CAPRI MODELLING THE SUPPLY RESPONSE OF PERENNIAL CROPS. IS THERE A WAY OUT WHEN DATA ARE SCARCE? preliminary version. Working Paper 97-09

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1 COMMON AGRICULTURAL POLICY REGIONAL IMPACT ANALYSIS CAPRI preliminary version Working Paper MODELLING THE SUPPLY RESPONSE OF PERENNIAL CROPS. IS THERE A WAY OUT WHEN DATA ARE SCARCE? Helmi Ahmed El Kamel and J.M.García Alvarez-Coque Technical University of Valencia

2 Helmi Ahmed El Kamel is research assistant at the Department of Economics, Sociology and Agricultural Policy, Technical University of Valencia. His current research is focused on modelling the supply response of perennial crops and econometric methodology. Adress: Technical University of Valencia Department of Economics, Sociology and Agricultural Policy Camino de Vera, s/n Valencia (SPAIN) Phone: Fax: helkamel@esp.upv.es José María García Alvarez-Coque, Ph.D. is a lecturer and research associate at the Department of Economics, Sociology and Agricultural policy, Technical University of Valencia. His current research areas are quantitative agricultural sector modelling. Adress: Technical University of Valencia Department of Economics, Sociology and Agricultural Policy Camino de Vera, s/n Valencia (SPAIN) Phone: Fax: jmgarcia@prv.upv.es The series "CAPRI, Working papers" contains preliminary manuscripts which are not (yet) published in professional journals and are prepared in the context of the project Common Agricultural Policy Impact Analysis, funded by the EU-Commission under the FAIR program. Comments and criticisms are welcome and should be sent to the author(s) directly. All citations need to be cleared with the author(s).

3 MODELLING THE SUPPLY RESPONSE OF PERENNIAL CROPS. IS THERE A WAY OUT WHEN DATA ARE SCARCE? 1 Introduction Basic Theory The Investment Decision The Production Decision The State-Space Approach Computable Models Final Comments References...18

4 MODELLING THE SUPPLY RESPONSE OF PERENNIAL CROPS. IS THERE A WAY OUT WHEN DATA ARE SCARCE? 1 Introduction Most perennial crop supply response studies evolve from the premise that decisiones about acreage changes must incorporate variables that capture long term nature of planting and removal decisions. As noted by French and Matthews (1971), perennial crop production is distinguished from the production of annual crops by the extended period between planting and subsequent output, the long period of output flowing from initial production or investment decisions, and the eventual deterioration of the productive capacity of the plants. Therefore, perennial crops pose additional challenges for economic analysis compared to annual crops. Planting decisions depend on profit expectations on time spans normally over ten to twenty years. Annual yields typically vary over the life of the crops. Age and variety composition of the crop vary over time depending on the exogenous variables of the farmer. The age and variety composition of the crop in turn influences the replanting-removal decisions as well as the quantity produced any time. Several studies have provided a structural approach for estimating separate equations that represent individual productive decisions, such as new planting, replanting and removal of trees. These include French and Bressler for lemons (1962); Arak (1968) for coffee; Albisu and Blandford for oranges (1983); French, King and Minami for cling peaches (1985); Hartley, Nerlove and Peters (1987) for rubber; Behr (1990) for apples; and Perera (1995) for tea. Most of these studies account to some extent for the age distribution as a determinant of the planting-removal decisions. For many perennial crops there is limited or not data on new planting area, removals and area in individual age groups. The problem remains of econometrically estimating perennial crop supply response with aggregate acreage and production data while still accounting for agegroup dynamics in a meaningful way. Several studies have attempted to use the kinds of information typically available. This is the case, for example, of the first empirical aggregate supply response studies that appeared in the sixties within the econometric framework. Bateman (1965) and Behrman (1967) adapted the Nerlove s model, developed for field crops, to perennial crop cultivation. In the early seventies, French and Mathews (1971) examined the decision processes of asparagus producers and detailed many of the basic relationships between unobservable grower expectations and the use of observable factors. This autors, provided a more complete model of supply response with five equations: two separate equations describes plantings and removals, and are combined to depict desired bearing area. A fourth equation explains variations in yields and the last specifies the relationship between unobserved expectational variables and observed data. Changes in yields and acreage were then combined to explain changes in output. Estimation of the structural system was not possible because of data limitations. Acreage is specified as a function of lagged prices and average harvested area in different periods. The estimated coefficients could not be used to recover the structural parameters and then there is a loss of information about plantings and removals, aspects which 1

