François Bonnieux

F8990~IFORSI

Keywords: non-point pollution control, compulable gcncral equilibrium models, agriculture, farming practiccs, envirolllllcntal impacts

Modelling slrategies to integrale ecology and economy are reviewed with an emphasis on non-point pollution due to farming activities. In this context three crucial issues must be considered: the nLlmber of firms involved, the spatial dimension and the stochastic nature of natural phenomena. The link of economic models with biophysical models is discussed From both a theoretical and an empirical perspective. Several Integrated Biophysical. Economic Production (IBEP) models are given. They are instruments to simulate the consequences of pollution control and fanning practices on a series of environmental and economic indicators such as nitrogen losses. crop rOlation, farm relUrns but they rely on maintained economic hypotheses wllich restrict their validiry. Computable General Equilibrium (CGE) models provide an alternative approach in which ecollomic links are integrated in a more realistic framework. But on the other hand the modelling of biophysical processes is over simplified. Therefore these modelling strategies happen to be complement ofeach other.

KeY\I'ords: Bio-economic modelling

I. Intl'oduction.

The decade of the 1970s saw the limirs to growth cOlltroversy alld the begillllillg of the ellvirollmelltal crisis. MEADOWS el al (1972) argued that expollelltial growth ill resource extractioll alld ellv ironll1elltal degradation cou Id not be sustai ned through the 2 1" celllury. Despite the weakness of the model of industrial dy"amics they used. this issue is crucial alld was recelltly revisited. Illdeed sustaillability became a central issue of our time durillg the eighties WitJl the BRUNTLAND REPORT (1987). This Report fïnnly established the COllcept of sustainable developmellt as the basis for ail illtegrative approach to ecollûmic policy ill the comillg decades alld goes fUl1her by statillg that it is possible to achieve a path of a sustaillable development for the global ecollomy. The prescription is (0 leave to future generations a generalised capacity of producing social utility. Thu5 removing DOCUMENTATION ÉCONOMIE RURAlE RENNES 1111111111111111111111111111111111111111 • a 1 5 6 8 1 • distol1ions stemming from public policies and market failures which involve an inefficient use of natural resources may improve the prospects for sustainable development but will not guarantee il.

Modelling resources management raises a Illimber of technical issues. Models have gained in realism by taking into account the dynamic dimension of the involved phenomenon and control theory has provided the most straightforward method for analysing them. This approach has been very fruitful to understand the effect of the functioning of nalllrai systems on social optimum. But in order to obtain general results researchers were forced to omit a number of relevant topics. 50 there is a need for more empirically rooted models which would be more policy oriented. Indeed, it is necessary to tLirn to Illodels ÎntegralÎng biophysical and economic aspects, to il11plement bener polie)' instruments.

This contribution emphasises the J110delling of non-point pollution stel11ll1ing from farmillg aClivity. Il reviews several approaches \..\Ihich have been proposed to integrate ecological tèatures into economic models. It is organised as follows. The first section clarifies the nature of non-point pollution. The second section is devoted to non-point modelling therefore it focuses the link between bio-physical models and economic models. The following section provides empirical resuhs both at the farm level and at the regional level. These integrated models have a serious drawback since economic decisions are not endogenous as they do not depend on environmental impacts. Computable general equilibrium models (CGEM) provide an alternative modelling strategy which is considered in the last section .. This approach is based on the assumption that the activities in different production sectors have different effects on the environment and that these effects are proportional to the production in the sector. These effects can be discharged of different harmful substances or the consumption of certain resources. By integratillg natural resource accounts into a social accounting matrix, it becomes possible to slUdy some of the repercussions in the economy from, say, a charge on minerai fertilisers. ln comparison with the former approaches there is more emphasis on the structure of the who le economy but on the other hand the interface with the environment is very stylised and gives a less realistic piclUre. Moreover CGEM are based on a rather narrow description of technology so there is 110 beSl approach and in cach case study a compromise has to be achieved between over-simplification and over-sophistication.

Nature of uon-point pollution.

A substantial proportion of pollutants affecting aquifers, lakes, rivers and coastal ecosystems can be anributed to non-point sources. Although the information is patchy and the sources, types and amounts of poliutallls vary among countries, it is nowadays recognised that agriculture represents the major source of pollution of water systems. For example, using a model to predicl the nitrate leaching From the 1'001 zone of agricultural land, it has been shown that over 85% of the European agricultural area has nitrate levels at one meter below the soil surface exceeding 25 mg of nitrates pel' litre, the guide level specified in a European Directive relating to the quality of \Vatel' intended for human consumption. The maximum admissible concentration (50 mg of nitrates pel' litre) is exceeded in approximately 20% of the agricultural area (Stanners and Bourdeau. 1995 p. 68). Bener nutrient management is an essential element of the basis for the 10ng-rLlI1 improvement and sustainability of the social value created by agricultural activities. POlential for nitrate pollution of water resources comes from the integration of Iivestock and field crop production activities.

Public actions to correct a perceived market failure in agricultural chemical have focused on: (i) education and information 10 stimulate adoption of technological solutions. (ii) cost-sharing 10 finance transition ta alternative practices or technologies. (iii) taxes or subsidies to change priee structures to induce "idespread changes in fan11 production decisions. and (iv) regulatory standards to require changes in production decisiolls. 0ppoltllllities 10 enhance envirollmental performance slich as Ilutrient pollution of ground water are \Videly recogn ised to be specifie of farln site. Further, economÎc research has shown that the full set of determinants of farm production decisions also play an important raie. Among these laner determinants is a vast array of farm-specific factors as discussed above. This implies that the nature of strategies for enhancing the ellvirOllmental impacts of agricultural activities which are economically efficient from both a social and private perspective may often be farm specific.

Failure to recognise the importance of the interrelationships between farm practices and environmental impacts has led to many policy drawbacks. In this context there has been an increasing concern about their overall consistency. The non-point source problem is characterised by tlHee specific features (TOMASI el al., 1994).

The l1ull/ber ofjirms involved.

With point source pollution il is easier 1O observe the el1lÎsslûns of Îndividual agents and to determÎlle their respective contribution to the total pollution. When many pollllters are contaminating in a diffuse "ay it is no longer possible to attribule ambient pollution to the activities of any one. Consequently. it is impossible to define the individual liability of each farmer. Moreover, the larger the number of farms. the more likely the free-rider behaviour is. Indeed each farmer perceives its own pollution to be relatively small.

Tite spatial dimensioll.

The relationship between nitrate leaving the root zone and nitrogen applied depends chiefly on climate, soil and crop type, and the quantity of nitrogen present in the soil. Denitrification processes in the soil vary considerably according to the geological conditions. Hence the impact of an emission on the quality of the water is altered with the location of the application to the aquifer or the river. Concerning the fate of pesticides and their environmental impact, the distance of the water bodies and the organic matter content of the soil play an important l'ole.

The .51ochaslic na/lire ofIhe nalUral phenolIIena.

Hydrologic variables such as rainfall intensity, volume of rain, rainfall interception, infiltration, \Vatel' storage, are closely related to the polllltant loading from agriculturai areas. Thus, the transpol1 of pollutants and the magnitude of non-point source pollution are governed by stochastic processes. In consequence. for a given action by farmer. it is not possible ta forecast exactly the resulting impact on the envirollment because of the occurrence of random natura 1 events.

These three elements complicate the management of agricultural pollution. For point source pollution, without stochastic phenomena and where it is possible 10 observe the elllissions of each agent. il is well-knowll that a system of efnuellt taxes, or trallsferable discharge permits or quotas is efficient. For non-point pollution sources such standard economÎc incentives cannot be used \Vith the saille efficiency. Orherwise, two issues lie at the core of the problem of the design of relevant environmental policy in this context: (i) asymmetric information and (ii) moral hazard. The first issue follows from the fact that the regulator cannot observe fann specific information necessary for the successful design of policies. The second issue, moral hazard, emerges in IwO ways. First, under regulation, any action taken by the regulated agcnt may reveal information to the regulator. Recognising this, the regulated agent's behaviour must be viewed as conditioned by this possibility.

Second, given that behaviour reveals information, the regulator can be expeeted to benefit by designing policies that encourage the revelation of information necessary for the design of the regulation. However, where slich attempts are made, the possibility for moral hazard must be recognised.

Modelling non-point pollution.

This modelling approach to integrate eeology and eeonomy is oriented toward system analysis and operation research. Models are partial equilibrÎul11 models and are in general optimising Illodels sillce they try to answer the question of how to meet environmental goals in a cost-effeetive fashion. They can also Îllclude monetary measuremenlS of ellvirOllmenlal damage. The envirollmental componel1t assesses the envÎrol1mental impacts of alternative management practice. Il is built on physical resource models which have been developed and tested using existing data bases. The economic component is a partial equilibrium linear or non-linear optimising model. It predicts farmers' response to eeonomic and polie)' signais. and provides information on resource lise and welfare changes.

The interaction of agriculture with the envÎrol1l11ent can be thought of as integrating biophysical and economie production processes (WEA VER and HARPER, 1992;WEA VER, 1994). Modelling these proeesses presents an important opportunity for multidiseiplinary interaction which simultaneously stimulates diseiplinary researeh. Figure 1 summarises the main links of Integrated Biophysical, Economie Production (IBEP) models. Weather data and farmer' deeisions are entered into a biophysiealmodel which simulates nutrient losses and crop yields. Ali this information plus data cOllcerning various constraints (on crop rotations, acreage. capital) are combined in an input-output m311-ix. Finally. a mathemmical programming model estimates the amOlll1t of fertiliser and pesticides applied. and farm profitabilit).

