Direct payments, spatial competition and farm survival in Norway

Transcription

1 Drect payments, spatal competton and farm survval n Norway Hugo Storm* a, Klaus Mttenzwe b, and Thomas Heckele a a Insttute for Food and Resource Economcs (ILR), Unversty of Bonn b Norwegan Agrcultural Economcs Research Insttute (NILF), Oslo *Correspondng author. Insttute for Food and Resource Economcs, Unversty of Bonn, Nussallee 21, D Bonn, Germany. Tel.: ; fax: , E-mal address: hugo.storm@lr.un-bonn.de (H. Storm). Selected Paper prepared for presentaton at the Agrcultural & Appled Economcs Assocaton s 2013 AAEA & CAES Jont Annual Meetng, Washngton, DC, August 4-6, Acknowledgement: The research presented n ths paper has been fnanced by the Research Councl of Norway under grant no /I10 wthn the program BIONÆR. Storm receved a travel grant from the German Academc Exchange Servce (DAAD) fnanced by the Federal Mnstry for Economc Cooperaton and Development under project ID Hs work s also funded by the German Research Foundaton (DFG) under grant no Most of the work was conducted whle Storm was a vstng scholar at NILF. The authors are grateful to Grete Stokstad and Sven Olav Krogl from the Norwegan Forest and Landscape Insttute (Skog og Landskap, Ås, Norway) for provdng the farm coordnates used n the analyss. Copyrght 2013 by Hugo Storm, Klaus Mttenzwe, and Thomas Heckele. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded ths copyrght notce appears on all such copes.

2 Drect payments, spatal competton and farm survval n Norway Hugo Storm, Klaus Mttenzwe, and Thomas Heckele Abstract: We argue that nterdependences between farms are crucal for assessng effects of drect payments on farmers ext decsons. Usng spatally explct farm level data for nearly all Norwegan farms, a bnary choce model wth spatally lagged explanatory varables s estmated n order to explan farm survval from 1999 to We show that gnorng spatal nteractons between farm leads to a substantal overestmaton of the effects of drect payments on farm survval. To our knowledge, ths paper s the frst attempt to emprcally analyze the role of neghbor nteractons for farm structural change n general and for an assessment of the effects of drect payments on farm survval n partcular. Keywords: spatal competton, land market, farm structural change, drect payments, polcy assessment JEL classfcaton: C21, C25, Q12, Q13 1 Introducton In Norway, as n many other ndustral countres, drect payments are often legtmzed as a way to mantan a vtal agrcultural sector and, n partcular, to prevent the abandonment of farms. It s often argued that agrcultural supports ncrease farm proftablty and thus reduces farm exts. Ths argument s supported by Breustedt and Glauben (2007) n an regonal level analyss for Western Europe n whch they concluded to have found [ ] emprcal evdence that the former EU's Common Agrcultural Polcy (CAP) has probably reduced the structural change n agrculture durng the last decades of the last century va prce support and subsdy payment programmes [ ] (p. 124). Smlarly, n a regonal level analyss for the US Goetz and Debertn (2001) found that hgher [g]overnment payments reduce the odds that a country loses farms on net but addtonally that among the regons n whch the number of farms declne [ ] hgher payments accelerate the rate at whch farmers ext (p.1020). These studes analyze the effects of ncome support on net regonal farm ext. These aggregate regonal effects, however, mght mask potental dfferent reacton at the ndvdual farm level. An addtonal drawback s that they need to rely on regonal varaton n payment 1

3 levels or other farm characterstcs for dentfcaton. Ths renders varable defnton and nterpretaton more complcated. Indvdual farm level studes, such as Key and Roberts (2006), on the other hand allow or more drect analyss of the effects of farm characterstcs and payments. In ther farm level analyss farm survval for US farms Key and Roberts (2006) found a small but statstcally sgnfcant postve effect [of payments] on farm busness survval (p. 391). For an overall assessment of the effects of payments however an aggregaton of the ndvdual farm level effects s necessary. We argue that for such an aggregaton t s crucal to consder the nterdependence between farm behavor. Snce so far ths lnk s mssng n farm level studes, Roberts and Key (2008 p. 628) argued n favor of regonal level studes that: [Farm level] studes [...] consder effects of payments on the growth or survval of ndvdual farms, whch cannot predct the effects of an ncrease n payments on aggregate farm structure. Ths s because studes of ndvdual farms cannot account for how nduced changes on one farm affect other, neghborng farms [ ]. In ths paper we am to consder these nteractons between ndvdual farms n the estmaton and for an overall aggregaton of the effects nduced by a polcy change. Partcularly, the objectve of ths paper s to emprcally analyze the effect of drect payments on farm ext rates controllng for spatal farm nteracton usng ndvdual farm level data of nearly all Norwegan farms for 1999 and It s argued that gnorng the spatal nteracton between farms n the aggregaton of the results leads to an overestmaton of the effects of drect payments on farm survval. To our knowledge ths paper s the frst attempt to analyze emprcally the role of neghborng nteracton for farm structural change n general and for an assessment of the effects of drect payments on farm survval n partcular. The mportance of neghborng nteracton s long recognzed n the agent-based model lterature. Balmann (1997) dentfes spatal nterdependence of farms, the mmoblty of land, and the locaton of farms n space as mportant assumptons (among others). In hs model the spatal nterdependence between farms are consdered through nteracton on the local land market. Here, farms compete for the lmted resource land whch s mmoble and located at a specfc pont n space. The developed agent-based model s employed n further studes to analyze the mportance of sunk cost (Balmann et al. 2006) and the effects of decouplng for structural change n Germany (Happe et al and 2008). 2