5 can be affected in a different way by economic variables and by the age and clonal composition of the acreage. Nevertheless, this study continues to serve as a framework for perennial crop response studies when acreage age distribution data are unavailable. Consequently, because of data limitations, studies on perennial crops have to rely on greatly simplified reduced-form equations that may fail to catch important structural features of the supply response of perennials. A major difficulty with past investigations of perennial crop supply is their failure to distinguish the individual effects of harvest and investment decisions on crop output. A further example is the model provided by Wickens and Greenfield (1973) to examine the supply of coffee in Brazil, derived from a decision theoretic model in which investment was explicitly considered as a derived demand for capital. Although the authors attempted to quantify investment and harvest decisions separately, they estimated a single reduced form equation for coffee supply due to data limitations. This reduced-form supply function relates current output to past prices with a distributed lag in which the coefficients have a specific interpretation: after a short period corresponding to the length of the distributed lag in the harvesting equation, they are proportional to an age-yield profile. Wickens and Greenfield estimate such a reduced form using a generalized Almon lag and obtain a lag shape similar to the age-yield profile for cofee after three years. They suggested to use a similar reduced-form equation in situations in which only data on output and past prices are available: e.g. Parikh (1979) on coffee; Dowling (1979) on rubber. However, the yield curves of perennial crops are not necessarily well approximated by the polynomial form used as tested by Hartley, Nerlove and Peters (1987) for rubber in Sri Lanka. In addition to this criticism, as these authors suggest, in areas where replantings are important, models such as Wickens and Greenfield s, which use only acreage changes as a measure of new investment, fail to serve as adequate representations of supply reponse in perennial crops. This is especially obvious in cases where technical change is of the embodied variety, as in the case of high-yielding or early-season varieties, so that it cannot be implemented without investment. This leads to Akiyama and Trivedi (1987) to assert that an understanding of the determinants of new planting and replanting investment decisions of the producer is of key importance when trying to account for the observed difference in the patterns of development and change (p. 137). The question is raised when there is a lack of detailed data on new plantings, replantings, removal and age composition of perennial crops. While it is advisable to follow a structural approach for estimating separate equations that represent individual planting activities, needed data are quite demanding and usually unavailable. What can be done? Very often the alternative to the structural approach may be to resort to the single-equation reduced form, which may involve a considerable loss of information. The problem can be important in the context of the CAPRI project, where supply modules for fruit production in the EU regions have to be provided. This paper does not attempt to provide an unique solution to the posed problem. Our intention is to draw on the literature to review different alternatives that can be used depending on the available information. If finally, simplifications have to be made on structural models, it is advisable to be aware of the costs of such simplifications. It is also useful to review alternative approaches with respect to what has been typical in the literature on perennial crop supply analysis. Therefore, section 2 begins with a quick look to the theoretical considerations on the 2

6 producer s behaviour for perennial crop supply. Section 3 reviews the area response (investment) decisions. Section 4 analyses separately the effects of harvesting decisions on crop output. Section 5 reviews the State-Space approach where separate accounting for unobserved components is possible in the absence of data on new plantings and replantings. Finally Section 6, studies the use of flexible computational model, that can be calibrated including econometric evidence and a priori restrictions. Note that this discussion paper, for the sake of simplicity, does not discuss the modelling of price expectations nor accounts for risk considerations. 2 Basic theory Consider a perennial crop with n age categories. As made by Akiyama and Trivedi (1987) we can refer to capital as the homogeneous land planted with trees with some specified density. Denote A(t, i) the capital stock of vintage or age group i used at time t. In other words, A(t, i) is the existing area of the perennial crop at the beginning of year t which will be in the ith year of life during year t, (i = 1,2,..., n). Output is produced only by mature vintages and is assumed to be homogeneous. Total output is defined by: (1) Q(t) = i y(t, i) A(t, i) where y(t, i) is the average productivity, or yield per unit of capital. In general, y (t, i) would depend on the expected output and variable input prices. Two interesting special cases are: (2) y(t, i) = y(t-x, i) = δ (i), for any x and (3) y(t, i) = γ(x) y(t-x, i) In the case of equation (2), yields are assumed depending only on the age of the trees, and not upon the time at which they were planted. In the case of equation (3) the productivity of trees of age i changes smoothly with time at a rate determined by the function γ(x). Both cases are not uncommon in perennial crop supply literature 1. In fact, for year t it is possible to distinguish between an actual output Q(t) and a potential output Q*(t), this one being defined by an empirical (constant) age-yield profile and actual empirical estimates of the age distribution: (4) Q*(t) = i δ*(i) A(t, i) where δ*(i) may be standard yield values based on field experiments. The potential output Q*(t) represents the effect of the existing stock of trees. Estimation of potential output would ignore weather, labour inputs, fertiliser use and the effects of varietal 1 See, e.g. French and Mathews (1971), Hartley, Nerlove and Peters (1987), Knapp and Konyar (1991). 3

