An integer programming dynamic farm-household model to evaluate the impact of agricultural policy reforms on farm investment behaviour

European Journal of Operational Research 207 (2010) 1130–1139

Contents lists available at ScienceDirect

European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor

Innovative Applications of O.R.

An integer programming dynamic farm-household model to evaluate the impact of agricultural policy reforms on farm investment behaviour Davide Viaggi a,*, Meri Raggi b, Sergio Gomez y Paloma c a

Department of Agricultural Economics and Engineering, University of Bologna, Viale Fanin, 50, 40127 Bologna, Italy Department of Statistics, University of Bologna, Via Belle Arti, 41, 40126 Bologna, Italy c European Commission, Joint Research Centre (JRC), Institute for Prospective Technological Studies (IPTS), Edificio Expo, C/Inca Garcilaso 3, 41092 Seville, Spain b

a r t i c l e

i n f o

Article history: Received 13 September 2009 Accepted 11 May 2010 Available online 15 May 2010 Keywords: OR in agriculture Dynamic models Household models Multi-objective models Investment

a b s t r a c t We develop a multi-objective farm-household dynamic integer programming model to simulate investment behaviour in different policy and price scenarios, with a particular focus on the decoupling of the Common Agricultural Policy (CAP). The model takes into account the characteristics of individual assets, including ageing and fixity through the explicit consideration of transaction costs. A case study application in the context of arable farming in Northern Italy is provided as an example. The results emphasise different patterns of reaction of different farm-household types over time, as an effect of the varying opportunity costs of resources and initial asset endowments. Overall, this application highlights the potentialities and limits of the methodology. In particular, the approach proved to be effective in providing a variety of results depending on the individual features of each farm-household, such as the differences between: (a) a ‘no reaction’ attitude; (b) an adaptation of farm activity and assets; and (c) a radical reaction pattern guided by high-income alternatives to farming. This highlights the potential of this tool as a generator of ideas and working hypotheses. We argue that, in view of the further developments of the CAP, the use of instruments able to account for multiple objectives, dynamics and investment choices will become even more relevant in the analysis of EU agricultural policy. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction and objectives Mathematical programming models have found extensive use in agricultural economics applications. Broadly speaking, two main areas of application can be distinguished: (a) support to farm-level decision making; and (b) support to policy decision making, e.g. through the simulation of farm reactions to policy effects. Both areas of application now include several tangible examples, and indeed a large body of literature. A wide literature review of the tools used to support firm (farm) decision makers (point (a) above) is provided by Ahumada and Villalobos (2009), who focus their attention on the different components of the supply chain related to crop production. The review emphasises the variety of different approaches and applications. In fact, examples of the uses of mathematical programming for farm planning purposes range from crop harvesting schedules (Prestwidge et al., 2009; Bohle et al., 2010) to whole farm models (e.g. Pannell, 1996; Annetts and Audsley, 2002; Recio et al., 2003). When included in operational tools, mathematical programming may be complemented by a user-friendly interface (e.g. Prestwidge * Corresponding author. Tel.: +39 051 2096114; fax: +39 051 2096105. E-mail addresses: [email protected] (D. Viaggi), [email protected] (M. Raggi), [email protected] (S. Gomez y Paloma). 0377-2217/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.05.012

et al., 2009) or act as the basis for proper decision support systems (Recio et al., 2003). The area of policy support (point (b) above) has attracted comparable attention in recent years. This includes a variety of applications at different scales and with differing scopes, including interaction with physical and biological processes (Janssen and van Ittersum, 2007; Buysse et al., 2007), and stimulating innovation in modelling designs and calibration techniques. The use of mathematical programming farm models for policy support is also the subject of this paper. In this field of research, a special area of interest in Europe has been the study of the Common Agricultural Policy (CAP) of the European Union (EU). The CAP is the largest component of the EU budget and a major driver of farmers’ choices. A number of different models are used to assess its impact on farm behaviour. Individual farm or territorial programming models are widely used in this context. However, in most cases models are characterised by a comparative statics approach that does not take into account investment behaviour. This is most properly addressed through a multi-period decision structure, taking into account expectations and dynamic effects (see Gardebroek and Oude Lansink (2004) for a general model). Relevant exceptions exist, most frequently concerning territorial models such as AgriPoliS and RegMAS, which deal with structural changes and land transactions and hence include some

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

investment mechanisms. Yet results are often not provided in terms of investment behaviour (e.g. Happe, 2004; Lobianco and Esposti, 2008). In addition, these models maintain a rather simplified approach to the investment decision making process, generally based on gross margin maximisation by farm units. Another stream of research develops a refinement of the basic profit-maximising model in the direction of accounting for uncertainty. Examples are provided by the Real Option Approach (Pyndick, 1991), or by Stochastic programming (Heikkinen and Pietola, 2009). A few papers have attempted to refine the choice of investment by taking into account the wider perspective of the multiple objectives of the whole decision making unit, mostly represented by the farm-household. An example is provided by Wallace and Moss (2002), who present a recursive strategic weighted goal-programming model, including adaptive expectation formation, where household consumption objectives are mediated with farm expansion and other farm-related objectives. Contrary to most of the literature using a multi-objective approach, they also cast the problem in a dynamic framework and include investment concepts among the objectives. Along the same line, Gallerani et al. (2008) adopt a multi-objective dynamic programming household model to assess the impact of CAP and market scenarios on a selected sample of 80 farmhouseholds in eight EU countries. This paper aims to present the methodology developed in the context of this study, and to discuss the design and calibration problems associated with a multi-objective dynamic programming model of farm-household behaviour the objective of which is to simulate farm-household reactions to policy and market scenarios. The paper develops the discussion of the theoretical and empirical models, as well as implementation, and provides a case study concerning six arable farms in Northern Italy. The term ‘‘farm-household model” in this context refers to a well established category of models in agricultural economics in which the household is the unit of analysis (embedding the farm) and which treats the allocation of household and external resources (labour, land, capital) on- and off-farm, as well as the production and consumption decisions, driven by the maximisation of farm-household utility, as endogenous and inseparable (Chayanov, 1966; Singh et al., 1986; Taylor and Adelman, 2003). Following the prevailing perspective of this literature, the paper focuses mainly on the use of such a model for policy simulation purposes aimed at providing support for the public decision maker. The paper is organised as follows. In Section 2 we illustrate the model. In Section 3 we discuss its implementation, calibration and validation, while in Section 4 we provide the illustration of a case study. The paper continues with a discussion in Section 5 and closes with some final remarks.

2. The model 2.1. Theoretical model Taking into account the large body of literature on farm investment behaviour (for a review, see Gallerani et al., 2008) and the number of determinants highlighted in the literature, we focus on a model which is able to provide: (a) a detailed technical representation of investment assets (age, value, non-divisibility); (b) an accurate representation of the decision making unit, identified as the farm-household (multiple objectives, on-farm vs. off-farm use of capital and labour, liquidity constraints); and (c) a sufficiently good representation of exogenous variables affecting household decisions (prices, policy payments).

