An econometric system to assess the economic impact of water restriction policies in Spain

The objective of the Spanish government-funded project GESMO (Gestión integral del acuífero 08.29 Mancha Oriental), is to develop new tools for the evaluation and monitoring of water policies. These tools have to be capable of matching resource exploitation with reserve sustainability, applied to aquifer 08.29 in the Eastern Mancha, Spain. A decision support system (DSS), was developed as part of the GESMO project, that integrates two different systems within one computer application. One, an hydrogeological model, simulates the River Júcar basin and its associated aquifer. The other, an econometric system, is capable of predicting the evolution of regional crop maps, crop yields and crop prices, thus allowing the determination of the regional gross product of crops. This paper describes mainly the economic system of the DSS, a set of econometric models. Those used for crop allocations are the most important for the DSS. The approach followed for the specif ication of the DSS is proposed as a provisional method based on information from the pre-quota period to estimate likely responses of farmers in a post-quota period. A brief description of the overall structure of the DSS and an example of one of its possible applications are also included in the paper. Additional key words: decision support system, econometric models, simulation, water management.


Introduction
In the early part of the past century traditional farming in Mediterranean countries gradually began to be replaced by irrigated farm lands, making irrigation increasingly more common in those places with enough water available.This changeover generated several advantages.First, irrigated crops are more profitable than dry-land crops.Second, many of these crops are associated with agro-food industries whose activity boosts regional economic wealth.Finally, as a result of the change in the production system and the increase in profitability, a significant ancillary industry usually emerges specialised in canal building, drill testing and the installation of irrigation systems.
The need to balance regional economic advancement with conservation of natural resources has brought water policy to the environmental, social and economic forefront in countries where demand for water is high and the resource itself is scarce.
In Spain, effects of this kind are becoming more apparent in inland areas where intensive agriculture has always depended on exploitation of aquifers, whose piezometric levels have rapidly fallen in places such as Albacete and Ciudad Real.This fall has led to the continuous application of restrictive policies on the exploitation of water resources, based upon extraction quotas.
The objective of the Spanish government-funded GESMO project is to develop management tools to help in matching resource exploitation with reserve sustainability in the aquifer 08.29, located in Eastern Mancha, Spain (Martín de Santa Olalla et al., 1999).Two types of end products should result from this project: i) a decision support system (DSS) for the definition of water-use policies, including economic-impact and reserve level simulators within a single multcriteria/ multi-purpose decision-making environment; ii) measurement of monitoring and control systems employing teledetection and simulation of crop water needs.
This paper describes the specification and estimation of the economic subsystem of the DSS.This is made up of three groups of econometric models: i) crop allocation systems of equations based on CAP (Common Agricultural Policy), crop prices, assigned aquiferwater quota and piezometric levels which serve to dynamically simulate the areas devoted to crops; ii) agricultural yield models which allows prediction of the expected yields of crops; iii) time-series models with which to optionally make short-term predictions of agricultural prices.

General system description
The overall purpose of the DSS designed within the GESMO project is to provide a simulation tool helping to solve that problem for the Eastern-Mancha Irrigation Board, both with a short and a long term horizon, thus also helping them to better negotiate with the Júcar Hidrographic Confederation water restriction policies to be applied.
More detailed DSS objectives are: 1. Adapt the general USGS Modflow model to a broader architecture, substituting the input files with a global database and designing a simple windowsbased input-output interface.
2. Design a general aquifer recharge model based on historical rainfall and levels of water in the Júcar river.
3. Use crop transpiration and irrigation models to calculate the demand for water for any crop map in the target area.
4. Design an econometric model to dynamically determine crop maps from input variables that specifically include the water quota.
5. Design an econometric model to calculate crop yields from specific input variables.
6. Design an econometric model to forecast shortterm crop prices from historical values.
7. Integrate all these elements in a global DSS able to evaluate complex climatic, regulatory and economic scenarios as a whole.Design different tools which can be used to evaluate these scenarios both for the short and long term.
The global system architecture is shown in Figure 1.The sectorial economic impact subsystem is composed of several models.Their goal is to dynamically determine, on the basis of water availability (quota), some agricultural policies (subsidies, set-aside rates) and also of the average piezometric level (determined by means of the hydrogeological impact subsystem), the regional gross product of crops (gross output less gross input) every year up to a target year.Such models are built on the basis of econometric techniques.The hydrogeological impact subsystem simulates the evolution of the aquifer up to the target year depending on the meteorology specified in the scenarios and the crop map determined in the sectorial economic impact model.The result is, for each year, the map of the average water depth in the saturated layer (measured by the piezometric levels) of the aquifer in accordance with the grid specified when defining the system.

