Centre for Efficiency and Productivity Analysis

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1 Centre for Effcency and Productvty Analyss Workng Paper Seres No. WP03/2009 Ttle MEASUREMENT OF AGRICULTURAL TOTAL FACTOR PRODUCTIVITY GROWTH INCORPORATING ENVIRONMENTAL FACTORS: A NUTRIENTS BALANCE APPROACH Authors Vet-Ngu Hoang and Tm Coell Date: School of Economcs Unversty of Queensland St. Luca, Qld Australa ISSN No

2 MEASUREMENT OF AGRICULTURAL TOTAL FACTOR PRODUCTIVITY GROWTH INCORPORATING ENVIRONMENTAL FACTORS: A NUTRIENTS BALANCE APPROACH by Vet-Ngu Hoang 1 and Tm Coell School of Economcs The Unversty of Queensland St Luca, 4072, Queensland, Australa 23/5/ Emal contact: v.hoang@uq.edu.au

3 Abstract Ths paper develops a new measure of total factor productvty growth n agrcultural producton whch ncorporates envronmental effects. The new measure s called the Nutrent-orented total factor Productvty (NTFP) Index, and ncorporates a materals balance condton. NTFP measures changes n nutrent-orentated effcency and can be decomposed nto effcency change (EC), technologcal change (TC) and nutrent-orentated allocatve effcency change (NAEC) components. An emprcal analyss, nvolvng country-level data from OECD countres durng , s provded usng DEA methods. Estmates of mean techncal and nutrentorentated effcency are and 0.526, respectvely. Estmated mean NTFP growth s 1.5% per year, wth nutrent-orentated technologcal progress contrbutng 0.8%. Keywords: Total factor productvty, envronment, nutrent balance, DEA 2

4 1. Introducton Durng the past three decades, the envronmental sde effects of economc actvtes have receved ncreasng attenton n publc and poltcal debate. Ths rases the need to adjust tradtonal methods of measurng effcency and productvty n order to take nto account envronmental effects. Sgnfcant efforts have been made to ntegrate envronmental concerns nto tradtonal techncal and economc performance measures (Scheel 2001; Tyteca 1996). Generally, these envronmental performance measures are derved by makng adjustments to standard parametrc and non-parametrc effcency and productvty analyss technques (Coell, et al. 2007). The tradtonal approach that the majorty of these studes have taken s that the envronmental effect s modeled as ether a bad output or an envronmentally detrmental nput n producton models (e.g. Ball, et al. 1994; Färe, et al. 1989; Renhard, et al. 2000; Shak and Perrn 2001; Tyteca 1997). These methods, however, face two crtcsms. Frst, they fal to allow for both ncreasng desrable output and reducng undesrable output at the same tme (Chung, et al. 1997). Secondly, Coell, et al. (2007) shows that these methods often do not satsfy the materals balance condton. Chung, et al. (1997) proposed the use of a drectonal dstance functon whch allows for smultaneous expanson of desrable output and contracton of undesrable output. Whle ths method overcomes the frst crtcsm, ths approach also fals to satsfy the materals balance condton, whch we show later n ths paper. Recently, Coell, et al. (2007) suggested the use of an alternatve modelng approach that uses the materals balance condton n dervng an envronmental effcency measure 2. They consder the stuaton where the envronmental polluton s caused by the balance of nutrents, equal to the dfference between nutrents n nputs and nutrents n outputs. In order to reduce polluton, one could reduce the nutrents balance by, for example, reducng the nutrent amount contaned n the nput vector. Compared wth the tradtonal approach, ths method does not nvolve the ntroducton of any extra varables nto the producton model and satsfes the materals balance condton. 2 Lauwers et al (1999) and Renhard and Thjssen (2000) also proposed effcency measurement methods that ncorporated the use of the materals balance condton. The former study estmated effcency scores usng DEA technque whle the latter study nvolved the econometrc estmaton of a shadow cost system. 3

5 In ther study, the materals contents of nputs s treated n an analogous way to the way n whch nput prces are used n a standard cost effcency calculaton, and hence exstng parametrc and non-parametrc technques can be used to estmate the effcency scores. Gven a fxed output vector, the envronmental effcency s defned as the rato of the smallest techncally feasble nutrent balance over the observed nutrent balance. The envronmental effcency can also be decomposed nto techncal effcency (TE) and allocatve effcency (AE) components. In ths paper, we use ths nutrents balance approach to measure the envronmental effcency of the natonal agrcultural sectors n OECD member countres n terms of both ntrogen and phosphorous balance. We term ths envronmental effcency measure as nutrent-orentated effcency (NE) whch s then decomposed nto TE and nutrent-orented allocatve effcency (NAE). We also construct a nutrent-orented total factor productvty (NTFP) ndex. Ths ndex s an envronmentally adjusted Malmqust productvty ndex whch ncorporates the tradtonal total factor productvty (TFP) nformaton along wth envronmental factors. The paper s structured as follows. Lterature on the nutrents balance approach and exstng methods of measurng envronmental performance s revewed n Secton 2. The development of the nutrent-orented total factor productvty (NTFP) ndex s presented n Secton 3. The emprcal analyss of agrculture n OECD member countres for the years of s dscussed n Secton 4, followed by concludng comments n Secton The nutrents balance approach and exstng methods The nutrents balance condton n agrcultural producton The nutrents balance condton s a partcular form of a materals balance condton whch s ruled by the law of mass conservaton or the frst law of thermodynamcs (Daly 1987). Ths law states that the materals n a producton system are not lost and that materal nputs end up n ether stock accumulaton or materal outputs. In other words, the materal nputs are transformed nto desrable and undesrable outputs. Ths law has been used wdely for the purposes of economc analyses (Daly 1987; 1992; Georgescu-Roegen 1971; Kneese, et al. 1970) and especally n agrcultural producton (Coell, et al. 2007; Hartmann, et al. 2007; Parrs 1998; Renhard, et al. 1999; Renhard and Thjssen 2000). 4