1131

The chosen approach is a multi-objective dynamic model of the farm-household. This approach is implemented by way of a dynamic integer programming model, which is particularly suitable to represent inter-temporal decisions with non-divisible assets (Hillier and Lieberman, 2005, for an example see van Asseldonk et al., 1999). The theoretical model for household-level decision making, based on the multi-objective approach, follows the following maximisation approach:

Max Zðxt Þ ¼ F½z1;t ðxt Þ; z2;t ðxt Þ; . . . zq;t ðxt Þ; zQ ;t ðxt Þ

ð1Þ

s:t: xt 2 X;

ð2Þ

xt P 0;

ð3Þ

where Z(xt) = farm-household utility expressed as a function of the value of the vector of decision variables xt; X = feasible set; xt = vector of the values of decision variables for each time t; zqt = value of objective q in time t as a function of the vector of decision variables xt; q = 1, 2, . . . , Q = farm-household objectives; t = 1, 2, . . . , T = time (years) in the planning period, with T = time horizon. The objective function is a representation of farm-household utility. The farm-household is expected to maximise a function defined as a combination of multiple objectives, each defined as a function of the set of decision variables. By maximising the value of total utility, the model quantifies farm reactions to prices and policies in terms of a set of decision variables (xt), including crop mix, labour allocation (on-farm vs. off-farm), capital allocation (on-farm vs. off-farm) and investment/disinvestment. Most of these variables, in particular crop mix, are extensively used in the mathematical programming models applied to agriculture and their previous applications can be found in the literature cited in Section 1. The main peculiarity of this model, together with the investment variables, concern on- and off-farm resource allocation, in order to represent the household rather than farm decision process, and dynamic liquidity management, which is needed to guarantee a realistic inter-temporal representation of liquidityconstrained investment decisions. The maximisation is subject to limitations to the range of values of decision variables, represented by constraints to the feasible set, and by non-negativity constraints. We describe this in detail in the empirical model by illustrating first the objective function, and then the constraints to the feasible set. 2.2. Empirical model: objective function The use of multi-objective programming is proposed when attempting to interpret household behaviour (instead of simple farm optimisation) as an alternative to the Net Present Value (NPV) approach in order to take into account multiple objectives (e.g. consumption, leisure, household worth) that may be relevant in household choices. However, whether farm-households make investment choices in a way that is better represented through multi-objective decision making is an empirical issue. In practice, and in the long run, the objective function may often be relaxed to a unique objective represented by the maximisation of the net household cash flow. This may be a debatable issue in theoretical terms, but it is acceptable to think that there could be cases in which criteria other than profit maximisation add little to the fitness of the model, and cases where they may be among the determinants of the results. In all cases, the NPV model can be taken as a benchmark. Following these arguments, multi-objective thinking can be seen as consistent with the household having a shorter vision with respect to the full time horizon usually adopted in the NPV maximising models. Consequently, the choice of this study is to run models in two forms:

1132

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

(a) a fully dynamic NPV maximising model; (b) a recursive dynamic multi-objective model. The form of the model to be used for the simulation of the investment behaviour of each farm-household is then chosen based on the best validation. Models (a) and (b) differ in the structure of the objective function and the algorithm for the solution (recursive vs. non-recursive), while the feasibility set is identical. The recursive model is first solved as fully dynamic for a shorter time horizon (n). Then, the choices for year 1 are kept fixed and the model is solved for the horizon from time 1 + 1 to n + 1. The procedure continues in the same way, moving forward 1 year at each step, until the initial time is equal to m, which is the number of years for which we seek to generate results from the model. The time horizon for each run is chosen according to that most likely used by the farmers, and is derived from their answers concerning future variables. In case (a), the objective function is expressed by the NPV of total household cash flow over the time horizon. It takes the following form:

Max NPV ¼

X

qt Y t

ð4Þ

t

where p Y t ¼ yat þ ylt þ yct þ yIt  ytc t þ yt ; X X xi;t gmi  v pz tpz ; yat ¼

ylt ¼

ð5Þ ð6Þ

z

i

X

out

lh;t wout h 

X

in

lj;t win j ;

ð7Þ

j

h

yct ¼ ct r   cþt r þ ; XX  XX þ Im;t;s km;s  Im;t;s km;s ; yIt ¼ m

ytc t ¼ TC ypt ¼

s X X 

X

m

m

s

Im;t;s km;s þ TC

s

xi;t wi;t þ Wdt ;

Yearly household income (Eq. (5)) includes farm gross margin from farm activities (Eq. (6)), net household labour income (Eq. (7)), capital costs (Eq. (8)), net costs for investment/disinvestment (Eq. (9)), transaction costs (Eq. (10)) and CAP payments (Eq. (11)). Transaction costs have been included to avoid unrealistic indifferences with respect to buying and selling an item, or keeping it (asset fixity). Eq. (6) represents the total gross margin from farming activities calculated as the difference between the sum of gross margins from individual activities, and the sum of costs for purchasing (additional) investment services. As it is designed, such a cost for investment services cannot be allocated to individual activities (see also Eq. (21)) and hence is not accounted for in the calculation of the gross margin of individual crops (i.e. in Eq. (22)). Wages and profitability of off-farm uses of capital (interest rates) are potentially uncertain parameters. However they are treated in a deterministic manner, since considerations on the causes of their variability would go beyond the scope of this paper. In case (b), the objective function takes a multi-objective structure. Depending on the information collected about the preferences of the farm-households, the achievement of objectives is treated in two different ways:

XX þ m

ð8Þ ð9Þ Iþm;t;s km;s ;

ð10Þ

s

ð11Þ

i

where (v = variable); qt = discounting factor; Yt = total farm-household income (v); yat = household cash flow from production activities, including farming (v); ylt = household cash flow from labour, calculated as the difference between income from external labour of household members and payments for hired labour (v); yct = household cash flow from liquid capital management, calculated as rents from investment in non-durable goods minus the cost of credit (v); yIt = cash flow from investment and disinvestment activities (v); ytc t = transaction costs connected to investment/disinvestment (v); ypt = cash flow from agricultural policy payments (v); xi,t = degree of activation of productive activity i (v); gmi = gross margin from productive activity i; v pz = purchased amount of investin ment service z; tpz = price of purchased investment service z; lj;t = lain bour purchase of type j (v); wj = cost of labour purchase of type j; out lh;t = labour selling of type h (v); wout h = wages from labour selling  of type h; cþ t ; ct = purchase of liquidity (access to credit), investment of liquidity in non-durable goods outside the farm (v); r+, r = interest rate paid on credit, interest rate gained on liquidity  and related uses (e.g. bonds); Im;t;s ; Iþ m;t;s ; I m;t;s = number of capital goods, investment and disinvestment activities of type m and age s at time t (v); km,s = value of capital good m, depending on age; TC+, TC = transaction costs on, respectively, investment and disinvestment as a percentage of the value of investment/disinvestment; wi;t ; Wdt = area based and decoupled payment (v), respectively; i = activities (e.g. crops); j = labour type for purchase (non-household); h = labour type for selling (household); m = types of capital goods; z = investment services; s = age of capital goods.