Economic impact of water restriction policies
The auxiliary subsystem helps to integrate the results of both previous subsystems, to configure scenarios and to automatically generate new ones.Additionally, the auxiliary subsystem allows for automatic sensitivity analysis of selected parameters.It also enables the display of simulation results in different formats (tables and graphics).
The user interface serves to define and store scenarios and also to select the analytical tools of the system to be used.
Structures of the hydrogeological and sectorial economic impact subsystems are very different.The former, based on finite differences, is a geographic nu-merical model able to represent piezometric levels.The latter, a set of statistical/econometric equations, models prices, yields and land allocation trends.

The sectorial economic impact models
Figure 2 illustrates the structure and behaviour of the sectorial economic impact models.
The most important section of the economic subsystem is the crop allocation model, an econometric model that dynamically simulates the evolution of areas allocated to the main irrigated crops.To do so it relates

Variability of parameters
Sensitivity analysis -Parameter to be changed -Target variables cultivated areas with several explanatory variables: delayed prices and yields, average piezometric level of the aquifer, compensatory payments, obligatory setaside rates and water availability (quota).The estimated areas are used for both the calculation of the gross regional product and as hydrological subsystem inputs to obtain estimates of piezometric levels.
The DSS always has to use the crop allocation model whatever analysis might be conceived.However, the DSS can optionally use the two other sections of the sectoral economic impact model: the models for the estimation of yields and prices.Therefore, the values of these groups of variables may be either the outputs of the respective econometric models or exogenous scenarios assigned by the user.In fact, for analyses at equilibrium (i.e.analyses which try to identify longterm steady-states of the system) exogenous yields have to be provided to the DSS given that the yield models use time trends as explanatory variables which would make impossible for the system to reach any equilibrium.Econometric price models (ARIMA) are expected to be used only for short-term analysis; longterm price expectations should be provided exogenously to the DSS, given the well-known characteristics of that kind of time series models.Given its higher importance within the DSS, only the crop allocation model is described here with detail.

The theoretical crop allocation model
The crop allocation model was developed before the quota policy was enacted.Hence, although the model is intended to evaluate likely responses during the postquota period, its parameters could only be estimated based on information from the pre-quota period.The Economic impact of water restriction policies 529

Exogenous scenarios
Yield models

Crop allocation model
approach we propose here is focused on solving this problem and should be seen as provisional until data corresponding to the post-quota period become available.This approach could be interesting for other researchers face with the same situation.
Before the enforcement of quotas, the main restriction on the allocation of surface area was land availability.In that period, farmers allocated a portion of their land to each crop.This portion varied according to the profitability that the crop offered.Thus, for the pre-quota period it is generally possible to estimate econometric relationships of the form where s it is the surface area allocated to crop i in t, A t is an n-dimensional vector in which each element a it measures the profitability of crop i in t, S t = and ε t is an error term.This system of equations explains how the λ it portions change over time in terms of relative changes in the profitability of each crop and the availability of arable land.
Multiplying each s it in [1] by ν i , the average unit needs for each kind of crop, yields q i = ν i s it is then an estimate of the annual water-needs of the surface s it and Q t * = is the estimate of total regional water-needs.Here, water-needs are used as proxies for water consumption assuming that farmers of the region supply water to crops proportionally to their theoretical needs.Once each ν i is known, the ψ i functions can be estimated for the pre-quota period.This way, f ˆij is an estimate of the fraction that q i represents over Q t * , while the ψ i functions reflect decisions about the allocation of those (estimated) waterconsumption fractions which are related to the profitability of crops and Q t * .For estimations concerning the post-quota period, Q t * will be replaced by the quota Q t and, given a scenario A t o , the estimate of s it will be The model uses functional forms which ensure, for every t, the additivity restrictions This is achieved with the multinomial extension of the logit model, due to Theil (1969), which is extensively employed in surface-allocation models (Bewley et al., 1987;Allanson, 1988;Burton, 1992;Ibáñez and Pérez, 1999): x k are explanatory variables, ε i are random shocks and α i and β ik are unknown parameters.
It is assumed that the variance-covariance matrix of the shock vector is of the form (Σ ⊗ I), where Σ is a square n × n matrix whose elements σ 2 ij represent variances when i = j, and covariances when i ≠ j, and where ⊗ is the Kroneker product.
The ψ functions chosen admit the following linearisation (Bewley, 1986): where f * is the geometric mean of the f i fractions and where The variance-covariance matrix of the new shock terms maintains the form (Ω ⊗ I); however, the matrix Ω is now singular due to the fact that the sum of the n u i -terms is null.The rank of such a matrix is (n-1).
The explained, or dependent, variables of the linearised models [3] have no clear economic meaning and so it is difficult to add dynamic-adjustment schemes to these models with a theoretical support.Thus, two schemas with the ad hoc inclusion of lagged dependent variables have been tested: -Restricted dynamic specification: n-1 dependent variables are included in every Eq.[3]; each of them is lagged one period (one must be eliminated since [4] would imply the existence of perfect multicollinearity).This specification is similar to that of the partial-adjustment generalized model (Hunt and Upcher, 1979).
-Unrestricted dynamic specification: the dependent variable itself is included in every Eq.[3], but lagged one period.This specification is similar to the well- known simple partial-adjustment model, or Nerlove's model.In this case, it can be observed (Bewley et al., 1987) that the relationships [4] imply that all parameters associated with lagged dependent variables are the same in the n equations.