4 Despte the recognton n the agent-based model lterature, emprcal studes concerned wth spatal nteracton n farm structural change are rare. An excepton s Huettel and Margaran (2009) who analyze the effects of nteractons on the land market for farm structural change. They consder dfferent theoretcal frameworks of strategc competton to characterze farm behavor on the land market leadng to several hypotheses concernng the relatonshp between ntal farm structure and farm growth whch are then tested emprcally. Even though ther theoretcal model s based on nteracton on the land market ther emprcal model does not explctly consder nteracton between farms. Instead they model farm sze developments as a Markov process n whch transton probabltes between sze classes are explaned by regonal or tme varyng varables. In contrast, our approach s based on ndvdual farm data and does consder spatal dependence between farms explctly. Smlar to our approach, Wess (1999) analyzed farm survval and farm growth n Upper Austra usng farm level data. He recognzes farm nterdependence and the competton for land and labor; Farm exts are a precondton for the farm sector to change ts structure snce land and labor are reallocated among remanng farms [ ] (p. 104), but does not consder t n hs emprcal applcaton. In other areas such as land use/cover change, spatal dependences and nteractons on the land market are more wdely recognzed (see Irwn and Geoghegan 2001 and Verburg et al for a revew). Gellrch and Zmmermann (2007) focus s on drvers of land abandonment n the Swss mountans. In some respect land abandonment s smlar to farm structural change snce the reasons to abandon land and to ext farmng lkely overlap. Ther model s based on an economc framework takng off-farm employment opportuntes, the share of part-tme farmer and polcy varables nto account. Gven ther objectve, however, ther model looks at the regonal scale and not at the ndvdual farm level. Spatal correlaton s thus consdered between neghborng regons nstead of ndvdual farms. One reason for the lack of emprcal models analyzng spatal nteractons between farms mght be the scarcty of spatally explct farm level data. The avalable data source for Norway thus provdes a unque opportunty to analyze spatal aspects of farm structural change on the farm level emprcally. We estmate a spatal bnary choce model to explan farm survval usng own as well as neghborng farm characterstcs. 3

5 The remander of the paper s structured as followng. Frst, a theoretcal model for farm sze and nteracton on the land market s derved. Based on ths hypothess about potental drvers of farm survval are dscussed. In secton 3 an overvew on the avalable data base s gven. The emprcal model wth the specfcaton of the spatal weghtng matrx as well as defnton of dependent and explanatory varables s gven n secton 4. The regresson results and the results of polcy scenaro smulatons are presented n secton 5 and 6. Secton 7 concludes. 2 Theoretcal model and Hypothess In order to dscuss the spatal nteracton on the land market and to gude the selecton of explanatory varables a smple spatal competton model s developed. The model s nspred by a unform delvery model (Graubner et al. 2011) and a Hotellng spatal competton model adapted to accommodate farm structural change. The general dea s that farms occupy that area for whch ther wllngness to pay (WTP) per hectare, adjusted by transportaton cost, s greater than zero and exceeds that of all compettors. As n the Hotellng spatal competton model we consder two farms A, B located at both ends of a lne wth length one. All avalable agrcultural area s of homogenous qualty and spread equally along the lne between the two farms. Farm WTP for one unt land s equal to the margnal value product of land.e. the resdual return to land after cost for all other producton factors, ncludng opportunty costs for labor and captal, are accounted for. Each unt of cultvated land tes labor and captal that could otherwse be employed or nvested outsde the farm, therefore, can also be nterpreted as the dfference between the on-farm ncome per area unt and the forgone offfarm ncome nduced by cultvatng that area unt. In some cases can also be larger than that dfference (.e. the margnal value product of land) f farmers derve non-pecunary utlty from beng self employed or see farmng as a way of lfe (Key and Roberts 2009). For a specfc plot r on the lne net WTP, r, s determned as the dfference between and transportaton costs t whch are assumed to be proportonal to the dstance between plot and farm. Net WTP for a specfc plot s thus A r tr and r t 1 r A B. B 4

6 Both farms compete on the land market and occupy ths area for whch r s postve and exceeds that of the compettor (Fgure 1). Farms are ndfferent for plot r, characterstc by A r B r, from whch we can solve for the specfc farm sze equal to 1 sze sze A B A B t r 2t A B t 1 r 1. 2t (1) Relevant for the objectve of the paper, s a specal case whch arses when net WTP of one farm exceeds that of the compettor ( A t B ext of B or A t B ext of A ) for all avalable land. In ths case one farm quts farmng whle the other takes over all agrculture land (Fgure 1). WTP for land dffers between farms due to dfferent characterstcs of the farm busness and the farm holder. Of partcular nterest wth respect to the research queston s the effect of drect payments on WTP and therefore fnally on farm ext. Key and Roberts (2006 p. 391) found emprcal evdence that government payments have sgnfcant postve effect on farm survval. He argued that ths mght be explaned by the possblty to bd up prces on the land market and for other fxed resources. Payments mght releve lqudty constrants allowng farms recevng more payments to acheve a more effcent scale and reman n busness longer (p. 391). Payments mght also make farmng more proftable relatve to alternatve occupatons, thereby reducng ncentves to ext agrculture (p. 391)." 1 We assume that for each plot there s always at least one farm wth a postve net WTP such that no land falls fallow. 5