1. objectives for which there is a degree of flexibility (compensability/trade-off) are incorporated in the objective function; 2. objectives that are ‘absolutely’ to be achieved are incorporated as constraints in the model, particularly if related to the consumption component. These two conditions can be thought of as compensatory and lexicographic quality of the objectives, respectively. However, for the same objective the two conditions are not mutually exclusive, and it is admissible to fix a minimum constraint for some objective, and at the same time allow the possibility of maximising that objective above that level. For flexible objectives (case 1 above), which the household accepts to trade-off against each other, a simple multi-objective function is used (Romero and Rehman, 2003):

Max Z ¼

X

xq zq :

ð12Þ

q

In this formulation, the objective function is the linear sum of a normalised value of the indicator zq related to each attribute q, multiplied by the respective weight xq. The value of each attribute is calculated using a specific procedure, depending on the nature of the objective (e.g. household net worth, leisure). Most objectives derive from the activities performed on the farm (e.g. crops) and are generally calculated as the average value of objective/attribute zq over time:

zq ¼

1XX aiq xit ; T t i

ð13Þ

where aiq = coefficient quantifying the change in the value of objective q as a result of a unit increase in activity i (see also the case study section for further details). In case there is a minimum level of certain objectives below which the farmer is not willing to accept the plan (case 2 above), constraints are added, such as:

zq P zmin q ;

ð14Þ

where zmin = minimum achievement required for each objective. In q the model, zq takes the role of a variable, while zmin works as a q parameter. These constraints are to be handled carefully, as they could lead to infeasibility and should be used only when there is realistic strong opposition to some very low value of an objective. In addition, zmin could be a very subjective and uncertain value to q

1133

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

judge, even for the decision maker. In the empirical application of the present model, this is dealt with by asking this parameter directly to the farmer/householder and limiting its use to two well defined sets of objectives: (a) farm-household consumption; (b) decisions about ownership of non-productive assets (e.g. a house) (see also model calibration). The use of such constraints is compatible with both the NPV and the multi-objective model. 2.3. The empirical model – constraints and feasible set The constraints defining the feasible set are organised into six sub-groups: (i) investment and capital; (ii) activities; (iii) liquidity, credit and external investment; (iv) labour; (v) payments; and (vi) non-negativity constraints. The first sub-group (i) describes investment and capital relations through the following equations:

Im;t;s ¼ Iþm;t1;s1 þ Iþm;t;s  Im;t;s ;

ð15Þ

km;s ¼ cm;s km;0 ; XX Im;t;s km;s þ vt ; Kt ¼

ð16Þ

m

ð17Þ

s

Im;1;s ¼ Iim;s ;

ð18Þ

Im;T;s

ð19Þ

¼ Im;T;s ;

where cm,s = depreciation coefficient for capital goods; Kt = value of household capital stock (v); vt = liquidity; Iim;s = stock of capital good m on the farm in the initial year. In Eq. (15) capital at time t is related to capital at time t  1, plus investments, minus disinvestments for each single asset. The variables Iim;s represent the number of individual assets, defined by their type (m) and age (s) and are defined as integer variables. Eq. (15) is verified for each year (t). The value of each capital good is calculated in Eq. (16), based on the initial value km,0 and the depreciation coefficient cm,s. Depreciation is assumed to be linear with age. Land is not depreciated. The value of the total household capital is calculated in Eq. (17) as a sum of the depreciated value of all capital assets, plus the value of liquidity vt. Eqs. (18) and (19) are included to control for the beginning and the end of the actual time horizon considered. Eq. (18) assigns the initial capital endowment and Eq. (19) forces the model to sell all capital at time T. This is necessary to allow the model to take into account the salvage value of all capital when taking decisions close to the end of the time horizon. The value of the household’s capital stock can be subject to uncertainty. The main source of uncertainty affecting the capital stock value, when the data come from survey information, concerns available liquidity at time zero v0, as this is clearly a sensitive piece of information to ask the farmer. In using our models, not knowing this parameter with a reasonable degree of precision is a significant difficulty, as it affects investment possibilities throughout the planning horizon. This could be solved in the case of consultancy, when individual data are kept totally confidential. In the empirical application of our model, instead, we dealt with this assuming a v0 high enough to ensure that the stated plan was feasible. As for the value of the other non-monetary assets (physical and non-physical), in the model this is treated as an analytical result of the sum of the value of each asset (by specific type and age), multiplied by the number of such assets owned by the farm at each point in time, which represent a rather high level of precision, though achieved in absence of related accounting data. Activity management (ii) is represented through the following equations:

X

xi;t ai;s 6 rhss ;

i

X

xi;t ai;z 6

X

ð20Þ

Im;t;s v m;z þ v pz ;

ð21Þ

m

i

gmi;t ¼ li pi;t  ei;t ;

ð22Þ

where rhss = right hand side representing the availability of resource s; ai;s ; ai;z ; ali = technical coefficients with respect to farm resource s, investment services and labour use; vm,z = amount of investment service z produced by investment m; pi,t = product price of activity i; li = yield of activity i; ei,t = variable costs of activity i; s = farm resources and constraints (different from land, labour or capital). Eq. (20) is the standard set of constraints of a mathematical programming model ensuring that the solution is compatible with the availability of resources defined by rhss for each resource s. However, land, machinery, quotas and production rights are treated elsewhere in the model, in the category of investments, and are described in specific equations. Eq. (20) also covers relevant technical and economic constraints in addition to the standard issue of resource availability. These differ considerably from case to case and have been designed consistently with each individual farmhousehold decision-making conditions. In general, the most common issues have been: (a) management of intermediate products, such as feeding with own-produced fodder, use/handling of organic waste from animals; (b) crop rotation; and (c) market constraints. Eq. (21) connects crops, capital goods and service rental through the use of the notion of ‘‘investment services” z (e.g. hours of work of specific machinery). Each capital good m can produce some amount of service z (vm,z) per year, which is used by farm activities. The availability of capital goods can be substituted by the purchase of the service v pz . Eq. (21) ensures that the amount of capital services required by farm activities is available from capital goods plus rented services. Eq. (22) is a simple computation of gross margin, subtracting the variable costs of each activity from the gross revenue from the sale of products. The main uncertain component in this group of equations are prices and agricultural product yields. Yield uncertainty is not treated directly and the models run based on average expectations concerning this parameter. On the contrary, prices are directly handled as uncertain variables by using them as one of the two main scenario parameters in the analysis (together with payments). Liquidity, credit and external investment are managed through the following sub-group of equations (iii):