7 improvements over time. The harvesting decision will be given by: (5) Q(t) = f [Q*(t), π (t), π e (t), Z(t)] where actual production Q(t) may differ from Q*(t) because of current profits π (t), expected normal profits or long-term profit expectations π e (t), and other variables Z(t) including weather conditions and a possible upward trend. As regards to the investment decision, we start from the age group dynamics, given by: (6) A(t+1, i) = A(t, i-1) - R(t, i-1) where R(t, i) denotes removals of age group i in period t and R(t, 1) = 0 (i = 2,..., n). By definition A(t, 1) = N(t), where N(t) denotes new plantings (or investment). Such model involves the choice by the farmer of optimal values of R(t, i) and N(t). Several attempts have been made to present a model of a competitive firm which chooses levels of R(t, i) and N(t) to maximize net discounted revenue 2. We can hypothesize that investment decisions are based on expected profitability of the perennial crop π e (t), and on a capital utilization factor of the perennial crop U(t). Thus, plantings in year t are given by: (7) N(t) = N [π e (t), U(t)] High levels of investment are associated with high levels of the capital utilization factor, which would involve the need for increasing the stock of capital. The utilization factor can be approached in different ways as we will see in the next section. As seen in equation (7), current profits are not likely to matter much for new planting and long term expectations may play some role. The optimization also involves the choice of the subset of mature age groups which can be considered as uneconomic. Given the decline in yield which occurs after a particular age (although not uniformly for all perennial crops) it will obviously pay at some point in the life cycle of a stand to remove it and possibly replant with a new variety. Thus, the tail of the age distribution can be expected to be removed in any year or, expressed in other terms, removals R(t, i) will tend to be higher for higher i. Removals R(t, i), of course, occur for other reasons, such as storm and desease, and because of profit expectations and new opportunities. For example, growers can compare current profits (short term expectations) π(t) relative to longterm profit expectations π e (t), in order to decide whether to remove at any year. Denote V(t) as the stock of uneconomic age groups, which would depend on the expected 2 Knapp and Knoyar (1992) obtain optimal values of R(t,i) and N(t) as a function of the existing acreage in each age group and future prices. Trivedi (1986) provides a model of optimization which also involves the distinction between additions to the capital stock from new plantings from those which come about from replanting currently uneconomic area under the same crop. A similar distinction is followed by Hartley, Nerlove and Peters (1987) and Kalaitzandonakes and Shonkwiler (1992). 4

8 age-yield profile for the perennial crop. Denote R(t) the total acreage of removed trees R(t) = i R(t, i). Therefore, removals can be formulated as: (8) R(t) = R[π(t), π e (t), V(t)] Equations (7) and (8) are generic for the investment decision and equation (5) for the harvesting decision of the perennial crop grower. The exact equation used will depend upon the way in which the different variables are specified. Apart from the profit variables π(t), π e (t), which are also difficult to approach when annual crop supply is analised, difficulties appear to elicit the potential output Q*(t), the capital utilization factor U(t) and the stock of uneconomic age groups V(t). Also, it happens to be a lack of data on plantings N(t), removals R(t) and the capital stock of each age group A(t, i). One wonders about the kind of simplifications that are acceptable in a context when available data are poor and scarce. The following discussion will not concentrate on the approximation of the profit variables π(t) and π e (t). The different studies (French and Mathews (1971); Albisu and Blandford (1983); Hartley, Nerlove and Peters (1987)) have normally based current and expected profitability on current and past product prices and input prices, such as labour and fertilizers. When available, measures of profitability per hectare should be used to take into account the income fluctuations due to weather conditions. 3 The investment decision The utilization factor that influences decisions on plantings may be approximated in different ways. One possibility is to define the utilization factor U(t) as the ratio of output to capital. Total capital stock could be represented by long-run responses involving adjustments in the size of the stock of trees when the utilization factor (output to capital ratio) is suboptimal and the output level is constrained by inflexibilities (number and effect of producing trees). The output level could be specified as a potential output Q*(t), whereas capital would be represented by the total stock of trees or total area planted A(t) 3 : (9) U(t) = Q*(t) / A(t) But estimation of potential output, at least as given by equation (4) would require an empirical age-yield profile and, what is more difficult, data on the age distribution of the perennial crop in each year. Although there are alternative specifications for Q*(t) compared to that of equation (4) (see next section), we would like to suggest a simple way of specifiying the output to capital ratio. Albisu and Blandford (1983) consider output as closely related to the bearing area (harvested area) A b (t) : (10) U(t) = A b (t) / A(t) Thus the last formulation would imply that potential output is, in fact, related to the bearing 3 Alternatively, Hartley, Nerlove and Peters (1987) include in the right hand of the new planting equation only the potential output Q*(t) and not the ratio otuput to capital. In fact, the size of the potential output might influence the number of the hectares newly planted. 5

9 area. Once the plants start to produce, production level cannot be easily modified in the shortrun. Removal can be assummed to be given by the size of the uneconomic age groups, as expressed in equation (8). It is usual to specify the variable V(t) by the area covered by the tail of the age distribution or the ratio of area with old plants to total area. Thus, V(t) can be given by: (11) V(t) = A o (t) / A(t) where A o (t) = old bearing area of the perennial crop. Although area A o (t) is technically observable, very often we will not have data to measure it. Therefore, it will be necessary to seek some closely associated variable that could substitute A o (t). A possible procedure, suggested by French and Mathews (1971) is to let old age acreage be proportional to total acreage. To account in part for the bias produced by periods of sharp increase or decrease in acreage, French and Mathews specified A o (t) as a function of the average harvested area during the previous five years: (12) A o (t) = g [A b (t) ] where A b (t) is the average harvested area during the past five years (t-5, t-4, t-3, t-2, t-1). As explained in section (1) it is desirable to formulate separate equations for plantings and removals, but unfortunately data pertaining to plantings N(t) and removals R(t) are usually unavailable. In section (5) we will describe a possible way of scaping this informational problem. For the moment, a possible alternative 4, with the cost of a loss of structural information, is to calculate net investment, instead of a separate accounting of plantings N(t) and removals R(t): (13) A(t) - A(t-1) = A t = N(t) - R(t) where, from substitution of N(t) and R(t) for equations (7) and (8) in equation (13), net investment A t would depend on current and expected profits (π(t) and π e (t)) and from the other variables affecting plantings and removals (utilization factor U(t) and the uneconomic stock V(t)). Unfortunately, it is also common that the variables measuring U(t) and V(t) 5 are not observable and it could force us to a last resort simplification to describe A t, based on a rational distributed lag approximation, suggested by Wickens and Greenfield (1973): (14) A t.= α0 + (β1-1) A(t-1) + β i A(t-i) + ϕ i p(t-i) i = 2 i = 0 l where p(t-i) are the prices in period t-i (i = 0,... m) and α0, β i.and ϕ i..are parameters of the function. A random error term should be added to the right-hand of equation (14). 4 See French and Mathews (1971), Albisu and Blandford (1983). 5 See equations (9) to (11). m 6