7 Fgure 1: Farms competng on the land market, (1) sharng the avalable agrcultural area, and (2) takeover of all area by one farm and ext of the other. demand A demand A α A demand B αb α A 0 r* 1 demand B 0 1 α B sze A sze B sze A (1) (2) Source: Own llustraton Based on these arguments we expect a postve nfluence of drect payments on. It remans unclear, however, of whether the absolute amount of payments or measured n relatve terms (e.g. on a per labor hour bass) s more relevant. Ths relates to the queston of whether total farm ncome or the on-farm wage rate (.e. total ncome over total labor requrement) s more mportant n determnng. Wth perfect labor markets we expect that s prmarly determned by the dfference between the on- and off-farm wage rate wth the total farm ncome beng less mportant. Farms too small to generate a full ncome but wth a relatvely hgh on-farm wage rate per hour would take on an off-farm employment n order to fll the remanng ncome gap. Wth mperfect labor markets, however, ths mght not be possble and farmers mght need to choose to ether contnue farmng, wthout a full ncome, or to qut farmng, takng on the alternatve off-farm employment. In ths case s prmarly determned by the dfference between total on- and off-farm ncome, wth the on-farm wage rate beng less mportant. Accordngly, under fully functonng labor markets we expect that drect payments per labor nput are more mportant than total drect payments n determnng whle under mperfect labor markets we would expect the opposte. On the other hand total farm ncome or total payments are a measure for the absolute sze of a farm and t s argued by others that the absolute sze of a farm s mportant n multple aspects, besde than the ones dscussed. For Norwegan mlk farms, Flaten (2002) showed 6

8 that, productvty ncreases wth farm sze partcularly due to a more effcent use of labor. Wess (1999 p. 105) consders the roll of technology and argued that [e]ven f the technologcal advances are scale neutral [ ] ther adoptons tends to favor larger farms snce they may have more access to nformaton and fnancng and may also have a larger set of management sklls. Roberts and Key (2008 p. 630) argued that [b]orrowng constrants could cause a farm s cost of captal to depend on ts net worth such that lager farms, havng more collateral, face lower borrowng costs. Wth respect to government payments the authors further argued that they [...] rase the net worth of a farm, makng t less costly for a farmer to obtan fnancng to ncrease farm sze. Smlarly, antcpated payments may gve farm operators more leverage wth agrcultural lenders (p.630). To assess the relevancy of these arguments for t s mportant to recognze that farm sze can be approxmated n multple ways reflectng dfferent dmensons of farm sze. Total ncome or total payments for example reflect the economc sze of farm whle total cultvated area or the total labor nput reflect the nput sde of producton. In general, the dfferent measures are expected to be hghly correlated such that n prncple the arguments apply smlarly to all three measures. However, some of the arguments mght match better to specfc measures than other. Total area and total drect payments, for example, mght be a more drect measure of farm collateral whle total labor requrement mght be more relevant to asses scale effects. Followng from ths we expect that all three measures are mportant n determnng wth each representng slghtly dfferent effects. Besde these factors that are of prmary nterest wth respect to the research queston there are plenty of others factors that mght be mportant for determnng farms WTP for land. To lmt the dscusson here, however, we restrct attenton to those varables avalable n the emprcal applcaton. The productvty of a farm for example should have a postve nfluence on the on-farm ncome and hence on WTP. The farm share of lease to total land should, ceters parbus, have a negatve effect on farm net worth and hence ncrease captal cost and decrease. Further dfference n WTP can arse due to dfferent farm 7

9 specalzatons and the specfc polcy envronments of that specalzaton. These mght nclude dfferent legal requrements for specfc producton types or specfc polces for sngle specalzatons 2. Equally mportant as characterstcs of the farm busness are personal characterstcs of the farm holder (see among other Wess 1999, Key and Roberts 2006). However, the age of the farm holder s the only varable avalable n the emprcal applcaton. Key and Roberts (2006) argued that [a]ge may be correlated to knowledge about the frm s compettve abltes wth older owners able to acqure more nformaton (p. 383). Addtonally, the fnancal lqudty of the farm holder mght ncrease over tme wth older owner beng able to accumulate suffcent net worth to obtan a certan scale of producton (p. 383). On the other hand beyond a specfc age farm development s strongly dependent on the avalablty of successor. Farms mght ncrease ther sze before retrement f a successor s avalable or f not mght decrease n sze n order to prepare for an ext. The theoretcal effect of age on farm growth and survval s thus unclear. From (1) t follows that farms own sze s postvely related to own but negatvely related to neghborng. In general we thus expect the effects of neghborng characterstc on own sze to be the opposte as the effects of own characterstcs. Ths means for total drect payments, for example, where we expect a postve nfluence on WTP that own sze s postvely related to own payments but negatvely related to neghborng payments. A Farm growth and survval therefore depends on the relatve dfference between WTP,, between farms,.e. farms occupy that area for whch ther dfference between on B and off-farm ncome exceeds that of ther compettors, for both consderng transportaton costs. Wth respect to the payments, ths mples that n a stuaton where changes n payments are the same for all farms also changes by the same amount for all farms. Changes n payments could be the same n case of decoupled payments or coupled payments when farms producton program are exactly the same. Snce there s competton on the land 2 Wthn the study perod, for example, the government bought large quanttes of mlk quota rghts whch mght have had an effect on mlk farms but no drect effect on other. 8

