fntroduction An important objective of nonparametric estimation of technical inefficiency is the development of recommendations for adjustment of factors of production. Impûcitly, these recommendations must be limited to adjustments which are economically efficient. Where technologies are homothetic, expansion paths are rays from the origin. Within this context, recommendations for radial adjustments for technical efificiency are consistent with achieving economic efficiency if adjustment is proposed along the expansion path relevant under the current price structure. In this sense, measures of radial technical eftciency ETE) would be of interest to managers because they provide recommendations that are consistent with economic efficiency. This correspondence betïveen radial technical adjustment and economic efficiency dissolves when technology is nonhomothetic. A similar situation occurs when the set of technical possibilities is constrained by quasi-fixity of factor services. In this case, even for homothetic technologies, the expansion path will deviate from a radial path. Such fixity might occur as a result of temporal, regulatory, or other constraints (e.g. exogoneity of flows) on adjustment. Within decision horizons where such factor services can not be controlled, reçommendations for their radial adjustment would be of little interest to managers. Where the marginal productivity of such services is nonnegative at their constrained level, radial adjustment through disposal of such services would be economically inefficient. This problem ïvas recognized by Fanell (1957) though he maintained a focus on radial technical adjustment.t Hal[ and Winsten (1959) reconsidered the issue by distinguishing between controllable and noncontrolable variables. More generally, the issue is a case of

I

The issue was also considered in a wider context by Fâre and Lovell (1978) who introduced input specific me:rures of input technical inefEeiency to-generalize the Farrell measure. These << Russell > input efficiency measures are interpretable as nonradial and were shown to provide identificaton of efficient firms from the primal. In contrast the Farell input and output measures provide difierent rankings of firm efficiency. While Fâre and Lovell's Russell measure achieved its objectve of providing a unique means of identi$ing technical efEciency from the primal, Kopp noted that the measure lacks a useful dual interpretaton. measurement of subvector technical efficiency (STE) as studied by Kopp (1981); Fâre, Lovell, and Zieschang (1983); and applied by Banker and Morey (1986), Kamakura (1988), Adolphonsorq et al. (1990). For the case of a single quasi-fixed factor, Banker and Morey (1986) demonstrated that the resulting estimate of subvector technical efficiency will be less than or equal to a corresponding estimate of unrestricted or radial technical efficiency.

In this paper, a formal proof is provided of the relationship between RTE and STE for the case of an arbitrary vector of quasi-fixed factors. Next, the paper establishes that, in general, a type of magnification effect occurs as the vector of quasi-fixed factors is expanded.

That is, for a particular firnr, as the number of quasi-fixed factors is increased (decreased) the STE estimate decreases (increases). In analogy to the Le Chatelier -Samuelson principle, the proposition states that as the opportunity for adjustment of variable factors is reduced, so the extent of technical efficiency is reduced. Going further, we evaluate the impact of fixity of factors on the efficiency rank of firms.

The presence of efficient markets and opportunities for instantaneous adjustment of factor services in many industries limits the applicability of subvector technical efficiency.

However, where ideal economic conditions fail to exist, or where economic conditions are distorted by regulatory constraints, subvector measures of technical efficiency are warranted.

To evaluate the empirical implications of use of RTE measures in the presence of quasi-fixed factors, we present estimates of RTE and STE for a sample of French cereal farms drawn from the FADN (Farm Agricultural Data Networ$ farm record system for 1990. The bias of the RTE measure is evaluated. Given the conditionality of STE estimates on the composition of the subvector of quasi-fixed factors, the robustness of firm efficiency rank is evaluated as the number of quasi-fixed factors is varied.

Technical Efficiency with Quasi-Fixed Factors Input based and output based measures of technical efficiency popularized by Farrell indicate an identical proportion by which either all inputs or all outputs may be reduced to place a firm on a particular technical frontier of reference. The usefulness of such aggregative indicators has been criticized because they fail to provide input specific recommendations for adjustment l99a). While the Russell measure of technical efficiency introduced by Fâre and Lovell provides input specific estimates, [START_REF] Kopp | Measuring the Technical Efficiency of Production: A Comment[END_REF] noted it lacks a corresponding dual measure. More generally, it may be of interest to access the technical efficiency of subvectors of inputs or outputs. The presence of quasi-fixity of subvectors is an important example. The notion of subvector technical efficiency was considered by Fâre, Grosskopf, and Zeischang (1983) for the a single factor case and by Fâre, Grosskop{ and Lovell (L994) for the general case. The input based measure of subvector efficiency can be defined following these studies for a set of "Ifirms indexed j: 1,....J, each with access to the same technology that transfoûns a vector of inputs ri €l{ into a vector of outputsy, eRY .

More generally, for the set of firms define a (I x ^|fl input matrix X and a (I x M) output vaî =A and vL,r7= 112,...,N1. For convenience, the partition is identical for all firms.

The elements of Xu are assumed variable and those of XY are assumed quasi-fixed. Each element of X can be equivalently writteî xJ = lxl,x). Suppose the technology satisfies the augmented regularity conditions adopted by Banker, Charnes, and Cooper (1934)2. The production possibilities set P can be written: 2 That is, the set of production possibilies is defined by: P = {(x,y) \ y > 0 may be produced from r > 0) satisSing: IPtl : (x,,y,) e P Vj: I, ...., J lP2l : P is a regular seÇ i.e. nonempty, close4 and satisSing the origin condition that y j = 0 f x l = 0 . P = {(x',xo,y):xu > x' A,xî > xo A,! < rl,,!n, = U" e Rl } tll i=r where ,"--(4,\,...,)"r) is the intensity vector. F;ach 1,, denotes the intensity at which activity j is undertaken. By equation ( 1), the jth frrm's production plan (xi,\,1) belongs to the production possibilities set, i{, and only i [, 1xl,xl,l) lP4l: P isconvex: V(r,y)ePand @,neP,Yq e [0,1] ; a(x,y)+(1-a)1l,yyef

[P5] : P is the intersection of all sets satisfyrngPl tO P4.

More formally, P2, P3 and P4 each define linear constraints that define closed subspaces. The intersecton of these zubspaces satisfies P-l and defines a convex envelop that may be written: {,' J ,4

,y):x>214,,y <ZAiJi,Zl, =!,x j à o v7 :1,.. j=t j=r 5 P_ j=r hypothesis are considered variable and controllable by the manager. Efficient adjustment is defined as conditional upon the levels of quasi-fixed inputs. A direct comparison of these two measures can be made within the context of linear programs that allow their nonparametric estimation following the approach of Data Envelopment Analysis. To allow a convenient comparisoq define a base linear program from which the two measures can be drawn as special cases: minB, = (E;,EI)

s.t.
Elxi >-X')" 1*; > x'r Yj <v" J Zx, =l j=r where X enl,ni e&,1 e\ Define .R; the solution to program "R" defined by the base program (4) augmented by the constraint that R, -El =E,Y. Similarly, define program ",S" as the base program augmented by the constraints that SY = ET and I = L. Solution of program ,S results in ,SrY consistent with (3). Banker and Morey graphically compared the solutions (R'Si ) for the case where x] is a scalar. For the general case where .rf is a'vector, they noted that any optimal solution to program.R is a feasible solution to program ^S.

Their proposition is as follows.

Proposition 1 (Banker and Morey, 1986) For anyi SrY < Rl where Sri is the solution to program ,S for firm7 and R; is the solution to t4l 6 program.R.

Formal proof follows directly by reference to the underlying input requirements sets derived from equation (1). In the absence of a constraint on x', , WoEramR was derived from equation (2). For rt fixed, program ^9 follows from equation (3). To compare the solutions to program R and program ,S, write equation (2) in terms'of the constrained level of xl-, say {: n,@i,il,t1) = min{Ri:R,xj er1n,rl,t),R, .&} tsl Given that R, e & , free disposal (assumed by P3) implies R,Il <7i nd t"1n,Il,t) c t'(xl ,t) Simply stated, the constraint set for program R is contained within that of program ,S. It follows that: R1(\,!)> si@i ,ri ,t) t6l By similar logic, define program,f-1 where an arbitrary element ofxn is fixed, e.E.* . Program J*I can be written as: si'{x;' ,X! ,xi ,t) = toin{si-' ,t-'*i-' e t*t1r! ,ri ,!),Si-' . &} l7l However, program,9 can be rewritten: si@i,ri,\,!1)=min{s;:qx;-1 e/'-l1^sjt!,xi,t),s; .&} t8l Gven that Sixl < x! ,itfollows that: /*l(s;I;,î; ,!) c I"'(Il,Il ,)i) and S; > S;-' . These results provide the basis for the following proposition.

