Isabelle Piot

Dominique Vermersch

Robert I ) Weaver

Agriculture's Environmental Externalities: fs There a Free Lunch? DEA Evidence for French Agriculture

Thç existence of technical inefficiency ofiers the opportunity for a 'free lunch' not typical$ consistent with neoclassical theory. Within the context of management of external efrects of production processes, when external effects are related to the use of particular inputs, elimination of technical efffrciency through reduction of input use represents a means of reducing external impacts. An tmportant example is found in agriculture where substantial environmental impacts are generated by particular inputs. Within this context, this paper considers the usefrrlness of Data Envelopment Analysis for estimation of potential input reductions and assessment of potential reductions of envirônmenal 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 opportunities are of particular interest where input reductions could lead to improvements in the external effects of a prôduction 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 and/or transformed, resulting in off-site impacts of the input use.

In this paper, v/e consider the usefulness of Data Envelopment Analysis (DEA) for identification of potential agricultural 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 cohsidér the usefulness of Russell measures of input specific technical efficiency. Next, we apply the methodology to assess the existence of a free lunch type of opportunity for reduction of inputs in French cereal production. Of particular interest are opportunities to reduce pesticide and fertilizer use.

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 paper, 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 efficiency 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]Kumbhakar, 1988). 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 ofthese 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 efficient 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 radial 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 efficiency would follow the ray AE to point E.

Alternatively, if technology were nonhomothetic, economically efficient adjustment would follow a nonlinear expansion pattr,'eg. 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. Within 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 I provides an illustration. Suppose Jf,is fixed at Xft. 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 inefEcient. Instead, adjustment would proceed along AR.

The implications of this problem for the measurement of technical efficiency were recognized by [START_REF] Farrell | The Measurement of Productive Efficiency[END_REF] though he maintained a focus on radial technical adjustment. Hall and Winsten (1959) 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]Fâre, Lovell, and Zieschang (1933); and applied by [START_REF] Banker | Efficiency Analysis for Exogenously Fixed Inputs and Outputs[END_REF], Kamakura (1988), Adolphonsorç et al. (1990). The input based measure of subvector efficiency can be defined following these studies for a set of -Ifirms indexedT: 1,....J, each with access to the same technology that transforms a vector of inputs r, eÀf. into a vector of outputsy, eRy . More generally, for the set of firms definea(J xN/ input matrix Xanda (JxM) output matrix I. Suppose the input matrix is partitioned so X-(X',X') where vc{1,2,...N} \,ith vni=A and ywV = {L2,...,W\. 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 can be equivalently written x, = (xl,\ ). Suppose the technology satisfies the augmented regularity conditions adopted by Banker,Charnes,and Cooper (198a). That is, v/e suppose the set of production possibilities is defined by P={(y,r)\y>Omaybeproducedfromx > 0} , satisfying:

[r1] : (!i,x) eP Vi :1, ...., J lP2l:P is a regular set, i.e. nonempty, closed, and satisSing the origin condition that y, = 0 if xi=0 ' ' lP3l :P is consistent with free disposal of inputs and outputs : V(y,.r) eP if x> x and y -< y, then (y,I) e P .

[PJ] :P is the intersection of all sets satisfying PI to P4.

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

(trrl P =.{0,x): x>l),,x,,y <ZAli,Z)', =1,1 eRll where )"=(4,\,...,As) istheintensityvector. Each X,, denotestheintensityatwhichactivity j is undertaken. To consider the measurement of technical efiiciency we partition the input vector into a subvector of variable input and a subvector of quasi-fixed factors , i.e. y = (xu ,xv) and write the production possibilities setP : J P={$l,x',x'):xu > x'x.,xî > xol,J <n",>)"j =U" eRl \ tll j=r By equation (l), the jth firm's production plan lO1,xi,xl) belongs to the production possibilities set, i{ and only il, (1t,,xj,x",).p . Input based radial technical efficiency (RTE) is defined following Farrell (1957), Charnes, Cooper, and Rhodes (1978), and Fârg Grosskop{, and Lovell Q99\: R,(!,,x,)= min{nr:n, x, eI$t,),R,.&} l2l where (yr) ir the input requirements set. The interpretation of,R7 as a radial measure follows from its scalar dimension which implies each factor will be reduced by the same nonnegative proportion. By comparisorç FÊire, Grosskop{, and Lovell defined subvector technical efficiency (STE) as follows:

si(t,,xl,xi1= min{sj:sj.x' e r(yj,x;),s;.&} t3l where f 0 j,x;) is the input requirements set conditional upon the level of quasi-fixed factors.

The distinction between ^R,1 and ,f; rests squarely on the application of an equiproportional reduction (thus, subaggregative) tci the entireverSus a subvector of inputs, where the elements of the subvector are by maintained hypothesis considered variable and controllable by the manager. Efficient adjustment is defined as conditional upon the levels of quasi-fixed inputs.

Figure I provides a direct comparison and illustration of these alternative measures. Suppose technology is homothetic, then À7 would be estimated by AE/AO while ,9; would be estimated by AR/AO. It is clear from Figure 1 that, in general, Ài > ,9i, a result that is proven formally in Piot and Vermesch (1995).

The usefulness of aggregative estimates of technical efficiency such as rR; and ^9; 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 Fâre and Lovell (1978) provides such input specific estimates. Rather than estimating equiproportional reductions as do JÇ and,9i in

[l] and [2] 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 pulposes of this paper (Kopp, 1981).

An Applicaton to French Cereal Production

In this section, we present estimates of radial, subvector, and Russell technical efficiency for a sample French cereal farms drawn from the Farm Agricultural Data Network (FADI.I) 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 specialued in soft wheat and matze, Vermersh et al. (1992). The sample caracteizes +Sol" 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.

We 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 l, we represent the product vector as including two outputs (cereal output (soft wheat and corn), 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. We 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 francsr. 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 I verify the specialization in cereal production by the sampled farms. Cereal production accounted for over two-thirds of their revenues and occupied almost 75o oîtheir 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 whrch maintain alternatives to Hypothesis 1 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 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 .R, when quasi-fixed exists according to Hypothesis 1. Based on our preferred specification, Hypothesis 1, Table 2 indicates that a 13% adjustment in inputs 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 the 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 alternative 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 7l under our preferred specification Hypothesis 1, to only 36 under Hypothesis I Economic data whether expressed in volume or value, reflects both technical and allocatve inefficiency. Past studies of technical efficiency have used both volume and value.

2 Fiire and Primont (1938) pres€nt results that indicate that use of value aggregate data will result in negatively biased estimates of technical efficiency. Thomas and Tauer (1994) have noted tlat measurement bias fiuly occur when linear aggregation is used. 3One AWU equals 2200 hours of labor.

V. This suggests that the distribution of the efficiency estimates is substantially different depending on the efficiency measure used (/ï or S/) 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 l3Yo 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: fu,,t=Qt-l)xr-s, where t, is the estimated technical efficiency score, x1y is the observed âtâ's input use , and s;,7 is the estimated slack variable for the ftt''s input and the fh fum. As reported in Table 4, this potential adjustment is substantial. For fertilizers, an estimated 15% 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 ihputs. Table 5 indicates that well over a 10%o 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 zero. The resulting estimated increase in yield is substantial, under Hypothesis I a2lYo increase in yield is estimated as possible for the subset of inefficient firms.

Tables 2 -6 report 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 l5Yo reductions are estimated as possible for fertilizers and for pesticides. The number of firms that are estimated to be efficient in their use of each input varies across inputi 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.

  x):x> xA,y <n",Zlr =L,l eRl i=1

Table 1 .

 1 Summary of data for efficiency analysis(188 French cereal producers, 1990)

Table 2 .

 2 Technical efficieniy estimates(Summary statistics)

Table 3 .