10 market, a change n by the same amount for all farms wll not cause changes n farm sze or farmers survval decson snce the relatve dfference n WTP between farms, A B, stays unaffected. One can also thnk of the effect of a full captalzaton of payments n land rents (Latruffe and Le Mouël 2009). In a stuaton n whch farms do not receve the same amount of payments (e.g. due to dfferent partcpatng rates (Roberts and Key 2008 p. 630), dfferent farm specalzatons or because per unt subsdy rates dscrmnate between land and herd szes as s the case n Norway) the relatve dfference A B would change. Here, an ncrease n payments would lead to growth and an ncrease of the lkelhood of survval for favored farms and a declne and an ncreasng lkelhood of farm ext of the other. Payments should therefore ether have no effect f they are the same for all farms or accelerate structural change f the changes dffer between farms. Fnally, t s mportant to pont out that the presented model only accounts for spatal nteractons on the land market whch are assumed to be mportant but whch mght not be the only way farm nteract whch each other. One other mportant type of nteracton s technology adopton and knowledge transfer (Rogers 1995, Berger 2001). Case (1992), for example, found evdence that the probablty of adoptng a new technology ncrease wth neghborng adopton. Consequently an actve cooperate network rases technology dffuson and wth t farm productvty. Neghborng farms are also mportant to mantan an actve network of supplers and processors. Overall, an actve corporate network should thus ncrease farm proftablty and hence WTP for land. For the background of the model presented above the effects of an actve cooperate network on farm sze should cancel out f all farms proft smlarly ( would ncrease for all farms alke). However, larger farms are more lkely to adopt a new technology (Feder and Slade 1984) and mght also be more mportant n mantanng an actve cooperate network of supplers and processors. Therefore, small farms mght beneft more from larger neghbors as large farm do from small ones. In ths case, WTP of farms wth larger neghbors ncreases more compared to farms wth smaller neghbors. Based on ths reasonng neghborng sze can also have a postve nfluence on own WTP and hence farm sze and survval. Whch effects domnate n the end, the negatve due to competton on the land market or the postve due to an actve cooperate network, remans an emprcal queston. In general all cases where we do not fnd the 9

11 opposte sgn of neghborng characterstcs compared to own characterstcs hnts at nteracton between farms other than the competton on the land market. 3 Data The analyss s based on data from the Norwegan Drect Payment Regster for the years 1999 and The regster contans nformaton about agrcultural area by crop and number of anmals by type of anmal (126 dfferent crop and anmal actvtes are dstngushed) for every farm that apples for drect payments. Elgblty for drect payments s subject to certan condtons, one of whch s a mnmum economc sze of the farm (measured by turnover) n order to prevent hobby-farms from recevng subsdes. As a consequence, the total numbers of acreage and/or anmals may be somewhat underestmated when compared wth other offcal sources such as slaughter statstcs or the decennal total farm census. Indvduals and legal enttes managng agrcultural area or keepng anmals elgble for drect payments may apply for subsdes by fllng n data n the regster. The regster lnks the amount of acreage and anmals wth busness dentfcaton and property numbers. Addtonally, farmers socal securty numbers are avalable contanng the brth date. As the unt of analyss we rely on the property number. Property unts present n 1999, but not n 2009 are assumed to have left the sector. Some potental measurement errors arse from ths choce: We dsregard f farms splt ther actvtes n dfferent busness unts. Small farms may ncdentally have left the sector n 2009, but appled for subsdes n 2008 and Table 1 shows the number of farms covered n the database for the two measures mentoned above and compared to the number of farms recorded n other statstcs. Table 1: Number of farms for varous accountng measures Property number (NAA 2011) 66,892 45,460 Busness number (NAA 2011) 66,832 45,420 Number of farms (Statstcs Norway 2011) 70,740 47,688 Source: NAA 2011 and Statstcs Norway 2011 Table 1 reveals that there are small dfferences between the measures to dentfy farms. For all practcal purposes regardng the analyss, the number of propertes and the number of 10

12 busnesses appears to be the same. Further, the numbers are somewhat lower than the number of farms provded by the Statstcal Offce (Statstcs Norway) due to certan sze lmts regardng the elgblty of drect payments. 4 Emprcal model and estmaton The paper ams to explore the effects of own and neghborng drect payments on farm survval. Therefore, we estmated a spatal probt model where we consder the ext decson between 1999 and The model can be nterpreted as a latent utlty model wth the latent varable denoted as y. The latent varable determnes the outcome of the observed survval ( y 1 f y 0 ) or ext decson ( y 0 f y 0 ). In some sense t relates to the dfference between own and neghborng WTP for land dscussed n secton 2. To reflect these dfference and to estmated the effects of neghborng nteracton, y s specfed to be a lnear functon of own, X, and neghborng characterstcs, WX wth W beng a spatal weghtng matrx defned below. For estmaton two dfferent model specfcaton are consdered, a spatally lagged explanatory varable model (SLX) y = Xβ + WXθ + ε ~ N, 2 0 I (2) whch assumes d normal errors and a spatal Durbn error model (SDEM) y = Xβ + WXθ + u u Wu ε (3) whch relaxes the assumptons of the SLX model by allowng for spatally autocorrelated errors (LeSage and Pace 2011 p. 22). The SLX and SDEM specfcaton are chosen over the more common spatal autoregressve model (SAR) of the form y Wy Xβ ε, snce they allow greater flexblty wth respect to the drect and ndrect effects of explanatory varables. As shown by Pace and Zhu (2012), n the SAR model the ndrect effects have the same sgns as the drect 11