10 In fact, this kind of formulation is similar to one which would be obtained if adaptative expectations had been assumed. A special case would be the use of the Nerlove s model, and the Wickens and Greenfield s formulation is very similar to it although the last one is derived from an optimising model which maximizes expected discounted revenue net of planting costs subject to a vintage production function. 4 The production decision A major problem with the determination of the output level in perennial crops is the need for distinguishing clearly between the long-run and short-run dimensions of the production decisions. The long-run decisions determine the potential output, which in turn is a function of investment decisions taken in the past, normally with a lag of several years (a tree usually yields significant production only after five to seven years of life). The short-run decisions are influence by current values of economic variables and determine the production actually harvested in any year (harvesting decision). In order to clarify the decision process, it would be advisable to account separately for potential production Q*(t). When the age distribution and an empirical age-profile are available, it is possible to calculate Q*(t) directly (see French, Gordon and Minami (1985); Hartley, Nerlove and Peters (1987)). At the regional level, as in many CAPRI regions, data for estimating variables δ*(i) and A(t, i), are not at hand. Therefore, equation (4) would not be directly calculated. This involves that specific assumptions between Q*(t) and other observable variables have to be made. To take an example, Akiyama and Trivedi (1987) distinguish known total productive capacity (potential output) existing at some arbitrary origin, from the subsequent additions to that capacity arising from new planting in subsequent periods. In fact, old capacity may be assummed to be changing at an unknown proportional rate λ 2, which reflect the joint effects of technological change and of reduction in productivity of the old stock of trees. Denote Q o (t) the old stock at year t; and (15) Q o (t) = exp(λ 2 t) Q*(0) where Q*(0) is the potential output at t = 0. Given data on total newly planted and replanted areas from t = 1 onward and an age-yield profile with data about δ*(i), it is possible to construct the potential output determined by addition to the planted area since time 0. Assuming that this added output, denoted by Q n (t) is also subject to technical change at a constant rate λ 1: (16) Q n (t) = exp(λ 1 t) δ*(i) N(i) i = 1 t Combining (15) and (16), the potential output Q*(t) = Q o (t) + Q n (t) can be constructed. Akiyama and Trivedi introduce it in a vintage supply function where dependent variable is the actual output Q(t) and the right hand incorporated the potential output as well as (exogenous) price variables. This leads to an expression that is non-linear in the unknown parameters but 7

11 that can be estimated by non-linear least squares. However, in many cases the age-yield profile is not available and, what is worst, newly planted and replanted areas are not observed at the regional level. This situation makes the desirable distinction between long-run and short-run decisions more complicated. The failure to construct separately the potential output Q*(t) may lead to a direct estimation of the actual output Q(t) in a single reduce-form output function. Of course, with the cost of losing structural information. This is what happens with the Wickens and Greenfield s model (1973), that ends up in a final reduced-form output equation where actual output depends on lagged areas and a distributed lag function of prices. The output response coefficients (with respect to lagged prices) of the Wickens and Greenfield s formulation exhibit the shape depicted in figure The actual estimation of the output response coefficients were facilitated by an Almon polynomial distributed lag. See, Wickens and Greenfield, p