 3 Technical efficiency estimates (Frequency) Environmental Extemalities: Is There a Free lrlnch? DEA Evidenoe for Frenc{r Agriculture

				Mean		Std-Dev			Min		Max
	Outputs
	Cereal @ Other products (F)			487t72 199014		303618 141785			36392 393		r494657 804672
	Quasi-fixed inputs Cereal acreage (ha)			59.5		32.4			9.8		2t4.9
	Other acreage (ha)			22.4		18.1			0.5		131.5
	Labor (AWD			1.3		0.5			0.8		5.0
	Variable inputs
	Equipment @			rr3463		7L827			12402		382560
	Fertilizer (F)			85209		47036			10025		304896
	Pesticides			72543		5r20t			2258		278440
	Seeds			37398		2373r			1184		111519
	Others (F)			30274		4T32L			153s		364914
	Hvootheses	Mean			Std-Dev			Min			Nfax
	Hv: All inputs	0.9319		0.0969			0.6223			I
	variable
	Hl: Land & labor	0.8773		0.1552			0.5158			I
	fixed
	H2: Cereal acreage	0.9262		0.t072			0.6006			1
	fixed
	II3: All land fixed	0.9271		0.1047			0.6006			I
	H4:Labor fixed	0.8915		0.1386			0.5158			1
				Hv	H1			H2	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	15.4	t2	6.4	26	13.8	22	lt.7	t7	9.0
	between 0.85 and 0.95		35	18.6	l3	6.9	33	t7.6	3l	16.5	l8	9.6
	<0.85		36	19.1	7L	37.8	40	21.3	42	22.3	64	34.0
												13

Table 4 .

 4 Potential input reduction(7o)

Table 5 .

 5 Potential Change in Cereal Yield (All producers)

Table 6 .

 6 Potental Changein Cereal.Yield (Iechnically inefficient producaers)

	Inputs		Hv		HI
		Mean	Std-Dev,		Mean	Std-Dev.
	Cereal acre,age	-10.68	12.53		-10.21	t4.L2
	Other acreage	-15.68	2L.96		-15.45	22.96
	Labor	-8.65	t2.30		-5.88	11.99
	Equipment	-8.71	12.t2		-13.10	16.18
	Fertilizers	-12.33	L6.T4		-t5.49	18.56
	Pestcides	-11.99	L5.7T,		-L3.72	16.91
	Seeds	-1 1.15	L5.62		-I4.65	t7.97
	Others	-r2.26	18.83		-14.81	19.24
			Mean	Std-Dev		Chanee (7o)
	Observedyields (F/ha)		8063	2425
	Optimal yields (F/ha)
	Hv		9L66	2456		13.68
	HI		9118	23L6		13.09
	TT2		8980	2389		LL.37
	H3		8939	2392		10.86
	H4		94L3	2430		16.74
			Initial Yields (F/ha)		Optmalvields (F/ha)
		Mean	Std-Dev	Mean	Std-Dev	Change (70)
	Hv	763I	t975	9674	1999	26.76
	HI	7480	1809	9525	1702	27.34
	H2	7565	1908	9295	1907	22.87
	IB	7557	L946	9262	194t	22.56
	H4	74',12	1802	10026	1802	34.18
						L4

Table 7 .

 7 Non radial technical efficiency mea$rement

Table 8 .

 8 Potental input reduction(7o)

				-t		0.82 and I Between	0.6 and 0.82 Between	< 0.6
		mean	Std-Dev	nb	%	nb	%	nb	%	nb	%
	Hv Cereal acreage	0.8603	0.r762	.95	50.5	22	tt.7	52.	21.7	19	l0.r
	Other acreage	0.7191	0.3270	90	47.9	t2	6.4	11	59	75	39.9
	Iabor	0.9327	0.1308	136	72.3	l6	8.5	29	15.4	7	3.1
	Equipment	0.9269	0.1396	127	67.6	28	14.9	25	13.3	8	4.3
	Fertilizers	0.8152	0.2259	93	49.s	19	10.1	32	11.0	44	23.4
	Pesticides	0.8190	0.2342	96	51.I	2l	tr.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	5s.9	8	4.3	T7	9.0	58	30.9
	Mean	0.8364 0.1815	92	48.9	11	5.9	62	33.0	23	12.2
	HI
	Equipement	0.8926	0.I762	111	59.0	29	15.4	32	17.0	16	8.5
	Fertiliers	0.8280	0.2200	98	52.1	t6	8.5	35	18.6	39	20.7
	Pesticides Seeds	0.8507 0.8041	0.2100 0.2563	r03 96	54.8 5l.l	22 L6	Il.7 8.5	31 30	16.5 16.0	32 46	17.0 24.5
	Others	0.736s	0.3098	98	52.1	8	4.3	11	5.9	7L	37,8
	Mean	0.8224 0.2022	93	49.5	8	4.3	52	27.7	35	18.6
				Hv					H1
			Mean		Std-Dev		Mean		Std-Dev
	Cereal acl.ea,ge		-13.97		t7.62
	Other acreages		-28.46		32.70
	Labor		4.73		13.08
	Equipment		:7.3L		13.56			-L0.74		17.62
	Fertilizers		-18.48		22.59			-t7.20		22.00
	Pesticides		-18.10		23.42			-14.93		21.00
	Seeds		-16.37		23.69			-19.59		25.63
	Others		-21.45		21.66			-26.35		30.98

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 inefficiency 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 conceming 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 alternative 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 I'efficacité technique en présence de fixités factorielles : une application à l'économie céréalière, Revue d'Economie Politique,105,3 Thomas A.C., Tauer L.W. (1994), Linear Input Aggregation Bias in Nonparametric Technical Efficiency Measurement , Canadian Journal of Agricultural Economics,42,77'86. Vermersch D., Boussemart f.P., Dervaux B.,.Piot I. (1992)


Catherine Benjamin

Alain De Janvry

Elisabeth Sadoulet

Labor Market Imperfections and Classes ofFarm Households: A Predictive Typology ofMexican Ejidatarios

. In tllis latter case, households are endowed with different levels of asset (mainly land) and maximize expected utility in a stochastic environm~nt characterized by access to working capital limited by collateral ownership and by moral hazards associated wilh hired tabor, implying the need to incur supervision costs. Rational cl!oice by these households leads them to chose differential labor strategies, and thus to belong to different labor regimes, i.e. social classes.

In this paper, we start by briefly reviewing these contrasted approaches to the construction of household typologies. We ilien propose an alternative mode! of household behavior that introduces transactions costs in access to labor markets and household labor qualities with differential opportunity costs. This allows us to construct four household classes corresponding to labor regimes, where the predictive characteristics are assets per unit of low-skill adult household labor, and endowment in higb-skill Iabor. We t11en use data from a 1990 survey of ejidatario households in the State of Michoacan in Mexico to cbaracterize membership to t11ese categories.

We then extend the concept of assets to include productive assets, human capital assets, and social assets.

 DOCUMENTATION ÉCONOMIE RURALE RENNES 1111111111111111111111 IIIII

regarding the differential intensity of labor use per unit of land across labor regimes wben assets per unit of lowskill adult bousebold labor increases. We test for this regularity using the Michoacan household data. The observed class-specific relation between labor intensity (or yield) and farm size per unskilled adult bas important policy implications for the targeting of institutional assistance to different classes of farmers if the policy objective is to increase land productivity.

II. Types of Typologies

Labor regimes contrast households who sell labor (hire out), are self-sufficient in labor, and hire in (employers). Descriptive typologies then describe both the asset position of these household classes and regularities in their efficiency in resource use.