St ¼ Y t  C t ;

ð23Þ

vt ¼ vþt1 St1 þ cþt ;

ð24Þ

XX m

þ

Iþm;t;s km;s þ

s

X j

in

lj;t win j;t þ

X m

v pm tpm þ

X

 xi ei þ ytc t þ c t 6 vt ;

i

ð25Þ cþt 6 dK t ;

ð26Þ

where St = savings (v); d = maximum debt/asset ratio permitted in the country. This group of equations defines the relationships between capital, liquidity and investment. First, savings St are defined as the difference between income Yt and consumption Ct (Eq. (23)), all variables quantified at the household level. Liquidity at year t (vt) is defined as the sum of liquidity of year t  1, the savings of year t  1 and the amount of external capital purchased (credit) cþ t (Eq. (24)). In Eq. (25), all liquidity requirements in a given period (liquidity requirements due to investment, payment of external labour, variable activity costs, machinery service rental costs, costs of credit and off-farm investments c t ) are constrained to liquidity availability. The access to credit cþ t is constrained to some share d

1134

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

of total capital owned (Eq. (26)) in order to guarantee that borrowing is compatible with national laws regarding the availability of collateral. The model then works with access to credit constrained only to capital availability (and not to other personal requirements). However, credit and external investment (e.g. bonds) are treated in a simplified manner with respect to the refunding mechanism, as both are treated as yearly variables (e.g. no mortgage refunding structure through periodic quotas is provided in the model). Labour is constrained by the following equation (sub-group iv):

X

out

in

xi;t ali þ lh;t 6 Lth;t þ lj;t ;

ð27Þ

i

where Lth;t = labour availability of type h in the household. Eq. (27) constrains labour use to labour availability at the farm-household level. Labour use includes both on-farm and off-farm activities of the farm-household. Labour availability includes both own household labour and purchased labour. Decoupled payments are managed by the following equation (v):

Wdt ¼ SFP

P

u i xi;t ni

n

;

ð28Þ

where SFP = Single Farm Payment, i.e. the payment scheme presently provided by the European Union for farmers; n; nut = total and used payment entitlements (v) in each year, where the latter depends on the crops cultivated. Payments are calculated based on owned entitlements, after adjustment based on eligible land uses. Note that in this formulation payments are not traded (neither are they sold or purchased). Also, this formulation does not apply in cases where the potential eligible area is higher than the number of entitlements, the occurrence of which is not relevant to farms included in our case study. Future (after 2013) payments are directly handled as an uncertain variable by using it as one of the two main scenario parameters in the analysis (together with prices). Non-negativity constraints (sub-group vi) are added for the following parameters: in

out

xi;t ; lj ; lh ; Im;t;s ; Iþm;t;s ; Im;t;s ; cþt ; ct ; St ; vt P 0:

ð29Þ

3. Model implementation procedure, calibration and validation The model application was initially designed to complement a survey aiming to assess the effects of the 2003 CAP reform (decoupling of the direct payments) on farm investment behaviour. The survey was conducted by way of in-depth face-to-face interviews with the head of each farm-household, using a detailed questionnaire. The survey was conducted in the second half of 2006 (see Gallerani et al. (2008) for details). The modelling exercise was performed on a sub-sample of the farm-households surveyed, selecting those farm-households deemed most representative of each system for the most relevant features, based on expert judgement and (ex post) with respect to the availability of information from the survey (i.e. also knowing farm attitudes, intentions and all information collected in the questionnaire). For each area and system, attention was focused on households with a higher percentage of income obtained from agriculture. Calibration was performed separately for each farm-household (i.e. the model was parameterised using data from each farmhousehold and was calibrated/validated with respect to the stated behaviour of individual households). The feeding of parameter values mainly used data from the survey. In particular, the questionnaire provided information about: (a) value, duration and age of present and potential (those that the farm would consider buying) farm assets; (b) household credit conditions; (c) farm labour

availability and off-farm incomes; (d) farm-household objectives; (e) actual mix of farm activities and criteria for the choice of activity mix (e.g. crop rotations); (f) intentions concerning future investments and farm activities. In most cases, primary data were sufficiently complete and accurate to enable a complete calibration of the model. This was also possible as the modelled farms were only a sub-sample of the whole sample, the selection of which was also based on the quality of individual data availability. However, existing secondary data were considered where available and deemed necessary, in particular for the calculation of the gross margin of farm activities and to complement data deficiencies due to incompleteness of some information from the questionnaire, e.g. concerning asset duration or value. Transaction costs proved to be a very complicated issue to be expressed in numerical terms, and we were not able to collect the needed amount of information through the survey. Accordingly, during the testing process, we sought to estimate a reasonable labour time for the conclusion of transactions, plus the associated administrative costs. The conclusion was that, while this value may vary considerably from one farm to another, and from one transaction to another, it has been approximated as a uniform percentage of asset value (20%). The list of objectives and their ranking was also collected by way of the questionnaire. In the questionnaire, a closed list was proposed to the farmers, taking into account potential household objectives including the following: household worth, household consumption, household debt/asset ratio, diversification in household activities, income certainty, and leisure time. Weights were derived from the ranking of objectives given by the household, using the rank reciprocal formula (Wallace and Moss, from Stillwell et al., 1981). Minimum requirements, leading to objectives that could not be traded-off, concerned only consumption (Ct) and decision about ownership of non-productive assets (e.g. a house). As the latter were defined on an individual basis, they are not handled separately in the model, and are rather treated through the generic activity constrains. Consumption was also left as a free variable, included in the objective function, with a lower bound represented by the minimum income requirement and an upper bound determined by income possibilities and saving requirements for investment. On the contrary, the ownership of non-productive assets, when relevant, is treated only as a constraint and is not connected to additional objectives in the objective function. The initial year was 2006 and for this year asset choices were constrained to assets already available on the farm. The calibration process was performed by including decision rules/constraints in the model derived from the questionnaire, and in particular concerning: (a) allowable activities (derived from past, present and possible future activities as stated by the farmers); (b) technical connections between farm assets and crops; (c) rotations and interconnections between activities (e.g. forage and livestock); (d) the constraining effects of contracts; and (e) an estimation of liquidity needs, if not available. The validation of the model was performed by: (a) comparing the model’s output (activity set and investment) with the real behaviour of farmers in the base year; (b) comparing the model’s output (activity set and investment) with the intentions stated by the farmers for the next 5 years under actual conditions (baseline scenario, see below). The first comparison reflects the classical approach to model validation that can be found in the literature (Hazell and Norton, 1986; Howitt, 2005). The second comparison is specifically used here given that information about activities and intended investment behaviour for the coming years was provided by the survey. Specifically, this included verifications of: (a) the feasibility of the stated investment and activity plan; (b) the calculation of the