6 In agrcultural producton, economc agents (.e. farmers) use many dfferent nputs whch contan a varety of nutrents (e.g. ntrogen, phosphorous and sulphur) to produce crop and lvestock products. These nutrents are needed for crop and lvestock producton. They are present n varous nputs such as feed, seed, plantng materal, fertlzers, purchased anmals, manure, sol, underground water, and even n ar. The materals balance condton mples that the balance of nutrents equals the nutrent nput mnus the nutrent output. If the nutrent balance s postve, t goes nto the envronment through land, ar or water and (potentally) causes polluton. As part of an ecosystem, agrcultural producton actvtes are regulated by the law of mass conversaton, mplyng that the nutrents balance condton holds true. Ths suggests that measures of effcency and productvty growth n agrcultural producton have to satsfy the test of the materals balance condton. Methods of measurng envronmental performance Hstorcally, undesrable outputs have often been gnored n producton economcs. However, recently there has developed a growng lterature proposng dfferent ndcators lnkng envronmental and economc performance of producton actvtes. Tyteca (1996) provdes a detaled lterature revew of the dfferent methods that have been used to measure envronmental performance of organzatons. Hs paper rased a varety of ssues relatng to the development of envronmental performance ndcators, ncludng concerns about aggregaton, normalzaton, standardzaton and accountng. The author also stresses the potental usefulness of the effcency measurement lterature n dealng wth these ssues. Pttman (1983) was one of the frst to attempt to ncorporate polluton nto conventonal productvty measures. He proposed an ndex number methodology that was derved from a theoretcal model where the objectve was the maxmal radal expanson of desrable outputs and contracton of undesrable outputs, holdng the nput vector constant. Färe, et al. (1989) used non-lnear programmng technques to construct hyperbolc effcency measures allowng for the expanson of desrable output and the reducton of polluton as an envronmental detrmental nput at the same tme. Ths approach was used by Yasawarng and Klen (1994) and Tyteca (1997) n ndustral applcatons. Färe, et al. (1993) extended the work by Färe, et al. (1989) usng parametrc output dstance functons to permt easer measurement of the shadow prces of the bad outputs. 5

7 Färe, et al. (1996) proposed an nput dstance functon approach that could be used to decompose productve effcency nto nput effcency and envronmental effcency. More recently, Chung, et al. (1997) have used a drectonal dstance functon to estmate envronmental effcency and productvty measures. In Färe, et al. (1996), for each frm two nput-orentated DEA models were run. The frst model allowed for the conventonal proportonal contracton of all nputs gven the level of desrable and undesrable outputs, wth strong dsposablty assumed for all varables. The second model dd the same thng, except t mposed weak dsposablty on undesrable outputs. The envronmental ndcator was then defned as the rato of the effcency scores obtaned n the frst and second models. Tyteca (1997) then further adapted the Färe, et al. (1989) to derve envronmental effcency scores by measurng the degree to whch the polluton varable could be reduced gven the fxed levels of nputs and desrable outputs. In contrast to an output dstance functon whch seeks to ncrease both desrable and undesrable outputs smultaneously, Chung, et al. (1997) proposed the use of a drectonal dstance functon whch seeks to ncrease desrable output and reduce undesrable output at the same tme. The authors suggested scalng the output vectors accordng to a vector of drectons whch could be flexbly selected. The drecton vector they proposed was to ncrease desrable outputs and decrease undesrable outputs, n a manner proportonal to the observed values for that frm. The paper also llustrated how one could decompose a total factor productvty change measure (that ncludes undesrable outputs) nto effcency change and techncal change. In an agrcultural example, Renhard, et al. (2000) studed the effects of ntrogen polluton on dary farms n the Netherlands. The ntrogen balance calculated usng the materals balance equaton was the polluton varable of nterest. Ths polluton varable was modeled as the envronmental detrmental nput varable n the producton functon. The frst model nvolved the contracton of the polluton varable holdng the conventonal nputs and outputs constant. The second model allowed for the radal expanson of the outputs wth the both the conventonal nputs and polluton varable held constant. The thrd model was the nput-orentated verson of the second model, whch scaled down the conventonal and polluton nput varables gven the fxed level of outputs. These three models produced three types of effcency scores: an envronmental effcency score, an output-orentated techncal effcency (TE) score and an nput-orentated TE scores. 6

8 Satsfacton of the materals balance condton Coell, et al. (2007) show that most of effcency measures descrbed above do not satsfy the materals balance condton. Ths was done for groups of envronmental effcency measures whch are based on nput or output dstance functons (.e. Färe, et al. 1989); Färe, et al. (1996); Renhard, et al. (2000)). In the followng secton we also show that the drectonal dstance functon proposed by Chung, et al. (1997) also fals to satsfy ths condton. We frst defne some notaton. Consder the stuaton where there s a frm that produces a vector of m = 1,2,...M outputs, M q R + usng a vector of k = 1,2,...K nputs, K x R +. The producton actvty also produces emsson of possbly pollutng substances as a by-product. The amount of emsson s defned by the nutrents balance condton z = ax bq (1) where a and b are vectors of known non-negatve constants. Followng Coell, et al. (2007), we allow the possblty that some of nputs could have zero amounts of the nutrents of nterest, for example labour and machnery. Chung, et al. (1997) defne the producton technology by the output set n whch nput vector x s used to produce good output q and undesrable output u : P( x ) = {( q, u) : x can produce ( q, u)} (2) The authors defne the drectonal dstance functon D( x, q,u,g) = sup{ β : ( q, u) + βg P( x)} (3) where g s the vector of drectons n whch good output s ncreased and undesrable output s decreased. The drectonal dstance functon of Chung, et al. (1997) s llustrated n Fgure 1, where we depct the smple case of one desrable output and one undesrable output. The producton fronter s defned by the lne 0Y, whch corresponds to a partcular quantty of nput. The drecton vector g=(-u,q) s used to project pont A (the observed data pont for frm A) to pont 7