The feasibility of development of IBEP models has resulted from the development of a rich base of disciplinary kllowledge Ilecessary to model agricuitural contaminant flows into surface and ground water. At the same time, this knowledge has established the necessity of development of models that exploit multidisciplinary knowledge. This neeessity is evident given the multiple biophysical proeesses involved (c1imatie, hydrologie, agronomie). The neeessity of integrating eeonomic processes has come From a recognition that choice of production practjces and application of inputs interact \Vith biophysieal proeesses extensively. Firsl, the choice of production praetiees and input applications are responsive to farm site conditions and biophysical proeesses understood b) the farmer. On a second level. after inputs have been applied. the environmental effects are still sensitive to the interaction of the production ehoices and process \Vith biophysieal processes such as climatie. hydrologie. and agronomie processes. The final imperative for the I8EP approach derives from the fact that while eaeh of these diseiplinary proeesses is weil understood, individually they fail to provide a basis for underst3nding and predicting the envirollmental impacts offarm activities.

Farmers' d~CÎsjons

Constraints

/

Oepending on the issues of illlerest and the features of the \\atershed which is considered, the structure of IBEP models varies. Some emphasise the regional level (MAPP el al., 1994: WU el al.. 1996), whereas others look at representative farllls (HOPKINS el of.. 1996), or consider simplified types of farming slich as single crop or mixed farmÎng. According to ('heir structure these l110dels incorporate three sub-models.

The first category inciudes models sueh as WXGE , which incorporates a system to describe the climate. It simulates daily rainfall and average Temperature over a fifty year-period stochastically. Such a lime series is needed because, due to the inlrillsic non-linearily of elllission processes, lIsing average values would lead to a distorted description of phenomenon. This results from the stochastic nature of ciilllalic evellls. An alternative strategy is 10 rely on a system such as CERES to simulate plalll growth. It estimates the potential photosynthesis providing weather conditions and aClual photosynlhesis according to the available 3mOlll1ts ofwater and nitrogen.

The second category includes models focusing on pesticide and nutrient flows in the soil. Thus, GLEAMS (Groundwater Loading Effects of Agricultural Management Systems) targets pesticides. It consists of five sub-models which describe hydrologic processes. erosion. flows of pesticides, flows of nutrielllS and the yield of pesticides. GLEAMS reads a series of input variables inciuding soil properties (texture, organic matter, slope), climatic events (computed bya specific model) and farming practices. It predicts horizontal as weil as vertical movements of water, nutrients and pesticides. Indeed their environlllentai impacl depends on the location of the farm relatively to the river bed. Therefore the outcome of the model must be viewed as being an upper bound of the amoulll of pollution which cou Id reach lhe waler body.

According to WEA VER and HARPER (1993), GLEAMS can be summarised as follows: R = R('1\, (j),)

H = H(R;Q),.cDJ E" = E" (R.X"Q,;cD,) Cp =C"(H,XI'.X"Q,,E,,;cD,.cD,) YI' = Yp(CI')
where

R= surface runoff <p(' = c1imatic inputs <D \ = soil characteristics X,= tillage system, Q,= crop choice.
X p = pesticide application (method, quantity).

This system of five equations describes surface runoff, hydrologic processes (infiltration, percolation. leaching). water erosion, chemical processes for pesticides (degradation, volatilisation, sediment transport and vertical flow) and pesticide yield.

1 lItrient flows have been characterised by other models such as EPIC (Erosion Productivity Index Calculator) which integrates in a single framework the two above categories of models. It computes the following key variables (COSSERA T, 1991):

• potential bio-mass depending on foliar surface, c1imatic conditions and crop characteristics.

• water, nin-ogen and phosphorus crop requirements.

• rates between crop requirements and available quantities of \Vater. nitrogen and phosphorus,

• actllal output of dry mane!".

• actllal consumption of each crop.

The computation of each key variable involves the running of six sub-models \\ hich are devoted to hydrology, climate. erosion. nutrients, plant growth and fanning practices. This can be specified along the same lines as GLEAMS. Some models which combine EPIC and the pesticide sub-model of GLEAMS (Wu el al., 1996) are representalive of a variety of bio-physical models.

The third category includes profit maximising models. The fann production choice problem is considered with the usual constraints on acreage, crop rotation and livestock. But in addition environmental restrictions are also taken into account. They may integrate the links between farming practices and the application of fertilisers and pesticides. This modelling approach is flexible enough to incorporate envirolllllentai regulation5 and standards involving specifie constrainls. Therefore il is possible to assess both the economic and environ mental efficiency of a variet)' of instruments such as input taxation. decrease in priee or quotas whose COlll11101l objective is to abate polluling emissions.

Within a neo-c1assical framework. the fm"mer's optimising programme is written as follow5 (HOPK INS el al., 1996):

Max"L,Jr,C, -"L,fJ,X, + yY -"L,c",Z", -"L,,;,,,I,,, -"L,À"K p This general framework links on the one hand systems describing climate events. pollmant and Illitrient flews \Vith on the other hand optimising economic programmes. This linkage ean result in a more complex system such as CEEPES (Comprehensive Environmental Economic Policy Evaluation System). ft is an inlegrated agri-ecological economic system designed to evaluate alternative environmental strategies at the regional level (BO ZAHER and SHOGREN. 1997). Among possible strategies to redllce soil and water contamination. the ban of herbicides on corn and sorghllm has been specially considered. CEEPES is a meta-model which connects the six following components: RAMS (Resouree Adjustable Modelling system). WISH (Weather Simulation on Herbicide). ALMA AC (Agricul1ural Land Management Alternatives \\ ith umerical Assessment Criteria).

RUSTIC (Risk of Unsaturated/Saturated Transpol1 and Transformation of Chemical Concentrations). STREAM computes surface water concentration. RISK provides indicators of acute and chronic human exposure.

RAMS is a linear prograll1l11Îllg mode!.

The later is the economic component of the meta-mode!. It is a regional static model which maximises short-tenn profit. It translates information on weed control strategies (choice of herbicide and date of application) given by WISH into a set of technical and economic indicators related ta management practices, crop rotation, yields, COSIS and gross return. WISH is fed by ALMANAC which is a model that simulates crop growth. weed competition, and the interactions of management factors for a variely of soi 1 properties and cl imatic conditions. The models STREAM and RUSTIC simulate chemical concentration in ground and surface water for a series of management practÎces. Soil properties and c1imatic conditions are the main parameters of interesl. The volatilisation process of pesticides is also simulated. Finall, a set of environmental

Îndicators giving exposure values for humans and aquatic vegetation are available.

A" ide variety of simulation models are currently available for application to specific bio-physical systems. These include consideration of rainfall. plant gro,,~h. sediment transport, soil degradation. and other biophysical processes. In many cases. these processes have been integrated into specialised models useful for simulation of particular aspects of IBEP processes. each presents differelll ways of l11odel1ing parlicular processes slich as soil erosioll, pesticide leaching to the root Zone. nitrate pollution of surface and subsurface \Vater. Other Illodels exist for consideration of the aggregatioll of bio-physical processes within watersheds. Finally, depending on the analytical issues of interesl. models exist for eXlending water pollution processes illlo ecological process effects. For example, water pollution of a river basin or estuary can be related to pal1icular species or particular aspects of ecology.

The economic core of these models is a profit maximising component. Due to a lack of data its estimation and validation is often a difficult task. A methodology such as positive mathematical programming (HOWITT, 1995) offers an opportunity to deal with these issues. This method ailows to calibrate agricultural technology and resource use at the farm level. regional level as weil as sector level. Positive Illathelllaticai progralllming uses the farmer's crop allocation in the base year to generate self-calibrating models that accommodate heterogeneous qualily of land and liveslOck. Policy cOl1straints as \\ell as limitations put on the reSDurce base are easily taken into accOLint. Moreover nOI1linear calibration can take place at any level of aggregation.

EI11)li";cal results.

-/.1. Farm leve!.

Most analyses concern the United Sates and simple farm types. mainly arable farms. However there are same results on mixed farming. Let LIS consider a brief overview of some signifïcant swdies.

The empirical focus of JOHNSON el al, (1991) is on nitrate groundwater pollution in a Iwo couilly area in Oregon. They model a crop farm with irrigated alfalfa and potatoes, and therefore high levels of fel1iliser application (400-540 of Iha). The CERES model is used to predict crop yields under different input levels. Its output is used as input in a dynalnic optimisation modelto optimise irrigation and fel1ilisation decisions for each crop. Decision are taken on a daily basis according to expected \Veather. Finally there is a linear programming model 10 find the optimal crop mix \Vith in the context of various constraints on farm-Ievel nitrate pollution rates. This model is limited ta seven rotations which are currently practised in the area. Technical coefficients for nitrogell and water are given by the dynamic optimisation mode!.