1135

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

difference between the stated investment and activity plan on one hand, and the planned investment and activity plan generated by the model on the other. The latter measure is used as the validation parameter. An important issue in mathematical programming models is the existence of a flat response to the changes of decision variables from the objective function. Such a condition would hinder the information content of the simulations provided and their use by decision makers, either in cases where the model was addressed to support farmer’s decisions or where case simulations are used to support policy evaluations from the standpoint of the public decision maker (Pannell, 2006). In the case study reported in this paper, the occurrence of such cases depends in fact on the numerical feature of each individual farm model. Due to the high number of variables in the model, it is likely that flat utility areas exist. On the other hand, the use of integer programming and the inclusion of a limited number of investment options should at least avoid smooth flat objective function areas as a function of different investment choices. To test the stability of the model, a sensitivity analysis has been performed on the main calibration parameters connected to activities and constraints showing the lowest marginal values. This was performed on a case-by-case basis but the results are not provided in this paper as it is not possible to summarise such vast amounts of information, and because of the different variables utilised for the sensitivity exercise in each individual farm-household model. Taking into account the above considerations, the most robust interpretation of the model’s results should primarily rely on the direction (sign) of changes and, only secondarily, on specific monetary values. At the same time, the fact that the calibration was performed knowing (from the survey) stated intended behaviour (in terms of investment and activity mix) in at least two policy and market scenarios (baseline and decoupling – see below) leads to believe that simulated results are relevant in terms of real decision making. The model implementation and elaboration was performed using GAMS, the most common software for economic optimisa-

tion models (McCarl, 2004). Given the nature of investment choices (and possibly other components of decision making), the model is cast as a mixed integer problem. Preliminary analysis on test farms rendered satisfactory solution performance using the solver CPLEX, with 0.1% tolerance in the search for integer solutions. Solution time over the set of scenarios was rather variable (between 0.1 and 10 hours using standard desktop personal computers), depending on the size of the model (which depended in turn on the number of activities and assets considered in each individual farm). 4. A case study application As an exemplary application we illustrate here a case study represented by six farms located in Emilia-Romagna (Northern Italy). All six farms are specialised arable farms, family run, and two are organic (Table 1). Four out of six have some household members working offfarm. The land size is variable from 5 hectares to more than 300. The role of SFP is significantly variable, ranging from 2% to 57% of total farm income. Based on the questionnaires the objective function was set as illustrated in Table 2, which also shows the validation outcome. For the purpose of the model, annual values of objectives were measured with reference to intermediate variables of the model illustrated above for the first two objectives: household worth, measured by variable Kt, and consumption, measured by Ct. The cþ debt–asset ratio is calculated based on Eq. (26) as Ktt . Diversification is calculated in three steps. First, by dividing the total farm area by the maximum number of activities allowed in the model, a parameter xd is calculated, which represents a ‘‘maximum differentiation” measure, assumed as an equal distribution of land among all possible crops. Second, the difference ei,t = xi,t  xd is calculated for each crop. The degree of specialisation (non-differentiation) is provided by the sum of the positive deviations of such differences P NDt ¼ i eþ i;t , while the differentiation objective is measured as 1  NDt. In a model with so many parameters, uncertainty is more

Table 1 Summary features of farm-households/farms modelled. Household CODE

ITPCA15

ITPCA19

ITPCA23

ITPCA27

ITPEA51

ITPEA66

Legal status No. household members Age farmer Use external labour Members working off-farm Household debt/asset ratio Land owned (hectares) Land rented in (hectares) Land rented out (hectares) Technology SFP (euro) SFP/income ratio Number of rights (hectares)

Family run 3 44 Yes Yes 10% 17 106 0 Conventional 17,000 57% 33

Family run 5 45 Yes Yes 3% 65 45 0 Conventional 28,500 29% 101

Family run 3 47 No No 17% 0 24 0 Conventional 11,500 36% 40

Family run 2 61 Yes Yes 1% 324 0 0 Conventional 58,000

Family run 2 50 No No 0% 7 2.9 0 Organic 1500 3% 9

Family run 3 48 No Yes 0% 5

176

0 Organic 500 2% 5

Table 2 Objective function and validation in each model. Household code

ITPCA15 ITPCA19 ITPCA23 ITPCA27 ITPEA51 ITPEA66

Objectives and their weights Household worth

Consumption

Debt–asset ratio

Diversification

Uncertainty

0.27 0.67 0.18 0.25 0.18 0.55

0.18 0.00 0.00 0.00 0.27 0.00

0.00 0.00 0.27 0.00 0.55 0.00

0.00 0.00 0.00 0.00 0.00 0.27

0.55 0.33 0.55 0.75 0.00 0.18

Final validation

Type of model adopted

0.03 0.06 0.07 0.22 0.05 0.04

Mono Mono Multi Mono Multi Multi

1136

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

readily dealt with in the way the model is used (i.e. through sensitivity and scenario analysis) rather than incorporating more (specific) parameters. In particular, we considered the option of stochastic programming, but this proved to be too complicated for this already very articulated model and could have resulted in difficulties in solutions (given the high number of integer variables included in the model). However, we allowed for a specific objective to represent the degree of knowledge (certainty) about activity performance. This is calculated according to Eq. (13), where the coefficient aiq related to the (un)certainty parameter takes value 0 for crops that have never been cultivated by the farm-household, and 1 for crops which the farm-household has experience cultivating. All objective measures are designed in such a way that they are intended to be maximised by the farm-household. The model is used here to simulate decoupling and alternative scenarios. The scenarios considered are the following:  Scenario 1: (Baseline) Agenda 2000, with 2006 prices for agricultural products;  Scenario 2.1: (Decoupling) 2003 reform of the CAP with 2006 prices;  Scenario 2.2: Same as scenario 2.1, but with a price decrease of 20% compared to 2006 prices;  Scenario 3.1: Same conditions as scenario 2.1 up to 2013, then no CAP payment after 2013; prices of agricultural products remain at 2006 level;  Scenario 3.2: Same conditions as scenario 3.1, but payment reduction is gradual, with a linear reduction starting in 2014, bringing payments to zero in 2021;  Scenario 3.3: Same conditions as scenario 3.2, but with a price decrease of 20% compared to 2006 prices (same price conditions of scenario 2.2). In the scenario 1, the parameter wi,t includes payments under the Agenda 2000 regime, and Wdt is set equal to zero. In the other scenarios, Wdt is calculated through Eq. (28), and wi,t includes the few residual coupled payments under 2006 provisions. Models were solved on a 25-year time horizon (with steps of 8 years in the recursive version), setting the final year at 2030. This period appears to be long enough to assess the profitability of most investments, and is consistent with the timescale of at least some of the scenario exercises available at present (even if most of them stop between 2015 and 2020). We illustrate the results focusing on two selected outcomes of the model: the impact of scenarios on household income and the Table 3 Impact of the scenarios on household income – Italy: plain–arable. Alternative scenarios (% variation compared to the baseline) Baseline (euro/ hectares/years)

