulaton of manure management ntroduced by the European Unon n 1991 does not prevent the agglomeraton of hog producton. It may even boost agglomeraton n two ways. Frst, t may nduce a shft n manure management technology from manure spreadng to manure treatment whch s more proftable wth hgh levels of hog producton. Second, t may boost agglomeraton economes related to non-market spatal externaltes va shared nputs or producer organzatons. These results could be an nterestng llustraton of Porter s hypothess. Further nvestgatons requre a specfc focus. In partcular, t would be nterestng to open the black box of spatal externaltes by studyng the role played by agrcultural cooperatves n the spatal dffuson of knowledge. It would also be nterestng to examne n detal the manure management technologes used by farmers and how they change over tme n order to confrm (or not) our dfferent nterpretatons. Our theoretcal model could also develop and calbrate our emprcal results to examne other types of publc regulatons such as ambent taxes. 24