The base case. represellting actual fanner"s behaviouL is lIsed to assess alternative strategies for \\ale!" and nÎtrogen applications. The number of nitrogen applicatÎons is 1\\0 to tlHee rîmes higher under the optimal solutions than for actual behaviour. This can be obtained at a 10\V cos!. and results into a higher profit level \Vith a decrease in total Ilitrogen applied. A 25% drop of nitrogen application on corn, maize and potatoes illduces a lil1lited reduction in nitrate leachate rates but a significant decrease in yields (Table 1). The relevant strategy ta achieve an impolianl drop in leaching rates, around 70%. must be based on more serious changes of management practices, specially \Vith respect to \Vatel' lise. (1991).

A flat 100% tax on nitrogen would reduce profit for corn by 14%, for maize by 7% and for potatoes by 4%. This is consistent since the short-l'un elasticity of nill'ogen is rather 10\\. A tax put on leaching \\ould have a smaller impact on profit and would be more environmentally efficien!. Its implementatioll however poses major difficulties and involves large costs of monitoring and en forcement. These results show that a moderate shift in the timing and application rates of nitrogen and water can lead ta an increase in the profitabi litY of farms and in public benefits. In the specifie context which has been considered this strategy seems better than an input or an emission tax.

A bio-economic model linking Ihree models. WXGEN. GLEAMS and a profit maximising model has been applied ta 1\\0 different farm sites (HOPKI S el al. 1996). The first site has t\\O types of farms, crop and pig farms. The second site, \Vhere slopes are significant. is charac!erised by crops combined with dairy production. Four crop rotations. three tillage practices (conventional. minimum ane!no-tillage) and four fertilisation strategies (high or reduced rate combinee! with minerai fertiliser or minerai and organic feliiliser) are considered. Without nitrogen control policy. mixed farms have higher emissions than crop farms. Indeed. as compared ta applying minerai fertiliser. applying manure offers less ability ta adjust applied nutrients ta crop requirements.

Results confirm that tax rates (on nitrogen input or on nitrogen emissions) must be high in orcier to induce a significant drop in leaching rates. Retullls of crop farms decline more than returns of mixed farms. This poses a problem because the former farms pollute less than the later ones. Otherwise, due to input substitution mechanisms, a nitrogen lax may involve an increase in the lise of other pollllting inputs and therefore create cross adverse effects on the env;ronment. In this conte"t a policy based on standards \\'ould be more relevant. Nevertheless the revenue of a tax can be used in arder to compensate off-site damages. This is an argument for taxation. As expected. simulations show that a change in tillage practices can lead ta significan! benefits. A French study (CARPY-GOULART. 1997) achieves similar resulls.

Several detailed studies have considered the High Plains in the United States. Among them, MAPP el al. (1994) simulate the economic and environmental consequences of different nitrogen control policies. The physical component includes runofr. sediment flo\\'s and leaching processes. Both irrigated and dry crops (corn. sorghum. alfalfa and maize) \\ ith clirrently usee! rotations and practices are considered. and areas are classified into four types of soi 1. Tinee components are linked: a model of crop gro\\'th and pollutant flo\\'s (EPIC-PST), a mathematical programming model and an aquifer model (MODFLOW). EPIC-PST integrates the pesticide component of GLEAMS into EPIe. The output of this system is used by the mathematical programming model for a 25-year simulation run of envirollmenlal and ecollomic changes. Ils primary function is to allocate available land area and other production resûurces 3mong available crops and praclices 50 as to maximise regional net returns. Water withdra\\'als are computed and entered into MODFLOW. This is a modular. finite difference model which considers hydrologic factors.

Four nitrogen control strategies are compared to a baseline: one-third reduction in 10tal nitrogen application. one thire! reduction in llitrogen application pel' hectare. one thire! reduction in nitrogen application on targeted soils and one third reduction in nitrogen application on irrigated land. Broad policies have potential ta reduce nitrate runoff and percolation but have a large impact on fann income (Table 2). Targeted policies are less efficient from the environmental perspective but have a smaller effeet on incollle. ln the High Plains also, WU el al. (1996) rely on a slightly different f,.amework. The physical model. EPIC-PST, is linkecl with a system of economet,.ic equations which give the acreage response to priee and policy variables. Changes in these controlled variables can indeed affect both crop mix and management practices and finally nitrate runoff and leaching losses. Calculatiol1s are made for each of the 110 counties of interest. This framework therefore allows ta determine envirol1mental impacts of several policies at the regional level. Commodity programmes based on target prices and the Acreage Reduction Program have a significant impact 011 nitrate losses. However the impact varies widely across areas. For instance it is negligible in sOllle parts of the region. On the other hand the elasticity of nitrogen losses is relatively high in counties with large nitrogen lasses. They tend to be those that have a large acreage of corn or are heavily furro\\ irrigated. This result would favour targeted pol icies.

Table 3 illustrates the consequences on net retullls of an herbicide ban [START_REF] Bouzaher | Modeling nonpoint source pollution in an integrated system in[END_REF]. They significal1tly vary across regions and whether the ban is on atrazine or t,.iazines. Net return loss ranges from 0% for a ban of atrazine in the Corn Belt to 3.8% for a ban of The ban of herbicides lead to large acreage changes in crop mix. In the Corn Belt, shifts are similar for atrazine and triazine ban: -13% for corn, -16% for sorghum and + 15% for soybean. This involves a change in management practices which can accelerate erosion processes. Indeed banning atrazine and to a lesser extent triazines increases the reliance on conventional tillage compared to no-tillage. This perverse effect makes herbicide ban questionable. However negative impacts are moclerate if crosscompliance constraints are anached with the implementation of agricultural policy. Indeed the potential confliet between the goals of soil conservation and the reduction in non-point pollution can be overcol11e by a trade-off between two environ mental objectives. The simulations for the Toulouse area emphasise the influence of climate condition 011 nitrate losses: they range from 19.1 kg/ha/yr to 67.7kg/ha/yr with an average equals to 37.8kg/ha/yr. Under the reforlll farllling practices leacling to a significant decrease in nitrogen lasses \vith a very limited diminution in farl11 returns should be implemented. Therefore a constant income objective is likely to be reached under a pollution drop. With the no-reform scenario, there is a conflict between the profitability goal and the environmental goal. The adoption of new farming practices WOu Id involve a decrease both in nitrogen losses and farm returns.

A tax leading to a similar reduction in nitrogen losses has also been considered, its rate is very high as it equals 200%. Such a tax would result inro a dramatic decrease in farm returns with mainly a drop in irrigated area. The outcome of these simulation is very similar \Vith results obtained elsewhere (RArNELLI, 1991). These results rely on a maintained hypothesis which assumes that fm'mers are technically efficient. But there is empirical evidence that a number of farmers are not efficient, corresponding farms are then included in the interior of the production set. It is well-established that the response of input demand to Ct tax on minerai fertiliser is greater for non-efficient farmers than for efficient farmers (VERMERSCH el al, 1993). For non-efficient farmers, a tax on fel1iliser is expected (0 induce bath a decrease in nitrogen consumption and an increase in profitabilîty. According to this argument, most optimising models tend to over estimate the detrimental effects of taxation on profitability. This is especially true in mixed farming cOll1bining crops and beef, as non-efficiency is a relatively serious problem [START_REF] Piot-Lepetit | Détermination des marges de manoeuvre des élevages à panir de la mesure des inefficacités 1[END_REF].

AMIGUES el al (1998) also considered a French version of EPIe. It is linked with a dual econoll1etric model which has been calibrated with a panel of farm data collected in a 5mall region of South Western France. Corner solutions are cOllsiclered in order 10 take into aCCQunt the absence of cellain crops on farms. The treatment of risk is emphasised in this fi•amework. Yield response to fertiliser and pesticide application is 1l10delled as weil as farmers' behaviour facing a production risk.

Envirol1l11ental Îndicators refer (0 the quality of surface \-Vater. Table 4 refers to ll1ixed farming where beef production is combinedwith irrigatedmaize. dry maize or corn. First of ail the impact of a tax on production costs is similar across the tlHee categories.

Moreover the response of fertiliser demand to taxation is high as the estim3ted own-price elasticity is over one. This contrasts \Vith Illûst optimising Illodels which rely on llol1-elastic fel1iliser demand equations but il is consistent \\ ith respect to the above argument on non-efficiency.

Concluding comments.

The management of non-point source pollution. originating mainly From agriculture. raises specific problems because it is impossible 10 observe individual emissions and their environmental impacts. For these reasons the adoption of Pareto optimal policy measures is impossible. Bul. emissions are correJated with climatic conditions and physical features of the site where pollutillg activit"ies take place. Biophysical models. such as Ihe Erosion Productivity Impact Calculator, which perform weil LInder a \,vide range of conditions, give key parameters to estimate the ullobservable illdividllal emissions. In consequence, the implement"ation of regulatory policies becomes possible, even if there are second best solutions. In coupling these biophysical models with mathematical programming models, it is possible to forecast economic impacts on agriculture of various scenarios targeting a desiredlevel of pollution. 1ntegrated B iophys ical Econom ic Prod uct ion models ra ise many tech nica 1 problems re lated ta biophysical modules. But they rely on economic hypotheses \\hich drastically limit their validity. In order to predict the oulcomes of the scenarios of interest, the economic model must deal \\ ith a l1umber of policy instruments sllch as taxation. standards. individual or regional quotas. Because of a wide diversity of production activities and few empirical constraints. the optimisation procedure reduces the realised number of activities. The problem of overspecialisation is the main difficulty that many programming models meet. The traditional approach relies on constraints for calibrating the

Figure 1 .