13 effects and the rato between ndrect and drects effects s constant across varables. Ths s an undesrable property for our purpose snce we expect n general the drect effects of own payments to dffer from the ndrect effects of neghborng payments (see secton 2). The SLX model s estmated usng standard probt maxmum lkelhood estmaton technques. We then test for spatal error dependence usng three dfferent test prncples approprated for probt models that are dscussed and compared n Amaral et al. (2012). Specfcally, two dfferent Lagrange Multpler test proposed by Pnkse and Slade (1998) and Pnkse (2004) as well as a test based on a generalzed verson of the Moran s I statstcs proposed by H. Kelejan and Prucha (2001) s appled. All three test statstcs are asymptotc 2 1 dstrbuted. The test statstcs are equal to 258.9, and 192.7, respectvely, and thus clearly lead to an rejecton of the H 0 -Hypothess of no spatal autocorrelaton. Snce autocorrelaton can lead to bas n the probt model the test results ndcate that the SDEM model whch consdered the spatal autocorrelaton n the errors mght be more approprated. Estmaton of a SDEM probt model for a sample of over 60,000 observatons, however, s challengng from a computatonal perspectve. Most exstng estmaton technques such as McMllen (1992), Beron and Vjverberg (2004) or LeSage (2000) are only applcable for relatvely small sample szes of a couple of thousand observatons (see Pace and LeSage 2011 for a more detaled comparson and a dscusson of the lmtatons wth respect to large samples). The major dfference between a standard probt model and a probt model wth spatally correlated errors (or the SLX and the SDEM model) s that the lkelhood functon s no longer based on unvarate truncated normal dstrbutons but, due to the dependence between observatons, becomes a multvarate truncated normal dstrbuton. Ths ncreases computatonal needs especally for large samples. Therefore, Pace and LeSage (2011) proposed a smulated maxmum lkelhood framework for probt models wth spatally autocorrelated errors capable of handlng large sample szes. Ther approach s based on the GHK (Geweke-Hajvasslou-Keen) algorthm to approxmate the ntractable multvarate ntegral of the multvarate truncated normal dstrbuton. The general dea of the GHK algorthm n ths context s to replace the jont multvarate truncated normal densty by a product of condtonal denstes. Ths product of condton denstes has a sequental order n the sense that each condtonal densty only depends on pror varables n the sequence. Usng specfc realzatons of the random varables allows calculatng the sequence of condtonal 12

14 denstes. By repeatng the calculaton R tmes, each tme wth a dfferent realzatons of the random varables, a numerc approxmaton of the multvarate truncated normal dstrbuton can be obtaned. One obstacle of the approach wth respect to large samples s that the number of operatons requred for the GHK algorthm depends on the number of non-zeros n the Cholesky lower trangular matrx of the covarance matrx 3. Pace and LeSage (2011) argued, however, that n most spatal applcaton each observaton mght only depend on a lmted number of neghbours such that the sparsty of the varance-covarance matrx can be exploted n order to reduce the computaton burden of the GHK sampler. They further propose to adopted the GHK algorthm to rely on a Cholesky decomposton of the precson matrx (.e. the nverse varance-covarance matrx) nstead of the varance-covarance matrx snce n many stuatons t has greater sparsty. In our specfc mplementaton for the SDEM model we also rely on the precson matrx beng equal to 4 I W I W. (4) As recommended by Pace and LeSage (2011) the sparsty of the precson matrx or varance-covarance matrx can be ncreases by an approprate orderng of the observatons. In our mplementaton we use the Matlab (Verson R2013a) buld n functon symamd() for an symmetrc approxmate mnmum degree permutaton appled to the precson matrx to reorder the observatons and to ncrease the sparsty of the precson matrx. For the GHK algorthm, we follow Pace and LeSage (2011) and employed a scrambled Halton sequences where we skpped the frst 1,000 values and used only every 101st value (Matlab default). For each lkelhood evaluaton we used R 15. Optmsaton s performed wth the Matlab 3 For a dense varance-covarance matrx there are n n 1 n non-zeros elements. 4 The varance-covarance matrx s gven byvar u wth 1 Beron and Vjverberg (2004 p ). I W, see for example 13

15 Optmzaton Toolbox usng a constrant maxmsaton solver wth an nteror-pont algorthm. Dervates are approxmated numercally usng forward dfferences. Wth our mplementaton t s possble to estmate the SDEM model wth 64,488 observatons n around 5.2h hours usng Matlab Parallel Computng Toolbox wth 12 workers on a Intel Xeon E (2 processors) where we allow to parallelze the R repettons of the GHK sampler. 5 The dependent varable n the analyss represents farm survval n 2009 of all farm actve n 1999 and s equal to one f a farm s stll actve n 2009, zero otherwse. We consder a farm as actve f at least one producton actvty s observed for the farm n the payment data base. Because of mssng observatons due to mergers of muncpaltes t was necessary to exclude 11 muncpaltes from the analyss 6. As explanatory varables we consder some that can be derved from the payment data base as well as from addtonal statstcs such as the 1999 farm census. As dscussed n secton 2, wth respect to the research objectve to explan farm ext, the most mportant varables of nterest are related to dfferent types of farm ncome such as the total ncome, the on-farm wage rate and changes n the on-farm wage. Of partcular nterest s the roll of drect payments n ths respect. In order to separate the nfluence of drect payments on farm survval we dvde farm ncome nto market returns and drect payments. It s mportant to note that what we call market returns also substantally depends on polcy decson snce market prces are strongly affected by admnstratve prces. Snce the actual market returns for each farm are unobserved we consder an average market return for each producton actvty. Therefore, market return rates are derved from the reference farms data collecton (NILF 2000 and NILF 2009). It contans nformaton of around 30 reference farms that are selected to represent the dversty of the Norwegan farm sector wth respect to sze, 5 Ths s lower as the speed reported n Pace and LeSage (2011), who clam to estmate a sample of sze n around 4 mn on a standard laptop computer wthout parallelzaton, but snce our focus s on a sngle estmaton no further mprovements of the mplementaton s pursued. 6 Muncpalty codes 529, 716, 718, 1154, 1214, 1418, 1514, 1569, 1572, 1576, and