2.1

2.2

3.1

3.2

3.3

2006–2013 ITPCA15 346 ITPCA19 1395 ITPCA23 866 ITPCA27 676 ITPEA51 5903 ITPEA66 117,944

16 5 10 3 1 0

14 25 21 19 22 0

16 5 10 4 1 0

16 5 19 3 1 0

20 25 21 20 22 0

2014–2021 ITPCA15 381 ITPCA19 1431 ITPCA23 948 ITPCA27 766 ITPEA51 6745 ITPEA66 –

17 9 14 3 1 0

14 30 22 19 24 0

18 22 6 47 3 0

4 17 7 20 2 0

41 38 34 49 25 0

impact on investment. The former is represented by the variable Yt in the model. The latter is presented in two forms: (a) the total monetary value of investment/disinvestment represented by yIt in Eq. (9); and (b) a qualitative summary of the numerical change  of selected investment goods, represented by Im;t;s ; Iþ m;t;s ; Im;t;s in the same Eq. (9). The delivery of the results year by year would have made the outcome of the model impossible to illustrate in this paper. However, averages of the entire planning horizon would not provide hints about the dynamics of the results. For this reason, the results are given as an average of two shorter periods: (1) 2006–2013 and (2) 2014–2021. The first period corresponds to the present programming period of the CAP. Table 3 reports the impact on household income, showing the income per hectare in the baseline scenario (scenario 1) and the percent variation in the five alternative scenarios. In conventional farming systems, the total household income per hectare varies between 346 and 1395 euro/ha.1 The two organic farms show a relevant difference: (a) in farm ITPEA51 due to the cultivation of high value added crops (pumpkin, tomato, watermelon), and (b) in the case of ITPEA66 due to high non-farming income (about 80% of the total household income). The latter is rather unique among the cases considered in this sample as it is the only one in which household members have high-income activities offfarm; as a result, income from farming is almost irrelevant compared to the whole household income. Reaction to decoupling shows changes in both positive and negative directions. ITPCA15 and ITPCA23 show a positive change. The remaining farms show a negative effect of decoupling. This effect is relevant (3% to 5%) for the two conventional farm-households, while it is irrelevant for the two organic farms. The latter effect is mainly due to a higher degree of decision-making independence from the CAP (ITPEA51) with respect to the farming activity, and due to the low relevance of income from farming (ITPEA66). The reduction of prices by 20% (scenario 2.2) causes a reduction of about 30% of income for all farm-households, with the exception of ITPEA66 which is never affected to a significant degree. This effect remains basically the same in the second period (2014–2021). The total removal of payments after 2013 (scenario 3.1) affects farm-households only in the second period and in a very differentiated manner, with the extreme case of ITPCA27 showing a 47% drop in income due to the large amount of payments from which the farm benefits. The gradual reduction of payments (scenario 3.2) results in a 7– 21% decrease in income compared to the decoupling scenario (scenario 2.1). The last scenario (3.3) provides for a decrease in prices by 20% and a gradual reduction of payments, which result in a drop in income in the first and, most remarkably, in the second period. Table 4 expresses the reaction to decoupling and associated scenarios in terms of investment/disinvestment, as measured by variable yIt in Eq. (9). As in the previous table, values are reported in euro/ha per year, for the baseline scenarios and as percent variations compared to the baseline for the other scenarios. The pattern of investment in the baseline shows varied behaviour across farms in the period 2006–2013, and more homogeneous behaviour in the second period. In the period 2006–2013, only ITPCA19 shows a clear investment strategy, while the positive investment of ITPCA27 is negligible in size. ITPCA15 and ITPCA23 show the beginning of a tendency towards a modest disinvestment. ITPEA51 and ITPEA66 reveal a strong disinvestment strategy based on the re-allocation of resources to non-farming activities. 1 This measure is rather atypical, as it tends to associate total income produced, including off-farm, with land. However, we do not use it to measure land productivity, but rather to understand the relevance of the main farm asset (land) on the overall economics of the farm-household.

1137

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139 Table 4 Impact of the scenarios on investment – Italy: plain–arable.a Baseline (euro/ hectares/years)

2.1 (%)

2.2 (%)

3.1 (%)

Table 5 Impact of the scenarios on selected investments – Italy: plain–arable. 3.2 (%)

2.1

2.2

3.1

3.2

3.3

2006–2013 Land Farm buildings Tractors Tillage machinery Harvesting machinery

= = = = =

= = = = =

= = = = +

= = + = +

= + = = =

2014–2021 Land Farm buildings Tractors Tillage machinery Harvesting machinery

= = + + =

= = + + 

= = + = 

= = =  

= = =  =

3.3 (%)

2006–2013 ITPCA15 39 ITPCA19 511 ITPCA23 101 ITPCA27 14 ITPEA51 5907 ITPEA66 43,555

0 127 0 3533 0 0

2 127 2 4423 0 0

0 127 4 15,191 0 0

0 127 120 3675 0 0

1154 127 0 15,237 0 0

2014–2021 ITPCA15 64 ITPCA19 65 ITPCA23 128 ITPCA27 33 ITPEA51 3474 ITPEA66 –

0 40 96 112 0 –

15 40 38 28 0 –

0 40 93 114 0 –

0 40 66 119 0 –

114 40 42 100 0 –

a The percent deviations for farms having an initial negative value of investment have been included in the table by calculating the percent deviation on the absolute value of initial investment, and adding the sign consistent with the direction of change, i.e. minus () if investment was decreasing and plus (+) if it was increasing. This applies for figures in bold in the table.