Proposition 2

The input based subvector efficiency-of firm7 varies systematically with the number of quasi- fixed factors which constrain its adjustment of variable factors. As v decreases fromMto 0, ST = R, = Srf-t 2...) Srl 2...> Sro = I tel An Application to French Cereal Production Propositions I and 2 establish that estimates of radial technical efficiency will, in general, over estimate the efficiency of firms which face constraints on adjustment due to quasi-fixity of factor services. In this section, we present results which allow an empirical evaluation of the magnitude of such biases as well as-an illustration of the magnification ef[ect presented in Proposition 2. The application is based on a sample of 188 French cereal farms drawn from the Farm Agricultural Data Network (FADN) data set for 1990. On average, cereal production accounted for at least 70 percent of their total gross product. In all cases, the farms were specialized in soft wheat and maize, Vermersh et al. (1992). The sample caracterues 45o of the French cereal farms sampled in the General Agricultural Census of 1988 and in this sense, the sample may be interpreted as representative of population of cereal producers in France.

To proceed, we estimate RTE and STE as alternative hypotheses concerning the fixed of factor services. Under a maintained hypothesis that we label as Hypothesis 1, we represent the product vector as incuding two outputs (cereal output (soft wheat and corn), and other outputs (mainly, oilseeds); five variable inputs (fertilizer, pesticides, seeds, other intermediate inputs, and equipment); and three quasi-fixed factors (area cultivated under cereal, area cultivated in other crops, and labor (family and hired)). This represents our prior concerning the quasi-fixity of factors. We include labor in the vector of quasi-fixed factors given that family labor accounts for 95o of labor used in the sample. All variables except land and labor are measured in 1990 French francs3. Available data necessitated linear aggregation of valuesa.

Land is measured in hectares, while labor is measured in annual worker units (AWU5).

Equipment services were measured based on estimated value, a five year amortuatiory as well as maintenance expenses, rent, and machinery cooperative fees. Equipment is viewed as variable due to the presence of active rental markets. Descriptive statistics presented in Table I verify the specialization in cereal production by the sampled farms. Cereal production accounted for overtwo-thirds of their revenues and occupied almost 75Yo of their cultivated area. Fertilizers and pesticides dominated expenses.

Estimation of the technical efficiency scores under various maintained hypotheses of quasi-fixity were based on solution of the programs presented in equations ( 2) and (3). Solutions were implemented using linear programming software available in SAS/OR. Results are reported in Table 2 -4. Alternatives to Hypothesis I for the specification of the quasi- fixed factor vector include Hypothesis V where all factors are variable and Hypotheses 2-4 which maintain alternatives to Hypothesis I as defined in Table 3. First, Table 2 indicates that the number of firms identified as technically efficient (based on a technical efficiency score of unity and slack variables estimated as zero) under alternative hypotheses ranged betwen 88 and 93. This indicates robustness of the classification of efficient firms under the alternative hypotheses. Details on the charactersitics of these efficient farms are available from the authors. However, similar robustness is not found across ranges'of inefficiency. For example, the number of firms found with scores below .85 varies from 71 under our preferred specification Hypothesis l, to only 36 under Hypothesis V. This suggests that the distribution of the efficiency estimates is substantially altered by the efficiency measure used @TE, vs. STE) and by the specification of the quasi-fixity of inputs.

Table 3 presents a different view of the distribution of efficiency scores. Results indicate that the mean and standard deviation of scores varies across specification. On average, the estimated technical efficiency score under Hypothesis I (land and labor fixed) was .8773 compared to .9319 under Hypothesis V (all factors variable), indicating that a substantial upward bias results from use of .R7 when quasi-fixed exists according to Hypothesis 1.

Further, Table 3 indicates the extent of the magnification effect presented in equation ( 9) can be substantial in quantitative terms, depending on the factors that are fixed. The differences between efficiency estimates based on Hypothesis V vs. Hypothesis I is also apparent from I to 37.8% compared to only 19J% under Hypothesis V.

Conclusions

These results have two important implications. First, where factors are quasi-fixed, both the level of efficiency and the distribution of efficiency among firms may be substantially over estimated when based on Hypothesis V. TVhile econometric study of efficiency has necessarily recognized the importance of accurate specification of input variability and fixity, these results highlight the importance ofthis specificaiton decision for nonparametric studies of technical efficiency. Second, the under estimation will provide a misleading basis for recommendations to firms concerning existence of opportunities for input adjustments as well as for more global recommendations concerning the existence of generic opportunities for input adjustment.

  Summary of data for efficiency analysis (188 French cerealproducers, 1990)

  eP. Input based radial technical efficiency (RTE) is defined following Farrell(1957), Charnes, Cooper, and Rhodes (1978), and /(yr) is the input requirements set derived from (l). The interpretation of .Ry as a radial measure follows from itd scalar dimênsion which implies each factor will be reduced by the same nonnegative proportion. As an alternative, Fâre, Lovell and Zeischang defined asymmetric technical inefficiency where the scalar reduction \ is applied to only one element of x;. More generally, Fâre, Grosskopf, and Lovell define subvector technical efficiency (STE) the input requirements set conditional upon the levels of the quasi-fixed factors. The distinction between lRy and S.1 rests squard on the application of a common proportion of reduction(thus, subaggregative) to a subvector of inputs which by maintained

	Fâre, Grosskop{, and Lovell (199a):
	R1(x1,1)= min{Rr:Rrx, elgt,),R,.&}	tzl
	[AE] 'Pisconsistentwithfreedisposalof (î,!) e P .	inputsandoutputs V(x,y)eP if x>x and t(y,then

where as follows:

si@i,xi,l1)=rin{q:s,xu et'(xr,,l),sr.&} t3l where I'(x;,y)is

Table 2 .

 2 Technical efficiency frequency

Table 3 .

 3 Technical efficiency measurement

			Hv		H1		H2	H3		H4
		nb	%	nb	%	nb	%	nb	%	nb	%
	=l	88	46.8	92	48.9	89	47.3
	between 0.95 and I	29	t5.4	t2	6.4	26	13.8
	between 0.85 and 0.95	35	18.6	l3	6.9	33
	<0.85	36	19.1	7L	37.8	40

Economic dat4 whether expressed in volume or value, reflects both technical and allocative inefficiency. Past studies of technical efficiency have used bothvolume and value. a Fâre and Primont (1983) present results that indicate that use of value aggregatd data will result in negatively biased estimates of technical efficiency. Thomas and Tauer have noted that measurement bias may occur when linear aggregation is used. 5One AWU equals 2200 hours of labor.


Keywords: Data envelopment analysis, radial technical efficiency, nonradial technical efficiency, cereal production, environmental impacts

The existence oftechnical inefficiency offers the opportunity for a "free lunch" not typically consistent with neoclassical theory. V/ithin the context of management of external effects of production processes, when external effects are related to the use ofparticular inputs, elimination oftechnical efficiency through reduction of input use represents a means of reducing external impacts. An important example is found in agriculture where substantial environmental impacts are generated by particular inputs. Within this context, this paper considers the usefulness of Data Envelopment Analysis for estimation of potential input reductions and assessment of potential reductions of environmental impacts of agricultural inputs. An application for French cereal production provides estimates that indicate that substantial potential exists for reduction of input use and environmental impacts.

Introduction

The potential for a "free lunch" is always viewed with suspicion by economists.