16 specalzaton and locaton. Data s collected on an annual bass and each reference farm summarzes nformaton from several farms wthn the Norwegan farm data accountancy system, comparable to the EU s Farm Accountng Data Network (FADN), to mnmze farm specfc varatons. The reference farms are the bass for the annual negotatons for the adjustments of the market support and drect payments and thus are central n the desgn of Norwegan agrcultural polcy. Based on these reference farms nformaton about the market return per unt of producton actvty s derved. A full cost accountng s appled consderng fxed costs, deprecaton and captal costs. Labor costs are excluded n order to derve the return to labor. The derved per unt rates are then multpled by the producton actvty levels of each farm observed n the payments data base, resultng n the total market returns per farm. Due to data lmtatons t s not possble to dstngush market return rates wth respect to dfferent farm sze or locaton. It s thus lkely that the actual market return of a farm dffers from the derved average market return. Nevertheless, we expect that the derved measures provde an approprate approxmaton of the dfference n farms market return that arse due to dfferent producton programs. Due to these lmtatons all ncome measures based on the market returns needs to be nterpreted as the potental or expected ncome gven a farmer s producton program. In the followng we wll use the terms ncome or on-farm wage to descrbe ths expected ncome of a farm. The drect payments per farm are calculated usng actual payment rates and elgblty rules. Most of the payments are based on current levels for anmals and crops and dfferentated by regon and farm sze. Usng the observed producton actvtes n the payment data base and consderng the specfc regon and sze of a farm the drect payments can be calculated rather accurately for each farm. Total ncome s defned as the sum of total market returns and total drect payments. To derve farms on-farm wage rate, the average labor requrement s calculated for each farm based on ts actual producton program usng estmated labor nput use coeffcents. The potental wage rate of a partcular farm s than obtaned as the rato of total drect payments or total market returns over total labor requrement. Addtonally, we obtan a measure for the potental change n the on-farm wage rate f the farm would not have altered t sze or producton program. For the calculaton we keep the producton program constant to the 1999 level, even though we have observatons on the actual producton programs durng the perod. 15

17 The reasonng s that changes n the producton program mght already be the results of changes n ncome opportuntes that we am to measure. A more detaled descrpton of the way the varables are derved s provded n Storm and Mttenzwe (2013). As dscussed n secton 2 for a theoretcal perspectve t remans undeceve of whether the total ncome or the on-farm wage rate s more mportant for farmers WTP for land and hence farm survval. In the emprcal applcaton we thus nclude all the varable just dscussed, namely the total drect payments n 1999 (dpay99) and the total market return n 1999 (mreturn99) as a measure of total farm ncome as well as the drect payment and market return per labor requrement n 1999 (dpay99/reqlabo and mreturn99/reqlabo) und the change n the latter two (C.DPayLabo and C.mRetLabo), as measures of the on-farm wage rate. Addtonally total agrcultural area (area), total observed labor nput n 1999 (obslabo99) and estmated labor requrement for 1999 (reqlabo99) 7 are ncluded. These three varables together wth total ncome are all measures for the absolute sze of the farm and therefore postvely correlated (Table 2). Table 2: Correlaton coeffcents between dfferent measures of the absolute farm sze area obslabo99 reqlabo99 dpay99 area obslabo reqlabo dpay99 1 Source: Own calculaton. 7 See Storm and Mttenzwe (2013) for detaled nformaton about the estmaton of the labor requrements. 16

18 Table 3: Descrptve statstcs and defnton of varable codes (n=64488). Codes Unts Mean Medan Max. Mn. Std. Dev. Age of farm holder age year Farm area area daa* Agrcultural labor nput Estmated labor requrement Total drect payments obslabo hour reqlabo hour Dpay 1000 Nkr Total market return mret 1000 Nkr Rato observed over estmated labor requrment Rato leased area over total area Dummy f farm has mlk cows Dummy f farm has sheep Dummy f farm has poultry Dummy f farm has sows Tot. market ret. per labor req. n 1999 Tot. drect pay. per labor req. n 1999 Change n market returns per labor structure equal to 1999 Change n drect pay. per labor structure equal to 1999 * daa = 1/10 ha. laboobs/req rato landlease/tot rato hasmlk bnary hassheep bnary haspoultry bnary hassows bnary mretrun/ reqlabo dpay/ reqlabo 1000 Nkr/hour 1000 Nkr/hour C.mRetLabo 1000 Nkr/hour C.DPayLabo 1000 Nkr/hour