12 FIGURE 1 OUTPUT RESPONSE COEFFICIENTS β i i Source: Wickens M. R. and Greenfield J. N., The first decreasing coefficients of the lag function correspond to the short-run price response (the harvesting decision ) while the coefficients start to increase proportionally to the yield curve of the perennial crop, ending with decreasing values. Actual production is, therefore, determined by short term decisions (a function of lagged prices one or two periods) and by long-run decisions (a function of lagged prices with higher weights of past periods e.g. 10 to 15 years ago). This approach must be observed as an improvement compared to the Nerlove s model that does not capture the dynamic structure of the tree crop supply. However, as said in the introduction to this paper, the Wickens-Greenfield formulation has been severely questioned (see e.g. Akiyama and Trivedi (1987)) because of the failure to provide separate structural information of long-run and short-run decisions and because the polynomial function does not necessarily approximate the yield function. Besides the estimation of the output function requires long time series to take consideration of prices lagged too many periods (eg. about 10 years) 7. This is complicated at the regional level for many products, thinking of CAPRI. In certain cases, we can simplify the obtention of the actual output in any year, if we adopt the assumption that actual production is the same as potential production. In other words, the harvesting decision is not affected by short-term profit variables. In addition, in many perennial crops, potential production can be assumed as not determined by any lagged variable for periods covering downward from t to t-m, where m is relatively high. For example, in citrus fruit production, present harvests depend on decisions taken over 7 year ago, because the yields of this crop are not significant until the trees are 7 year old or older. In this case, if we were simulating over time spans of 4 to 6 years (eg. CAPRI), we could attempt to forecast output without a structural formulation that explains the output variations. Therefore, actual output of perennial crops could be taken as exogenous in the various CAPRI price simulations. That is, (17) Q(t) = Q[Q(t-1) Q(t-2),...,Q(t-k), t] where actual output Q(t) could be estimated based on time series and different methods 7 The natural cut-off point of the Almon function is shortened by taking first differences in the estimating function (Wickens and Greenfield (1973), p. 438). In spite of this, the lenght of the lag function was only shortened from 20 to 9 years. 9

13 (trends, autoregresive specifications, Brown method, Holt method and ARIMA models) 8. Where data about newly planted and replanted areas are available, output predictions Q(t) could be improved by using information of plantings lagged m years before N(t-m). A basic assumption would be: (18) Q(t) = φ0 + φ1 N(t-m)+ u t. where u t. is a random error and m could be determined by a search process around the time span that farmers are concerned about obtaining competing production from new plantings. Again, in the last specification, a difficulty could arise from the very long data series required for estimating equation (18). An solution is proposed by French and Mathews (1971) where we can assume that the area expansion is associated with an increased proportion of plants in the young bearing age group, thus reducing the average yield of the perennial crop activity. Thus we might approximate the average yields in year t by (19) y (t) = δ0 + δ1 [A(t) - A(t-h)] + v t where h is a small number such as 2, 3, or 4. Where it is possible to approximate the proportion of young orchards in total area, denoted by A y (t)/a(t), the yield equation would take the form (20) y (t) = ω0 + ω1 [A y (t)/a(t)] + w t The last equation assumes that the age-yield profile is relatively constant, once a tree becomes productive. As follows from this discussion, solutions exist to the information problems. However, it is not advisable to give an unique and general solution, because it will depend on the kind of data available and on the realism of the assumptions adopted in each case. 5. The State-Space Approach Econometric studies of perennial crop response have usually resorted to single reduce-form equations for aggregate output or acreage, or estimates on individual new planting/removal equations. The first approach has been criticized because it does not adequately account for the structural relations that describe planting and removal decisions, while the second approach requires detailed data which are not always available. Is there a way out? Some authors (Knapp and Konyar (1991), Kalaitzandonakes and Shonkwiler (1992)) have proposed a State-Space aproach to allow the separate estimation of the qualitatively different planting and removal decisions. Let us describe the basics of this approach with a simple example. Assume that data on total change in acreage area A t are available but there is no information about new plantings and removals for all the studied period (e.g. data on these variables are available just for one year). Denote column vector x t as that formed by the unobserved variables of the system, that is new plantings N(t) and removals R(t). 8 See Cases (1994) for a comparison of several methods of forecasting without theory. 10

14 Assume that the system dynamics is represented by the model (21a) (21b) x t = F x t-1 + G z t + e xt A t = H x t + e At where H = [1 : -1] is the matrix that relates the vector x t to the variable A t (H x t = N(t) - R(t)). F is a transition matrix that allows dynamic interactions between paths of plantings and removals by permitting lagged values of both plantings and removals to influence current plantings and removals. Vector z t include such variables as prices and costs, which are considered to be observable and exogenous to the dynamic system. Elements of matrix G include the response effects of the unobservable endogenous variables to the observable vector z t. Both equations include error terms. Thus e xt describes the process noise, while e At is the measurement noise of A t. The unknown parameters of the system (to be estimated) are given by the elements of matrices F and G, while the unobserved variables (to be recovered) are elements of vector x t. In fact, the model given by equations (21a) and (21b) is a special case of the well known State-Space model, which allows for dynamic interdependencies among unobserved variables. The behaviour of the dynamic system can be described by the evolution of the unobserved variables, called state variables, which cannot be determined exactly by direct measurements. Instead, we can use indirect measurements of the state variables, called measurement variables, which are functions of the state variables and are, in fact, corrupted by random noise. In the system given by equations (21a) and (21b) the state vector is x t, while the measurement variable is A t. Thus the perennial crop problem is reformulated as a State- Space model. There are many methods to estimate the unknown states of a dynamic process from noisy data taken at discrete real-time intervals, the most well known being the Kalman filter. This method provides the general solution to the recursive, minimised mean square estimation problem within the class of linear estimators. The Kalman filter gives optimal estimates of the state variables and their variance-covariance matrix for given information, including given values of the parameters, the variance-covariance matrices for the error terms in (21a) and (21b) and initial conditions represented by the expectations and variance-covariance for the state variables at t = 0. The log-likelihood function is then estimated. Iterations over the values of the parameters are then conducted to find maximum likelihood estimates of the unknown system parameters. A special case, which simplifies parameter estimation is that studies by Kalaitzandonakes and Shonkwiler (1992). They assume that total plantings A t are measured without error (e At = 0) and that the initial observable state vector x o is deterministic, in which an estimation process without the Kalman filter may be obtained. Assumming that e At = 0 and basing on the initial state vector x o, the repeated substitution of (21a) in (21b) provides a reduced form of the statespace system in which A t is expressed exclusively in terms of the observable x o and z t ; that is (22) A t = H F t x o + H F t-j G z j + H F t-j e xj, t t 11