9 B (whch s techncally effcent). Ths nvolves expandng the desrable output (q) and contractng undesrable output (u). From the dagram, t can be shown that q q 2 1 = β and hence u u 2 1 = 2 β. 3 The materals balance condton appled n ths model ndcates that at ponts A and B, respectvely, we have 4 u = ax bβq (4) and (2 β )u = ax bβq. (5) Then combnng (4) and (5) we obtan ( ax 2bq)( β 1) = 0. (6) 1Equaton (6) has two solutons: β = and ax = 2bq. The frst soluton ( β = 1) means that only effcent frms satsfy both the drectonal dstance functon measure and the materals balance condton (.e. any nteror pont n the producton technology such as pont A n Fgure 1 s not feasble). The second soluton ndcates that the amount of nutrent n the nput vector must always be exactly equal to double the amount n the output vector. Nether of these solutons are a desrable feature of a drectonal dstance functon. 3 Ths s because BC q q 0D q tg α = = and tgα = = CA u u DE u ths gves u2 q2 = 2 = 2 β u q gve q2 q1 u u 1 2 q1 =. After some arrangement, u 1 4 Note that z=u n ths case. 8

10 q g=(-u 1,q 1 ) q 2 B Y E α q 1 D C A -u 1 0 u 2 u 1 u Fgure 1: Drectonal dstance functon wth drecton vector g=(-u,q) 3. Nutrent-orentated effcency and productvty measures Coell, et al. (2007) utlse an alternatve envronmental effcency measure that nvolves the ncorporaton of the materals balance condton nto the producton model. In these models, the desrable output vector was fxed and undesrable outputs were vewed as the net balance of nutrent content as defned n (1). Whenq s fxed, the surplus balance s mnmzed when the aggregate nput nutrent content ( N = a' x ) s mnmzed 5. In ths method, nstead of mnmzng nputs, they mnmzed the aggregate contents contaned n the nput vectors. Ths s done on the grounds that a frm s more envronmentally effcent f t produces a lower nutrent balance. N( q, a) = mn{ a' x x, q P} where P s the output set (7) x The nput vector that contans the mnmum nutrent content s donated nutrent content equals to N denoted e = a' x e x e and the mnmum. The nutrent content at the observed nput vector s N = a' x. The techncally effcent nput vector s denoted by x t. These three nput vectors are llustrated n Fgure 2, for the smple case where there are two nput varables. The slopes of the so-nutrent lnes reflect the ratos of nutrent contents of the 5 Ths excludes the case where the nutrent balance s negatve. The realty s that there s the postve balance of nutrents used n agrcultural producton. The postve balance goes to the envronment and makes the envronment polluted. A postve balance s denoted as surplus. 9

11 two nputs. The ntercepts of these lnes represent the total amount of nutrent (N) contaned n the nput vectors x, x e, x t. The so-nutrent lne passng through the observed pont (x 1,x 2 ) has a larger ntercept than the lne passng through the techncally effcent pont (x 1t,x 2t ). Smlarly the so-nutrent lne passng through the techncal effcent pont has an ntercept that s larger than the lne passng through the nutrent mnmsng pont (x 1e,x 2e ). x 1 soquant (x 1,, x 2, ) (x 1t,, x 2t, ) (x 1e,, x 2e, ) so-nutrent lne a'x so-nutrent lne a'x t so-nutrent lne a'x x 2 Fgure 2: Nutrent mnmsaton Next, we defne nutrent-orentated effcency (NE), techncal effcency (TE) and nutrentorentated allocatve effcency (NAE). TE( q, x) = mn{ θ θx, q θ Y }, (8) where θ s a scalar takng a value between zero and one. The optmzaton problem. nput vector and hence Nt = a' x t x t s the soluton to ths s defned as the nutrent content at the techncally effcent Nt. TE = N = a'x t a'x =θ (9) Followng Coell, et al. (2007), the nutrent-orentated effcency measure (NE) of a frm s defned as the rato of the mnmum nutrent content over the observed nutrent content: 10

12 N a' x NE e = e =. (10) N a' x NE then can be decomposed nto techncal effcency (TE) and nutrent-orentated allocatve effcency (NAE): NE = TE x NAE, (11) where N N a' x a' x e e NAE = =. (12) t t TE relates to the operaton of the frm on the fronter of the producton technology (.e. the producton possblty curve) whle NAE relates to usng the correct nput mx gven the observed nutrent contents. All three effcency measures take values between zero and one. The value of unty ndcates full effcency whle less than unty mples neffcency. As noted n Coell, et al. (2007), NE can be estmated followng a procedure smlar to estmatng cost effcency n whch the vector of nutrent contents of the nputs (a) s used nstead of prces. There are some advantages of usng ths nutrent-orentated effcency measure. Frst, n the settng of dstance functons and fronter functons (.e. revenue, cost or proft functons), ths approach allows the estmaton of shadow prces of nutrent reducton and the estmaton of effects on nutrent reducton by polcy changes (e.g. taxaton). Ths was dscussed n Coell, et al. (2007). The second advantage s that these nutrent-orentated effcency and productvty measures are applcable to the analyss of both ndvdual nutrent flow and aggregate flow of varous nutrents. In agrcultural producton, for example, there are concerns on the balances of varous thngs, such as ntrogen, potassum, phosphorous, sulphur and carbon. Ths approach can quantfy envronmental effcency and productvty measures by applyng the materals balance condton to the balance of dfferent ndvdual nutrents or to the aggregate balance of all these nutrents. The aggregate balance of dfferent nutrents needs a choce of weghtngs for dfferent nutrents. 11