19 Further, n lne wth the dscusson n secton 2 the age of the farm holder 8 (age), a rato of leased to total agrcultural area (landlease/tot) and a rato between observed labor nput and estmated labor requrements (laboobs/req) as a measure of farm productvty s ncluded. As a rough measure to reflect specalzaton specfc polcy envronments dummy varables for ndcatng f a farm has mlk cows (hasmlk), sheep (hassheep), sows (hassows) or poultry (haspoultry) are consdered. Descrptve statstcs of all explanatory varables along wth ther varable codes, are provded n Table 3. In the regresson analyss all varables are z-standardzed by subtractng the mean and dvdng by the standard error. A requrement for the estmaton of model (2) and (3) s to specfy a spatal weghtng matrx W. The spatal weghtng matrx should be constructed n order to closely approxmate the neghborng relatons between farms. Ths task s challengng n general and n partcular for the background of the heterogeneous farmng regons n Norway, varyng from small scale berry producton areas wth hgh farm densty to extensve sheep grazng regons wth low farm densty per unt area. We also expect that neghborng relatons and the sze of the local land market to dffer between regons. In rather dense regons the dstance between farms and the felds farmers compete for are lkely smaller than n regons wth only few farms. From the 1999 farm census, data about the drvng dstance to the furthest feld s avalable and can be lnked to the payment data base. We expect that these data carres some nformaton about the regonal structure of the farm sector, the dstances farmers are wllng to travel and hence the dstance over whch farms compete for land. Usng ths data the medan drvng dstance to the furthest feld n each muncpalty s calculated. The medan s used n order to elmnate the nfluence of potental outler and zero observatons that cannot be dstngushed from mssng observatons. Neghbors of a farm are then defned as all farms that are wthn a radus of ths medan muncpalty drvng dstance. Addtonally, the maxmum number of neghbors s set to 20 (nearest neghbors) n order to prevent farms from havng an unrealstcally large number of neghbors. Fnally, the farms 8 For observatons where age s mssng n the data base we mputed the mean age. The age s mssng for example for all farms where the owner s not a natural person. In total we have 495 or 0.77% mssng observatons for age. 18

20 dentfed as neghbors are weghted by ther nverse dstance, gvng nearer neghbors a larger weght compared to neghbors further away. One common crtcsm of spatal regresson models s that the neghborng relatons are defned n a rather arbtrary fashon and do not necessarly represent the true neghborng relaton between farms. Even though we base our defnton of the neghborng relatonshps on emprcal data ths crtcsm remans vald. However, as ponted out by LeSage and Pace (2011), n most cases the results of spatal regresson models are less senstve to the defnton of the spatal weghtng matrx as commonly beleved. In order to explore the senstvty of our results to the defnton of the spatal weghtng matrx we repeat estmaton of the SLX model usng two alternatve defntons of neghborng relatonshps: Frst all farms wthn a fxed radus of 2km are consdered as neghbors and, secondly, the 5 nearest farms are consdered as neghbors. As can be seen n appendx A-1), the results are largely unaffected by the defnton of the neghborng relatons. 5 Regresson results In the followng the results for a model wth and wthout the spatal nteractons are presented. Dstngushng between the two models allows us to hghlght how the concluson regardng the effects of drect payments changes when gnorng spatal nteractons. The regresson results for the non-spatal model as well as the results for the spatal model usng the SLX and SDEM model specfcaton are reported n Table 6. It can be seen that the coeffcents wth respect to the non-spatally lagged varables dffer only slghtly between the three specfcatons. Ths allows us to dscuss the non-spatal results frst and to hghlght the dfferences wth respect to the spatal model n the followng. The non-spatal regresson results are presented n the left part of Table 6. Except for the market return and ts squared term, the dummy varable ndcatng f a farm has poultry (haspoultry) and the squared term of the estmated labor requrement (reqlabo99^2) all explanatory varables are hghly sgnfcant. The nsgnfcant squared terms where dropped n from the model specfcaton. Statstcal sgnfcance s comparatvely easy acheved wth more than 60,000 observatons, but says lttle regardng relevance. A measure of the explanatory power of the overall model s the percentage of correctly predctng the bnary choce. Wth the non-spatal model we are able to correctly predct the ext/survval decson 19

21 n 72.64% of the cases. Compared to the nave model, whch correctly predcts survval n 62.72% of the cases, ths s a total gan of 9.93 percentage ponts. Table 4: Percentage of correct predctons of farm survval between 1999 and 2009 wth dfferent model specfcaton of the non-spatal bnary choce probt model wth respect to the absolute sze of a farm. Nave All other non-spatal explanatory varables Full Model and Area and obs. Labor and est.req Labor and drect payments % Correct Dff. to full M Source: Own estmaton. To assess the explanatory power of ndvdual varables, we can explore how the percentage of correct predcton changes wth or wthout the varable under consderaton. Overall we found that the varables related to farm sze (area, obslabo99, reqlabo99, and dpay99) are most mportant explanng farmers ext/survval decson (Table 4) wth a postve relatonshp between farm sze and survval. A model wth all explanatory varables except these varables related to the absolute sze would correctly predct farm ext/survval n 67.58% of the cases whch s 4.86 percentage ponts more than the nave model and 5.01 percentage ponts less than the full model. Further, t s nterestng to note that all varables related to the absolute sze can explan more or less the same snce the percentage of correct predcton wth only one of the four varables s only slghtly lower as the percentage of correct predcton wth all four varables (Table 4). The mportance of the remanng varables s relatvely evenly dstrbuted wth each varable addng only lttle to the overall explanatory power of the model. Of specfc nterest s the mportance of the on-farm wage rate (mreturn99/reqlabo and dpay99/reqlabo) n 1999 and the change n on-farm wage rate from 1999 to 2009 (C.DPayLabo and C.mRetLabo). Both have a postve nfluence on farm survval but, ndvdually and together, add only a lttle to the overall explanatory power of the model (Table 5). 20