This strategy is extreme in the case of ITPEA66, for which it is optimal to sell all of the land and related farm assets. In the period 2014–2021, all farms maintain a prevailing investment behaviour, due mainly to the renewal of existing assets. As usual, ITPEA66 does not follow this behaviour pattern. Given that it totally disinvests in the first period, there is no more activity or investment/ disinvestment in the second period. Comparison across scenarios is hence not relevant in this case. Compared to the baseline, decoupling (scenario 2.1) brings about no change in the first period in four cases out of six. This is related to asset fixity and transaction costs that are properly interpreted by integer programming: in spite of the fact that incentives change under decoupling, the change is not high enough to justify a costly change in asset endowment. In the remaining two cases decoupling causes disinvestment. This is particularly relevant in the case of ITPCA27, which was the farm with the largest amount of payments. This demonstrates a clear effect of decoupling in the direction of reducing the profitability of farming or hindering the payment-based expansion of the farm that was envisaged at the baseline (Agenda 2000 scenario). The strong disinvestment policy is justified by the possibility of alternative capital allocation in off-farm activities, while the farm can continue to benefit from the payment. In the period 2014–2021 the pattern is the same for all farms, except ITPCA23 which increases investment. This late reaction is likely due to the (low) age of assets which did not allow for profitable investment in the initial stages, but also shows an attitude towards increasing asset endowments rather than disinvesting. In both periods, the degree of reactions are quite high as a percentage compared to the investment pattern at the baseline. This is not surprising as the baseline scenario provides no change in the context for about 25 years, and the adaptation to the previous policy changes (in place for 5 years) had already occurred. Price decreases tended to cause no change in the first period, and a mixed strategy in the second: ITPCA15 decreases investment compared to the decoupling scenario (2.1), ITPCA19 and ITPCA51 show no change, while ITPCA23 and ITPCA27 increase investment. The outcome is that, at least in the medium-term, all strategies are possible, even when prices decrease and the investment strategy highlights a stronger ability of the farm to adapt, as in the case of ITPCA23 and ITPCA27. Payment cuts (scenarios 3.x) also caused a reduction in investment, though the reaction was even more complex than

in the previous scenario, due to the fact that changes in payments concern only the period 2014–2021. Compared to the decoupling scenario, the removal of payments in the second period (scenario 3.1) causes relevant changes only in the case of ITPCA27, which already reacts with a major disinvestment in the first period, anticipating the reduction of profitability in the second. Once again this is easily motivated by the fact that the farm (and the household) is highly payment-dependent. The opposite strategy is adopted by ITPCA23, which adapts through an increase in investment, albeit small. This strategy continues with a higher value in the second period. The remaining results are basically the same as in scenario 2.1, demonstrating that the removal of payments does not produce any change in investment behaviour. Interestingly enough, scenario 3.2 (gradual reduction of payments) mainly brings about relevant changes, compared with scenario 2.1, in one farm, i.e. ITPCA23. These changes are not a partial version of the ones in scenario 3.1 (as could be expected), but are rather characterised by an increase in investment in both periods, higher in the first and lower in the second. The latest scenario (3.3) assumes that a 20% reduction in prices is associated with the situation in scenario 3.2. This results in a mixed effect in the period 2006–2014, with only two farms showing a difference with respect to the decoupling scenario (2.1): both ITPCA15 and ITPCA27 react with strong disinvestment. This effect repeats in the second period, with ITPCA15 showing the most noteworthy increase in disinvestment. ITPCA23 is the only farm that tends to maintain the same strategy (the result is not substantially different from scenario 2.2). Table 5 provides a summary of investment behaviour in physical terms, summing across farms and comparing the different scenarios. For most typologies of assets, behaviour is characterised by stability of investment patterns across scenarios. Among the different assets, land never shows changes, whilst farm buildings show an increase only in the last scenario. Tractors are the category showing the most frequent changes, all of which are positive. Tillage machinery does not change in the first period, increases with decoupling and price reduction, and decreases with the gradual reduction of payments either with or without price decreases of 20%. Harvesting machinery tends to increase in the first period, and to decrease in the second. 5. Discussion The results emphasise the potentialities and limits of the methodology. The approach proved to be very effective, particularly in providing a variety of (sometimes apparently contradictory) results depending on the individual features of each farm-household, hence highlighting the potential of this tool as a generator of ideas

1138

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

and anecdotal hypotheses. In this study this is further emphasised by the choice to model individual households, rather than average or representative ones. Despite the relatively narrow scope of the paper (one farming specialisation in one area), the model nonetheless allows for the recognition of different typologies of farming and of relationships between farming and household decisions. The first typology (represented by farm-household ITPCA15) is characterised by minimal reaction to policy and price scenarios, mainly due to limited alternatives. Contrary to the first typology, a second typology can be identified in farm-household ITPEA66, which is characterised by the high opportunity costs of resources, and a strategy marked by abandonment of agriculture activity altogether. Finally, a third typology is represented by those farm-households with higher flexibility, i.e. capacity to react to policy and market scenarios through the adaptation of agricultural activities (ITPCA19, ITPCA23 and ITPCA27). This group demonstrates in a more pronounced manner how articulated investment reactions can be, when ageing assets interact with policy timing, and activity adaptation interacts with the combination of assets required by each activity. As discussed in Section 1, the main objective of the model is to support policy analysis from the point of view of the policy decision maker, rather than supporting farmers’ adaptation to policy and investment decisions. However, the model can be of some interest for this second use as well, though we did not test it for that purpose, and the discussion can only be based on inferences from the indirect experience carried out. With regard to its potential use as a support to farm decision making, the model developed will likely not be of much use to provide farmers with an optimal solution that can be directly applied as a normative prescription for farm choices. This use would be hindered by uncertainty in the calibration parameters, and potentially flat responses of the objective function to different combinations of decision variables. However, the use of such a tool could allow farmers or, more likely, their advisors, to learn more about the dynamics of costs, management options and investment options in light of future policy scenarios, and to anticipate external conditions through early implementation of appropriate strategies. The use of the model through testing several values of exogenous parameters or different investment options can also provide insights into the stability of income and the optimality of investment choices, hence allowing for a pragmatic approach to uncertainty which could, also be suitable to support farm advice. This could open avenues for its use as a farm planning tool, following other successful examples, such as Prestwidge et al. (2009). Use of this kind is not feasible with the model in its current form, as it would require at least: (a) the development of a user-friendly interface; (b) a thorough editing, as it is presently designed for research purposes only; (c) a revision of endogenous and exogenous variables, in order to allow for the direct evaluation of different potential farm investments, rather than only of external policy and market variables. In addition, an application to support farm choices would likely require a careful consideration of the balance between individual costs for data entry and calibration, versus the informational benefits for farmers (see Pannell (2006) for more thoughts on the concept of information benefits). This would likely render the model useful only to those farmers considering major structural changes or investments, for which the likely benefits of more informed decision making would balance the costs of using more sophisticated tools. 6. Final remarks Mathematical programming tools are widely used for the purposes of policy analysis in agriculture. Compared to econometric