13 Coell, et al. (2007) dscussed the case when there are two nutrents, whch requred two materal balance equatons. If there are two nputs and one output, the equatons are: z = a x + a x b q (13) and z = a x + a x b q. (14) If the chosen weghts are v 1 and v 2, the aggregate balance equaton becomes v z + v z = v a + v a ) x + ( v a + v a ) x ( v b v b ) q (15) ( and the method proceeds normally. For example, a natonal agrcultural system uses dfferent types of energy, feed, fertlzer, pestcdes and seed n ts producton and pollutes NO x, PO x, SO x or CO x to the envronment. The materals balance equaton n (15) can be used to estmate the aggregate balance of materals gven a partcular choce of weghts for the dfferent materals. The thrd desrable feature of ths approach s that t avods the potental correlaton between the undesrable outputs and conventonal nputs n emprcal studes. For example, one mght want to compare the envronmental performance of crop farms whch produce ntrogen to the envronment. The producton model can have ntrogen as an undesrable output whle fertlzer as an nput. Statstcal data for ntrogen s normally estmated by usng the formula (fertlzer) (ntrogen content factor). Consequently, multcollnearty s a potental problem n ths model. Ths problem, however, s not present n the materals balance condton approach because n (2) there s no undesrable output vector. Snce the surplus balance of nutrents causes polluton, some countres (especally OECD member countres) have started regulatng the use of nutrents n agrcultural producton. One of the most common envronmental polces nvolves the regulaton of the lmt of emsson that the farmer can pollute to the envronment (Dowd, et al. 2008; Nam, et al. 2007; Pretty, et al. 2001; Sterner and Kohln 2003). Under ths regulaton, farmers are taxed or leved on the nutrent balance whch exceeds a specfed lmt. One example of ths regulaton framework s 12

14 the Mneral Accountng System (MINAS) whch montors the nutrent balance of farms n the Netherlands (Van Der Brandt and Smt 1998). Under such an envronmental regulaton system, the farmers operate under a nutrent balance constrant. Applyng the nutrents balance condton equaton n (1), one can separate two dfferent types of nutrent constrants restrctng the behavour of the farmers: (a) gven that the output vector s fxed, the lmt on the nutrents balance means that the farmers operaton s restrcted by the maxmum level of nutrents n nput and (b) gven that the nput vector s fxed, the lmt on nutrents balance suggests that the farmers are requred to acheve the target of mnmum total quantty of nutrents n output. These two types of nutrent constrants however can be modeled n a smlar manner to the modelng of frms operatng under a cost budget restrcton and revenue target restrcton. Färe and Grosskopf (1994) provde technques to measure effcency and productvty performance of the farmers usng cost- and revenuendrect technologes. The applcaton of these prce-based technques to nutrent-based problems could be an nterestng area of future research. Nutrent-orented total factor productvty In ths secton, we use the nutrent-orentated effcency measure to construct a Nutrentorented Total Factor Productvty (NTFP) ndex. Ths ndex bulds upon the concept of the nput-orentated Malmqust TFP ndex frst proposed by Caves, et al. (1982a; b). The ndex s constructed by measurng the radal dstance of the observed output and nput vectors n perod t and t+s relatve to two reference technologes: technology n perod t and technology n perod t+s. Frst, usng technology n perod t as a reference technology, the Malmqust nutrent-orentated TFP ndex for perod t and t+s s defned as changes n the nutrent-orentated effcency n perod t+s over perod t: M t NE =, (16) NE t,t+ s t,t where the frst and second superscrpts refer to the reference technology and tme perod respectvely. The subscrpts refers to the nput-orentaton. For example, t,t s NE + refers to the envronmental effcency score calculated usng the observed data for a frm operatng n tme 13

15 perod t+s relatve to the reference technology from tme perod t, usng an nput-orented framework. Smlarly, usng the technology n perod t+s as a reference technology, a Malmqust nutrentorentated TFP ndex may be defned as: NE = (17) t+ s,t+ s t+ s M t+ s,t NE Our NTFP change ndex (NTFPC) s then defned as the geometrc mean of the two prevous ndces: NTFPC NE t,t+ s t+ s,t+ s t,t+ s = t,t t+ s,t NE NE NE 1/ 2 (18) All NEs n are defned as follows: t,t t,t t,t t,t a' x e a' x e a' x t t,t NE = = = NAE TE t,t t,t t, t a' x a' x a' x t t,t. (19) t,t NE can be estmated n a nutrent nput-orented framework (e.g. by a cost-mnmzng DEA) and t,t TE s estmated n a standard nput-orentated framework gven a nput vector x t,t of tme t t correspondng to a specfed output level ofq at tme t. NE t + s,t + s a' x a' x a' x = a' x a' x a' x t + s,t + s t + s,t + s t + s,t + s e e t = t + s,t + s t + s,t + s t + s,t + s t = NAE t + s,t + s TE t + s,t + s (20) t + s,t + s NE s estmated n a nutrent nput-orentated framework and t + s,t + s TE s estmated n a standard nput-orentated framework gven a nput vector specfed output level of t + s q at tme t+s. x t + s,t + s at tme t+s correspondng a NE t,t + s a' x a' x a' x t,t + s t,t + s t,t + s e e t = = t,t + s t,t + s t,t + s a' x a' x t a' x = NAE t,t + s TE t,t + s (21) 14