Neoclassical theory clarifies that hedonist producers may be expected to use all available inputs in a manner that is technically efficient conditional upon producer information and managerial ability. Market competition for scarce resources is viewed as the whip which cracks over the backs of entrepreneurs and shunts inefficient producers into other activities. In reality, such processes often work slowly and information access and utilization fails to guide all entrepreneurs to the same technically efficient frontier. Where such technical inefficiency exists, a type of "free lunch" opportunity to reduce inputs without reduction of outputs may exist. Such opporhmities are of particular interest where input reductions could lead to improvements in the external effects of a production process, e.g. those of agriculture on the environment. In the case of agriculture, substantial environmental impacts have been associated with fertilizer and pesticide use. The complexity of the biophysical processes through which these inputs are utilized imply that even under the most informed management, application of these inputs may exceed efficient levels. Further, these same processes result in even optimal applications being transported andlor transformed, resulting in off-site impacts of the input use. In this paper, we consider the usefulness of Data Envelopment Analysis (DEA) for identification of potential agricultual input adjustment which might result in improved technical efficiency and at the same time reduced environmental impacts. First, we consider the usefulness of DEA for assessment of technical efficiency in agriculture. The existence and importance of quasi-fixed factors renders typical radial measures of technical efficiency of little usefulness for agriculture. In their place, we consider the usefulness of a subvector measure of technical efficiency which acknowledges that it would be economically inefficient to radially reduce quasi-fixed factors. In addition, we consider the usefulness of Russell measures of input speciflc technical efficiency. Next, we apply the methodology to assess the existence ofa free lunch type ofopportunity for reduction ofinputs in French cereal production. Of particular interest are opportunities to reduce pesticide and fertilizer use. J On the Usefulness of DEA for Agriculture Nonparametric estimation of technical efficiency based on DEA has been recognized as an important tool for the development of recommendations for adjustment of factors of production (Brauer, 1990). Its usefulness as a means of constructing evidence relevant to the question that is the focus of this pâper, two issues are of concern. First, agriculture is characteized by factors of production which are persistently fixed, or very slow to adjust.

While land rental markets often exist, they operate only over long periods of time, and do not allow repeated, instantaneous adjustment. Similarly, for labor, transactions costs for labor market participation are often high enough to prevent complete integration of farms with rural labor markets, and rural labor markets with national labor markets. Second, the usefulness of DEA for assessment of possibilities for adjustment which might reduce agriculture's negative impacts on the environment must be questioned. Farrell measures of technical effrciency provide insights on total factor employment and propose equiproportional reduction of all factors necessary to attain technical efficiency [START_REF] Kopp | Measuring the Technical Efficiency of Production: A Comment[END_REF][START_REF] Kumbhakar | Estimation of Input-Specific Technical and Allocative Inefficiencies in Stochastic Frontier Models[END_REF]. While this type of aggregative measure of technical efficiency may be useful for some questions, the differential impacts of agricultural inputs on the environment would seem to beg for a measure of input specific potential for adjustment of input use. Before proceeding, it is useful to consider each of these issues in some depth.

In the measurement of adjustment necessary to attain a technically efficient input bundle, the path between a technically inefficient point and an efficient one must be limited to economically efficient points. That is, only economically effrcient adjustment is of interest.

Where technologies are homothetic, expansion paths are rays from the origin and recommendations for radial adjustments for technical efficiency are consistent with achieving economic efficiency under the given price structure. In this case, measures of rudiaI technical efficiency (RTE) would be of interest to managers because they provide recommendations that are consistent with economic efficiency. This correspondence between radial technical adjustment and economic efficiency dissolves when technology is nonhomothetic. Figure I illustrates this point. Suppose that technology is homothetic and the observed input bundle is at point A. Adjustment to achieve technical effrciency would follow the ray AE to point E.

Alternatively, if technology were nonhomothetic, economically effrcient adjustment would follow a nonlinear expansion path, e.g. OFA to point F. In this case, the radial adjustment AE would provide a biased estimate of the economically efficient adjustment AF.

A similar situation occurs when the set of technical possibilities is constrained by quasi-fixity of factor services. Such fixity might occur as a result of temporal, regulatory, or other constraints (e.g. exogoneity of flows) on adjustment. V/ithin decision horizons where such factor services can not be controlled, recommendations for their radial adjustment would be of little interest to managers. In this case, even for homothetic technologies, the expansion path will deviate from a radial path. Again, Figure 1 provides an illustration. Suppose X/is fixed at Xfr. Where the marginal productivity of its services are nonnegative at their constrained level, disposal of its services would be economically inefficient. It follows that adjustment along AE or AF would have to be ruled out as economically ineffrcient. Instead, adjustment would proceed along AR.

The implications of this problem for the measurement of technical efficiency were recognized by Farrell (1957) though he maintained a focus on radial technical adjustment.

Hall and [START_REF] Hall | The Ambiguous Notion of Efficiency[END_REF] reconsidered the issue by distinguishing between controllable and noncontrolable variables. More generally, the problem requires measurement of equiproportional adjustment necessary for a subvector of inputs which are variable. This type of subvector technical efficiency (STE) has been studied by [START_REF] Kopp | Measuring the Technical Efficiency of Production: A Comment[END_REF]; Fiire, Lovell, and Zieschang(l9S3); and applied by [START_REF] Banker | Efficiency Analysis for Exogenously Fixed Inputs and Outputs[END_REF], [START_REF] Kamakura | A Note on the Use of Categorial Variables in Data Envelopment Analysis[END_REF], Adolphonson, et al. (1990). The input based measure of subvector efficiency can be defined following these studies for a set of -/firms indexed j: 1,....J, each with access to the same technology that transforms a vector of inputs x, e R! into a vector of outputsy, e Ry . More generally, for the set of firms define a (I x N) input matrix X and a (J x M ) outputmatrix I . Suppose the input matrix is partitioned so X:(X',X') where vc.{I,2,...N} with vÀv =O and vvV = {I,2,...,N}. For convenience, the partition is identical for all firms. The elements of Xu are assumed variable and those of Xt are assumed quasi-fixed. Each element of X canbe equivalently written x, = (xl,xl ). Suppose the technology satisfies the augmented regularity conditions adopted by [START_REF] Banker | Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis[END_REF]. That is, we suppose the set of production possibilities is defined by f ={(y,x)\y>0maybeproducedfromx > 0}, satisffing:

[P1]: (!i,x) eP Yi :1, ...., J lP2l: P is a regular set, i.e. nonempty, closed, and satisffing the origin condition that y-= g if x, =g . lP3l :Pisconsistentwithfreedisposalof inputsandoutputs: V(y,x)eP if I2x and y < y, then (!,f) e P . lpll : P is convex: V(y,x) e P and (y-,I) e P,Va e [O,t] ; a(y,x)+ (1 -cr\y,f; e f [P5] : P is the intersection of all sets satisS'ing Pl to P4.

More formally, P2, P3 and P4 each define linear constraints that define closed subspaces. The intersection of these subspaces satisfies PI and defines a convex envelop that may be written:

(trll p= ]g,x),x>>?u,x1,! <ZLiyi,Ir, = 1,I €Ri I Ir'='i+it) (y,x);x> XL,y <h,ZL, = 1,1. eRj j=t where t"=(\t,\,...,?ur) isthe intensity vector. Each )', denotes the intensity atwhich activity i is undertaken. To consider the measurement of technical effrciency we partition the input vector into a subvector of variable input and a subvector of quasi-fixed factors , i.e. 1), the jth firm's production plan (l,,xj,xj) belongs to the production possibilities set, if, and only if, (y j ,xl ,xi) e P . Input based radial technical efficiency (RTE) is defined following Farrell (1957), Charnes, Cooper, and Rhodes (1978), and Fitue, Grosskopf, and Lovell Q99$: R,(!,,x)= tnir$r:R,x, el(y),Ri.&) l2l where /(yr) is the input requirements set. The interpretation of $ as a radial measure follows from its scalar dimension which implies each factor will be reduced by the same nonnegative proportion. By comparison, Fâre, Grosskopf, and Lovell defined subvector technical efficiency (STE) as follows: sj(l,,xl,xï)=minfrl:srïru = I"(yj,xuj),s; =&) t3l where I'(y,,x|) is the input requirements set conditional upon the level of quasi-fixed factors.

The distinction between & and S", rests squffely on the application of an equiproportional reduction (thus, subaggregative) to the entire versus a subvector of inputs, where the elements of the subvector are by maintained hypothesis considered variable and controllable by the manager. Effrcient adjustment is defined as conditional upon the levels of quasi-fixed inputs.

Figure 1 provides a direct comparison and illustration of these alternative measures. Suppose technology is homothetic, then R, would be estimated by AE/AO while S", woutd be estimated by AR/AO. It is clear from Figure 1 that, in general, R; > S", , a result that is proven formally in Piot and Vermesch (1995).

The usefulness of aggregative estimates of technical efficiency such as R, and Si provides a limited basis for answering the question of interest in this paper. Instead of equiproportional adjustments in inputs, it would be of interest to have estimates of the potential for input specific reductions which could result in achieving technical efficiency.