Barraclough distinguishes four labor regimes: sub-family farms (SF) wbicb sell labor, family farms (F) which are self-sufficient in labor, muitifamily medium farms (MFM) which hire a few workers, and multifamily large farms (MFL) wbich hire a large number of workers. The asset characteristics of these household types is then observed, particularly farm size. For perfotmance, yields and other productivity indices are observed to see if there exists an inverse relation from SF to MFL, thus justifying redistributive land refotm on an efficiency basis. The hunch is that there are labor market imperfections whicb allow smaller farms to benefit from cheap captive labor, and thus achieve higher levels of factor productivity. The systematic empirical application of these concepts across Latin American countries was fundamental in the subsequent design of land refotms in the 1960s and 70s, under the aegis of the Inter-American ColillDÏttee for Agricultural Development.

Utsa Patnaik is concemed with social differentiation which is based, in ber perspective, on the ability for some farmers to extract a surplus through the hiring of labor and the need for others to surrender surplus through the sale of labor. Her labor regimes are defined by a "labor-exploitation" index E defined as: Since the E-index measures the net between h and/ 0 , bouseholds could simultaneously sell and bire labor. The average asset position of each household category can tben be observed. Assets include land, Iivestock, machinery, farm tools, and non-farm productive assets (see Akram-Lodbi (1993) for an application to Pakistan). Indicators of perfotmance such as land and labor productivity and residual farm profits ~r hectare can be calculated by class.

E = (h -fo)IJ;,
2 [START_REF] Roemer | A General Theory of Exploitation and Class[END_REF] For Mexican households, CEP AL develops a typology which is also based on labor strategies. Households are classified into four categories of employers:

Peasants with less than 25 days of hired labor per year, Tran.sition farmers with between 25 and 500, Small entrepreneurs with 500 to 1500, Medium entrepreneurs with 1500 to 2500, Large entrepreneurs with more than 2500.

Peasants are in tilm divided according to the amount of land (in hectares of quality equivalent based on yield): infra-subsistence (S4ha) for whom land is insufficient to feed the family and the household is a net buyer of food; subsistence (4-8ha) who can feed themselves but cannot cover depreciation of capital; stationary (8-12ha) who can cover both food and replacement needs; and surplus (~12ha) who can save. Elaborate characterizations of the asset position and other characteristics of these household types are then given, as well as indicators of their performance.

Predictive typologies are based on extensions of the work of Eswaran and Kotwal. In their own work, they assume that households maximize a utility function in income and leisure, where income is derived from farm production, the sale (or hire) of labor, and the rentai (out or in) of land. Credit is obtained on the basis of land owned A which serves as collateral. Credit is thus constrained by asset ownership. Total bousehold assets n• is thus the sum of the rentai value of land owned at the rental rater and the collateral value of this land B(A):

n• = rA + B(A).
There are in addition, moral hazards in hired labor (h) behavior, with the need to incur supervision costs, s(h). Household time can thus be allocated to labor hired-out (f 0 ), own-farm work if), or supervision of hired tabor (s(h)). Optimal household behavior, given its initial asset position B., thus defines a typology of classes corresponding to endogenous labor strategies:

Asset position

Hire out Own-farm work Supervision Class fo /;

s(h) B. <K + 0 0 Agricultural worker K <S,. n• < 13i• + + 0 Laborer<ultivator 13i• <S,. s• < s; 0 + 0 Self cultivator s; <S,. s• < s; 0 + + Small capitalist B• > s: 0 0 + Large canitalist
Assets thus predict class membership. Optimum behavior in the constrained Pareto-efficient world of credit constraint and moral hazards on hired labor also predicts several regularities in yield and land-to-labor ratio across classes as assets rise. Specifically, the land-to-labor ratio is constant in the smallholder class and strictly increasing afterwards; yield is constant in the smallholder class, and strictly decreasing across the other classes. [START_REF] Carter | Imperfect Market Environments: Theory and Analysis of Agricultural Decollectivization in Latin America[END_REF] extends this mode! by specifying particular functional forms for the fu~ctions describing credit rationing and supervision. This allows to predict the shape of the restricted profit (land rent) function across classes. The land endowment ( A) at which this function peaks is expectedly the farm size toward which land transactions would make farm holdings converge. He consequently uses this model to anticipate the type of land consolidation that may occur as farms compete for land and simulates how specific policy changes may affect the distribution of land across classes of households.

m. A Model of Household Behavior and Endogenous Labor Regimes

The model which we develop here bas as a purpose to accommodate a commonly observed labor strategy, namely existence of households who both sell and hire labor. It also incorporates the existence of wide price bands in labor transactions costs, with low effective wages received and high effective wages paid. [START_REF] Lopez | Structural Models of the Farm Household that Allow for Interdependent Utility and Profit Maximization Decisions[END_REF]. In subsequent extensions, we ~Jlow for the existence of some captive family labor, supervision costs on hired labor, and price bands in relating to the product market, implying that some households are net sellers of food, others self-sufficient, and yet others net buyers.

The household considered bas two categories of family labor, unskilled labor in quantity / and skilled labor in quantity / 2 , with opportunity costs w! and w; on the labor markel, respectively The household can also hire h workers at unit cost wh. These costs include search in finding employment or in hiring, and supervision of hired workers. Unskilled tabor is defin~ as family members which are cheaper than hired workers, while skilled labor are members with higher opportunity cost than the hired workers' cost to the farm: w! < wh < w;. Family labor allocates its time between on-farm work (J/ and J/), off-farm activities (J; and/}), and borne time or leisure (fi 1 and fi 2 ).

The household produces a single output q with a fixed amount of capital (land) A and tabor. Family labor and hired workers are perfect substitutes in agricultural activities, despite their differential skills and opportunity costs. The household maximizes a utility fonction, which is the sum of income and the utility of home time for family members:

1 2 1 1 2 2 1 ( J/+J;)+12{1-f/+J}) max q(A,h+J;+J;)-whh+w 0 J 0 +w 0 fo+ful 1 2 , h.f/ .J/ .f] .f} f f
subject to non-negativity constraints h, J;', J;2. Jo', fo2, fi' = J' -J;' -J;, and J/ = /2 -J/ -J} ~ 0. The production fonction q is assumed to be linear ~omogenous, increasing, strictly quasi-concave, and continuously differentiable in its arguments. The utility function u is increasing and strictly concave in home lime. These assumptions on fi.) and u(.) ensure that the problem admits only one solution given by the Kuhn-Tucker conditions:

(1)

(2) wbere q' is the marginal productivity of labor, and µh,µf ,µf ,µ!,µ; ,µJ, and µf are the slack variables and Lagrange multipliers associated with the non-negativity constraints.

(3) (4) (5) (6) (7) q' -Wh+ µh = 0 I I ) ) 0 q -u -µ, +µ; = q' -v' -µf + µ; = 0 w! -u' -µJ + µ! = 0 w2 -v' -µ2 + µ2 = 0 0 1 0 µ~ ~ 0, J:, ~ 0,
These non-negativity conditions imply the following properties for the solution:

Proposition 1. Skilledfamily labor never works onfarm. This is sbown by substituting (1) and ( 5) in (3), which gives:

ar.d hence J/ = 0.

Proposition 2. If there is hired labor, no unskilledfamily 'Iabor works ojf-farm. If the bousehold is biring, h > 0 and µh = O. From (1), q' = wh, and ( 2) and ( 4) give:

and hence J; = 0.

Proposition 3. If unskilled family tabor works ojf-farm, there is no hired labor. Similarly, if /; > 0, µ! = 0, and substituting ( 2) and ( 4) into (1) give:

and bence h = O.