16 t,t NE + s s estmated n a nutrent nput-orentated framework and t,t s TE + s estmated n a standard nput-orentated framework gven a nput vector t specfed output level ofq at tme t. x t, t + s of tme t+s correspondng a NE t + s,t a' x a' x a' x t + s,t t + s,t t + s,t e e t = = t + s,t t + s,t t + s, t a' x a' x t a' x = NAE t + s,t TE t + s,t (22) t NE + s,t s estmated n a nutrent nput-orentated framework and t TE + s,t s estmated n a standard nput-orentated framework gven a nput vector specfed output level ofq t+ s at tme t+s. t +s,t x of tme t correspondng a Followng Caves, et al. (1982a; b), the standard nput orented Malmqust TFP ndex s defned as TFPC TE t,t+ s t+ s,t+ s = t,t t+ s,t TE TE TE 1/ 2, (23) whch can be decomposed nto 1/ 2 t+s,t+ s t,t t,t+ s TE TE TE = = t,t t+s,t t+ s,t+s TE TE TE TFPC TEC TC, (24) where TEC s techncal effcency change and TC s the geometrc mean of two techncal change ndces, evaluated at the perod t and perod t+s data ponts, respectvely. Thus, usng equatons 18 to 24, we have NTFPC NAE NAE = t,t+ s t+ s,t+ s TFPC t,t t+ s,t NAE NAE 1/2 (25) and hence t,t + s t + s,t + s NAE NAE NTFPC = TEC TC TEC t,t st,t = TC NAEC + NAE NAE 1/2 (26) 15

17 Techncal effcency change (TEC) refers to changes n techncal effcency of the observed unt aganst the techncally effcent unt; techncal change (TC) refers to the shft of the techncally effcent fronter; and nutrent-orentated allocatve effcency change (NAEC) measures the effect of allocatve decsons on envronmental performance. 4. OECD Applcaton The OECD has recently released a report on the envronmental effects of agrculture of ts member countres for the years from 1990 to 2004 (OECD 2008). Ths report was the latest output from the broader project of establshng envronmental ndcators for agrculture whch began before The unque feature of ths report s that t brngs together the most up to date comparatve data on the envronmental performance of agrculture n OECD countres. One of the man ponts of dscusson n ths report relates to the estmaton of gross ntrogen and phosphorous balances of member countres over the survey perod. In our study we utlze the data provded by ths project to estmate the envronmental performance of these member countres by constructng nutrent-orentated effcency and productvty measures. The scope of ths paper focuses on both the ntrogen and phosphorous balance. In terms of the eutrophcaton effects, the choce of weghts s straghtforward n ths case: the eutrophyng power of phosphorous s known to be ten tmes more than that of ntrogen (Coell et al. 2007). The boundary of natonal agrcultural producton system Fgure 3 provdes a dagrammatcal representaton of the boundary and the flow of ntrogen n a natonal agrcultural producton system. Ths fgure s extracted from Hoang and Alauddn (2009) whch s a modfed verson of the farm gate method of accountng for ntrogen and phosphorous flows. The agrcultural producton of a country s consdered to be a black box n whch there s an nteracton of lvestock and crop producton actvtes. Insde the box, harvested fodder crops and grazed grass are consumed by the lvestock and the excreton of the lvestock s a source of fertlzer for crops. The nput sde of the box ncludes fertlzer (.e. norganc and organc but not manure), feedstuff, seeds and plantng materal, purchased breedng/baby lvestock, plus bologcal ntrogen and phosphorous fxaton. The output sde has three man groups: marketed lvestock products, marketed crop products, and all ntrogen and phosphorous-contanng tems 16

18 (e.g. fodder crops, grass, manure) exported to other countres or used for non-agrcultural purposes. The sol surface method whch was used by OECD (2008) s an alternatve method of accountng nutrents balance. Ths method defnes the nutrent balance as the dfference between the nutrent nflows enterng nto the sol and nutrent outflows gong out of the sol. Gven the objectve of our research s to use the nutrent balance as ndcators for the envronmental performance of the whole natonal agrcultural sector whch nvolves both croppng and lvestock actvtes, we decded to use the modfed farm gate method. Ths s because ths method s more accurate and delvers a more meanngful nterpretaton (Hoang and Alauddn 2009). Specfcally, there are three man mportant advantages of usng the modfed farm gate method over the sol surface method. Frst, OECD (2008), n mplementng the sol surface balance method, estmated ntrogen content n manure by multplyng the number of lvestock wth a partcular coeffcent whch relates to the amount of manure produced n a year and how much ntrogen s n each unt of manure. Ths way of estmatng the nutrent content n manure potentally causes hgh uncertanty. The modfed farm gate method does not have manure n the nput or output terms because they are contaned wthn the black box. Secondly, as noted n OECD (2008), there s a double-countng error n ther calculaton regardng atmospherc deposton of ntrogen nto the sol. In the modfed farm gate method, ths tem s not present therefore t avods ths double-countng error. Thrdly, the computed nutrent balance produced by the modfed farm gate method delvers more valuable economc and envronmental mplcatons than the sol surface method (Hoang and Alauddn 2009). For example, under the sol surface method, n order to reduce the nutrent surplus, a country can reduce fertlzer supply and lvestock manure. Theoretcally, an easy way of reducng lvestock manure s to scale down the sze of lvestock producton 6. However, scalng down the lvestock producton s not always economcally feasble, especally n those countres where lvestock producton s a man agrcultural producton actvty of ther agrcultural sector (.e. where lvestock producton s more proftable than crop producton). Also, under the sol surface method, the use of manure for crop producton as a way of 6 One can also reduce the lvestock manure deposton nto the sol by exportng the lvestock manure from agrculture to other commercal actvtes. However, ths s not always economcally feasble. 17