15 j = 1 j = 1 t = 1,... T where parameters can be directly estimated through maximum likelihood procedures. Once the parameters are estimated, unobserved plantings and removals can be derived through the use of the Kalman filter. Although the implied series cannot be falsified by the real world, empirically reasonable, system parameters and derived state variables open a way of validating the supply model. The main advantage of this approach is the possibility of recovering the unobserved states of the system 9. The question remains about the property of ability to forecast the future of such system. Within-sample forecasts of total Florida grapefruit plantings were obtained by Kalaitzandonakes and Shonkwiler (1992) for two estimated models, the first derived from the Nerlovian partial adjustment model, and the second derived from the state-space approach. The results indicated that the explanatory power of the single-equation Nerlovian model was lower than the dynamic unobserved components model. However, there is a need for testing such model for out-sample forecasts. Furthermore, a comparative study is needed with singleequation models based on less naive assumption than the partial adjustment equation tested in the quoted work. 6. Computable Models Regional data are frequently fragmentary and of poor quality so that they cannot support precise estimation of key structural parameters of a supply model for perennial crops. This can justify the implementation of computable models that calculate the supply response under alternative assumptions about related variables such as age-yield profiles, new plantings, removals, and supply elasticities. This approach can make computationally implementable a great number of equations, permitting speed and flexibility in evaluating policy. In our case, the model would consist of computable expressions for the system formed by equations (4), (5), (6), (7) and (8). Once the expressions are formulated, the model can be calibrated using historical data and parameter estimates that are not obtained from a fully econometric model because of the limited time series data used in their estimation. Needless to say that sensitivity analysis is essential in this kind of approach. For example, according to Trivedi and Akiyama (1992), the output equation expressed by (5) is defined in the following terms: (23) Q(t) = f 1 [Q*(t)] f 2 [π (t-i)], i = 0... m where f 1 [Q*(t)] is a function of the potential output, normally expressed as a percentage of potential production that is actually produced in any year; and the second term f 2 [π (t-i)], represents the current and lagged effects of (own and substitute crop) profits, denoted by the vector π. 9 As Kalaitzandonakes and Shonkwiler (1992) point out, knowledge of the measurement and state vectors over a finite time segment must include sufficient information to enable the system s state to be completely identified (p. 348). 12

16 Given an age profile, potential output could be constructed as in equation (4), from empirical data and the size of surviving stock of vintage i trees A(t, i), where this variable is given by the accumulation equation (6), which provides the investment decisions. New plantings can be specified in a simpler way than that given by equation (7). For example, Trivedi and Akiyama assume that new planting of cocoa are a function of prices lagged one period (as a proxy for the expected future real producer prices). In the computable model by Behr (1990), annual new plantings are determined as a function of lagged gross receipts per hectare and a variable representing risk aversion. Assume that we avoid to incorporate risk considerations. Then Behr s equation for new plantings could be specified as follows: (24) N(t) = C π3(t) e where C = constant; π3(t) = average of profits (t-1, t-2, t-3), and e = planting elasticity. As far as removals are concerned (see equation (8)), it seems quite difficult to specify a computable equation that takes into account removals, death and losses from the existing stock. One sensible solution is to rely on expert assessments to provide alternative assumptions about rates of removals, according to regional conditions and possible policies 10. For example, Fernandez, Serra and Recaj (1994) constructed a computable model under different hypothesis about the rates of removals that would provide a balance between supply and demand for Spanish lemons. A further simplification of the computable model would be that discussed in section 4, which assumes that actual production equals potential production. This assumption has already been adopted by the computable models by Behr (1990) for apples, and for lemons. In both cases, potential (actual) production is constructed from an empirical age-profile, as given by equation (4). Actually, both models recognise that actual production in any year is the result of lagged decisions taken a long time before 11. A possible representation of this approach is given by figure 2, where there is (1) a physical module, based on the dynamic system including the age distribution of the orchards and the potential production and, (2) two economic modules, based on the way plantings and removals are specified. Both variables can be defined in terms of behavioural equations but it could be interesting to modify the forecast according to experts assessments. Although the model illustrated in figure 2 is rather simple, in terms of methodological concept, it is also true that the number of involved elements can make it somewhat cumbersome, specially if we wanted to apply it to a high number of products and regions. For example, Fernandez, Serra and Recaj (1994) just studied the Spanish lemon but the model incorporated 10 producing regions, 2 varieties and 50 age groups to perform forecasts along 13 years. Note that a model based on age-yield profiles and age distribution of cropped areas should make a distinction between the different productive varieties for each crop, taking into account that age-yield profiles of old and new varieties are normally different. Again, data 10 For example, Valencian Government gives an aid for hectare replanted by citrus, because of the fight against the long decline virus. Over 2000 hectares per year are expected to be replanted, under the current program, until the year In the case of lemons, the time span between the planting of a tree and the age when the tree has a competitive production is about 15 years. 13