The empirical crop allocation model
Given the form of the shock variance-covariance matrix, the parameters of all the ψ functions must be estimated as a group.Due to the singularity of the Ω matrix, it is necessary to eliminate one arbitrarily chosen equation before making the estimation; however, the parameters of the eliminated equation are recovered by [4].
The estimation has been calculated by applying the Full Information Maximum Likelihood method to historical data series.The choice between each restricted or unrestricted dynamic specif ication has been made according to a ratio test of the likelihood of either approach.
Profitability of each crop has been reflected by the return/ha (area times yield) or by the price obtained for each crop.Specifications have included (n-1) ratios of the return or price with respect to one used for reference purposes.In 1993-1994, the compensatory payments given to COP (cereal, oilseed and protein) crops established in 1992 by the reform of the CAP, were added.For those years, the set-aside rates stipulated by the reform were also included as explanatory variables.Production costs were not considered as such, but the average piezometric level of the aquifer was included since this is a variable directly related to the cost of water.The average piezometric level is the output of the other main subsystem of the DSS, the hydrologic model of the aquifer.
Data employed are annual and correspond to the period 1973-1994; data on cultivated areas and yields correspond to the province of Albacete, which is the aquifer's exploitation area.Prices obtained by farmers are national and will be addressed further when the price estimation model is described.Data on surfaces, yields, and prices are taken from the Yearbook of Agricultural Statistics (Anuario de Estadística Agraria), a publication of the Ministerio de Agricultura, Pesca y Alimentación (MAPA, 1985(MAPA, -1997)), the Spanish agency for agriculture, pisciculture and food.Estimates of each crop's water need were supplied by the Instituto Tecnológico Agronómico Provincial de Albacete (ITAP).Average piezometric levels were calculated by averaging the mean annual depths obtained by probing 11 spots corresponding to the different hydrogeological areas of the aquifer 8.29 (Fernández, 1996).The measure chosen for each area corresponds to the median depth of all measures pertaining to the same area and covering the historical series 1973-94.Figure 3 shows the path of the calculated average depth, which reflects the progressive overexploitation of the aquifer.
Crops considered are those planted most frequently and/or those with the highest value within the area, evaluated in 1994.These include; wheat, barley, corn, sunflower, lucerne, potato, garlic, onion and other vegetables (lettuce, melon, pepper, tomato, green beans, peas, fava beans).Thus n = 9 for the allocation system shown in [3].The direct, single stage estimation of the corresponding 8 equations would have given rise to a problem of degrees of freedom.To avoid this, a hierarchical-allocation scheme was chosen, which is customary in other surface-allocation models (see, for example, Wolfgarten, 1989;Burton, 1992;Ibáñez and Pérez, 1999).This scheme assumes that the farmer will proceed by stages, first allocating groups of crops and then separating each group into its component crops.Each stage implies the estimation of a system of type [3], which ensures the overall additive consistency of the schema.
Figure 4 illustrates the hierarchical structure adopted.As the figure shows, in the first stage water volumes are allocated to COP and non-COP crops (S-I allocation system).This way of grouping seems realistic given the fact that COP crops have support prices and other aids to ensure a significant part of each year's incomes, whereas the other crops lack such insurance against risk.Thereafter, the volume of water corresponding to each modelled COP crop is specified by means of the S-II allocation system, and that of the non-COP crops by means of the S-III system.
As can be seen in Eq. [4], the parameters of Eq. [3] measure deviations from average values, implying that a zero value of any of these parameters does not mean a non-significant effect of its corresponding explanatory variable but rather an average effect.The consequence is that the conventional t-statistics have no value for the validation of the estimated Eq. [3].Hence the final validation of the estimated crop allocation equations took into account: i) Their ability to recreate historical data series, evaluated by comparing graphs of actual and predicted values as well as by means of Theil's U 2 -statistics (Kost, 1980).
ii) The rationality of the elasticities derived from parameter estimates.
Estimated short-run elasticities, shown in Table 1, describe the average percentage change in the volume of water allocated to each crop, or group of crops, in response to a one percent change of the variable given in the top row, all else being equal.
The main check for the rationality of the estimated elasticities is that all of the own income or price elasticities are positive (except in the case of potato, where the value is virtually zero).The existence of positive signs outside the principal diagonals can be attributed to associations among crops within the traditional rotations of the area.A 1% increase in the total amount of water (the remaining variables being unchanged) is associated with an average 0.32% increase in the allocation of water to COP crops and with an average 0.61% decrease in the allocation of water to the other crops.As a result, the allocation of an increase of the quota Q t for the groups of crops in the S-I system is not likely to be homothetic.In other words, the farmer is likely to respond to greater availability of water for a given year by favouring COP crops.Similarly, if the amount of water for COP crops increases by 1%, all else being equal, corn would be the favoured crop.Finally, an increase of 1% in the amount of water available to the non-COP crops would favour lucerne and onion.
Elasticities relative to the average piezometric level must be interpreted in a similar way.In response to a 1% increase of the piezometric level (i.e. an increase of water extraction cost), the favoured crops would be the COP group once again, and more specif ically wheat and barley.The favoured non-COP crops would be potato, garlic and other vegetables.