19 abatement s mplctly gnored. On the other hand, under the modfed farm gate method, one can thnk of maxmzng the recyclng of manure from the lvestock producton for crop producton actvtes to reduce the nutrent balance. Ths s arguably more economcally attanable. Consumed fertlzers Feedng stuff Cattle Lvestock products Seeds, plantng materals Purchased lvestock Crops Manure Crop products Nutrent-contanng tems exported or used for nonagrcultural purposes Input and output varables Surplus balance lost to the envronment through runoff, leachng and domestc agrcultural volatlzaton Fgure 3: Modfed farm gate method of accountng nutrent balance The emprcal analyss n ths paper nvolved annual data on 28 OECD countres durng the perod The bologcal nutrent fxaton and nutrent removed from the system for non-agrcultural purposes are not ncluded n our analyss because of a lack of data and ther nsgnfcant contrbuton n the balance 7. The stock of lve anmals was treated as an nput for lvestock producton. An ncrease n the lve anmal stock n any year was credted to the output n that year. Smlarly, any decrease n the lve anmal stock was debted to the output. 8 7 OECD (2008) estmated a very nsgnfcant amount of nutrent n these three categores. 8 In a year, a country could have a negatve change (decrease) or a postve change (ncrease) n the stock of lve anmals. A postve stock change s treated as extra output and added to the output. A negatve stock change s treated as nput and subtracted from the output. Yeld, defned as tonnes per head, s used to convert number of head of stock nto tonnes. However, there are a few of negatve values (49 out of 392x155= data ponts) n the output quantty because of negatve stock change. There are some potental explanatons for ths: (1) measurement error due to the use of yeld to convert the number of head data nto tonnes data, (2) the negatve stock change of a partcular lvestock but ths anmal was not for lvestock producton actvtes (e.g. breedng or recreatonal purposes) and (3) n that year a country could have reduced or stopped the producton of a partcular lvestock commodty therefore lve anmals were slaughtered but data on producton of that commodty was not recorded. If any of these s the real reason for a negatve data pont n the output sde, t s however reasonable to change t to zero. Settng negatve values to zero s also for the sake of protectng the dataset from losng observatons. 18

20 The natonal agrcultural producton system has 131 crop commodtes and 24 lvestock commodtes on the output sde and seven man categores of nputs (.e. land, labor, energy, fertlzer, feed and seed and plantng materal, machnery, pestcde, and water). Ths paper used DEA 9 to estmate effcency scores under the assumpton of constant return to scale (CRS) producton technology 10. Due to degrees of freedom constrants, we aggregated the 155 output commodtes nto one aggregate output varable and the 61 commodtes n feed and seed nto one aggregate feed and seed (FnS) varable. On the nput sde, we dd not nclude nformaton on water and pestcde because of ncomplete data. The nput-output matrx n the system then becomes One output term: aggregate output Fve nput terms: fertlzer, land, labor, machnery and aggregate FnS. There are three data requrements for each nput and output varable: quantty, ntrogen content and phosphorous content. For aggregatng output commodtes nto an aggregate output term, we also need prce data of 155 commodtes of 28 countres n 14 years ( ). 11 For the aggregate FnS term, we need quantty and prce data of 61 commodtes to aggregate them nto one aggregate FnS nput term and ntrogen and phosphorous content of these 61 commodtes to aggregate nto one aggregate nutrent content for the aggregate FnS nput term. The man source for quantty and prce data was FAO s webste (FAOSTAT). Data for ntrogen content of the output commodtes was compled from varous food composton tables of OECD member countres See Appendx 1 for bref descrpton of the DEA method & software used n ths paper. 10 There are three reasons why the CRS assumpton s more approprate than varable return to scale (VRS) assumpton n the emprcal work n ths paper. Frst, the analyss nvolves the use of aggregate country-level data (Coell and Rao 2005). Secondly, Grfell-Tatje and Lovell (1995) found that the Malmqust TFP ndex may not correctly measure TFP changes when VRS s assumed. Thrdly, the nput terms do not have any tems that capture the factors whch causes scale neffcency (e.g. sector governance errors, corrupton, bureaucracy). 11 All aggregaton s done usng a multlateral Fsher ndex. 12 These countres reported mcronutrent values (ether ntrogen content or proten content or phosphor) n 100 g of a partcular commodty of edtable food. Ths s actually part of a number of nternatonal projects of constructng nternatonal food composton table such as FAO s Infoods (avalable at 19

21 Quantty data for land s n 1,000 hectare unts of agrcultural land from OECD (2008), quantty data for labor s the total populaton workng n agrculture from FAO, quantty data for fertlzer s total tonnes of actve nutrents (ntrogen, phosphorous and potash) from FAO and OECD (2008), quantty data for machnery s the total number of agrcultural tractors, balers, ploughs, harvestng machnes, seeders, threshng machnes, and mlkng machnes. The nutrent contents for labor and machnery are zero. The nutrent content for land s also assumed to be zero. 13 The ntrogen and phosphorous content of fertlzer s calculated as the rato of total (weghted) ntrogen and phosphorous fertlzer over total actve nutrent quantty. In order to estmate the quantty of the aggregate output term, we calculated transtve Fsher quantty ndex numbers usng prce data as weghts. There are some zeros n the orgnal quantty and prce data n some countres due to data mssng. The zero quanttes were left as zeros. Mssng prces data were flled usng the Country Product Dummy (CPD) method developed by Summers (1973) 14. The same technques were used to calculate the quantty data for aggregate FnS nput term. Another aggregaton job was requred for the nutrent (.e. ntrogen and phosphorous) contents of the aggregate FnS nput term. There were three steps nvolved n creatng ths aggregate nutrent content. Frst, we constructed quantty ndces (QI j ) of country j wth prces as weghts (ths step s dentcal to the frst step n aggregatng the output term). Second, we calculated total nutrents (TN j of country j) that are contaned n all tems n aggregated terms (TN j = EU s EUROFIR (avalable at and LANGUAL (avalable at From these resources, we collected food composton tables of thrteen OECD countres ncludng Australa, Belgum, Canada, Denmark, Fnland, Italy, Japan, New Zealand, Norway, Span, Sweden, Swtzerland and USA. 13 The best ndcator of nutrent content of land should be the nutrent content n the sol that the crops can access to. At the farm level, ths data can be drawn from nutrent test of sol qualty. However at natonal level, the sol test estmate s mpossble. However, we dentfed three possble ways of settng land nutrent content: (1) the nutrent content s zero, (2) balance of nutrent estmated by the sol surface balance approach and (3) the accumulatve nutrent accumulated from the balance of nutrent estmated by the sol surface balance approach. All of these three treatments face dfferent crtcsm. When nutrent content of land s set to zero, ths means that the nutrent content n sol s not used by the plants. Ths s a very strong assumpton. However, gven the practce that there was overuse of fertlzer n OECD countres over the survey perod (OECD 2008) and the fact that the major amount of nutrent comng to the sol leaches deep under the ground and becomes naccessble to the plant, ths assumpton sounds to be reasonable. The second and the thrd treatment, however, have measurement errors and some dffcultes n nterpretaton. For example, OECD (2008) estmated the net balance of nutrent of Hungary n 1991 was negatve, ths negatve balance does not have any nterpretaton regardng how much nutrent n the sol n 1991 was used by crops. 14 A detaled descrpton of the CPD method s provded n Appendx 2. 20