We now lurn to the derivation of the bousehold's optimal labor strategies. Solution of the problem reveals that the bousehold's optimal strategy depends on its initial land endowment per unit of unskilled family labor, A• = At/. This result thus explains bow differential labor strategies emerge endogenously as a consequence of rational cboice bebavior in the contexl of unequal initial asset distribution. Note firsl tbat, from Proposition 1, the housebold's objective function is separable:

(8) mp, q(A,h+/;1)-whh+w!J;+/1~ 1-; +, 0 +n;i~ w;J}+/ 2 1 Ji [ ( /, 1 1,1 )] [ { •, .2/+2fo2 )]- h,/; ,/ 0 f /; .fo .
Hence, skilled labor lime is allocated between home time and off-farm work in order to equalize the marginal utilily of home time witb the wage:

v' (1-/} If 2) = w;.
With constant retums to scale in production, the first tenn in (8) can be divided by /1, and rewritten:

(9) '' .t:' 5 May 20, 1994 where h• is the ratio of hired workers per unit of unskilled family tabor, and /;°1 and / 0 • 1 are the shares of family tabor spent on-fann and off-farm. The optimal household strategies regarding the allocation of unskilled family labor and the potential employment of agricultural workers are as follows:

[ ( • • • 1 • 1 • 1 ( • 1 • 1 )] max qA ,h +/; )-whh +wof 0 +ul-J; -/ 0 , h•.t,
Proposition 4. Labor regimes depend on land endowments per unit of unskilledfamily labor. These regimes, which define classes, are the following: a. For A• < ~, J; > 0, il = 0, and h = O. The household does not cultivate, and all family labor is hired out. b. For ~ S: A• < A;, J; > 0, il > o." and h = O. The household cultivates with family tabor, and hires out. c. For A; s: A• < A;, /; = 0, il > 0, and h = O. The household is self-sufficient in farm tabor. d. For A• ~A;. J; = 0, il ~ 0, and h > O. The household cultivates with family labor and hired workers.

Households whose asset position A• is so Iow that the marginal productivity of even one unit of their labor would be inferior to the off-farm opportunity wage w! 'do only off-fann work for a wage. Once A• ~ ~. households allocate their labor to both own-farm work and work hired out. They are thus worker-peasants or semiproletarians. As the assets become more abundant, all unskilled family tabor is absorbed in the family farm. There is a range of asset positions (At to A;) that corresponds to the family farms. With yet more assets, the households hire labor in. This proposition is demonstrated as follows. Consider first the case where there is off-farm work of unskilled labor, J; > 0. From proposition 3, there is no hired labor, and equations ( 2) and ( 4) give q'(A•,,e 1 )=w!-µJ. LetAo bedefinedby q'(~.0)=w!. Since q'(A .. /;°1) isanincreasingfunctionofA• and a decreasing fonction of /;°1, for A•<~. q'(~.0)< w!, hence µJ >0and,C 1 =0. There is no cultivation, and all family labor is hired out For assets above ~, allocation of family tabor between on-farm and off-farm work is defined by: As A• increases, on fann labor increases and off-fann labor decreases, until all family labor only works on-farm. This threshold A; is defined by: For assets above A; there is no off-farm work by unskilled family labor. Consider now the case where there is hired labor, h• > O. From proposition 2, there is no off-farm work of family tabor, and equations (1), (2), and (4) give:

Hence, the marginal utilities of family labor and of hired labor are equal to wh. The shadow price of family labor w! + µ! is equal to the hired workers' wage wh. Since u'(l -/;°1) is an increasing function of /;°1, this labor strategy is chosen for sufficiently large value of A•. The lower limit at which the household hires workers is A; defined by:

(12) q'(A;, /;°1) = u'(l-,C 1 ) = Wh.

6

May 20, 1994

Since wh > w;, (11) and ( 12) show that A; > A;. This leaves a range of values for A•, Ai• < A• < A;, for which households neither hire workers in nor hire unskilled family Iabor out. This defines the range of family fanns.

For these households, the shadow price of family Iabor w!h = w! + µ; is defined by: q'(A .,J;°1) = u'(l-.f/ 1 ) = w!h

It is a monotonie function of A•, increasing from w! to wh as A• increases from Ai" to A; . This establishes proposition 4.

These labor strategies give the following typology of households:

Classes Assets A• =Al/ J; J/
0 0 + 0 0 + 0 0 + + 0 + 0 0 0 0 0 0 0 0 Costoffann Iabor WI 0
Proposition 5. Labor intensity (J/ + h) / A (or equally land yield) is constant over the assets range of the worker-peasant class, strictly decreasing for the family farmer, and constant although at a lower level for the rich farmers. Labor productivity q !(!/ + h) is constant over the assets range of the worker-peasant class, stricUy increasing for the family farmer, and constant at a higher level for the rich farmers.

With a CRS production function, the marginal productivity of labor is a monotonie decreasing function of labor intensity, and average Iabor productivity q !(J/ + h) is a monotonie decreasing function of labor intensity. Hence proposition 5 derives directly from the variation of marginal productivity of farm labor across classes established above.

IV. The Data and a Descriptive Typology

The Mexican land tenure system established by the land reform of 1917 divides property rights over land between the private sector and the social sector. Each sector occupies half of Mexico's arable land and half of the irrigated land. The social sector is composed of 28,056 ejidos and ethnie communities which each contain a number of families that can range from as few as 20 to as many as four or fi ve hundred, with an average of some 100 families. In this sector, the land tille is held by the community and individual households have usufruct of a plot of land and often access to common grazing and forestry lands. While .bouseholds in the ejidos were in principle forbidden to divide the land among descendants, in practice much division has occurred.

7 [START_REF] Roemer | A General Theory of Exploitation and Class[END_REF] .,

In the ethnie communities, divisions were legal. The result is that a significant share of the social sector today is composed of very small famts where households engage in both subsistence agricultural production and the sale of labor. The majority of famts are self-sufficient in labor, while yet others, larger and better endowed in productive assets or with smaller families, engage in the hiring of salaried labor.

In December 1991, the Mexican Congress approved a constitutional amendment that put an end to further land redistribution and offered to ejidos and communities the right to assign individual tilles, which can be privately traded, to those currently usufructing the land. Wbile little titling bas yet occurred, as the legal process of identifying individual rights over land is highly complex and conflictual, the reform is well under way. In addition, as part of structural adjustment induced by response to the debt crisis, Mexico bas engaged in thorough reforms of the role of govemment in agriculture, with massive descaling of state fonctions and privatizations of most parastatals engaged in marketing and the provision of inputs. Further, trade bas been liberalized, including through joining GA TT and NAFT A, and extensive credit and factor subsidies have been terminated. Only corn and beans remain protected, but their prices are being rapi<lly brought to the international market price level, and a scheme of direct income transfers, PROCAMPO, has been initiated to compensate farmers for the welfare Joss.

These massive reforms of the land tenure system and of the institutional context for agriculture have generated considerable interest in obtaining a better characterization of households in the social sector, and in particular in developing a typology of these households. This typology should be able to capture the great degree of heterogeneity in that sector, and yet summarize il according to the main determinants of differential performance. Of specific importance is to anticipate how different categories of households in the social sector will respond to the reforms in progress and what type of complementary reforms should be put into place to prevent this sector from rapid disintegration, and its households from abandoning the land and migrating enmasse to the cities and the United States.

The data we use are from a 1990 survey of the social sector conducted by the Ministry of Agriculture and Hydraulic Resources (SARH) and the Economie Commission for Latin America (CEPAL). We work with data for the state of Michoacan, where the traditional coexistence between social sector and private lands is well represented and where there is an extensive peasantry as well as an active labor market., both local and through seasonal migration to the United States. The survey consists in 1204 complete observations of households in ejidos and communities. The extension service regroups these farms in 13 Rural Development Districts (DDR) which are defined to have agroecological homog~neity and whicb we use to characterize the regional context of each ejido.

We divide, in Table 1, the households based on the six labor regimes (excluding agricultural workers for which we have no data) identified in the household mode!. The three categories--sellers of unskilled labor, selfsufficient, and employers--can ail sell skilled labor if they have some. A laborer has been classified as skilled either if he/she is employed in the manufacturing, services, or construction sectors and/or if he/she has at least six years of education. In Table 1, the self-sufficient households are used as the reference category relative to which t-tests on differences of means are calculated.