The Russell measure of technical efficiency introduced by Ftire and Lovell (1978) provides such input specific estimates. Rather than estimating equiproportional reductions as do R, and .S", in [1] and l2l above, the Russell approach estimates input specific reductions necessary to move from an observed input bundle such as point A in Figure I to the efficient isoquant or frontier. While this measure does not provide a dual basis for statement of the proportion by which costs may be reduced, we are not interested in such statements for the purposes of this paper (Kopp, 1981).

An Application to French Cereal Production

In this section, we present estimates of radial, subvector, and Russell technical effrciency for a sample French cereal farms drawn from the Farm Agricultural Data Network (FADN) data set for 1990. On average, cereal production accounted for at least 70 percent of their total gross product. In all cases, the farms were specialized in soft wheat and maize, Vermersh et al. (1992). The sample caructerizes 45%o of the French cereal farms sampled in the General Agricultural Census of 1988 and in this sense, the sample may be interpreted as representative of population of cereal producers in France.

V/e consider the sensitivity of estimated technical efficiency to alternative specifications concerning the fixity of factor services. Under a maintained hypothesis that we label as Hypothesis 1, we represent the product vector as including two outputs (cereal output (soft wheat and com), and other outputs (mainly, oilseeds); five variable inputs (fertilizers, pesticides, seeds, other intermediate inputs, and equipment); and three quasi-fixed factors (area cultivated under cereal, area cultivated in other crops, and labor (family and hired)). This represents our prior concerning the quasi-fixity of factors. W'e include labor in the vector of quasi-fixed factors given that family labor accounts for 95% of labor used in the sample.

All variables except land and labor are measured in 1990 French francsl. Available data necessitated linear aggregation of values2. Land is measured in hectares, while labor is measured in annual worker units (AWU3). Equipment services were measured based on estimated value, a five year amortization, as well as maintenance expenses, rent, and machinery cooperative fees. Equipment is viewed as variable due to the presence of active rental markets. Descriptive statistics presented in Table 1 veriff the specialization in cereal production by the sampled farms. Cereal production accounted for over two-thirds of their revenues and occupied almost 75% of their cultivated area. Fertilizers and pesticides dominated expenses.

Estimation of the technical efficiency under various maintained hypotheses of quasi- fixity were based on solution of the programs presented in equations ( 2) and (3). Solutions were implemented using linear programming software available in SAS/OR. Results are reported in Table 2 -6. Alternatives to Hypothesis I for the specification of the quasi-fixed factor vector include Hypothesis V where all factors are variable and Hypotheses 2-4 which maintain alternatives to Hypothesis I as defined in Table 2.Table 2 presents the sample mean and standard deviation of estimated scores across alternative specifications. On average, the estimated technical ef{iciency score under Hypothesis I (land and labor fixed) was .8773 compared to .9319 under Hypothesis V (all factors variable), indicating that a substantial upward bias results from use of $ when quasi-fixed exists according to Hypothesis 1. Based on our preferred specification, Hypothesis 1, Table 2 indicates that a 13% adjustment in inputs I Economic data, whether expressed in volume or value, reflects both technical and allocative inefficiency. Past studies of technical efficiency have used both volume and value.

2 Fâre and Primont (198S) present results that indicate that use of value aggregated data will result in negatively biased estimates of technical efficiency. Thomas and Tauer (1994) have noted that measurement bias may occur when linear aggregation is used. 3One AWU equals 2200 hours of labor. I could be effectuated without loss of outputs. This suggests that substantial extensification could occur with accompanying benefits for the environment. Further, Table 2 indicates a type of the magnification effect occurs as ths number of fixed factor is reduced. This property is motivated theoretically in Piot and Vermersch (1995). Table 3 presents results concerning the distribution of estimated efficiency scores. First, the number of firms identified as technically efficient (based on a technical efficiency score of unity and slack variables estimated as zero) under alternative hypotheses ranged between 88 and 93. This indicates robustness in the classification of efficient firms under the altemative hypotheses. Details on the characteristics of these efficient farms are available from the authors. However, similar robustness is not found across ranges of inefficiency. For example, the number of firms found with scores below .85 varies from 71 under our preferred specification Hypothesis 1, to only 36 under Hypothesis V. This suggests that the distribution of the efficiency estimates is substantially different depending on the efficiency measure used (R, or Sr.") and the specification of the quasi-fixity of inputs.

Table 4 translates these estimates of technical efficiency into possible reductions in input use. While Table 2 suggested that a l3%o equiproportional reduction in all inputs would be possible, actual potential input reduction must recognize that many firms do not use particular inputs or produce particular outputs. For these firms and product choices slack variables are estimated. Table 4 defines potential input adjustment as: dxo, =(ti-L)xo,-so, where I is the estimated technical effrciency score, x;,ristheobserved h'h'sinputuse, and s7,7 is the estimated slack variable for the h'h'sinptil and the ith firm. As reported in Table 4, this potential adjustment is substantial. For fertilizers, an estimated l5%o would be on average necessary, while for pesticides a nearly equal reduction would be recommended. This represents a substantial reduction in inputs which generate environmental impacts. Table 5 reports an alternative perspective on these results. While technical efficiency could be attained by input reduction, an equivalent approach would be to hold inputs constant and achieve increased output by efficient use of inputs. Table 5 indicates that well over a 10o% increase in yields could be expected on average across the sample. Table 6 excludes efficient firms from this calculation given that their adjustment would be zerc. The resulting estimated inuease in yield is substantial, under Hypothesis I a27Yo increase in yield is estimated as possible for the subset of inefficient firms.

Tables 2 -6 rcport estimates based on equiproportional reductions in either the entire input vector as under Hypothesis V or a subvector of variable inputs as under Hypotheses 1 - 4. Russell measures of technical efficiency allow the reduction of inputs to vary across inputs.

Tables 7 and8 report results for the Russell measure of technical efficiency. These results provide yet another basis for insight into the potential for adjustment of agricultural inputs which affect the environment. From Table 7, we see the distribution of technical efficiency varies across inputs substantially. On average,over I5o reductions are estimated as possible for fertilizers and for pesticides. The number of firms that are estimated to be efficient in their use ofeach input varies across inputs and this variation is pronounced across different ranges of the distribution. In Table 8, these results are translated into potential reductions in inputs necessary to attain technical efficiency. Results again corroborate that substantial reductions in fertilizers and pesticides would be necessary.

Conclusions

Technical inefficiency definitionally provides an important basis for opportunities for adjustment of inputs without loss in outputs. This paper has considered the usefulness of DEA analysis as a tool for assessing the extent to which opportunities for input reductions might exist in agriculture. Of particular interest are opportunities to reduce inputs which impact the environment. The paper first clarifies that in agriculture the presence of quasi-fixed factors renders traditional radial measures of technical inefficienay are not useful. Instead, the paper proposes the use of measures based on subvector technical effrciency or Russell technical efficiency.

The results reported in this paper have two important implications for the use of DEA in agriculture. First, where factors are quasi-fixed, both the level of efficiency and the distribution of efficiency among firms may be substantially over estimated when based on Hypothesis V. While econometric study of efficiency has necessarily recognized the importance of accurate specification of input variability and fixity, these results highlight the importance of this specification decision for nonparametric studies of technical efficiency.

Second, the under estimation will provide a misleading basis for recommendations to firms

  x = (xu,xt) and write the production possibilities set P : J P = {(y,x',xo):xo ) Xu}",xn > Xi}r,,y < n,I }", =1,}u.Ri } tll j=r By equation (

Table l .

 l Summary of data for efficiency analysis(188 French cereal producers, 1990) T able 2. Technical efficiency estimates (Summary statistics)

Table 3 .