17 requirements to apply this approach to over 200 regions and the whole fruit sector, as CAPRI would require, are significant. Let us discuss some further simplifications that can help us to avoid some of the information problems. Normally, the most difficult part of the model deals with the estimation of the potential output. Assume that we do not want to know with the age distribution of the crop area. This implies that equations given by expression (6) will disappear from the system. If we formulate hypothesis on new plantings and an empirical age-yield profile, then potential output for a particular variety could be given by the sum of expressions (15) and (16): (25) Q*(t) = exp(λ 2 t) Q*(0) + exp(λ 1 t) δ*(i) N(i) i = 1 where Q*(0) and N(i) can be estimated from historical data, and λ 2, λ 1, δ*(i) from expert assessment. Finally, let us assume that we are in the worst situation where there is scarce information on the empirical age-yield profile of particular varieties. Then we could resort to equations such as (17) to (20), with calculated parameters rather than econometrically estimated. A possibility would be to combine trend estimation with expert assessments. For example, we could forecast output by expression (17), where actual output of perennial crops could be taken as exogenous in the various CAPRI price simulations, and afterwards checking and correcting the trend estimation by expert judgements. This method makes sense in a context of multiple regions and the need for combining fruit products in aggregate mixed activities such as apples, pears and peaches, other fruit or citrus fruits. t 14

18 FIGURE 2 EXAMPLE OF COMPUTABLE MODEL FOR PERENNIAL CROPS INPUT BASE YEAR DATA AND PARAMETERS A( 0, i ) R( 0, i ) * δ ( i ) N( 0 ) REMOVAL MODULE (EXPERT ASSESMENT) R( t, i ) ITERATION FOR YEAR t A( t, 1) = N( t ) A( t + 1, i ) = A( t, i 1) R( t, i 1) i = 2,... Q( t ) = δ ( i ) A( t, i ) i * NEW PLANTING MODULE (BEHAVIOR EQUATION) N( t ) PRICE DATA t 1, t 2, t 3 END 15

19 7 Final comments At this stage may be redundant to recognise that the modelling approach for perennial crops is a matter that depends on the aims of the model and on the available resources, in terms of data. Thus, where over 200 hundred regions are to be modelled and aggregate fruit activities (eg apple, pears and peaches) are concerned, needless to say that a detailed approach based on specific data for the different varieties and age-yield profiles can be extremely costly. What this paper has intended is to supply an overview of the different approaches that take the time series as starting point for the modelling of perennial crops. Interestingly we advocate for a mixed approach that does not support an unique modelling approach. That is to say, depending on the data available on each region, the present paper provides the methodological elements to apply different approaches to different regions, depending on the available information and on the assumptions that could be admitted in each region. This does not mean that we should avoid harmonisation in basic definitions and economic concepts, especially those referred to the productive activities considered in the model, and to other basic economic variables such as prices, gross margins, cost positions. Of course, we should avoid methodological inconsistencies between the modelling approach adopted for different regions. This paper has tried to present the subject in a way that any approach can be understood as a simplification of more general models, so inconsistencies could be minimised. Before starting with a further specification of the modelling approach for the CAPRI perennial crops and regions, we prefer to stop here, given the fact that this could be the result of a consensus between the different viewpoints expressed within the framework of the CAPRI seminar. 16

20 8 References AKIYAMA, T. y TRIVEDI, P. K. (1987). Vintage Production Approach to Perennial Crop Supply: An Application to Tea in Major Producing Countries. Journal of Econometrics, Vol.36, Nº1, pp ALBISU, L. M. and BLANDFORD, D. (1983). An Area response model for perennial plants and its application to Spanish oranges and mandarins. Euro. R. Agr. Eco., Vol.10, pp ALSTON, J. M.; FREEBAIRN, J. W. y QUILKEY, J. J. (1980). A Model of Supply Response in the Australian Orange Growing Industry. Australian Journal of Agricultural Economics, Vol.24, pp ARAK, M. (1969). Estimation of Asymetric Long-Run Supply Functions: The Case of Coffee. Canadian Journal of Agricultural Economics, Vol.17, pp ASKARI, H. y CUMMINGS, J. T. (1977). Estimating Agricultural Supply Response with the Nerlove Model: A Survey. International Economic Review, Vol.18, Nº2, pp BATEMAN, M. J. (1965). Aggregate Regional Supply Functions for Ghanian Cocoa, Journal of Farm Economics, Vol.47, pp BEHR, H. C. (1986). A Market Simulation Model for Perennial Crops. Acta Horticulturae, Nº184, pp BEHR, H. C. (1987). Evaluating long term effects of different market policies for perennial crops in the enlarged European Community. Acta Horticulturae, Nº203, pp BEHR, H. C. (1988). Efectos de las diversas políticas agrarias comunitarias en el sector hortofrutícola de la CEE. Investigación Agraria. Serie Economía, Vol.3, Nº2, pp BEHR, H. C. y ANDERSON, J. L. (1990). A Policy Analysis Model for Fruit Crops. Acta Horticulturae, Nº276, pp BEHRMAN, J. R. (1968). Monopolistic Cocoa Pricing. American Journal of Agricultural Economics, Vol.50, pp CASES, B. (1994). La predicción de cosechas en citricos. Comparación entre diferentes métodos. Investigación Agraria. Serie Economía, Vol.9, Nº3, pp COLMAN, D. (1983). A Review of the Arts of Supply Response Analysis. Review of Marketing and Agricultural Economics, Vol.51, Nº3, pp DOWLING, J. M. (1979). The Supply Response of Rubber in Thailand. Southern Economic Journal, Vol.45, Nº3, pp FERNANDEZ, Y.; SERRA, P. y RECAJ, Y. (1994). Un análisis sobre la producción española de limón: evolución previsible a medio plazo. Investigación Agraria. Serie Economía, Vol.9, Nº2, pp FRENCH, B. C. y BRESSLER, R. G. (1962). The Limon Cycle. Journal of Farm 17