The data show that 62% of the households are self-sufficient in farm labor, 33% are employers, and 5% are sellers of unskilled labor. However, when the sale of both unskilled and skilled labor is taken into account., 17% are sellers. These figures still under-represent the extent of participation to the labor market because labor income for these households mainly derives from migration to the United States which was under-reported as the survey focused on housebold members present in the farm. For one ejido community in Micboacan, [START_REF] Fletcher | Migration and the Transformation of a Mexican Village House Economy[END_REF] report 11 % of household income derived from wages, commerce, and handicrafts, 28% from remittances, and 61 % from agriculture, Iivestock, and fisberies. However, for our analysis, with remittances derived from skilled tabor, the opportunity cost of tabor for farm work remains unaltered by this missing information.

Households who are sellers of tabor have a higher number of adults and also of unskilled adults than the other categories, but there is no difference in the number of unskilled adults within each category between those who sell skilled tabor and those who do not. The average age of adults is clearly younger in a1l classes for households who sell skilled labor than for those who do not. And the average level of education of adults is higher for all skilled tabor-selling households. Skilled workers thus appear to be additional adults within each households and younger adults. Education plays a further role: employers have a higher level of education than self-sufficient and seller households. Education thus appear to be related to both the sale of skilled labor and the employment of others.

The reason to sell or hire unskilled tabor is clearly established by the productive assets position of the households relative to the number of unskilled workers. Sellers have smaller farm sizes, less inigated land, and less animals of all types than self-sufficient households. Employers bave more land and perennial crops, with irrigation the key differentiating factor. They do not have more animais as livestock is a tabor extensive activity that does not create significant employment.

Among social assets, greater access to (constrained) credit is a distinguisbing feature of employers. In addition, those who sell skilled labor also have more access to credit among both sellers and employers, suggesting the key role of education in accessing credit.

Dîfferent regîons offer different opportunities to join organizations (an endogenous choice). The opportunity to join an organization is represented by the regional density of farmers participating to organizations. The data shows that bouseholds who sell labor are in regions with tess organizations while those who employ are in regions with more credit organizations. Labor market conditions are also quite varied across regions. Those wbo bire out unskilled labor do so more when the local (municipio and state) markets are more active. By contrast, those who bire ~ut skilled labor do so more in DDR where there is more participation to the national or international tabor market. Among those who employ, there is more hiring when there is more participation to the local and international la~r market. This suggests that hiring-in is in part to replace migrants. High skills are exported and replaced by local unskilled workers. The self-sufficient are located in areas where there is a less active local labor market and less participation to international migration. It is thus interesting that the more intense the labor market, the more both sale and purcbase of tabor.

Among indicators of performance, use of capital equipment such as tractors and trucks is more prevalent among those who hire tabor and also among those self-sufficient and sellers wbo have skilled tabor. The role of participating to the labor market as a source of liquidity that can compensate for lack of access to credit is revealed by observing househotd behavior within the self-sufficient class. Those with skills bave less access to credit, but more use of capital equipment, suggesting that liquidity derived from skilled labor wage earnings substitutes for credit.

Labor intensity shows no significant differences among household classes, suggesting Oie need to controt for the influence of other variables as we will do in what follows. Participation to the product market as seller of a marketed surplus is also a very important detenninant of falling into the employer category. This may reflect larger farm size and a higher share of irrigated land in a trivial manner, or it may reveal more subtle differences for which we need to control for the relative influence of determinants of labor regimes. Those who hire labor out have much less participation to the product market.

V. A Predictive Typology

We now tum to a multinomial logit mode! to predict belonging to the three labor regimes: sellers of unskilled labor, self-sufficient, and employers (Table 2). We should recall that the mode! in Section III predicted that educated labor which commands an opportunity cost above the cost of hired labor should be hired out, and eventually replaced by unskilled hired Iabor. It also predicted household appurtenance to labor regimes on the basis of assets per unit of unskilled bousehold labor. In the multinomial logit analysis, average adult education and productive assets per unit of unskilled labor should thus be predictors of labor regime.

With these three labor regimes, the sale of skilled labor is present in ail three regimes. However, education should influence differentially the probability of pertaining to a regime. For the sellers of unskilled labor, education would increase the sale of skilled labor, and decrease the sale of low skill tabor for a given family size. Hence, the average level of adult education would tend to reduce the likelihood of being a seller of unskilled labor. By contrast, bigher education among employers would increase the sale of skilled labor and increase the employment of substitute unskilled labor. Hence, education should increase the probability of belonging to the employer class.

In Table 2, the self-sufficient group is again the reference group. We can see that there are well recognizable exogenous household characterisûcs which allow to predict labor regime. However, the predicûve power of the logit for the seller group is zero, in spite of several significant explanatory variables (Table 3). This is because the criterion used in logit maximizes predictive ability for the whole sample, thus discriminating against the predictive power of small groups. In Ibis case, the seller group is only 5% of the total number of observations. It is not surprising tbat Ibis group is poorly represented in the overall estimation. For the other two groups, the logit predicts correctly 70.7% of the self-sufficient households and 65.6% of the employers.

The results show tbat average adult education lowers the probability of being a seller bousehold and bas a non-significant effect on the employer category. Productive assets per unskilled tabor lower the probability of hiring out, particularly farm size and cattle ownership, while they raise the probability of being an employer, particularly farm size and the share of land whièh is irrigated. The other variables are shifters which enrich the concept of assets used in the model beyond education and productive assets per unskilled tabor. Tractor and truck are used as indicators of technological regimes, and they increase the likelihood of being an employer. Access to credit, an exogenous variable under a severely credit constrained regime, is also a strong determinant of being an employer. Those with larger marketed surpluses sold on the market are also more likely to be employers. This is after controlling for farm size and irrigation. Since credit is constrained, il should indicate greater insertion in the money economy, and hence greater ability to generate the liquidity needed to bire workers. It also may signal households who are more effective in reducing transactions costs in accessing product markets.

Regional availability of organizations is only significant for access to equipment and it increases the probability of being an employer for those located in a DDR with higher density of such organizations. Local labor market conditions increase the likelihood of selling labor (while decreasing that of hiring which is not 10 May 20, 1994 ,I correct). Greater regional opportunities for migration to national and international tabor markets, using a social network concept where the density of regional migration increases the expected net benefits from migration, also induces more selling of tabor.

Policy implications are interesting. Say that the objective of policy is to break away from self-sufficiency which is associated with poverty and high exposure to natural shocks. The two roads are sale of wage tabor and becoming a successful small scale entrepreneur who can start to hire tabor. For the first road, the key policy instruments are (1) education that will increase the sale of skilled labor and reduce that of unskilled, and (2) a more developed local labor market and better established migratory networks. For the second road, the key instrument is to capitalize households, particularly in irrigation, animais, and capital equipment. Access to credit and availability of local organizations for access to equipment are also important. This stresses the importance of institutional development., and this in a context where government support bas been withdrawn from credit and technology as a consequence of privatizations and descaling of government budgets.

Reconstructing new institutions able to deliver these services to households of the social sector is thus fundamental.

VI. Performance Indicators by Labor Regimes

If the household mode! with differential labor skills and with price bands in accessing the labor market is correct, the reduced form of the model predicts that labor intensity (J/ + h)/ A should be unrelated to assets per unit of adult labor in the seller and employer categories, and falling in the self-employed category. As was shown in proposition 5, this is because the first two categories have exogenous labor costs equal to w! and wh, respectively, while the shadow wage w!h of family labor rises with assets per adult worker. In Table 4, we test this proposition by giving the results of a regression analysis of labor intensity within each tabor regime.