 3 Technical efficiency estimates(Frequency)

				Mean	Std-Dev			Min		Max
	Outputs Cereal (F)			487172		30361 I			36392		r494657
	Other products (F)			199014		14t785			393		804672
	Quasi-fixed inputs
	Cereal acreage (ha)			59.5		32.4			9.8		214.9
	Other acreage (ha)			22.4		t8.l			0.5		131.5
	Labor (AWV)			1.3		0.5			0.8		5.0
	Variable inputs
	Equipment (F)			tt3463		71827			12402		382560
	Fertilizer (F)			8s209		47036			10025		304896
	Pesticides			72543		51201			2258		278440
	Seeds			37398		2373t			I 184		1 I l5l9
	Others (F)			30274		4t321			I 535		3649t4
	Hypotheses	Mean			Std-Dev			Min			Max
	Hv:All inputs	0.9319		0.0969			0.6223			I
	variable
	Hl: Land & labor	0.8773		0. I 552			0.5158			1
	fixed
	H2: Cerealacreage	0.9262		0.1072			0.6006			I
	fixed
	H3:All land fixed	0.9271		0.1047			0.6006			I
	H4:Labor fixed	0.8915		0.1 386			0.5158			I
				Hv	HI		II2		H3		H4
	Estimated Technical Efficiency	nb	%	nb	%	nb	%	nb	%	nb	%
	:l		88	46.8	92	48.9	89	47.3	93	49.5	89	47.3
	between 0.95 and I		29	t5.4	t2	6.4	26	13.8	22	tl.7	l7	9.0
	between 0.85 and 0.95		35	18.6	13	6.9	JJ	t7.6	31	l6.s	18	9.6
	<0.85		36	19.1	7l	37.8	40	2r.3	42	22.3	64	34.0

Table 4 .

 4 Potential input reduction (%)

Table 5 .

 5 Potential Change in Cereal Yield (All producers)

Table 6 .

 6 Potential Change in Cereal Yield (Techrically inefficient producers)

	Inputs		Hv		H1
		Mean	Std-Dev		Mean	Std-Dev
	Cereal acreage	-10.68	12.53		-t0.21	14,r2
	Other acreage	-r 5.68	21.96		-15.4s	22.96
	Labor	-8.65	12.30		-5.88	t1.99
	Equipment	-8.71	12.12		-13. l0	16.18
	Fertilizers	-12.33	t6.14		-15.49	18,56
	Pesticides	-11.99	15.7t		-13.72	t6.91
	Seeds	-l 1.15	15.62		-14.65	t7.97
	Others	-t2.26	18.83		-14.81	19.24
			Mean	Std-Dev		Change (%)
	Observed yields (F/ha)		8063	242s
	Optimal yields (F/ha)
	Hv		9166	2456		13.68
	H1		91 l8	2316		13.09
	H2		8980	2389		11.37
	H3		8939	2392		10.86
	H4		9413	2430		16.74
			)		Optimal yields (F/ha)
		Mean	Std-Dev	Mean	Std-Dev	Change (%)
	Hv	7631	1975	9674	r999	26.76
	HI	7480	1809	9525	r702	27.34
	H2	7565	1908	929s	t907	22.87
	H3	7557	t946	9262	1941	22.56
	H4	7472	1802	10026	I 802	34.18
						I6

Table 7 .

 7 Non radial technical efficiency measurement

Table 8 .

 8 Potential input reduction (%)

				:l		Between	Between	< 0.6
						0.82 and I	0.6 and 0.82
		mean	Std-Dev	nb	%	nb	%	nb	%	nb	%
	Hv
	Cereal acreage Other acreage	0.8603 0.7191	0.1762 0.32',70	.95 90	50.5 47.9	22 t2	ll.7 6.4	52. lt	27.7 59	,t9 75	10.1 39.9
	Labor	0.9327	0.1308	136	72.3	l6	8.5	29	15.4	7	3.7
	Equipment	0.9269	0.1396	127	67.6	28	t4.9	25	13.3	8	4.3
	Fertilizers	0,8152	0.2259	93	49.5	l9	10.1	32	t7.0	44	23.4
	Pesticides	0.8190	0.2342	96	51.1	2l	11.2	27	14.4	44	23.4
	Seeds	0.8363	0.2368	103	54.8	23	12.2	22	lt.7	40	2t.3
	Others	0.7855	0.2766	105	55.9	8	4.3	l7	9.0	58	30.9
	Mean	0.8364	0.1815	92	48.9	1l	5.9	62	33.0	23	12.2
	H1 Equipement	0.8926	0.1762	lll	59.0	29	15.4	32	17.0	t6	8.5
	Fertiliers	0.8280	0.2200	98	52.1	l6	8.5	35	18.6	39	20.7
	Pesticides	0.8507	0.2100	r03	54.8	22	tt.7	31	16.5	32	t'7.0
	Seeds Others	0.8041 0.7365	0.2563 0.3098	96 98	51.1 52.1	t6 8	8.5 4.3	30 ll	16.0 5.9	46 7l	24.5 37.8
	Mean	0.8224	o.2022	93	49.5	8	4.3	52	27.7	35	18.6
				Hv					HI
			Mean		Std-Dev		Mean		Std-Dev
	Cereal acreage		-13.97		t7.62
	Other acreages		-28.46		32;10
	Labor Equipment Fertilizers Pesticides Seeds Others		-6.73 -7.31 -18.48 -18.10 -t6.37 -21.45		13.08 13.56 22.59 23.42 23.68 27.66			-10.74 -17.20 -14.93 -t9.59 -26.35		t7.62 22.00 21.00 25.63 30.98

Agriculture's Environmental Extemalities: Is There a Free Lunch? DEA Evidence for French Agriculture

concerning existence of opportunities for input adjustments as well as for more global recommendations concerning the existence of generic opportunities for input adjustment.

With regard to the question posed in the title of this paper, the paper finds that across altemative specifications and concepts of technical efficiency substantial evidence exists to support the notion that adjustment of technical inefficiency of farm use of fertilizer and pesticides presents an important opportunity for reduction of environmental impacts associated with these inputs. Piot I., Vermersch D. (1995), Mesure de l'efficacité technique en présence de fixités factorielles : une application à l'économie céréalière, Revue d'Economie Politique, 105,3 Thomas A.C., Tauer L.V/. (1994), Linear Input Aggregation Bias in Nonparametric Technical Effrciency Measurement, Canadian Journal of Agricultural Economics,42,77-86.

Vermersch D., Boussemart J.P., Dervaux 8., Piot I. (1992), Réforme de la Politique Agricole Commune : Evolution des rendements céréaliers entre infficacité technique et prixfficacité, Rapport pour le Ministère de L'Economie et des Finances, Direction de La


some environmentalists believe that nature has intrinsic value whether humans are around to sense and experience it or not, therefore they do typically recomnand the elimination of pollution. Economists tend to deal with pollution in a dlfferent way because thel'consider it occurs on1\, when one or more individuals suffer a loss of I'elfare' So pollution being a neçtative externaliti-there is an optirnal 1eve1 of pollution. The search for this efficient 1et'eI raises difficult problems because we need to kno;* the private beneflt of the polluter and the external cost.

Damage functions are ver!,'difficult to estimate in practice since they inyol-ve components whic[ do not have observable prlces, So speciflc val-uation methodologies are needed. Moreover the identification of damage categories is opening the way for disputes about their relevance because preferences for enyironmental assets are yery contingent ' But as suggested by Baumol and Oates (1988, pp.240-243\ there is good reason to belieye that the demand for ent'ironmental qualitl' will rise with income. This position is consistent with the recent emergence of the ent'ironmental movement uhich developed a consciousness about the value of environmental assets. Às a consequence the economist will have to put hj-gher vaLues on social costs since it can be expected that willingness to prevent environmental stress is going to increase in the future. Therefore 1t can be argued it is possible to reconcile ecology and econom)'.

The development of intensive livestock farming creates detrimerrtal effects which include amenitl' losses due to noiÉe, bad smell and aesthetic changes. But up to nolJ thel' are considered as being small compared t{ith the contamination and eutrophication of ground and surface waters, due to run-off and the leaching of animal uastee. There is now in France a great concern with the nitrate contamination becauee nitrate concentration in drlnfing water ls above the permit level of 50 mg/1 ln several areas. This paper is restricted to the nitrate component of pollution due to liquid manure and foeuses on nitrogen excess at the farm Ievel. This relevant variable 1s reviewed in the flrst point which is mainly descriptive, since using microdata farms are classified according to the level of nitrogen excess. There cIearll' exists a threshold for nitrogen excess abotre which farm operators are polluters. But the point is why they do not respect agronomical standards and so pollute the environment ? To deal with this problem an econometric model of farmers'behaviour in face of manure and mineral fertilizers is developed ln the second point. It is based upon a Tobit specification in order to take this threshold effect into aeeount. the third point is devoted to the econometric estimation on panel data for the years 1-982-86 and the dlscusslon of the results emphasizes technical and allocative lneff iciencies .