 1 Figure 1. Flow diagram of Integrated Biophysical, Economic Production (IBEP) models.

8 1 =

 1 outpul of cropJ pel' hectare. ~= acreage in a management practice i, y= number oflivestock units, Zm = hûurs machine m is lIsed.1", = dummy variable (1 if machine m is on fallll. 0 other\\ ise). and parameters are: ail = yield of crop) in management practice i, 13, = per-hectare variable cast of management praCl'ice i. y = net relurIl of livestock unît. livestock stock ing rate of management practice i. é m = per-hour variable cost of operating machine m. ~m = fïxed cost of machine m. ll,f' = kg pel' hectare of effluent p from management practice i. K,} = limit 011 effluent p in kg. À p = flat l'ale tax on effluent p. J[ 1 =unitary priee of cropJ, v = minimulll livestock Illllllbers.

  triazines in the Northern Plains. Losses per hectare are expected 1'0 reach a maximum of 4.1 %. Constant net returns in the COIll Bell resulls from the adoption of a new technology provided by low-II dosage herbicides which should be substituted to atl•azine. This change reveals to be profitable in severa! regions.

  Groundwater contamination is Ilot a seriolls problem in these regions and the concentration of the substances \~Ihich are considered, is below the benchmark. Surface water contamination widely varies across areas and according to substances. A ban of atrazine, especially on corn, would lead to an increase use of some triazines resu1ting illlO concentration exceeding benchlllark for several substances. A ban on triazines would not lead to a silllilar excess over the benchmark.[START_REF] Flichman | Politique économique et pollution des nappes par les nitrates en Europe C.R. Aead[END_REF] linked a French version of EPIC with an economic model which maximises expected utility under a series of constraints (financia!. political, physical and risk). The main objective is to assess the change in nitrate pollution which could result from the 1992-reform of the COl11mon Agricultural Policy. The study tm'gets six regions distributed in Italy, France, POl1ugal. Spain and the United-Kingdom. There are two regions in France: Toulouse area in the South West of the country and the Beauce in the Paris area. In orcier to calibrate the mode! a single type of farming has been selected in each region.

Table 1 .

 1 Effects ofa 25% decrease in nitrogen application (%).

		Maize	Corn	Potatoes
	Leaching rate	-4	-9	-2
	Yield	-14	-10	-22

Source: Johnson el al,

Table 2 .

 2 Impacts ofnitrogen control strategies (%).

	One-third restriction	Nitrate rllnoff	Nitrate percolation	Farm income
	Totalnitrogen	-41	-67	-19
	Nitrogen/hecta,.e	-30	-69	-25
	Targeted soil	-8	-27	-13
	Irrigated land	-12	-46	-10
	SOllrce: Mapp el al. (1994).

Table 3 .

 3 Impacts on net returns ofan herbicide ban (%).

	Atrazine	Triazines

Table 4 .

 4 Impacts on fel1il iser demand and costs of production of a tax on fel1iliser (%).

	Tax rate	Ferliliser demand		Costs of production
			Irrigated Maize	Maize	Corn
	20	-26.1	4.2	3.6	3.7
	40	-50.4	1 1.0	10.5	7.4
	60	-79.0	15.2	18.2	11. 1

Source: Anllgues el al (1998).


Ludo Peeters

~ T\>

AN ASSESSMENT OF ALTERNATIVE EMPIRICAL MODEL SPECIFICATIONS•

. are identified. Alternative dynamic specifications are estimated, based on flexible funetional forms. While our primary focus is on the use of a modified version of the Symmetric Generaliscd McFadden cost function with maoy outputs, the popular Translog cost function is estimated as weil for comparative purposcs. In illustration. the proposed modelling framework is uscd to estimate cost functions for the Belgian feedmix industry.

INTRODUCTION

The induced•innovation hypothesis is c10sely associated with the work of Hayami andRuuan (1970, 1971) and Binswanger (1974Binswanger ( , 1978)). Despite the faet that this hypothesis reccivcd considerable attention in the literaiure. malt econometric sludies failcd to model technical change as adynamie investment procas. In addition, OImstead and Rhode (1993) noticed thal one can ob!tt'Vc two distinct arguments in the induced•innovation hypothesis, which have becn cilher ignored or used interchangeably in many empiricaJ studies: (a) the "change variant", and (b) the "Ievel variant". The first v&riant is the conventional argument, in which c1uJn8~s in relative factor priees lead to tr:ehnical innovations that save the factor whieh becomes relatively more expcnsive. The second variant argues that even at constant relative factor price lt~ls, new techniques will he developcd and/or adoptcd to save relalively expcnsive factors.

•

Paper to be presented at the lJe Journées de Microéconomie Appliqute. Universit~de Li~ge, 6-7 June 1996. This paper presents the results of ongoing research. Ali errors remain ours. Comments are weleome.

•1• ln this paper. wc attempt (a) to identify and me&Sure the relative importance of these two variants of the induced-innovation hypothesis, and (b) to disentangle the "traditional" or "pure" factor substitution from the factor substitution (factor biases) resulting from prieeinduced technical change. To accomplish this, we slart from the framework proposed by Lasserre and Ouellette (1991) to estimate induced tcchnical change. by taking explicitly into account the necessary time lags involved in the innovation pracess. AI50. Fulginiti (1994) adopted a similar approach to separate pure substitution from substitution due to tcchnical change. Her approach was essentially based on the distinction hetween (a) "market priees"

guiding pure factor substitution, on the one hand. and (b) "normal priees" affccting the choice of technology, on the other hand.

Specifically, wc develop alternative empirical model specifications, using 5O•called nexible functional forms, which are grounded on duality theory. Unlike Lasserre and Ouelleue (1991). who used the popular and widely•used Translog (TL) cost function. our focus is on the use of a modifted version of the retatively new Symmetric Generalised McFadden (SOM) eost function with many outputs. Here. the TL cost function will only he estimated for comparative purposes. The prexnt study is also an extension of Rask (1995 l. ;n the sense that:

-2-.~. in factor proportions) is modelled as an investmcnt (adjuslment) proccss involving lime.

Ta assess the;r empirical performance. the propose<! model specil1cations are used to estimate induced innovation in the livestock feed induslry in Belgium. This empirical case presenls a true "tedooak cxample" of policy-induced changes in technology which took place in the European agri-food sector (known as Ihe "cereals substitutes problem"). The replacement of cereaJs by ather ingredients in livestock feeding is oot surprising. given the fact Ihal relative priees of cereals in the EU were high and persistently increasing during the last Ihree decades (prior to Ihe 1992 reform of Ihe Common Agricultural Policy).

matrix of unknown parameters. C. [c.J is an NxM matox of unknown paramelers. A ë [al,l] is an NxN matrix of unknown parameters. pis an Nx 1 column vector of current (market)

priees of aggregate feed inputs (indexed i J). p is an Nx t column "ectar of long-run cxpected

where A, denotes the Î-th row of the matrix A. and where p represents the vcelor of (nonobservable) "expected long•run priees" or "normal prices". which are a fUllClion of pasl input priees (defined in relative terms). The "normal priees" are defined as a geometrically-declining lag structure with constanl adjusunent parameter (À); they are allowed to interact with current "market priees". and the)' represent the "change variant" of the induced-innovation hypothesis.

The normal-priee term supplements the usual time trend. which is supposed to represcnt the "Ievel variant" of the induced The following notation will he used throughoui this section: N is the numbcr of (feed) inputs;

Mis the number of (compound (oed) outputs. a, '1 la"l is an Nx 1 colurnn vector of unknown paramelers. P, '1 [Q, 1is

I: I-M. e'p" l' for 1 1. .N (2) -)- -4- . t
. .

'ona-run. The inner products a'p,and ~'y, can bc interpreted as Iixed-weight priee and quantity indexes. where 0 1 and 4\ dcnote the cost share of input i and the value share of output k.

respectivcly. Non-jointness in input quanlilics wou Id itnply that the lIcssian matrill. vanishes (i.e.. Q is a null matrix). The estimation of the s)Istem of input demand and marginal-cost equations allows 10 caiculate thr'tt types of (aggregale or global) own-and cross-priee tlaSlicitics of input demand:

THE TRANSLOO COST FUNCTION

This last expression is similar to equation ( 9) in [START_REF] Rask | The structure of technlJlogy in Brazilian sugarcane production, 1975-87: an application of a rnoditied S)'mmelric Genenllized McFadden ~'o~l funclion[END_REF], bUI here it represents the (annual) rate of change in input demand due only 10 Ihe levtl variant of induced innovation.

(II)

(la) " cll"", J L S'--;i/ , , ( cll"
,,,

Sil -at ( cll",,, _ cllnC, J S -- I/~, ~, ( 4>Y,)[ ') 6 ( ~~y, ] = - a (1-.... + -+Y+Y' ,1 , , ' Il XII y, -À6,( ~;;, , •Y,' y,,(I-I)]]' for i = 1" .,N 4> Y, 1 TL modt'l wUh commml adju.f/menr paramt/u ~~" i!1 dllU'" cl' ],1
For comparalive purposes, we now formulale three versions of a dynamic Translog (TL) cost function with many inputs: (a) the TL cost function with a common adjustment faclor À.