22 K =1 ( x n +10x p ), where n j and p j are ntrogen and phosphorous content of sngle commodty j j j j tems (x ) among K tems of country j 15 ). Thrd, aggregated nutrent content (ANC j ) s the rato of total nutrent content dvded by TQ j *QI j where TQ j s total quantty of all the tems n the aggregated terms ( x j ). 16 K =1 Effcency scores Table 1 provdes basc descrptve statstcs for the dstrbuton of three DEA effcency scores: techncal effcency, allocatve effcency and nutrent-orentated effcency. The mean techncal effcency (TE) score of suggests that the average country should be able to produce ther current output wth 20.2% fewer nputs. The mean nutrent-orentated allocatve neffcency (NAE) score of 0.671, suggests that the average country could reduce nutrents by a further 32.9%, f they were to adjust the nput mx. Thus, the overall mean nutrent-orentated effcency (NE) score of ndcates that the average country should be able to produce ther current output wth an nput vector that contans 47.4% less ntrogen and phosphorous 17. Table 1: DEA effcency scores Effcency measure Mean Stdev Mn Max Techncal effcency (TE) Nutrent-orentated allocatve effcency (NAE = NE/TE) Nutrent-orentated effcency (NE) As dscussed earler, the relatve eutrofyng power of ntrogen and phosphor s 1:10 16 There were some mssng data n the nutrent content of feed and seed commodtes n some countres. Ths was essentally because we dd not have access to ther food composton tables. However, we beleve that nutrent contents n food commodtes n countres of smlar bologcal and weather condtons do not vary much. Based on ths assumpton, we appled nutrent contents of Korea to Japan, Mexco to USA and Canada. Nutrent content n Austra, France, Greece, Hungary, Iceland, Ireland, Netherlands, Poland, Portugal, and Turkey are estmated usng the average of Belgum, Denmark, Fnland, Italy, Norway, Span, Sweden, Swtzerland, and UK. 17 It should be noted that these country-level NE scores should not be nterpreted correspondngly as a partcular amount of damage caused to the envronment by the nutrents balance. Ths s because that locatonal characterstcs (e.g. sol type, topography and ranfall) vary from country to country and the estmated scores do not capture polluton abatement actvtes that countres could be engagng n. However t s also of nterest to ncorporate abatement actvtes nto the model f data s avalable. 21

23 Fgure 4 graphs the movement of mean nutrent-orentated, nutrent allocatve and techncal effcency scores over the 14 years perod. The movement of nutrent-orentated effcency scores n many years was n the opposte drecton of the techncal effcency scores. The mean nutrent-orentated effcency scores were around 0.52 over the survey perod. It saw a bg drop n 1991, 1992 and n Fgure 5 shows the changes n the output levels 18. Combnng these two fgures, we observed that the drop n nutrent-orentated effcency levels n 2002 was prmarly due to a drop n output whle the fall n 1991 and 1992 was apparently due to more ntensve use of fertlzer Techncal effcency Nutrent allocatve effcency Nutrent-orentated effcency Fgure 4: Mean techncal, nutrent-orentated allocatve and nutrent-orentated effcency scores 18 Whch are measured by changes of the average values of output quantty ndexes. 22

24 Output ndex SnF ndex Fgure 5: Output and nput ndces Fertlzer ndex The result also ndcates that there are only three countres whch were effcent n terms of the use of ntrogen and phosphorous. They were Hungary (n 1991 and 1992), Swtzerland (n 2000, 2001, and 2003) and the Netherlands (n the remanng years). There are some nterestng factors that may partly explan the hgh nutrent effcency n these three countres durng these perods. For Hungary, ths achevement happened durng the early years of the transton perod from central economy to market economy. Durng the perod before 1990, the farmng producton used an excessve amount of fertlzer. But the shft had moved farms from an ntensve producton orentated system to adopton of more extensve producton methods. The more extensve farmng was lnked partcularly to a large decrease n use of commercal fertlzer and feed and seed. The quantty of fertlzer appled on farms n 1991 and 1992 were less than 48% and 28% of the amount used n 1990 respectvely. The use of feed and seed also dropped by 5% n 1991 and 26% n 1992 from 1990 accordngly. The use of machnery however ncreased sharply n these two years whle the output level n 1991 was nearly the same level n Ths fndng s consstent wth OECD (2008). 23