1-NJ.trogen exceas from intensive aninal production at the farn IeveI Due to the changes in society, with urbanization and the increase ln purchasing power, the meat dernand has considerably increased in the last decades. On the suppl)' side, a converging set of technological advances, fiâit'tlf in poultry and plg production, has made it possible to respond to the needs that arose. These advances hal'e been adopted in Fratrce in the sixties by the most dynamic farmers genera11l'settled in smaLl holdings located in regions without employment opportuni ty.

During the seventies cheap inport of feedstuffs contributed to the possibilities for development in intensive stock-keeping. But the intensification at the European leveI has led to overproduction and to lower profit margins, Bo that the Êcale of operatlons has enlarged leading to eonsiderable anlmaJ waetee per unlt of Land in some cases. The pollutlon effects of the inteneification has been lncreased by a parallel development towards regional specialization to such an extent that more than one-half of in onI1' one region, namell' French pig production is now located Bri t tanl' Àccording to the number and the type of livestock it is possible to estimate the avalaibi.litl, of fertilizer components of animal origin per farm. But otherxise artificial fertllizers are bought and h'e have to take the total amount of nutrients into aceount. If the application rate iu cultivated land of total nltrogen from aninal or mineral origin, is more important that the extraction, which depends on the t]'pe of crops and fields, damage to environment ensues. We can assume that these damages are proportional to the excess of nitrogen.

In fact, the effects of nitrogen surplus are nore complicated because groundwater pollution depends on the nitrogen cycle in the soils. Furthermore the effects of on-site nanure spreading are related to the nature and the state of the soil. Soils can be distinguished as being ni-1, poor, average and good. This classification has to be compared with weather conditions, which ultimately leads to three kinds of gurface : those on which slurrl'spreading is unsuitable at any tirne of year, those on which it is unsuitable onll'in winter, and those on u'hich slurry can be spread at any time of year. So the relationshlp between a certain amount of fertilizers and the consequent damage is not a sirnple one.

The nitrogen excess is estimated from the French farm accountancy data network, a representative sample of fu11 time farms giving detailed informations on 6500 units. À panel with 489 intensive animal farms is selected from I9BZ to 1.986. fntensive anlmal farming is defined by a ratio of stock-keeping per hectare (number of animals corresponding to one cow one year over than 1.5), and the total nitrogen is expressed in kg of mineral nutrient. Some holdings do not produce erops and they have only animals and they export manure. But export flows of rnanure are unknown therefore farms with less than 5 ha are excluded from the eample and are not taken into account in reeulte reported belox.

Às lndicated in table L along the five years surpluses reach high val"ues since the grand mean of total animal and mineral nitrogen excess per ha equals 176 kg varying from a minimum of 170 kg in 1985 to a maximum of LB1 kg in L986. But the dispersion of these results is ver)'important as shown by the staudard-de*iat,.lt. It is possible to compare the grand mean of 176 kg with results reported by other authors, as for instance Becker, L989, p.191who did simllar calculations for Lower-Saxon\/ in FRG. For the same period, he obtains surpluses varying from 324 to 347 kglha, twice the French result.

The importance of the variance concerning the French results may be explained bl' differences between t!'pes of farming. This point 1s clear in table 2 ilhere the distribution of holdings b]'type of farming according to the difference between total supply of nitrogen and total plant fixation is given. For all types of farming, deficit units accoullt for LZ & ; balanced units for 9 & and excess units for 79 %. The break-down by type of farming in table 2 shows that excess units are more numerous among intensive livestock farms (85 $) than in nixed farms (78 *). Reversely there 1s a lack of nitrogen in L4 * of the mixed farms, agalnst B % in intensive livestock farms. Àrable farming occupies a mediunr range in both cases.

Table 3 provides other data concerning the distribution of farms according to the leveI of nitrogen availibilitl'.

It is assumed that 30 kg of nitrogen per ha is an agricultural threshold belou which there is no utilization b)' the crops. So this level corresponds to a negative excess. The figures in table 3 shov; a steadl' rate of farms, about one-harf, for which there is an important excess, over 1-00 kg/ha, whire the number of high porluting units, f or r+hich excess is greater than 200 kglha, has declined from ZL.2 % in 1982 to L5.9 * in 1986. But the rate of very higl'r poltuting farms, for which the difference between total supply and utilization by prants exceeds 500 kg per ha stirl renains stable 4.L t to 4.9 %. Moreover there is an increase of the number of units below 30 kg per ha from 21,.0 in 1982 up to zj.l in 1986.

Farner behaviour and nanure utilization

Manure spreading involves costs but generate benefits for the farmer since organic nitrogen can be substituted for bought fertilizers. sometime those benefits are not enough to balance epreading costs Eo the free diepoeal hypotheeie ie not met, but ueual.J.y manure epreading ls a prof ltabte procegÊ at the farm level.

For a given level of output the total amount of avallable organic nitrogen is fixed but usually too emall to fu1filI plant requirements. Thus the cost mininizer has to determine the optimal level of mineral nitrogen he has to purchase. Therefore nitrogen exceËs is not consistent with a cost minimizLng behaviour because it shows technical and allocative inefficiencies. Moreover nitrogen exeess creates soclal costs because a fraction of nitrogen spreaded is not assimilated by the crops.

Let us begin, then, by introducing a model similar wlth one which has been considered to take into account land and family labour fixity (Vermersch, 1989). The farmer wlshes to minimize the cost of production subject to the relevant constraints concerning the technology and predetermined levels for fixed factors. Note that this cost-minimizing hypothesis encompasses the profits maximizing one which is more restrlctive. The input-vector is divided into two for variable inputs and z for fixed inputs. contains all input bundles (x,z) which can give in the hyperplan 7.ç .

We ehaIl dlstlnguish three categories inpute: Iand T, family labour Lrr and nltrogen through liquld manure Nr .

sub-r'eetors x

The set X (y) Y, and z lies of fixed provieion There is a constraint on land availability (br)TsT and the fixed cost of land is Ptf. If this constraint ls binding then it is possible to infer the long-run equllibrium level for land (Bror+n and Christensen,198f i Guyomard and Vermersch, 1989 ) . For arable farms , there is econometric evidence that this optimal leve1 is greater than T so in the long-run there is a pressure touiard an increasing acreage of farm holdings. Therefore land is a quasl-fixed factor because if the constraint (br ) l.las relaxed farmers would adapt farm acreage in order to meet farm size optimality, this process would result into more land under cultivation.

The constraint input and it is given by : (bz ) relates to the familv labour (bz) L > Lr

The quantity Lr of available family labour provides the lor+er bound for the total amount L of labour input. This constraint is not necessarily binding because some farm operators have to hire rdage earners because there is no enough family labour avaitable on the farm : Lt is smaller than the solution of problem t1l for labour. If Iabour is demanded in amount smaller or equal to Lr then the constraint is binding. The latter case is often observed and involves a low mobilitl' of agricultural labour due to poor job opportunities. Fami1l' labour is a semi-fixed input.

Farms can be classified into two categories according to whether or not the family labour constraint is binding. For the first category for which the constraint is effective there is 6ome hired labour on the farm. Therefore given a costninlmizing behaviour, the optimaL level of labour lnput equals famil-y Labour pl.us htred labour. The baelc idea is to use this informatlon to derlve the optlmal LeveL of input for the eecond category of farms for whlch the constraint is not binding.

À Tobit specification can be used to handle these two categories of farms Vermersch (1989) has estimated a tobit model using a sample of arable farms in France. The optimal level of labour has been calculated for each farm. Very often, there 1s a disequilibrium which is characterized by an excess of famlIy labour. Prices and technolog!'given there is tuo much fanily labour on farms.

Regarding nanure utilization farms can also be classified into two categories so the Tobit specification can be extended to this new problen. FormaIIt' the manure constraint ls:

(ba) N 2 Nr

Nr equals nitrogen provision through liquid manure, thus the farmer has to spread this mininum quantitlz. The total amount effectively spreaded is equaled to N which includes Nr plus nltrogen Nc provided by chemical fertilizers. Thus Nr and Nc are substitutable.