E~dllU'

'1 = --" cllnp, E.'iH1 dllU' '1 = --"- dlryJ" 1 and I.RI dlnx C•~11l E'I = ___ "::" '1 ~lnp,. "'ï'='}. 1993),
This mode! was de\lcloped În [START_REF] Peeters | Measuring biases of technieal change: the case of cereats displacement in livell>tock ration formulation in Belgium[END_REF]. Assuming a common parameter of adjuslmenl as" al

(1 -~)OE" (18)
Alternatively, given expression (la), wc could wrilC

The expression in (12) stems from apply;ng a convenlional Koyck adjustment scheme tO the traditional TL specification. This Koyck trallsformation is accomplished as fol1ows:

r, ~S,lX, -E S,X) , (S, -.l',') X, -E (S,S,lX, '" (19) S = a ... Lh"lnplf " , , ,
where L ",tlny~, + a,,' ~~'(p, l'P. l'P, J' ),

.,

for ail ;

(\4)

where Y, '= as/a, and X, '= c11nx/c1/, or in matrix notation:

r ~(S -S'®.I)X ~nx (20)
The Koyck transformation: multiply ( 14) by À and lag one period, then substract this from ( 14), toobtain (12).

However, due to the singularity of the matrix n, it is not possible to solve for X '= (olnx, lai).

Therefore. we use an alternative approach by rearranging expression (t0) as follows

as" 1 alnC, as"

1 ~as, -- ._..- -_ . L..(-)Inp ClI Su ClI c1, SIl , a, JI " ~'O = L a,pnp" 1 • ).Inp,.. l ' Àllnp,,) , , ,
" OE E --'-,-Inp/l l' for ail 1

1 1 1 • 1\/. ( 15
)
Cllru" a,

OE,,(I-~)

.1'

" + L a j ,(1 -À)lnp" , (21)
The aggregate own-and cross-priee elasticities of input demand are calculated as

SHO E" '" E" clint" è1lry}" clint" ----- Cllnpj' 1 b" • S,,~~, SIl a" _~~~'r.:"ill Sn 6" 6" -9- (16) (17)
from which the (annual) rates of change in input demand due ta the level variant of induced innovation can easily bc derived. Some rcmarks: ln the TL case (estimation of cost shares), the Le Chatelier principle is not automatically satisfied, even though the proportionaJ adjustment of the cost shares to their equilibrium values is l•À < 1 (given that 0 < ). li: 1). Onl)' if ail < 0, then the long-run As can readily be secn, ail columns of the (symmetric) matrix M sum to zero (by constructi• on), a l'talUre which is required to ensure singularity of the mode!. Furthermore, the clements of the matrix M are l'ully dcfincd in lerms of N parameters À/, IJ" .,. À, own-price elasticity will be larger (in absolute value) than the short-run own-price elasticity.

However. if a t > O. then the long-run own-price elasticity will be smaller (in absolutc value) !han the short-run own-price elaslicity (Rerndl t'I ul. 1977, p..'O). 1I0w to intcrprcl a positive a.? If a .. > 0, demand for the ;•th input can be calle<! Msharc ineiaslic M , sillee an increasc in the priee of the ;'lh factor resu1ts În an increasc in the cost share of lhat factor. This and other problems with the cost share adjustmclli specification (sec Berndt ri al. The matrix M can be wrÎUen as (Moschini and Moro 1994, p.306):

where

À, 0 0 À, 0 À, 0 À, A, 1 and À 0 0 À . À.
Given the definition of P-IJ or p-lJ o, as functions of the ". ail elements of the matrix Mean he uniquely identified. Now, defining Sol = 9,,(') + 4>,('), wc get 4>,(') = SIl -9,,0, and

M " A H' L:' À, À (À 'À.) , , ". . -À, ' L,À, (23)
À,(À, ÀNI

1 • J ",' L7, À, ( 24
) 4>(') , AP, 1 • M[S, 1 -a, ,(')} (28) ( 29
) (JO)
The clements of the mat ri x Mare then:

-II, or -12- where S is a vecior 01 (;Ost shares..~is a diagonal matrilt wilh the cost shares as diagonal elements. and / is an identity malrilt of approprialc dimension.

We now formulate such an error correction modellECM) specification, starting from a restricted version of a first-order "autoregressive-distributed lag" or ADl.( l, t) model:

The annual changes in the cost sharcs duc 10 the levcl variant of induccd innovation are calculated as

L h"lnp" L (',.Iny••• a'l' , , as" il'
(

~1)OEtI L !J"OE,) 1
,., (351

'" a, L a,jlfVJjr 1 , L P" hlJ!", • ÀS" , , (36)
The (anoual) raies of changc in input demalld duc 10 Ihe level variant of induecd innovation can be computed alollg similar lincs as in cquatioll (21). whcre èSj(l, has 10 be replaced by (35) inslead of (18). ln equilibrium (that is. in a situation in which therc are no changes in priees and output quantilies). we get the following relationship:

s:

D, L h'/ 1np)' • L (a,,' P,)lnp/' , , 1-1.
"c lm"

L I l • l • , " 1 " (37)
This ECM specification is an attractive alternative to the previous simple Koyck adjustment scheme. provided il is able to represent adequalely the data's dynamic properties and 10 generale plausible and meaningful parameter estimates (Friesen 1992).

The shorHun elastieitÎes of input demand are the same as for the TL case with a common adjustment matrix (Section 3.1). The long-run elasticities are defined as 1t;5 c1ear that the restricted ECM rorm permits to dislinguish (conceplually) belwecn (a) the equilibrium priees in the second !crm on the RHS. representing the shoU-run yel/ull:Nuljusled pure substitution effccts. and (b) the equilibrium priees in the third tcrm on the RHS. The measures of the level variant of the induced innovation can he compute<! along similar lines as for the previous TL specifications.

Ô,SII " (a," a'l)

L h"IfV}" L l',llnY Ir 1 L a,rô,lrv'" , , 1

EMPIRICAL APPLICATION

L h"l'V,,, L ",1 !nYl ' ' L a"ô,lrv'" 1 , .

(1 +' " ~("; ,~,) I~,,, , -( I"'~)(1-1)1

The proposcd mode! specifications arc applied to the Belgian fecdmix industry. The data used for estimation are constructed from an nua! observations on priees and quantities of aggregate This specification allows also 10 impose symmelry on the long-run parameters.

-

Estimation mtthod

To facilitate the cconometric estimation of the SOM model. the input demand equations in (3) and the marginal"COSt equations in ( 6 Therefore. wc decided 10 choose the value 0 for this parameter (note that in mosl cases reported in the litcrature. a zero lower bound would be binding, anyway). Hence. the SGM function wc eslimated is "semi-f1exible" in the sense of Diewert and Wales (1988) and Kohli (1994). The reduclion in fleltibility is not incompatible with the data (the drop in value of the log-Iikelihood is imperceptible). In the jt,;nl SOM case. the required convexity of the cost function with respect to the output qU311lities y was violate<!. Imposing the nceessary restrictions (or choosing a value of a for the relevant Cholesky value). we were nol able 10 reach convergence or to obtain meaningful results.

We testcd for non-jointness in input quanlities. In the SGM case. this tcst implies (hal ail the elements of the matri x Q be set equal to zero. In the TL case (the rcsults arc not reported here), this test requires the inclusion of the cosl function in the estimation process, and involves a number of non-linear restrictions (Ocnny and Pinto t 978. p.257). Exploratory estimations (not presented here) showcd that in both the SOM and TL,cases, Ihe hypothesis of non-jointness had to be rejectcd (with the eonventional5% significance level).

ln the TL case, with a restricted adjustment matrix M. the estimated characteristic rools of rnatrix M' are: -0.302,0.505. and 0.891. Since they are ailless than one in absolute value.

stationarity is satisfied. The estimated matrix Mis:

•18• r f , ... For the short•run dynamic elasticities ta be smaller than the corresponding long-run eluticities (Le.• the so-called Le Chatelier principlc), il is al50 necessary that the characteristic roots of the M matrix lie within the unit circle. This condition, however, is not sufficient (sec, for example, 8c:rndt il al., lm, p.30). Looking at the Jaults of the symmetric adjustment matrix model. il can he secn that the elasticities satisfy the Le Chatelier principle. There is. in general. no "overshooting" (which would he the case if the short-run cross-elasticities are larger than the corresponding long-run elasticities). This makes sense. Finally. comparing the two models (A. ~'jW M) and using the likelihood ratio test (LR = 32.2). the hypothesis of a comman parameter of adjustment is c1carly rejected (with 5" significance level and df = 3).

Il should he noted that for the Tl case. the common adjustment parameter version is not nested within the ECM version; heRCe. the log-likelihood value of the ECM version is not necessarily larger. Also. in the estimation of the ECM version of the Tl. the standard procedures of cointegration anaJysis were not conducted. We hope to explore this area in much more depth in the future.

ẼsTiMATED

PRieE ELASTICITIES OF INPUT DEMAND (CHANGE VARIANT)

The elasticities of input demand. which are mcasuring the change variant of the induced innovation process. are shown in Tables 2a and2b for the SGM and the Tl eost functions.

respectively. Nole that the reported elastieities are averaged over the values calculated for every sample point bc:twecn 1961 and 1991. Overall. the elasticities secm to he well-hehaved.

However. in the comman adjustment parameler version of the Tl. the Le Chatelier principle is not satisfied for additives. In the common matrix version of the TL. there are sorne instances of a sign reversai -from substitutability lO complementarity -for the cereals-proteins and substitutes-additives relationships.