21 Economics, Vol.44, pp FRENCH, B. C. y MATTHEWS, J. L. (1971). A Supply Response Model for Perennial Crops. American Journal of Agricultural Economics, Vol. 53, Nº3, pp FRENCH, B. C.; KING, G. A. y MINAMI, D. D. (1985). Planting and Removal Relationships for Perennial Crops: An Application to Cling Peaches. American Journal of Agricultural Economics, Vol.67, pp HARTLEY, M. J.; NERLOVE, M. y PETERS, R. K. (1987). An Analysis of Rubber Supply in Sri Lanka. American Journal of Agricultural Economics, Vol.69, pp KALAITZANDONAKES, N. G. y SHONKWILER, J. S. (1990). Planting Decisions for Perennial Crops: A Dynamic Unobserved Components Approach. American Journal of Agricultural Economics, Vol.72, Nº5, pp KALAITZANDONAKES, N. G. y SHONKWILER, J. S. (1992). A State-Space Approach to Perennial Crop Supply Analysis. American Journal of Agricultural Economics, Vol.74, pp KNAPP, K. C. (1987). Dynamic Equilibrium in Markets for Perennial Crops. American Journal of Agricultural Economics, Vol.69, Nº1, pp KNAPP, K. C. y KONYAR, K. (1991). Perennial Crop Supply Response: A Kalman Filter Approach. American Journal of Agricultural Economics, Vol.73, Nº3, pp NADDA, A. L. (1987). Supply response of Perennial Crops: A Study of Himachal Apples. Indian Journal of Agricultural Economics, Vol.42, Nº3, pp NARAYANA, D. (1994). Perennial Crop Production Cycle Models: Influence of High Yielding Varieties and Prices. Indian Journal of Natural Rubber Research, Vol.7, Nº1, pp NERLOVE, M. (1979). The Dynamics of Supply: Retrospect and Prospect. American Journal of Agricultural Economics, Vol.61, Nº5, pp PERERA, N. (1995). Modelling the Perennial Crop Sector in Less Developed Countries: A Case of Tea in Sri Lanka. Indian Journal of Agricultural Economics, Vol.50, Nº4, pp SAYLOR, R. G. (1974). Alternative Mesures of Supply Elasticities: The Case of Sao Paulo Coffe. American Journal of Agricultural Economics, 56, pp TRIVEDI, P. K. y AKIYAMA, T. (1992). A Framework for Evaluating the Impact of Pricing Policies for Cocoa and Coffee in Côte d Ivoire. The World Bank Economic Review, Vol.6, Nº2, pp WICKENS, M. R. y GREENFIELD, J. N. (1973). The econometrics of agricultural supply: An application to the world coffee market. Review of Economics and Statistics, Vol.55, Nº4, pp

22 List of CAPRI Working Papers: 97-01: Britz, Wolfgang; Heckelei, Thomas: Pre-study for a medium-term simulation and forecast model of the agricultural sector for the EU 97-02: Britz, Wolfgang: Regionalization of EU-data in the CAPRI project 97-03: Heckelei, Thomas: Positive Mathematical Programming: Review of the Standard Approach 97-04: Meudt, Markus; Britz, Wolfgang: The CAPRI nitrogen balance 97-05: Löhe, Wolfgang; Britz, Wolfgang: EU's Regulation 2078/92 in Germany and experiences of modelling less intensive production alternatives 97-06: Möllmann, Claus: FADN/RICA Farm Accountancy Data Network Short Introduction 97-07: Löhe, Wolfgang; Specification of variable inputs in RAUMIS 97-08: María Sancho and J.M. García Alvarez-Coque; Changing agricultural systems in the context of compatible agriculture. The Spanish experience Helmi Ahmed El Kamel and J.M.García Alvarez-Coque; Modelling the supply response of perennial crops is there a out when data are scarce? 19