There is no opportunity to sell Nr so the farner has to use it in the production process. Thus the (bs ) constraint is similar to (bz ) because Nr is an input whose utilization is subject to technical and allocative inefficiencies. In order to go forward let us lntroduce an agronomical standard Sr which equals, for a given crop mix, average nitrogen requirements per hectare. Sr is farm specific and above this standard pollution occurs. This expression completes nodel specification. It is with a specific threshold for each observation instead one for the whole sample.

3-Enpirical results

former I at ter

The problem involves two thresholds Sr T and Nr . The is a farm specific agrononical standard whereas the equals nitrogen provision througtr liquid manure. Following Shephard's Iemma, derived easily obtained. Then Iet us consider the specification for nitrogen demand : The output le represented by y i pr is the price of factor xr, f = 1,.,4 reepectivel.y : fueL, chemical fertilizers, capital (buil.ding and machinery) and feed. Ouaei-flxed factore zà lncl.ude famlLy labour and acreage under cultivatlon. data batrk is a panel of 500 f arms f or the period Lg82-1986 (see annex). Estirnates reported in table 4 has been calculated on the pooled sample uhose size is NT = bO0. In order to assess estimation significance a chi-sqttare statistic 1s provided. TabIe {. Moreover betxeerr , tti thin and cl ass ica lquasi generalized least square estinations are alsct corr'sldered. Each calculation has been run for three different cases : t-ratio and chi-square (Tobit Obtained values are consistent (annex). Thel-are closed to (Bonnieux and Rainelli, 19BB). model ) are in parenthesis. uith eross-sectional results values publ-ished elsexhere Furthermore, these elasticities generally decrease ( in absolute term) with the closerress (proximitl') of the nitrogten allocation to an ef f icient 1er.e1. Às a consequence, nltrogen taxation rlou1d irrduce a process xhich would reno\-e the observed inef f iciencies.

Formally

  ) reveals allocative and ma)-be technical inefficiencies because tço much nitrogen is spreaded so eostminimizer would have bought a smaller amount thatr Nc of chemical

  = âo + Er al Pr + b.y + Eu Cn,Zn t3l

  .able is the dependent t'ariable is explained by a Tobit model TabIe 5. Fertilizer own prlce elasticitl. (calculated at the eample mean)

Table 2 .

 2 Distribution of holdings by type of farmlng according the nitrogen availabiLity(cumulated data)

		def ici t units	balanced uni ts	excess uni ts	all %	units number
	Mixed farming cattle and dair\') (arable land+	1{ t	8t	78 t	100	162 3
	Àrable farming (cereals+sugar	9*	t_0 t	81 t	1-00	728
	beets+oilseeds )
	fntensive livestok (pig and poultry)	8&	7%	85 t	L00	78
	À11 farms	12%	9%	79 %	r-00	2429

Table 3 .

 3 Farm distrlbution according to nitrogen exeess (in t)

	N-Excess (in kg/ha)	82	83	84	85	85
	> 500	4.5	4.1	{.5	4.5	4.9
	> 300	7.6	7.8	ot	8.2	7.4
	> 200	2t.2	1,9 .2	1.7 .1	19 .6	15.9
	> 100	50.9	51.5	53. 2	50. i	48.9
	>50	72.4	72.6	72.2	72.0	71.1_
	>30	79.0	81 .0	80.2	77 .9	76.9
	< 30	21.O	19.0	l_9. B	22.1	23.L

Table 4 shoxs

 4 Tobit model f21 estimatiou with the parametrizatior: (31 .

  Tlre

Ànnex : Data and other resulte

We cattle units have used a panel per hectare (N=100) farms with five years nore than 1.5 (1982-1986). of for Four varlable inputs and two quasi-fixed factors are taken into account : the model is specified with prices for fue1, fertilizer, eapital and feed ; acreage under cultivation and family labour are included as fixed lnputs. z3 represents materials for which we have no price i 24 is livestock in cattle units. For the capital input, it 1s assuned that the service flow from the stock of capital is proportional to this stock and, as in Dornont and Sevestre (l-986), the user cost of capital is only the apparent interest rate. The 1evel of output 1s measured b]' cash saIes.


F Bonnieux

P Rainelli

D Vermersch

THE PROVISION OF ENVIRONMENTAL GOODS SY AGRICULTURE

Keywords: Amenities, Environmental goods, Wetland preservation, Agricultural Policy

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE PROVISION OF ENVIRONMENTAL GOODS SV AGRICULTURE ln some cases such as "point amenities", an attractive waterfall fo. example, the owner of the estate where the amenity is located can charge the consumer fer entry to that site. But here the existence of exact boundaries allow exclusion. So this type of amenity is mixed public good. ln other circumstances environmental values can be easily captured through the pricing of amenity-related goods. Through commercial marketing some eommodities produced in specific territories are sold over their "normal" price. The extra-price refleets the attributes of the territory: wilderness, quality of the natural resourees, cultural heritClge ... Institutional measures can enhance the eommoditisation, and labelling is one of the most efficient. By this mechanism exclusion is ereated.

Close to the pricing of amenity-related goods, is the case where the attributes of the environ ment are embodied in the property value (hedonic price method). Here the market ior these attributes is implicit through the premium the household accept to pay to enjoy such a countryside commodity. For example, Garrod and Willis, (1992), observed in a rural are" of the United Kingdom that Woodland and water have a positive influence (respectively .07 % and .05 %) on hou se priees, when marshland reduces house priees.

A more comp!ex form a marketiserl environmental product arises with "non point amenities" with non exact bo~ndaries when environmental entrepreneurs downstream or upstream are engaged.

But in any case for the development of a market to internalise the external benefits four necessary conditions can be identified (Crabtree, 1994):

-a well-defined set of property rights; this point is central to tne whole internalisation proeess.

-Iimited local free access to reduce the potential for local substitution -the ability to Iink use to payment and exclude nLln-paying users -a level of income net of transaction costs that produces an acceptable 'Blurn to investment The internalisation can be also obtained by other ways than commoditisatioi1 and pricing, (Blëehliger, 1994). There are actions by interest groups such as collective organisations or non-governmental organisations which buy ownership or buy specifie pro perty rights, or direct government intervention using taxes and subsidies. But some amenities have the characters of pure public goods. This applies most nctably to t'le nonuse types of amenity, such as existencE: values.

Environmental good demand

The value of these countryside goods calls for Contingent Valuation Method (CVM), since it is the only available technique which can capture existence value. Even if the value obtained may vary both over space and time, it may be of some interest to give some empirical illustrations of well-defined amenities.

ln SWGden various interesting stucl'~s [START_REF] Navrud | Pricing the European environment[END_REF] give information on Swede's Willingness-to Pay (WTP) to preserve endangered species living in forests. Kristrom's study shows that WTP amounts SEK 95 per person. In an other study Johansson obtains an average of SEK 85 to protect endangered species, but to protect them the exploitation of the forestry must be changed. To maintain an open landscape in areas already dominated by forF.!sts, [START_REF] Drake | The non-market value of the Swedish agricultural landscape[END_REF]. used CV to estimate the value of the agricultural landscape. He obta:n~a WTP of 78 ECU per person or 140 ECU per hectare. Similar monetary values have been obtained in the context of Austria [START_REF] Hackl | Subsidising external benefits: the case of agriculture and tourism in Europe[END_REF]. In U.K. CVM is used to value the benefits which residents and visitors might derive from alternative agricultural landscapes. In the Yorkshire Dales National Park people agree to pay the fa~mérs for avoiding abandoned either agricultural landscape. ThE: WTP amounts E 24 per household, [START_REF] Willis | Landscape values: a contingent valuation approach and case study of the Yorkshire DaJes National Park[END_REF]. Such results are valuable because they can serve as guidelines for è,rêc,t payments.

Environmental good supply

Ali the results reported refer to the preference of people about how much they are willing to pay the amenities provided by farmers. This is related to the demand side, but on the supply side there are few studies. To stimulate supply and determine the correct level of incentives to offer farmers CV apjJioac:h is relevant. The iswe can be illustrated using a case study [START_REF] Bonnieux | Contingent valuation and the design of agrienvironmental measures[END_REF].

The CV approach has been used to ask farmers how much they were hypothetically Willing To Accept (WTA) to change their farming practices and then to increase the provision of environment<>1 goods. The case study is concerned w!th the implementation of a standard payment scheme in a limite area of welland which has been designed an ESA. The functioroning of the standard payments is straighforward since ail farmers are offered the same price for accepting the same condition to protect and enhance the environment. Typica!ly "le conditions relate to the acceptance of constraints on farnl operations; four levels of management prescriptions were offered to farmers. ln this context several options to increase the provision of environmental goods are available . increasing the rate of enrollment, . offering additional options in the scheme ln order to design future policy a variety of scenario were conside~ed and fa~mers were asked to participate in contingent markets. 80th eligible and non eligible farmers were surveyed.