We see that the proposition holds clearly true for the self-sufficient group: for them, labor intensity falls sharply as land area per unskilled adult rises. Labor intensity is decreased by use of tabor saving technology (tractors), increased by irrigation, and increased by greater participation to the product market (greater liquidity and lower transactions costs).

For the employers, we find that there is a large fringe of small employers, with a share of hired labor in total labor less than half, where the relation ~tween labor intensity and assets per worker continues to decline. This suggests that the effective wage continues to rise, even thougb the wage of hired workers should be the (constant) opportunity wage. In the tradition of moral hazards and supervision costs, this indicates that there are rising supervision costs that need to be incurred, but that there are economies of scale in supervising, with the result that wages ultimately stabilize and the relation between labor intensity and farm size per adult becomes insignificant. This is what is observed in the group of 73 large employers.

We test this proposition by introducing a supervision variable in the labor intensity equation for employers. Since all employers are relatively small, supervision is insured by family members wbo work along with hired workers. The supervision variable is thus the share of family workers in total farm labor, J/ !(!/ + h) [START_REF] Frisvold | Does Supervision Matter? Sorne Hypothesis Tests Usding Indian Farm-level Data[END_REF]. Since this variable is endogenous, we instrumentalize il with the set of assets that characterize the household. The results in Table 5 show that supervision does indeed malter and that il increases labor intensity with an elasticity of 0.78. Fann size per unskilled adult remains significant, but with an elasticity of -0.46 which is smaller than the elasticity without supervision.

11 May20, 1994 For small sellers, the mode! is not confinned, suggesting that some other Jabor story is required to explain observed facts. In that category, labor intensity falls with farm sire per adult, even though the off-farm wage obtained by family members who hire out should be the constant opportunity cost of family labor. This suggests that not ail family Iabor is perfect substitute. For instance, it may be that, once men with a well established opportunity cost on the labor market have been fully hired out, the rest of the family is semi-captive labor, with low opportunity cost In this case, shadow wages would behave as they do in the category of selfemployed. Indeed, this would explain why we find the same inverse relation between Iabor intensity and assets per adult in the seller category as we do in the self-employed category.

The main policy implication of the observed inverse relationship between Jabor intensity (or equivalently yields) and assets per adult is to stress the relative efficiency of the family farm as a tabor regime. This superiority of the family farm originates in its low effective labor costs. The social sector reforms initiated in 1991 in principle free this farnily farm sector from govemment contrais and should allow it to reach higher levels of technical and allocative efficiency. However, in the overall context of reforms--that occurred mainly after the 1990 survey on the basis of which this relationship bas been estimated--, this family farm sector is now exposed to rapid elimination. This is because the reforms have dismantled the web of institutions through which this sector had access to credit, markets, modem inputs, technology, and information. Privatization of these services means that delivery by private agents is now principally reaching the larger commercial farms, mainly in the private sector, bypassing farnily farms in the social sector. To take advantage of the labor superiority of the family farm sector which emerges from the social sector reforms, a new set of institutions needs to be developed that can cater to this sector and increase its competitiveness. These institutions need to emerge from civil society, with selective assistance from the state within its reduced fiscal means. These agrarian institutions have been the object of analysis of the new institutional economics (Bardhan, 1989;[START_REF] Hoff | The Economies of Rural Organization: Theory, Practice, and Policy[END_REF] as well as of international development agencies (Anderson and de Haan, 1992). They include service cooperatives, group lending and credit unions, decentralized water users associations, privatized or mixed publidprivate extension services, grassroots organizations, etc. Like in many societies in Africa and Eastern Europe which emerge from decades of strong govemment contrai, these institutions are still Iargely missing in Mexico. Non-governmental organizations (NGOs) have a fondamental role to play in assisting this institutional reconstruction and in targeting it on the needs of poorer households. Freeing the land market without putting into place these supportive institutions creates the risk of rapid elimination of the family farm sector, at a high social cost. In our predictive typology of Mexican social sector fanners, predictions may well be that the family farm sector will rapi<;\ly disappear unless il receives urgent attention to consolidate is physical, human, and social capital.

  where h = labor hired-in, / 0 = labor hired-out, and J; = family labor working on the farm.

4

  and µ~f:, = 0 for m = i,o,l and n = 1,2 µh ~ 0, h ~ 0, and µhh = 0[START_REF] Roemer | A General Theory of Exploitation and Class[END_REF]

[START_REF] Roemer | A General Theory of Exploitation and Class[END_REF]

[START_REF] Roemer | A General Theory of Exploitation and Class[END_REF]

[START_REF] Roemer | A General Theory of Exploitation and Class[END_REF] ,/


Ludo Peeters

ESTI:\lATL'\G FEED DE,.\IAt'ill IN THE EC: THE STATE Of THE ART

This paper reviews the 'state of the art' in the field of modelling feed demand in the EC. After presenting a genera! conceptual framework, several methods for empirically estimating feed demand responses to price changes are c1assified. Also, a method is proposed for econometricallyestimating (1) the allocation of feed ingredients among different liveslOck categories, (2) the composition of the various livestock rations, and (3) feed input demand elasticities differentiated according to type of livestock, by using aggregate market data. The potentials of this method for covering all marketable feed ingredients will be explored. In conclusion, sorne pending research issues will be discussed.

Introduction

In conducting simulations of feed policy reforms, it is imponant for EC policy-makers to rely on empirically-justified parameters (elasticities) of feed substitution and allocation. In the past, a number of studies have been devoted to estimate such key parameters of feed input demand. The purpose of this paper is to review the 'state of the art' in the field of modelling feed demand in the EC. After the presentation of a genera! conceptual framework, we c1assify severa! methods for empirically estimating feed demand responses to price changes. Three broad categories of studies are distinguished: (1) studies using a synthetic approach;

(2) studies using a programming approach; (3) studies using an econometric approach. An overview of the existing literature is provided along with an appraisal of the merits and limitations of the various approaches. Next, we propose a method for econometrically estimating at the sarne time (1) the allocation of feed ingredients among different livestock categories; (2) the composition of the various livestock rations; (3) feed input demand elasticities by type of livestock. It will be shown that, under certain conditions, it is possible to net out liestock-specific demand-price relationships even though intermediate flows of feed ingredients are not observable; that is, by using aggregate market data (i.e., total marketable feed usage). In other words, this method will help in overcoming the problems of limited sub-sectoral and national effects. Fourth, the growing role of the compound feed sector should be taken imo consideration, which creates specific linkages between feed manufacturers and livestock producers (we retum to the specific role of the compound feed sectOr below).

;able 1 shows the distribution of livestock activities in te,ms of type of 0pè::tion (mixed, 'rational', integrated) as weil as type of output (beef/milk, pork, poultryieggs).

Obviously, one may observe sorne kind of 'skewness' in this distribution. Reading the table from the top-Ieft to the bottom-right one may generally observe: (1) a higher share of purchased feeds (straights and, in particular, manufactured compound feeds) in the total feed ration and, hence, a higher share of feed costs in total costs; (2) larger expansion elasticities;

(3) smaller substitution elasticities between marketable and nonmarketable feed ingredients;

(4) larger substitution effects between (a widening range of) individual feed ingredients.

Given these various types of livestock producers and the associated comolex feedlivestock linkages (in terms of both substitution and expansion effects), one should adopt a pragmatic approach, on a country-by-country basis, using a 'flexible' model that can be adapted to 'local' conditions. For example, the role and importance of home feed mixing by 'rational' livestock producers will serve as a basis for specifying commercial purchases of feed ingredients by farmers. Altematively, by analysing the production decisions of imegrated livestock producers, we could develop a specification for the demand for manufactured compound feeds. Finally, demand relationships for home-grown feeds such as cereals and forages could be specified using the production decisions of mixed farm operations.

where H = livestock herd (quasi-fixed input); Xi = vector of vanable inputs i where subscripts i = 1,2 correspond to feed and nonfeed inputs, respectively; L = vector oi livestock outputs (including the production of livestock ready for slaughter or livestock product for sale, such as mil!-: A = vector of land allotments for various crops. pasture and forage land required for the production of feeds des::r:ed for livestock; K is a vector or other quasi-fixed inputs such capital, infrastructure, family labour, and so on; T = time trend capturing the effect of technological change; A, fi and k = changes in the quasi-fixed factors.