-19-

The "Iong-run" elasticities of inpul demand nofloct\he teehnicaI chanBe impoct of past priees. The estimated elasticity values fOT the SOM suggest, for example. that a 10~illCreasc in the "normal priees" or priee expectations of cereals. ct/tris p<lribus, induces technical innovations leading, after a tapse of more than 12 ycars. ta a 1511 reduction in the ccreaJs content. Overa.Il. the signs of the long•term elasticitics are consistent with the change variant of the (cereals-saving and proteinlsubstitutesladditive-using> induced-innovation hypothesîs.

EsTrMATEO RATES OP CHANOB (LBVBL VAIIAf'(J').

The estimated (annual) rates of change in input demand or changes in input cost shues. which are representing the level variant of the induced innovation process. are given in Table 3. ln many eues, thcy are in lint with the cereals--savi"l innovation process which took place in the 8clgian fecdmix. industry. Only in the eue of the TL specification with a common adjusment pe.rameter À. the results are consistent with the Q priori expected substitutes-using innovation.

It should he noted that the measures presenteel in Table 3 are short-run. In the cases where a common adjustment parameter À is heing uled (including the ECM specification). one can c:a.sily derive the long-run mcasures (8iven a steady-state situation) by dividing cach short-run measure by l-À. They are not reported here.

Obviously. both the estimated measures of the change and level variants of induced innovation seem to bc very sensitive ta the ehoiee of functional form as weil as the particular dynamic specification. The pure substitution elasticities. however. are doser to cach other (exeept for the common matrix version of the TL).

SUMMARY AND CONCLUSIONS

'The aim of this paper was to discuss the application of a cost-function framework to masure pricc-induced innovation in production systems (affeeting factor proportions). Technical change was treated as the delayed result of a price-based investment process. Hence. induced innovation was modelled in adynamie fashlon (usinglagged priees). -31-Nole; l "" cereals; 2 '" cereal lubstitule.; 3 = high-protein food.; 4 '" additives.