Farmers facing an environmental scheme

The objective of this section is to develop a model of farmers' behaviour covering both eligible and non eliqible farmers. This section is structured as follows. The tirst paragraph is a brief presentation of some useful tools while the second and third paragraphs are devoted to the modelling of environmental scheme. In second paragraph we deal with eligible farmers and consider actual behaviour while the third paragraph emphasises the case of non eligible farmers and their contingent behaviour. It is shown that a similar model can be applied to an ex ante and an ex post perspective since there is a direct relationship between the WTA revealed in an hypothetical market and producer surplus variation.

Basic too/s

The production possibility set is by far the most general way of characterising farm technology since it allows for multiple inputs and multiple outputs [START_REF]Applications of duality theory[END_REF][START_REF]A characterization of the normalized restricted profit function[END_REF][START_REF] Mc | Cost, revenue and profit functions" in "production Economics, a dual approach to theory and applications[END_REF]. Here the farm's production possibility set is denoted T. Take any feasible production plan 1 in T and assume that:

1 =(x,y,z)
where x=(x, i o "l, .... n) and is a sub-sector of variable inputs Clnd Y=(Yjj~l, .... I) and is a sub-vector of outputs. The third sub-vector z requires some expianation as it ir.cludes two different components (i) quasi-tixed factors such as welland z'" and dry land Zh",; (ii) relevant socio-econoic characteristics (e.g. age, education) and the environmental attitude of the farmholder. The price vectors w and pare associated with vectors x and y.

A very basic set ofaxioms for T is considered : production;

(HT2) There is free-disposai for inputs and outputs: V(x,y,z)ETgiven (x',/)suchas xi",x,/~y,then (xi,y',Z)ET

I1 (p. w,z) =max[p'.y-w'.x . . F(x,y,z) =OJ :c.y [2]
This function is continuous, non-decreasing in p, non-increasing in w, homogeneous of degree one and convex in (p, w).

Hotelling's lemma which can be proved by direct application of the envelope theorem, it gives farm's demand x' and supply y':

. on

x =----- 1 éh1. on y = - } op} i =J, ... /1 j = J, .. ./ [3]

Modelling actual behaviour

Typically, management prescriptions involve a set of constraints on specifie inputs (e.g. pesticides, fertilisers) X;,s =0,1, .. S is the above bound associated with the se! of constraints imposed by levels of the environmental scheme. The corresponding prcmium equals p' per hectare of wetland enrolled in the scheme. Let us note that the non-enrolment case is also taken into account providing that s = O,x;' = +00, pli = O. Let us consider the farm's profit maximisation problem : of the corresponding variable inputs. The virtual price provides the marginal increase in restricted profit due to a marginal relaxation of the equality constraint x, = Xc .

Using the restricted profit function, program [4] can be rewritten as:

[6]

An alternative specification is

[7]
it is only valid where s # O. It does not cover the case where farmers do not join the scheme.

It must be emphasised that there is no direct Iink between the premium pS and the it follow~, usiflg the virtual priee tha!:

[8]

[9]

[10]

Condition [10J has a nice economic interpretation: the farmer chooses the agreement (x;, p )(x;,.) where the margina: cost Wc of tlle restricteci input equals the marginal revenue w, due to the production of marketed goods minus the valuations z",. ~p . This last term is u x, associated with the marginal value attributed to the negative externality implied by the use of xc' Tl1e environmental agency can determine the optimum premium associated with w, if it has complete information on the restricted profit function.

Modelling contingent behaviour

Non-eligible farmers are now considered and the objecti'/e here is to model the WTA for entering the environmental scheme. Let us begin with program [1] whose solution gives a reference profit function:

n (p, w,z)= nR(p, w_"x;,z)-w;X;

where X; denotes the optimal value of a specifie input generating external effects.

Farmers' WTA to limit the use of x, can be intcrpreted as being a premium:

[11]

(

  HT3) T is a strictly convex set. When the production possibility set sastisfies the axioms above, the transformation function F(x,y,z) =0 representing farm's technology, can be defined. It is assumed to be a differentiable function. The graph of the transformation function shows ail the technicallyefficient production plans. Providing there is a vector (w, p) of strictly positive prices the following profit maximisation program: Max p'.y-\1:' x x.y F(x,y,z) = 0 [1 J admits a solution. This predicts farm's market behaviour. A useful tool is the farm's profit n(p,w,z):

  TH~PROVISI;)N OF ëNVIRONMENTAL GOOeS BY AGRICULTURE Max p'.y-w'.x+ pS.zx If constraint (a) is binding then the profit function depends on the threshold s' being a solution of program[4]. If constraint (a) is not binding then the profit function depends on the price-vector Wc of inputs subject to environmental limitations. This result is true if the farmer does not enter into the scheme (i.e. s =0).The concept of a restricted profit function leads to an alternative interpretation of program [4]. Let us consider the farm's profit maximisation problem with the equality constraint Given Max p'.y-w_c'.x_ c w_c,xc,z)=max[p'.y-~c'x_, .. F(x_"x,.,y,z)=O] . This function is usefLiI in x_c•ydefining the virtual price (Lau, 1976) associated with the equality constraint Xc =x" Thus: anR w,. =-a-,it follows that Xc =Xc is a solution of program[1] where Wc is the price-vector

  impact on farm income imposed by the constraints on farm operations. At the optimum of program [6J the constraint (a) may possibly be not binding. This means thal a farmer can enler the program without modifying farming prac::tices. Therefore p' is an extra-income authority in charge of the scheme and eligible farmers. If an environmental agency has complete information on farm operations it can Iink compensatory payments and income loss due to more environ mental friendly practices. Instead of considering a finite number of levels in the environmental program, let us suppose that a cO:ltinuous choice is available to eligible farmers. A specifie agreement '5 then defined by x, and p(x".) with ~p < O. The premium is a decreasing function of the u x, above bound Xc for xc' The profit maximising problem is then rewritten : Necessary first order conditions follow. They are sufficient providing ( HT):

Table 1 Modelling actual behavlOur (ordered 10g1t multrnomlal) dependenl vall,JOlc 1 :: no agreemenl 2 :: lever 1 agreement 3 :z other levels

 1

	Intercept

as a percentage of lotal dry land

		0	ref.
	use on maize	< 105	0.97
			Il.281
		> 105	•0.75
			rD.7Ql
	use on wetland	< 25	-0.38
			10.261
		25• 50	/07:, 1.25
		>50	ret.
	n• of gross IIveslock unitslha	< 1.28	ref.
		1.28 -1.8	0.49
			10.221
		1.8 -2.6	2.56
			Il.00I
		> 2.6	2.87
			19.38\
	n• or employees	0	ref.
		> 1	0.42
			/057'
	Correcl predictIons		70.6%
	-2 IOQlikelihood		177.30
		35-60%	0.25
			10.13)
		> 60%	1.07
			(2.06\
		0%	ref.
	Malle	< 25 %	-0.71
			10.54\
	as a percentage ot total dry land	> 25 %	-2.32
			15.261\
	Intensification
	minerai nitngen (kglha)
		0	ref.
	use on maize	< 105	1.46
			(2.211
		> 105	1.67
			(2.89\
	use on wetland	< 25	1.09
			13.711
		25 -50	-1.79
			17.911
		> 50	ret.
	n• ot employees	0	ret.
		> 1	-0.41
			10.53)
	Correct predictions . 2 IOQlikelihood		85.8% 184.88	-

chemical fertilisers.

Table 2 is concerned with farmers' contingent behaviour. They were faced with a dichotomous choice: entering or not entering an hypothetical environmental scheme. Il is interesting to note that variables which describe farmers' attitude play an important role. The probability of entering the program increases with the number of farming bodies and farmers who favour of organic farming and green tourism are more likely to enter the program. There are differences between actual and contingent behaviour. The influence of the variables which describe land use (share of welland, grassland, maize, cereals) and intensification (use of minerai fertiliser and Iivestock units) is similar to the effects obtained with the ordered multinomial logit mode!.