The above production function can be adjusted to accommodate the three types of livestock operation outlined in the previous section. In the case of the mixed-enterprise farm, it is necessary to partition the vector of land allotments, A, between cereals, on the one hand. and forages and permanent pasture, on the other hand. In so doing, we are able to capture :he èynamic relationships betv..een these two categories of land use. Simil<ül), the set or ;'"".j input variables, XI' is divided between feed ingredients purchased off the farm and homegrown cereals. Another refinement relates to the farmer's possibility to choose among different crops and livestock enterprises, and the recognition that the underlying technology is characterised by sorne sort of jointness. Finally, livestock output, L, can be decomposed in such a way that it takes into account the dual purpose of raising cattle for milk production and beef slaughter. Given all these characteristics associated with a mixed-enterprise farm, the underlying production function should be extended as follows:

(2)

where Xll and X 12 = quantities used of compound feeds and home-grown feeds (cereals), respectively); Y, = production of cereals; A, and Ar = allotments of land devoted to cereals and forages, respectively; all other variables are defined as above. The total amount of land alloned to cereals and forages can be viewed as fixed and to be equal to Â.

In the case of a 'rational' livestock producer, a single-output perspective can be adopted, which means that all resources are geared towards the production of livestock.

Thus, the amount of land, A, owned or rented by the farmer is devoted to growing a -7-

The role of the compound feed sector

The role of the compound sector in the EC has been growing considerably over the last three decades. The supply of manufactured feed rations accelerated the rationalisation and speci~': sation/intensification of livestock production in various EC member counrries (espec:"':!y in those countries located near the major po.:s, s.

as the Netherlar.c5, Bèlg:t::n, and the northern pan of Germany).

In order to capture the substitution possibilities between feed ingredienrs used in the production of compound feeds, one can model the behaviour of the feed compounders separately (and independently) from the input decisions of the livestock producers. Feed compounders use least-cost LP formula to produce their balanced feed rations. Specifically, a multiple-input multiple-output static cost function framework can be used to establish complete elasticity matrices of feed demand (given the ability of feed compounders to 'inSt4rllaneously' adjust the composition of their feed :-.:~ons f~llo•.;•ii'i~fee..: ~~.:.: '::.::'&';5).

The cost implications of feed price changes will, in generaJ, be passed on to the livestock sector, given the low margins (values added) and the competitive structure of the EC compound feed sector (Mahé 1989, p.8/l0)

In producing balanced feed rations, the compound feed sector uses most of the imported feed ingredients (such as oilcakes, manioc, corn gluten feed) for which the trade regimes are different. Therefore, most of the raw products used by the compound feed sector are directly linked to the current agriculturaJ trade or 'substitutes' issue. It is obviously also the compound feed industry where the most dramatic changes with respect to feed demand have occurred. This aJl makes a separate analysis of the EC compound feed sector worthwhile on its own.

Modelling approaches ta estimate Ceed demand systems in the EC

The purpose of !his section is to describe the various modelling approaches for analysing feed demand in the EC. Three broad categories of studies are distinguished: (1) studies using a synthetic approach; (2) studies using a programming approach; (3) studies using an econometric approach. the CES function). The approach only requires a priori knowledge o'f the n direct pnce elasticities and input cost shares for feed ingredients, whereas other synthetic approaches require information on n(n-I)12 own-and cross-priee elasticities.

3.2, Programming approaches

Two types of srudy can be distinguished: (1) studies using a LP-based simulation approach;

(2) studies using a 'pseudo-data' approach.

LP-based simulation approach

This class of studies typica1ly uses a two-part model: (1) LP models are used to determine the adjustment in the composition of the livestock rations as weil as the priees of livestock rations following feed input priee changes; (2) a set of compound feed equations is used to estimale the priee elasticities oi compound ieed demand ior me various ii... ",.oc;" ,<:....ù.,. ~il these srudies no anempt is made to summarise, through a set of elasticities, the demand-price relationships for the various feed ingredients. Exarnp1es of this type of approach are provided by Leuck (1985); [START_REF] Peterson | The effect of trade restncuons on demand for imported feed ingredients in France[END_REF]; Hillberg (1986); [START_REF] Blom | A modelfo-the EC cereal and compoundfeed raw material marker: some preliminary resu/rs[END_REF].

The LP-based approach has a major advantage in that technica1-nutritional restrictions on feed substirution are explicitly taken into account. The comprehensiveness of the LP model is a considerable potential virrue in poticy analysis in which quite radical changes in the conditions are posrulated, since any results will remain fully consistent with the technicalnutritional restictions imposed. An additional advantage follows from the fact that EC feed compounders use LP models themselves to determine least-eost feed rations. As a result, the sarne method is used to analyse the adjustment in the composition of livestock rations.

Finally, the LP-based approach allows for an analysis at a disaggregated level. One should realise, though, that in the LP models do not coyer al1 animal feeds (forages and on-farm mixes of grains).

Pseudo-data approach

This class of srudies uses least-eost LP models to generate so-ealled 'pseudo data', by repeatedly solving the LP models for different sets of feed priees (Griffin 1978). The Many of these models, though, Jack a solid theoretical underpinnlng, and are specitled on an ad hoc basis, As a result, these models generally lead to biased and inconsistent parameter estimates.

:neorerically consisten; approach

These studies are based on the use of duality theory, which allows for greater flexibility in the specification of the demand for feed inputs and permits a very close relationship between economic theory and practice. Because, according to the principles of duality [START_REF] Fuss | Production economics: a dual approach to theory and applications[END_REF]Lopez 1982;[START_REF] Chambers | Applied production analysis: a dual approach[END_REF], there exists a ('reciprocal ') correspondence between the production and cost or profit functions, any one of these functions couId be econometrically estimated to derive input demand and/or output supply elasticities. In practice, the estimation of the dual cost (or profit) functions has proved to be more con-\ '0_:0_' --è ',so"ul 'or es"mau'n-~ulu'plp oU""'u' tp'''nolool'pS 'forp~,•p-thp 0,.. where w = vector of feed inputs; y = vector of compound feed rations.

• Assuming CRS and nonjointness in feed input quantities implies:

V G = ~J = 0 B = 0 yy Y. Y. and m t ,. r WTAW ) T J G = Ly.g.(W) G = y, -: ' -r -<7l... W C. ;.\ ••\ 0 W
where g.(w) = unit (marginal) cost of producing output k.

• Feed input demand functions are (Shephard' s lemma) :

-aggregate

x. = aG x .. aG .. [aiw _ >"0 WTAW) r .. CJ' , ow:

i aW i OT W 2 i (OT W ) 2 <7l Y , -ration-specifie wTAw ) J • ag, • [[aiw Xi = Y. dW, Xi .. Y. OT W -;'0. <7l... C'" W i ' (OT W )2
• Feed input demand elasticities are:

-aggregate

_ aX i w j [[ a. _ 0 aiw _ O. ajw .. 00. wTAw )<7lTy] w j E. -ow: E." _ J Xi OT W ) (OT W )2 ' (OT W )2 ' J (OT W )3 Xi -ration-specifie • a 2 g. W)
. [[ a.

Data availability

Using an econometric approach for estimating parameters of the demand-price response sun"ace, assumes the availability of an extensive set of statistieal infùrûlâciù" ùn p.-i~;O.i z,..-,.i demand/supply quantities for all feed Ingredients, compound feeds and livestock products, in each EC member country. Time series should be as long as possible (preferably going back to the 196Os). Such data conditions, however, are far from being satisfied in the EC, especially with respect to feed price-quantity data.