-32-~lr, ( -))-

~~~

  a mulJi~produet SGM COSI function is uscd. and (b) bi(J.{N tethnieal change <implying shifts

  (a) short•flln!in.sloflloneous or .fhort•runl.'ffut;(: claslicilics (rcprcsenling short-run but fullyadjusted pure factor substitution due 10 current "market price~changes. given the slale of the leChnology); (bl shnn-runld.vnumic ellstieities (rc:prcsenting shorHun bUI parlially•adjusted factor substitution due 10 price-induced changes in lechnology); (c) Jong-runldynomic elastitilies (representing long-run. fully-adjusted. factor substitution due to pricc-induced changes in the tochnology). The dynamic tlaSlicitits can be uscd 10 chracterisc the change variant of induced innovation. These elasticities are respectively defined as

(

  Koyck scheme): (b) Ihe TL cost function with a restricted (symmetric) adjustment matrix M: (c) the TL cost function formulated as an eTTOr correction model (ECM). The specification of the TL cost functions do nol a1low for autonomous (ilicks•neutral) technicai change. as dcfincd in Moroney and Trapani (1981. p.53), for example. and is similar 10 the one in Pecters (1995). where 19)

À

  . we can write the system of cost•share equations as The leve! variant of Ihe induced innovalion can he calcu!ated in two ways: (a) as the (annual) change of the input cosi shares. expressed in perccntage points (as. for eump!e. in Stevenson 1980). or (b) as the (an nuai) rate of change in input demand. expressed in percentages. The corresponding expressions for thesc measures are s, = e,l') • flop" • ÀI[S, 1 -e, ,01 is an Nx 1 vector of cost ,hares. 1' 1 is an Nx t vcctor of the logs of the input priees.A = (avl is an NxN matrix of unknown parametcrs. 1 is an idcnlily matrix of approprialc dimension. and 9 r t) an Nx 1 vc<:lor with clements 9,,0. wherc -):: a,' Lh,llflP},' L,•"loy., ' a,l'The anoual changes in the cost sharts due to the level variant of induced innovation are calculated as This expression 15 similar to r:quation (8) inPecten (1995), augmented with an exogcnous teehnica! change lcrm (linear lime trend), As w;lh the SGM case abovc, the familiar finn-arder autoregressivc spttific3tioll can be obtained by seHing A = O.

  O" A'PII • M'lS.•, . e; .(-)\ absolut.e value. Note that the characlcristic foots of matrix M are the same as those of malrix M'. plus one rool which is equal 10 zero (k=O), The thrce types of owo-and cross•priee elasticitics of input dcmand are dcfined as (in matrill nolation) 3.3 TL trror corrte/ion mo(ü/ lé'"' • (H • S'.\).\ /.:SHI '" tA • S'S).~, ,.;I.HI ~tAO' M) l ,.\o/Sl.~1 -change variant of indiced innovation has been represented Ihrough a pre-specified geometrie-Iag structure. Hendry (1995) and Banerjee tl al. (1993), amang others. have becn criticising such a modelling Slrattgy. advocaling instead the use of a more gcncral dynamic modelling framework. from which more restrictive dynamic specifications (such as the above geometrie-Iag structure) can be inferred and teste<!. This so-called MgeneraJ-to-spetificM approach is usualJy based on an error correction model (ECM) specification.

  Some rcmarks: First. for stability of the adjuslment process. it is requircd tha! ail characteristic rools 01 M lie wilhin the (0.1) interval. Second. the specilication permits "overshooling M . Third. symmetry of the "Iong-run/dynamie" Allen elaslicities of substitution is not necessarily salislicd. cven though the ~short-run/dynamie" Allen elasticities of substitution arc symmetrie. The stalionarity of the dynamic process is tested by cheeking Ihe values of the eharacteristie roots (cigenvalues) of the matrilt MO. As noled byBerndt and Savin (1975. p.944). the dynamic process is stationary if the roots of malrill. MO are less lhan one in .\3-This specilication presupposes only the eKistence of .thort-run (albeit lagged. by construction) and innll-run substitution cffects due to price-induced changes in technology through the incorporation of bath one-ycar-Iagged and lwo•year-laggcd priee variables on the RIIS. whereas the repanse of input demand 10 changes in eurrent market priees and/or OUlput quantities always oceurs in.~tanfanl'ously (full adjuslments). The levcl variant of induccd innovation is again represented through a shift term (time trend).

  fecd inputs and aggregate compound fecds outputs. for the period 1961-1991. The dala wcre lakcn from publications of the Nationallnstitute of Statistics ("Nationale Produkliestatislieken R ) and the Federation of Belgian Feed Compounders (BEMEFA). Il is estimated that the sample represents 85 %of tolal compound fced production in BelgÎum.Notice that the crror corre<:tion part (betwccn the brackets) only includes those terms representing the long-run equilibrium relationship betwecn cost shares and lagged (norma\) priees and a time trene:!. ln othcr words. the paramctcrs e" and P' 1 are representing the long-run rcsponses of input demand 10 changes and levels of !agged (normal) input prices. respectively.

  ) arc transformcd inlo nominal or current value terms by multiplying Iheir elemenls by the input priee iodeK and output quantity index. respective!y.Hence, the dependent variables are del1ned as R, = p,x, (; = 1, ...• M and F, = 8: :v (le = l, ...• M). Prior to estimation, additive error lerms are appended to each of Ihe equations. The error terms are assumcd to be joinlly normally dislributcd with 1.ero mcans and constant but unknown variances and covariances. Since the sum of Ihe lirst N (four) equations (Ep,x,) is identically equal to the sum of Ihe remaining M (thret) cqualions (tgl.\I~). the N+M (scven) equations in the system arc hoearly dcpendcnt. As a resuh. the covariance matrix of the error ttrms is singular. and olle or the equallons must bc droppcd bcforc estimalioll.The TL models are eSlimaled by employing the usual COSI share equalions. The cost function itself was not included in Ihe eSlimation process.The various models are estimatcd using the iterative 7..ellner technique (ITZEL). which is asymptotically equivalent to FIML. The ITZEt. estimates arc invariant to the cquation deleted (in ail the modcls wc arbilrarily dropped the input demand equation associated of the SGM and TL cost functions. and the associaled asymplotic standard errors, are reported in Tablesla to le. Overan. the estimation resulls are satisfaclory. ln the SGM case, global concavity of the cost function with respect to priees p and p was tested using a Cholesky deoemposition of the matrices Band A. respective!y. Preliminary estimalion showcd thal one of the Cholesky values was positive. indicating a violai ion of the concavily condition. Squaring this Cholesky value created problems of non•convergence.

  uu1tiriel (in the fil'lil J1IIt of the "'Ille).•rd in percenlage polnlJ for the Inf"U! cost ahlrel (in the lecond f-r1 of lhe. "'ble).

  •innovation hypothesis. Furthermore. we impose the usual symmetry and homogeneity restrictions on the matrices A il [exvl. 8

E [b.,J and Q il: [qUI]' ln other words. symmetry and homogeneity are assumed to hold both in the short-run and the The SOM functional form for a cost function with mUlI.v outputJ and constant rtturns 10 .fcalt is formulated herc. The propertics of the SOM COsl function will not bc discussed in this paper. sinee Ihey are sufficiently described elsewhere (e.g .• Diewert and Wales 1987; Kohli

1993)

. Note thal the empirical application 10 the Iivestock fecd induslry below would justify the assumplion of non-joimnt.'u in input quantities (Pecters and Surry 1993). However. we will s!.art our discussion w;th the (more general) joint cost function framework.

2. J

A modij;ed. Jully flexible. SGM ('lm .(unclio/l with man.v nutpu/of

is the k•th column of matrix C. Q. is the IHh row of matrix Q. and I<l is defined as in

  Pecters and Surry (1993) .

	t,' .!
			2 4>'y,	O'p,	O'p, ,	• (O'p,)'	(O'p, ,)'
			l'o(Y:QY, " . _ , _ , ' -, -, . -.---. -' -. -t a ,7'-Io.I-) Ày",QY,,] [e' ,y, ÀC'y,,) A,p" ( ' ( 1) (4)y,) (4)y,,) 4> Y, 4>y" Op"	(4)
	Given the above specifications. wc now present a straightforward extension of the theorem introduced by Kohli (1993):		[ .0 _,_, "y'-+"hy ,l_À 1 '1 P:YI P:Y(I-I) '~'y, ' " 4>'y, 1	-Ày(t-l)-lJ2ÀY(/-l)1 1 Il	)
	THEoREM.	TM fO.tl junction C(j d~fin~d in (1) is a Jully fl~x;blt cosl !unction al the point				r" 1 't'y, 1 , 1.:;:;-.	for; = l, .... N
	z• = (p.,y.,t.,p.), 'NIu!rt p dtno(e,f tlw vector (~r (mm-observable) "normal" priees. providtd
	thot. for .wrne p. H O. .v... O. and p • .. O. 'he followins condi,ions ort satisfied: l1btJpt =	Using (3) and (4), the "normal priee" term A,p, in (3) can be written as
	O.forolli; ~alJP" == O.foroll;; ~qihYh• = O,for011 k; L;a iJ " = J; E,ftu = J; ~8PI•=
	J; E,8Pr• = J; und E.4v.• = J,(Note that in the empirical analysis. below, it is assumed that	A,p,	A,P, 1	, {ail lagged lerms in Eq.(4)}.	for;	I •...N	(51
	p. = 1"", .v• = 1." and '-=0•1		8/p'I
			Nole that when the matrix A is equal to zero, the model reduces to a first•order autoregressive
	PR.ôbF. Sec the Appendix.	specification. Expression (5) can now be inscrted into the marginal or unit (feed) cost
			equations. whieh are also derived by applying Hotelling's lem ma to (1):
	Applying i1otelling's lemma to (1). while using the aggregate output index. ~'.v,. as
	a normalising factor (for easc of exposition), yiclds the following inpul demand equations: The full expressions for thesc claslieities arc ralher tedious (set. for example, Peeters and	K h = , 4> (P,'BP,] . [Q"y, -'1,4> Y,'QY,] (Op,) • p,'C, • 4>,(P,'A p,) VI • O'p ~y k (~yY , ,	(61
	Surry 1994); lherefore we will nol present them here (they are available upon request). In the
	• 6,Y,' • 'ilO,Y u " , • A,p, • a,,' where C. x" 4l~v, a/p, '1.0 ~Bp, 1 . ';.0 l <Qy, 1 ' (e'pi ' (~~)'i (',Y, ~~)'I • ~.(a;p,)' • (8p,)P u ' + 4l.(6'p,)y,I t 'IJ41.(8p,)y",', for ft . 1. M SGM case. Ihe Le Chatelier principle will always be satisfied wîth a common adjuslment parameter À. NOle that thest c1aslicities are aJl.1l.'t'J.!clft' elaslicilics: howe\ler. assuming non-l ' !.éP, (3) joinlness in input quanlitics would allow 10 calculate di-fuggrt'J<uft'd or output-specific O~(P~~!)' 4l~~', for 1 1. .N elasticities. along wilh the allocalion of the inpuls OVer the various outputs (Peeters and Surry
	where A" B,. and C, denotc the j•th row of the matrices A. B. and C. respectively. Note that	2.2	Measuring 'h~changt and levtl varianJs of induCf'd Îmlovalion