22 Table 5: Percentage of correct predctons of farm survval between 1999 and 2009 wth dfferent model specfcaton of the bnary choce probt model wth respect on-farm wage and changes n the on-farm wage Nave All non-spatal explanatory varables except Full Model on-farm wage changes n on-farm wage on-farm wage and changes n on-farm wage % Correct Dff. to full M Source: Own estmaton. Taken together the results ndcate that the absolute sze of a farm s more mportant than the on-farm wage rate per hour or changes n ths on-farm wage rate. As dscussed n secton 2 ths mght hnd to potental mperfectons on the labor market whch render the potental onfarm ncome per person or famly, as approxmated by the absolute sze of a farm, as more mportant than the on-farm wage rate per hour. It s useful to analyze the effects of the absolute sze and n partcular the effects of drect payments on survval n more detal. Overall, all varables related to the absolute sze of a farm show a postve nfluence (some wth decreasng rate) between farm sze and survval. To llustrate the relatonshp for drect payments, the survval probablty s calculated based on the non-spatal regresson results for an average farm, keepng all other explanatory varables fxed at ther means and vary only the total amount of drect payments. Fgure 2 shows that drect payments have a larger effect for relatvely small farms whch s levelng out for larger farms. Ths ndcates, as mentoned above, that farms need to have a suffcent sze to provde for the famly. Beyond that sze, addtonal drect payments do not much ncrease the probablty of survval anymore. 21

23 Fgure 2: Probablty for an average farm to stay actve between 1999 and 2009 for varyng total drect payments. The x-axs represents the 2.5% to 97.5% quntle of the observed total drect payments. Source: Own calculaton. From a polcy perspectve we could draw the concluson from the non-spatal fndngs that ncreasng drect payments would be one approach to ncrease the survval probablty of farms whch do not have a suffcent ncome potental wthout them. In the followng we explore how ths concluson s affected when consderng spatal nteracton between farms. The spatal regresson results for the SLX and SDEM model are reported n the rght part of Table 6. For model specfcaton we ncluded all varables, except the squared terms, as spatally lagged varables 9. The regresson results for the SLX and SDEM model almost 9 Snce the spatally lagged varables show less varaton we summarze varables that are hghly correlated and measure related aspects. Specfcally, the two varables for the on-farm wage rate mreturn99/reqlabo and dpay99/reqlabo are summarzed to one varable W_FarmWage99. Smlarly, the two varables for the change n on-farm wage rate C.DPayLabo and C.mRetLabo are summarzed to one varable W_C.nco99. The spatally lagged observed labor nput s excluded from the model specfcaton because of a hgh correlaton to the estmated 22

24 dentcal even so we found sgnfcant spatally autocorrelated errors wth a 0.12 n the SDEM model. Ths fndng mples that gnorng the spatally autocorrelaton n the errors, as ndcated by the sgnfcant n the SDEM model and the test performed n secton 4, does not result n a substantal bas of the SLX model estmates. The results wth respect to the non-spatal varables dscussed before stays almost unaffected ndcatng the non-spatal results are robust wth respect to the ncluson of spatal lagged explanatory varables. Overall the ncluson of the spatal lagged varables mproves the percentage of correct predcton only slghtly ndcatng that they have only lttle explanatory power for farmer s survval decson. Also the mportance of dfferent varables stays unaffected such that the fndngs dscussed for the non-spatal model smlarly hold for the spatal model. Nevertheless, wth respect to answerng our research queston consderng the spatal effects s crucal. For the non-spatal fndngs we concluded that the absolute sze of a farm s the most mportant factor n explanng farmer s survval decson and that, for the relevant range, the larger the absolute sze the hgher the survval probablty, rrespectve of how the absolute sze s measured. Ths result also apples for the spatal model but the effect of the absolute sze of neghborng farms s somewhat more complcated. When consderng only one spatally lagged varable for the absolute sze, we found a negatve nfluence between neghborng sze and own survval rrespectvely whch varable (w_dpay99, w_uaar or w_laboreq99) s used to measure the absolute sze. As dscussed above all three measures of the absolute sze of the farm are hghly correlated and the same holds for the spatally lagged absolute sze measures. Nevertheless, the large sample sze s suffcent to anyway dentfy dfferent coeffcents on the three varables (Table 6). Farms wth larger neghbors n terms of area and labor use havng a hgher survval probablty whle farms wth larger neghbors n terms of total drect payments havng a lower survval probablty. labor requrement that does not allow dentfyng both varables. The general model results and conclusons, however, are unaffected by the choce of whch to exclude from the model. 23

25 Table 6: Regresson results for the non-spatal probt, SLX and SDEM model to explanng farm survval. The dependent varable s equal to one f the farm stays actve between 1999 and 2009 and zero otherwse. Spatally lagged varables are denoted wth a leadng W_. Non-spatal probt SLX SDEM Varable Coef p-value Coef p-value Coef p-value const age age^ area area^ obslabo obslabo^ reqlabo mret dpay dpay^ laboobs/req landlease/tot mretrun/reqlabo dpay/reqlabo C.DPayLabo C.mRetLabo hasmlk haspoultry hassheep hassows W_mRet W_dpay W_area W_reqLabo W_landLease/Tot W_FarmWage W_C.nco W_hasMlk W_hasPoultry W_hasSheep W_hasSows rho n % Correct predctons Model % Correct predctons Nave Total Gan* *Change n "% Correct" compared to nave specfcaton. As dscussed n secton 2 a reason for ths fndng could be the multple ways farm nteract whch each other. On the one hand farms gan from an actve farmng neghborhood and cooperatve network due to technology dffuson or easer accesses to supplers or 24