Models for agricultural-yield estimation
In order to provide estimations of the yield per hectare for each crop i, the DSS include regression equations which can be optionally used by the user, as explained before.Such equations have the following general specification where y it = yield, t = time trend, h t = fertilizer price index, p it = crop price, s it = area, d it = dummy variable and ε it = random shock.
The linear trend is meant to show the effect arising from employment of new varieties and production technologies.The quotient between the fertilizers' price index and the price obtained by farmers allows taking the relative prof itability of that important production input into account.The variable representing cultivated areas tries to catch the effect on yields of allocating crops to soils of varying quality.Finally, the dummy variables are used to classify yields into three qualitative groups, namely high, normal or low, on the base of sampled information and to characterize respectively each group by d it = 1, d it = 0 and d it = -1.Thus, in designing scenarios for the DSS, just a single variable, the dummy d it , is needed to represent good (d it = 1), average (d it = 0) or bad (d it = -1) weather conditions.

Price prediction model
The limited extension of the area in which this work is applied imposes certain restrictions on the methodology to be employed for modelling prices.Farmers do not limit themselves to selling in markets within their own province.Commonly, they will trade in surrounding markets as well, as long as prices offered are appealing enough.Similarly, farmers of other regions may come to local markets when it is advantageous for them to do so.Thus, physical-output values corresponding to the province of Albacete (which are the only ones which can be estimated using the DSS) are likely to provide only very limited information with regard to prices obtained by farmers in the area.This turns out to be an impediment to the estimation of prices by means of inverted demand models, in which prices are mainly dependent on outputs.Hence, ARIMA models (Box and Jenkins, 1976) were used instead, which, as is well known, allow for predictions based only on data series concerning prices observed over time.
Since the price models has also a limited role for the functioning of the DSS, they are not explained further here.

The calculation of the gross regional product
The DSS obtain the regional gross product (GP) (gross output less gross input) by means of where: s it is the area allocated to crop i in t; y it is the yield of crop i in t; p it is the price of crop i in t; EI t is the regional electricity cost in t; and OI t are other regional input costs in t.
Regional cost of electricity was directly related by regression to the average piezometric level of the aquifer.Such regression is employed to estimate EI t from every average piezometric level, θ t, calculated in the hydrologic section of the DSS (see Fig. 2).
Other input costs, OI, are taken as fixed and equal to its average historic values.Once again, an exogenous value for this variable can be supplied to the DSS.
Accumulated gross product throughout a period of time is also calculated by the DSS.This is an interesting index for analysing and comparing results from long-term simulations under different scenarios All quantities of the economic section of the DSS are corrected for inflation by dividing each monetary value by the retail price index.A discount rate may be easily incorporated to AGP's expression for the DSS to calculate its actual value.Here, a null discount rate has been arbitrarily considered.