	the parameters a,r arc input-speciflc. whcrcas the y, and y" are common (unknown) scalars
	(which are necessary 10 ensure "full OexibilityW); 50. there is no redundancy in this	Dynamic priee elasticities of input demand and rates of change in input demand can be used
	specification. Now. applying the conventional Koyck transformation, we obtain the following	as descriptive meuures of the change and level variants of the induced•innovation hypothesis.
	input demand equations in estimable form:	respectively.
		•5•

= [BP'. À Bp, ') . v.o( p,

'Bp, -À P ' ,'Bp, ')

  1977, p.3\) can be avoided by using an alternative specification, such as the SGM, where a level-adjustment model is usually adopte<!.

			ÀL		(25)
			":IÀ,
		",	À,À) -L,À,'	" j	(26)
	3.2	TL model w;th rr.~'rktrd (Jymmt'Irid adjll.wmrnr matrix

Estimation of a singular system mcans that onc equation must be dcleted. Defining the matrix M'as an (N-I) x (N-l) matrix of unknown adjustment paramctcrs and having typical elcments P-./ =p.y'P-,,,. the elements of the matrix MO can bc estimated jo;nt!y with the structural parameters by rewriting the model as In5tcad of e5timating a demand system with ollly one coefficient of adjustmel\t, we 1l0W devèlop a model which is very similar to the one suggested by

[START_REF] Moschini | AUlucorrelation specification in singular equation systems[END_REF]

for autoregressivc, singular, equation syslems. This model inco'l'Orates N diffcrent coefficients of adjustment. Il ;5 a restricte<! version of the Nadiri-Roscn generalised Koyck adjustmcnt scheme, and can bc writlcn as: S,' ' " e;(•) • A/i" • M'[S,', -e; IC')} (27) s,e,o ' !Vi, 1 • MIS, 1 8, ,(')1 (22) whcre S; and e,'O are the veclOrs S, and 9l) with the lasl elements deletd. and A' is the matrix A with the last row delelcd. The clements of MO are

  representing the long-run substitution cffecls due 10 changes in the stale of the technology (i.e.• biases of pricc•induced lechnical change).Equation (36) can now easily bc rewrillen in an ECM form. This can be accomplished by .subtracting S~l from bath sidcs of (36) and then add and ~ubtract [C1 l 1 lnp}l.}on the RHS and rearrange to get

	I~' ., dlM II dlnp,	6 y .. S,/Sil S"	6"	(40)

Table le :

 le Parameter estimates for the Oolnt) TL cost function, common adjustmenl parameter A.

	j;
	"
	LoI-likelihood Mo S2.6; Not. .. 30 Nole: i,j. .. 1 20 poultry: 2 '"' pigJ: 3 .. cllitle Loa-like1ihood • Hl.): No~~30 Note: i.j -1 • ccreal.: 2 .. <;ereal 'l,Ibf,litule~; ) ,. high-prolein fe«l,; 4 .. addil;~" k '* 1 .. poullry; 2 .. pil~: ) .. caille Parunotor E-lilNltcd value Standard error Pllrllmeler &:IUlUIlcd v.lue Standard error bll 0.037 oms ., 0.475 0.0)) bl2 0.041 0.034 ., 0.449 0.063 bll -0.061 0.019 " 0,325 0.OS8 bl4 •0.017 0.014 .4 -0,249 0.123 b22 0.018 0.044 b2J -0.047 a.OZl ail -0.100 0.0)4 b24 -0.012 0.014 al2 0,061 0.037 b33 0.117 0.021 ail 0.009 0.022 b34 -0.009 0.008 al4 O.02S D.OIl b44 0.018 0.008 a22 -0.076 0.OS3 aU 0.023 0.028 d' -0.064 0.023 a" -0.030 0.014 d' O.... 0.021 a33 -0.041 0.015 dl -0.021 0.017 a34 0.008 0.010 <2, 0.029 0.023 a" -0,004 0,009 ,22 -0.047 0.024 . <2l 0.017 0.019 a'T -0.006 0.002 dl 0.01l 0.023 an 0,000 0.001 d' -0.018 0.022 a3T 0.003 0.001 d3 0.005 0.017 a4T 0.002 0.000 ,41 0.022 0.008 ,42 -0.020 0.006 ÀI 0.441 0.147 «Il •0.002 0.004 À, 1.280 0,358 À3 0.636 0.114 À4 -0.204 0.081	Log•likelihood .. 317.2: Nobl .. 30 Nole: i.j. 1 .. cereal.; 2 • cerNI ~u""liTuI6J: 3 = hiah•protoin (_il: 4 _ additives k .. 1 .. poullry: 2 -pi!.: J .. caule PUanlelt;f Est;malod vllue SWldlrd error Panrneter &titnltC!d ~11Ut; Sa..ndard t;tror bll -0,064 O.04S 011 -0.288 0.106 bl2 0.123 0.04\ 012 0.242 0.092 bn -0.065 0.021 on -0.008 0.052 bl4 0,006 0.019 014 0.054 0.043 b22 .o.osa 0.048 022 -0.394 0.114 b23 -0.034 0.024 023 0.232 0.062 b24 -oml 0.011 024 -0.076 0.039 b33 0.110 0.018 033 -0.295 0.065 b34 -0.012 0.010 034 0.011 0.026 "4 0.031 0.012 0.. -0,046 0.0]1 dl .0.018 0.030 ail -0.125 0.045 d' 0.041 0.021 al2 0.088 0.041 dl -0.02] 0.016 an 0.006 o.on ,21 -0.045 0.030 al4 0.043 0.019 ,22 0.01] 0.019 a22 -0.123 0,046 ,23 0.032 0.016 a23 0.07] o.on d' 0.040 0.022 a24 -om8 0.017 ,32 -0.035 0.015 a33 -0.094 0.019 d3 -0.004 0.011 a34 0.027 0.011 ,41 0.023 0.014 a" -0.0]) 0.013 c42 -0.019 0.010 c43 -0.004 0.007 ~IT -0,009 0.002 ~'T -0.003 0.002 d' 0.250 0.049 PJT 0.009 0.001 dl 0.164 0.030 I\4T 0.00) 0.001 dl 0.089 0.020 d4 0.497 0.077 À 0.4&6 0.077
	-27•	-28-

•• Tablolb: Parameter estlmates for the (non-Joint) SGM cost functlon l '"' cere.I,; 2 '"' t'l;IrCllI subsliTule~: J C" hialh'jlrtltcln fllt.'Jlb; 4 ... addilivek ~Table Id: Parameter estbnates (or the Qomt) TL cost functlon, restrlcted (symmetrk) adjustment ntatrb: M

Table le :

 le Parameter estlmates (or the Oolnt) TL cOlt (undlon, restrk:ted ECM .peclncatlon ~p Table 2.: FJastidties ror the SGM model specifICations, measuring the change \'Briant oC the Induced-Inno\'ation hypothesis Table 2b: Priee elasticities oC input demand for the Oolot) TL model specifications, measuring the change variant oC the Induoed~lnnovatlonhypothesLs Nole: l '" cereal~; 2 '" cere.1 sub!<lituteJI; 3 = high-rroleill feeds; 4 = Ilddilives.

										,
	'" ,]2 ," '14 '21 "2 <23 '24 <JI ," '" <J' ," "2 '" ,44 LoIL	Shorl-run instant. -0.862 0.5n 0.219 0.110 0.787 -0.809 0.090 -0.068 0.2]2 0.066 ..0.303 0.004 0.517 -0.234 0.021 -0.305 58.5	Joint SGM Short-run dYl1&1Tlk .(l.J8) 0.222 0.027 0.134 0.336 -0.309 0.115 .0.143 0.036 0.081 -0.132 0.015 0.667 -0.496 0.082 -0.253	Long-rull dynllmk -1.482 0.858 0.106 0.517 1.302 -1.195 0.447 ..0.553 0.138 0.]15 -0.511 0.058 1.583 -1.921 0.316 -0.978	Shorl-rWl imtlllll. -0.893 0.>64 0.207 0.123 0.835 -0.858 0.107 -0.084 0.220 0.079 -0.312 0.012 0.588 -0.293 0.058 -0.354 52.6	Non-joint SGM Soorl-rwl dyrwnic -0.421 0.241 0.016 0.170 0.368 -0.297 0.110 -0.180 0.024 0.076 -0.131 0,0]0 0.868 -0.635 0.162 -0.395	Long-rwl dynamic -1.364 0.769 0.050 0.545 1.175 -0.949 0.350 ..0.576 0.077 0.244 -0.419 0.097 2.773 -2.018 0.519 -1.263	," ,]2 ,Il ," '21 '22 m 2' 'li ,]2 ," ,]4 ," "2 <4l ,44 LoIL	" i t 1 , ) '~' Rellricled BCM specification Lona-run Short-run Shon-run Conunon adJusrment pt.r1uneler ~Rellricted adjustment matrix M Shon-T\Ul Shon-run Long.T\Ul Shon-run Short-run Long-run iMl&rll. dyrwni(.: dynamic insl&rlt. dynamic dynamic inllanl. dynvnic dynamic -0.635 -0.923 -1.5n -0.528 -0.922 -U23 -0.826 -1.069 -1.47 0.419 0.467 0.956 0.3S) 0.421 0.939 0.59] 0.597 0.93 0.123 0.330 0.330 0.154 0.3S7 0.204 0.144 0.319 0.307 0.072 0.127 0.246 0.021 0.144 0.380 0.089 0.152 0.230 0.750 0.714 1.447 0.544 0.646 2.619 0.887 0.893 1.396 -0.885 -1.208 -2.137 -0.687 -1.0\5 -3.100 •1.012 -1.632 -2.453 0.216 0.557 1.034 0.125 0.429 1.499 0.187 0.843 -0.082 -0.063 -<>.364 0.018 -0.061 -1.017 -0.061 -0.104 <>.2 0.144 0.366 0.366 0.177 0.395 -0.446 0.163 0.348 0.336 0.153 0.397 0.739 0.088 0.305 Ull O. 112 0.603 0.950 -0.]39 <>.860 -1.260 -0.307 ..Q.796 -1.434 ..Q.329 -1.l34 -1.576 0.042 0.097 0.154 0.042 0.096 0.567 0.034 0.184 0.290 0.374 0.667 1.299 0.107 0.756 1.l16 0.456 0.784 1.184 ..Q.303 ..Q.2J8 •1.2]1 0.051 -0.228 -0.573 •0.230 -O.J81 <>.964 0.191 0.464 0.747 0.\89 0.456 0.635 0.151 0.885 140<1 •0.261 -0.893 -0.814 ..Q.347 -0.984 -1.178 -0.377 -1.288 •1.628 317.2 333.3 316.3
										! 1 ,
							LoI-likelihood .. )16.3; Nobl: .. 30
							Nole:	;J .. 1 = cereals; 2 .. cereal subslirut~: 3 .. hilh-protein feeds; 4 .. Addilivee
								k .. 1 .. IlOU.Itry: 2 .. pi,s; 3 :0 clttle
										\
										~, . r,
			•29•						•30•	~

Table 3 :

 3 FAtlmated mean rates of change in inpul demand and changes in inpul cOS1 share5, measuring the level varianl of induced-Innovation Jures of the l.y"l y.ri..l! of indUl.:ed innoy.lion in !his Iabl" r"'l'relent Iyerlillid y.lues çalçu1lkd for eyery sarnple point lUld lU'e .fIJurt•tWl. 1be:y Ire npreued in percent.gel for the input deq

		SOM			TL
		Joint	Non.jolllt	Cummon À	Mlui" M	ECM
	ù1w,/iJr	•1.03	•0.86	-0.9]	-0.92	.1.24
	ôllUl/ô,	-0.21	-0.29	0.2S	-0.19	-o.6S
	ôllU,lô,	0.16	0.S8	0.1S	0.]1	1.46
	ôllU,là'	0.18	0.]9	0.49	4.48	1.99
	àS,là, as/ô,	•0.32 •0.02	-0.24 .(),O]	-0.32 0.06	.().33 -a.os	-0.46 .().1 S
	àS/à,	0.28	0.2]	0.2]	0.09	0.46
	èS/à,	0.06	0.04	0.03	0.29	O.IS
	Note:	Th. reported me'

-23-Hayami. Y. and Runan, V.W. (1970). Factor priees and technical chanae in aariculturaJ development:

the United States and Japan. 18*)-1960. JOf,jrrtQl of Po/ulcot EcOllOtrly 78: 1115-1141. Hayami. Y. and RUtlIn. V.W. (19'11). A&rltuJtIuuJ IHwIopmttv: An Inw'lotlonal PtrS/HCûw. Baltimore. MD: Johns Hoplùna University Prw (rev .. enl. cd .. 1985). Herdry. D.F. (1995). DynamIe EcOMfMtrlcs (Advanced Tekla in Econometries). Oxford University PreS!. -24-" -, KohIi. U. (1993). A symmetric l'lOnT\:,Ilized quadnuic GNP funclion ..nd the U.S. demand for imports and supply of UpolU. IflttrnolioMI ECOfIomic RtV;tw 34: 243.2SS

Table la: Paramtter estlmates rOI" lhe Oolnt) SGM c:ost rundlon

ApPENDIX PROOF OF THEOREM. The SOM cost function CO defined În (1) provides a second-arder differential approximation to C"{"). al the lXIint (p* ,y.,f-,p.), if the following conditions hold: Note that the "normal price", P. are allowed 10 interacl only wilh the "market priees". p. i ,. The proposed modelling framework wa,s used to estimate OO5t functions for lhe Belsian feedmix industry. The statistical results demonstraled that by using a modified SGM (or TL) cost funetion. it is possible to disentangle the pure substitution from lhe substitution due to price-induced technical change. It was shown that the pc:rsistence of feed price distortions rmplied by the CAP oriented the innovation process in the Belgian feedmix industry in a pronounced cereals-saving and protein-using direction. Overal!. the estimalion results were quite satisfactory. giving slrong evidence of the two variants of induced innovation. However.

the results revealed that large differences exist in the magnitudes of the estimated mcasurcs of induced innovation (i.e.. priee elasticîties of inpul dcmand and rates of change in input demand).

Now il can be shown that, due to the homogeneity of ~O and CO and Euler's Theorem, only lh.N(N-I)+lhN(N-I)+lhM(M-I)+(N-I)+(M_I)+NM+2 of the above restrictions. (A.l) lhrough (A.6). are independent (similar reasoning as in Kohli (1993». Note al50 thal the cost function as weil as lhe inpui demand functions are homogcncous of degree zero in p. Therefore. the following additional restrictions hold as weil:

V,:("(')p' = V,C'(')P' , 0