models, they allow for the incorporation of a wider number of detailed mechanisms and behavioural rules, enabling an ex ante evaluation of policies through the representation of such mechanisms with small samples. Disaggregated level models, such as farm or household models, can provide a very high level of detail in terms of objectives and technical representation of farming activities. This is particularly important when attempting to develop a policy-relevant representation of investment reactions to the decoupling of the CAP. On one hand we have a ‘dependent variable’ (investment choice) which is highly complex, and characterised by different assets, reaction times, fixity, ageing of assets, connection between assets and between assets and activities. Investment/disinvestment is represented by discontinuous decisions over time, which often make the comparability of investment patterns across scenarios difficult, particularly when dealing with a limited time frame. For the same reason, it is even more difficult to find consistency between theoretically-driven equilibrium models and real word representations of decisions over time. On the other hand, there are policy changes that affect investment indirectly through a number of interacting explanatory variables (location, specialisation, household characteristics, etc.). Trying to address this articulation of mechanisms necessarily involves a strong trade-off between the need for sufficient details for the development of models and the increasing limitations in the representativeness and extrapolability of the cases studied. The model illustrated in this paper, and its application to a case study represented by six farm-households in Northern Italy, confirms these features. We developed a multi-objective farm-household dynamic integer programming model to simulate investment behaviour in different policy and price scenarios, with a particular focus on the decoupling of the CAP. The model takes into account the characteristics of individual assets, including ageing and fixity through the explicit consideration of transaction costs. The model proves to be useful in terms of its ability to mimic the articulation of farm-household reactions to policies. Indeed, it allows for an appreciation of the different, and sometimes opposite, patterns of change under different decision-making conditions, affected by different household characteristics, farm assets and objectives. Extending the uses of the model to support farm decision making is also envisaged, although this is beyond the scope of this paper. Based on this experience, we argue that, following the decoupling of the CAP, the introduction of cross-compliance and the shift of more funds to rural development measures in the second pillar, the use of instruments able to account for micro-mechanisms has become more relevant in the analysis of EU agricultural policy. In fact, they are likely to become even more relevant in light of the further reforms envisaged at the end of the present programming period of the CAP (2007–2013). At the same time such instruments need to be used with an increased awareness that they are only one of the many, and growing number of, tools in the analyst’s toolbox.

Acknowledgement The Authors wish to thank the anonymous referees for their valuable comments and Frank Sammeth for an early reding of this paper. However, the responsibility for the contents of the article lies solely with the authors. The paper was funded by the IPTS, JRC-European Commission within the project Investment behaviour in conventional and emerging farming systems under different policy scenarios, CONTRACT 150369-2005. However, the views expressed in this paper are purely those of the authors and may not in any circumstances be regarded as stating an official position of the European Commission.

D. Viaggi et al. / European Journal of Operational Research 207 (2010) 1130–1139

References Ahumada, O., Villalobos, J.R., 2009. Application of planning models in the agrifood supply chain: A review. European Journal of Operational Research 195, 1–20. Annetts, J.E., Audsley, E., 2002. Multiple objective linear programming for environmental farm planning. Journal of the Operational Research Society 53, 933–943. Bohle, C., Maturana, S., Vera, J., 2010. A robust optimization approach to wine grape harvesting scheduling. European Journal of Operational Research 200, 245–252. Buysse, J., Van Huylenbroeck, G., Lauwers, L., 2007. Normative, positive and econometric mathematical programming as tools for incorporation of multifunctionality in agricultural policy modeling. Agriculture, Ecosystems and Environment 120, 70–81. Chayanov, A.V., 1966. The Theory of Economics of Peasants. The University of Wisconsin Press, Wisconsin. Gallerani, V., Gomez y Paloma, S., Raggi, M., Viaggi, D., 2008. Investment behaviour in conventional and emerging farming systems under different policy scenarios, JRC Scientific and technical reports, EUR 23245 EN – 2008, ISBN 978-92-7908348-8, ISSN 1018-5593, doi:10.2791/94554. Gardebroek, C., Oude Lansink, A.G.J.M., 2004. Farm-specific adjustment costs in dutch pig farming. Journal of Agricultural Economics 55 (1), 3–24. Happe, K., 2004. Agricultural policies and farm structures. Agent-based modelling and application to EU policy reform, IAMO Studies on Agriculture and Food Sector in Central and Eastern Europe 30. Hazell, P.B.R., Norton, R.D., 1986. Mathematical Programming for Economic Analysis in Agriculture. MacMillan Co, New York, NY, USA. Heikkinen, T., Pietola, K., 2009. Investment and the dynamic cost of income uncertainty: The case of diminishing expectations in agriculture. European Journal of Operational Research 192, 634–646. Hillier, F.S., Lieberman, G.-J., 2005. Introduction to Operations Research. McGrawHill, New York. Howitt R.E., 2005. Agricultural and Environmental Policy Models: Calibration, Estimation and Optimisation, MIMEO.

1139

Janssen, S., van Ittersum, M.K., 2007. Assessing farm innovations and responses to policies: A review of bio-economic farm models. Agricultural Systems 94, 622– 636. Lobianco, A., Esposti, R., 2008. The regional multi-agent simulator (RegMAS) assessing the impact of the health check in an Italian region. In: 109th European Association of Agricultural Economists (EAAE) Seminar. The CAP after the Fischler Reform: National Implementations, Impact Assessment and the Agenda for Future Reforms, Viterbo, Italy. McCarl, 2004. GAMS user guide 2004, Available from: . Pannell, D.J., 1996. Lessons from a decade of whole-farm modelling in Western Australia. Review of Agricultural Economics 18 (3), 373–383. Pannell, D.J., 2006. Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making. Review of Agricultural Economics 28 (4), 553–566. Prestwidge, D., Stainley, T., Skocaj, D., Di Bella, L., Higgins, A., 2009. Harvest planning for growers. Sugarcane International 27 (2), 22–26. Pyndick, R.S., 1991. Irreversibility, uncertainty, and investment. Journal of Economic Literature 29 (3), 1110–1148. Recio, B., Rubio, F., Criado, J.A., 2003. A decision support system for farm planning using AgriSupport II. Decision Support Systems 36, 189–203. Romero, C., Rehman, T., 2003. Multiple Criteria Analysis for Agricultural Decisions. Elsevier Science Publishers, Amsterdam. Singh, I., Squire, L., Strauss, J., 1986. Agricultural Household Models. Extensions Applications and Policy. The Jonhs Hopkins University Press, Baltimore. Stillwell, W.G., Seaver, D.A., Edwards, W.A., 1981. Comparison of weight approximation techniques in multiattribute utility decision-making. Organizational Behavior and Human Performance 28, 62–77. Taylor, E., Adelman, I., 2003. Agricultural household models: Genesis, evolution, and extensions. Review of Economics of the Household 1, 33–58. van Asseldonk, M.A.P.M., Huirne, R.B.M., Dijkhuizen, A.A., Beulens, A.J.M., 1999. Dynamic programming to determine optimum investments in information technology on dairy farms. Agricultural Systems 62, 17–28. Wallace, M.T., Moss, J.E., 2002. Farmer decision-making with conflicting goals: A recursive strategic programming analysis. Journal of Agricultural Economics 53 (1), 82–100.