25 In the Netherlands, the government had focused ts envronmental polces n agrculture on reducng the polluton caused by nutrent surplus. Thanks to these efforts, ths country ganed sgnfcant mprovement n terms of the ntrogen and phosphorous balance. The nutrent polcy has gone through three phases (Grnsve, et al. 2005; OECD 2003). The frst phase from 1984 to 1990 was to stop the ncrease n lvestock producton. The second phase from 1990 to 1998 nvolved a step-wse decrease of pressures resultng from surplus quanttes of anmal manure by usng applcaton lmts and a manure quota system. The thrd phase from 1998 to 2005 appled compulsory Mnerals Accountng System (MINAS) n whch the nutrent balance of farmers s montored. Under ths ntatve, ntrogen and phosphorous surpluses exceedng certan lmts were subject to leves. There was also a nutrent reducton budget of around USD 700 mllon through lvestock farm closure schemes durng (Grnsve, et al. 2005). The government also provded fnancal assstance n the form of tax reductons to the farmers (Beers, et al. 2002; Grnsve, et al. 2005). To comply wth nternatonal envronmental agreements, the agrcultural sector has been set targets for reducng ntrogen and phosphorous emssons nto the North Sea and ammona emssons nto the atmosphere (OECD 2008). In Swtzerland, there has been a growng emphass on the envronmental polces n agrculture. From 1993, Ecologcal Drect Payments (EDP) as a prmary fnancal assstance framework for farmers was granted on condton that the farmers adopt a set of envronmental management practces (OECD 2008). The revson of the Agrcultural Polcy Reform Programme whch provded the basc framework governng agrcultural polcy for the perod requred that any general drect payment to farmers meet fve envronmental crtera (Badertscher 2005; OECD 2004). A balanced use of nutrents, crop rotaton, sol protecton and mproved pestcde management are among these crtera. In addton, the Water Protecton Act requres farmers to lmt manure and fertlser applcaton per hectare; nstall facltes to store manure for at least three months; and adopt practces to prevent polluton of water by fertlsers and pestcdes. Under the Order on Hazardous Substances sol nutrent assessment s compulsory for each crop durng the growng season (OECD 2004; 2008). Table 2 reports the average values of the three effcency measures over the perod of 28 countres and ther rankngs. It notes that the rankngs change dramatcally between TE to NE. For the case of TE, Australa, Belgum-Luxembourg, the Netherlands, New Zealand, and Unted States have the best ranks. However n the terms of nutrent effcency, only the Netherlands retaned ther poston whle Australa dropped to 17 th rank, Belgum-Luxembourg 24

26 to 5 th rank, New Zealand to 21 st rank, and the Unted States to 20 th rank. The Fredman test confrmed there was a sgnfcant dsagreement between the rankngs n nutrent-orentated effcency scores and techncal effcency scores 19. Table 2: Average effcency scores for the perod Country Mean TE Rank Mean AE Rank Mean NE Rank Netherlands Swtzerland Greece Italy Belgum-Luxembourg Portugal Hungary Austra Mexco Turkey Denmark Czech Japan Span Poland Korea Australa Germany Sweden Unted States New Zealand France Canada Unted Kngdom Norway Fnland Ireland Iceland The result of the test: Fredman = 37.35, Kendall = 0.69 and p-value = We also dd a test on the rankngs n TE, NE and NAE whch gves p-value = 0.02, ths suggests the rankngs n the effcency consderatons are sgnfcantly dfferent (at 5% level of sgnfcance). 25

27 Nutrent-orented total factor productvty growth Table 3 reports the average productvty changes over the perod of the 28 member countres. In terms of nutrent balance, the OECD acheved a mean growth n NTFP of 1.5% per annum over the 14 year perod, compared wth 0.8% n the tradtonal TFP growth. Ths was due to the presence of technologcal progress n terms of the use of nutrents. The nutrent-orentated technologcal change was estmated to be around 0.7% per year over the survey perod. There were 12 countres experencng negatve growth n the nutrent-orentated productvty. Among these countres, decreased tradtonal TFP n eght countres caused the negatve growth n NTFP. On the other hand, the negatve growth n NTFP n the remanng four countres (Australa, Unted States of Amerca, Canada and Portugal) was attrbutable to the nutrent-orentated technologcal regress. New Zealand and Australa were the worst two performers n terms of NTFP growth. In these countres the reason for the negatve NTFP and TNC growth was because of overuse of ntrogen fertlzer. For example, the total consumpton of fertlzer n Australa ncreased 89.9% (63.7% for New Zealand, 29.5% for Canada, 27.9% for Unted States) from 1990 to 2003 compared wth an ncrease of 8.8% of all OECD countres. Span (10.9% growth), Denmark (9.8% growth) and Greece (5.0% growth) acheved the hghest NTFP growth. Ths achevement was manly due to sgnfcant growth n the tradtonal TFP for Span and Denmark and was manly due to nutrent-orentated technologcal progress for Greece. In the case of Korea and Iceland, ther envronmental performance mprovement was due to reduced (relatve) use of ntrogen and phosphorous content nputs, regardless that the tradtonal TFP decreased. Table 4 and Fgure 6 reports the average productvty growth for 28 countres n each of the years n the perod. There were four years (1993, 1994, 2002 and 2003) that experenced negatve growth n the nutrent-orented total factor productvty ndex, where the negatve growth was a consequence of both decreased tradtonal TFP and a reducton n nutrent-orentated allocatve effcency. From 2000 onwards, the OECD has seen a slght reducton n the nutrent-orentated technologcal growth. Ths nutrent-orentated productvty trend suggests that ether the easy gans n envronmental mprovements have been acheved, or that OECD countres may be startng to be less vglant n tacklng these envronmental ssues. 26

28 Table 3: Mean productvty growth, Country Mean TFPC Mean NAEC Mean NTFPC Australa Austra Belgum-Luxembourg Canada Czech Denmark Fnland France Germany Greece Hungary Iceland Ireland Italy Japan Korea Mexco Netherlands New Zealand Norway Poland Portugal Span Sweden Swtzerland Turkey Unted Kngdom Unted States Geometrc Mean