Results and discussion
Here we illustrate the utility of both the sectoral economic impact subsystem and the complete DSS by means of two different analyses.Firstly, two simulations of the isolated sectoral economic impact subsystem were carried out to assess the impact of a ceteris paribus restriction on the total quantity of water available for irrigation in the study area.In both simulations, the subsystem was allowed to evolve until equilibrium is reached.As it is explained before, both prices and yields have to be provided exogenously for this kind of analysis.
As a simplifying assumption, both simulations consider zero regional cost (i.e.EI t = OI t = 0 for every t).In this way, gross product equals gross output throughout the analysis.In scenario #1 all the exogenous variables were maintained constant since 1995 at their real 1994 values.Particularly, total water needs (or quota) were kept stable at 728.4 hm 3 .Values for scenario #2 were kept constant at their 1994 levels, except for the total quota, which has levelled out at a constant value of 655.6 hm 3 since 1995 (10% less than that in #1).Tables 2, 3 and 4 gather the results for water allocations, surfaces and gross output values resulting from these simulations.
As can be observed in the tables, a reduction of 10% in the total availability of water causes a reduction of 8.2% in the total irrigated area and a loss in regional gross output of 5%.The COP crops are the most heavily impacted, with a loss of 10% of their surface and of 17% of its output relative to the base scenario.
A brief explanation is necessary before presenting the analysis using the complete DSS.This system has shown stable steady-states for all of the long term simulations which maintain a constant scenario for control variables (including yields and prices).This very interesting result means that both regional gross product and piezometric levels of the aquifer, under a constant environment, are able to reach long-term stationary values.However, the existence of steadystates must be examined carefully: long-term equilibria of the system could occur at an overexploitation point, that is, a stationary, empty aquifer.This result is effectively obtained with the DSS under certain intensiveexploitation scenarios (i.e.quotas and crop prices too high).
That previous result led to our second illustrative analysis: a sensitivity analysis where the value of quota is varied and the system is simulated, for every quota, until equilibrium is reached.Figure 5 shows equilibria curves for the regional gross product and the piezometric levels obtained in that way for some fixed scenario of all exogenous variables other than quota.
The upper curve, corresponding to regional gross product equilibria, shows a maximum for a value of the quota around 3,600 m 3 ha -1 yr -1 .This value can be taken as the desirable quota from a long-term point of view, given that the corresponding equilibrium for the piezometric level is high enough to ensure sustainability of the aquifer.Of course, curves of Figure 5 will vary if the assigned scenario is altered.The DSS permits exploration of variations of the desired quota calculated under various situations.

Conclusions
The system designed amounts to an innovation in the field of decision support systems for managing water resources.Its main feature, hydrogeological criteria combination with agricultural sector economics (the biggest loser as far as water restriction policies are concerned) produces a tool to analyse the two aspects of these policies both in short-and long-term scenarios.
The system has been validated and delivered to Irrigator Corporation, where it is used to plan the agricultural year and design irrigation policies which are then submitted to the Hydrographic Confederation of the Júcar.
It is planned to develop the system to admit a very wide range of water resource management measures (transfers, collection of surface water, recharging pools, etc.) and extend the econometric model to more accurately estimate the trend in costs of production, introducing advances in irrigation technology, etc.
The Spanish National Hydrologic Plan (2001) introduces deep changes in water management at national level with a decisive influence in the Eastern-Mancha aquifer.The main innovations include the transfer of water from basin to basin, a new use of surface water, new government regulation of irrigation system, supporting increased irrigation efficien-cy, etc.This new framework leads to significant evolution of the system in order to support these new scenarios of water policies, far more complex than the former.

Figure 1 .
Figure 1.Sketch of the global architecture of the DSS (decision support system).

Figure 3 .
Figure 3. Trend in the depth of «08.29 Mancha Oriental» aquifer level.

User interface Scenario configuration Scenario analyser -Crop maps -Regional gross product Piezometric levels Sectoral economic impact subsystem Hydrogeological impact subsystem
Recio et al. / Span J Agric Res (2010) 8(3), 526-537 Hierarchical structure of the crop allocation model.

Table 1 .
of water restriction policies 533 Estimated average elasticities of water allocation to each crop or group with respect to returns or prices, total needs and piezometric levels

Table 4 .
Results of simulation: equilibrium gross output values (millions of €) 1 COP crops have a loss of 16.8%; non-COP crops have an increase of 0.3%.Total gross output has a reduction of 4.9%.SC1: scenario 1. SC2: scenario 2.