Long and detailed time-series data on feed prices and quantity are available only in two EC countries, namely Belgium and the Netherlands. Other countries, such as France, the UK, Denmark and Germany, also publish feed data series, but they tend to be less extensive and exhaustive in commodity coverage than in the Benelux. Consequently, there is still a need to develop a large data base in the EC that fits the criteria of econometric time-series analysis. While EUROSTAT developed (is developing) a homogeneous data base for feed supply (demand) balances in the EC, it is generally not adapted to the estimation needs associated with the models proposed in this paper.

Conclusion

In view of the predominant role of the feed-livestock sector in EC agriculture as weil as the importance of feed resources in international agricultural trade, it is crucial for policy-makers

  .r.~.....v ...... , l ... ....... • .... v.t" ........ ~v ..so-called flexible functional forms (FFF) , such as the translog or the (symmetric) normalised quadratic, allows for the estimation of demand elasticities without imposing a priori restrictions on the substitution parameters. The dual approach has been pursued in a number of studies: Mergos & Yotopoulos (1988);[START_REF] Surry | Econometrie modelling of the European Community compound feed sector: an application to France[END_REF][START_REF] Surry | The 'Constant Difference of Elasticities ' function with applications to the EC animal feed sector[END_REF];[START_REF] Folmer | ModelIing ECfeed demand[END_REF];[START_REF] Surry | Input substitutability in the EC compound feed industry[END_REF];Peeters & Surry (1993a,b,c).Mergos & Yotopoulos (1988) and Folmers et al. (1990) have built an integrated model covering both marketable and nonmarketable feed ingredients.Mergos & Yotopoulos (1988) estimated derived demand of feed inputs in the Greek livestock sector by using a multiple-input multiple-output (static) cost function. They adopted a two-stage procedure, by using an aggregator function for feed ingredients (weak separability).Folmers et al. (1990) estimated a EC feed demand system, as part of the general equilibrium-type 'European Community Agricuitural Model' (ECAM). In their model, a distinction is made between demand for marketable feed ingredients and demand for nonmarketed greenfodder. Several livestock categories and feed commodities are distinguished. Demand for commercial feed is derived from cost minimisation by national farmers. Greenfodder usage is determined by availability, restrictions on allocation to animal types, and minimum requirements. Their approach is strongly innovative, but it suffers from a number of important shortcomings

Table 2 :

 2 ModelIing approaches to estimating feed demand elasticities -",. ..,.-oImNl (J9n) ,....... ~!cueu/prokU. Danony (1.7.) ,....... _0

	'Oplimiain. agcot'

rd al. ÜD<u EC-. ..",...., Il<:lI}'I"'llH... II( '( i 1-1 I(ho (llulclll .Jll ,.,111/,•""'111<• ..... ,, j bv IV" .. "1/"'...,1,,, AI

Table 3 :

 3 Modelling framework for estimating livestock-specific 'parameters of feed

	substitution and allocation
	• G is a multiple-input multiple-output feed cost function (assuming zero substitution
	between feed inputs and nonfeed inputs and 'free' composition of feed rations):
	G = G(w,y)	G(w,y) = \ [W OTW T AW)<7l T y ... ;,ryTBY)OTW .. wTCy, : <7l T y

  Most models do not allow for the long-term, nonstationary movements in feed input demand which may be due to sorne kind of price-induced (cereals-saving) structural or teehnologieal change resulting from the persistence of the CAP cereals regime (Guyomard & Mahé 1992, p.19). The relative feed priees pre\'ailing in the EC play a-. ::npo:-..:c;1' role in eneouraging more and more feed compounders to invest in new equipment capable of handling nongrain feed components (such as manioc or corn gluten feed). One way of dealing with biased technological change is through the use of cointegration analysis (for example,Clark &

		-19-
	5.3. Price-induced technological change
	Youngblocd 1992).
	8 T w	J (8Tw) 2	' (8Tw) 2	' J (8Tw) 3 <7l. X/

8. a,w _ O. aJw

wTAw ) J w)

E. .. Y. E• .. Y. --.. 0.0. _

awiaw)

x,'

compound feed sector can be analysed by only considering the feed cost iunction. By assuming this admitted!y restrictive modelling framework, we may perhaps do injustice to the compound feed techno,ogy. Neverless, we believe that his exercise is wonhwhile because oi

(1) the imponance of the results, and (2) th elack of valid alternatives, due to the apparent nona 'ilability of the necessary data.

The proposed framework has been applied te the Belgian and Dutch compound feed sectors. The focus was limited to the feed ingredients used by the compound feed industries.

which is justifiable by the fact that in Belgium (or the Netherlands) nearly all marketed ieed ingredients are processed by industrial feed compounders. To keep the model manageable, four groups of (weakly separable) feed ingredients were considered: cereals; high-energy feeds, designated by the term 'cereal substitutes'; high-protein feeds, including corn gluten feed; additives (minerals, vitamins, other supplements). Also three output categories (livestock rations) were considered: poultry feeds: pig feeds; cattle feeds. The data used were prices and quantities of feed inputs (total quantities) and compound feeds (per type of 1234.

Extension to ail marketable feed ingredients

Although the share of manufactured compound feeds in the total feed ration is steadily increasing in most EC countries, not all purchased (marketable) feeds fIow through the compound feed sector. In the UK, however, an increasing proportion of livestock seems to be fed on rations mixed on the farm (Daw & Entwistle 1989, p.53). Therefore, the model proposed in the previous section, which was principally designed for the compound feed sector, should be adapted sc as to coyer all marketable feedS (whether purchased or homegrown) used by livestock producers.

Information on the breakdown of marketable (concentrate) feeds berween home-mixing activities and compound feed manufacturing is not always available. In these instances, one should adopt a pragmatic approach, and treat home-mixing in a similar way as industrial feed Appendix 1: Typology of Iivestock producers in the EC Three broad categories of livestock producing farms can be distinguished in the EC (Surry 1985):

(1) lmegrared livesrock producers: With only ~5::,all land base, these farmers raise poulrry or pigs by feeding mixed or compound feeds. In most cases, these farmers are fully integrated through contracts with either slaughter-houses or compound feeds firms. The objective function of these livestock producers consists of maximising a profit function, subject to a technological feeding process, with one livestock output and one (compound) feed input. In addition, the need to replace the flock of birds or herd of pigs on a regular basis must be part of the decision-making process.

(2)

'Rational' livestock producers: This class of livestock producers has !WO ways of feeding livestock: they can either mix their own feeds or purchase manufactured compound feeds. These farmers make a 'rational' decision by selecting the feed alternative leading to the highest expected net profit. These farmers have also the option of selling their home-grown cereals on the market.

(3)

Mixed ja17TlS: These multiple-enterprise farms grow cereals and other crops as weil as forages to be fed to beef and/or dairy herds. The model representing the economic decisions should include home-grown cereals which are mixed with other feeds in order to raise beef or dairy cattle, The economic objective of these farmers is te maximise the expected net returns of producing milk or beef using home resources.

The above categories of livestock producers can be found in ail EC member countries. For instance, integrated livestock producers will mainly operate in the poulrry sector in Belgium, the Netherlands, France and Germany. Balanced feed rations are provided by the compound feed sector. A similar situation exists in the Benelux, where penetration by compound firms Appendix 2: Estimation results for Belgium , Estimated values for the 1984/85 season using technical information (fixed input-output coefficients) .

• Weighted average for 1ayers and broilers, where the weights are equal to the shares in total compound feed production for pou1try (0.65 and 0.35, respective1y). e Standard (complete) dairy feed.


Elisabeth Chevreau

M Dufour

Michel Duron

In vitro neoformation of woody plants (apple, pear, weigela)

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