COMMON AGRICULTURAL POLICY REGIONAL IMPACT ANALYSIS CAPRI preliminary version Working Paper 98-01 EV-Risk analysis for Germany Thomas Heckelei and Wolfgang Britz University of Bonn Universität Bonn
Thomas Heckelei, Ph.D. is a lecturer and research associate at the Institute of Agricultural Policy, University of Bonn. His current research areas are quantitative agricultural sector modelling and econometric methodology.. Wolfgang Britz, has a post-doc position as research assistant and lecturer at the Institute for Agricultural Policy, University of Bonn, and is specializing in quantitative economic modelling. In the CAPRI group Bonn, he is responsible for the methodological concept and the EDP realization. Address: Institut für Agrarpolitk, Universität Bonn, Nußallee 21 D-53115 Bonn Phone: Fax: +49-228-9822923 URL: E-mail: +49-228-732323 (Heckelei) or 732502 (Britz) http://www.agp.uni-bonn.de heckelei@agp.uni-bonn.de or britz@agp.uni-bonn.de 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).
EV-Analysis for Germany 1 Introduction and layout of the study... 1 2 Data base... 2 2.1 SPEL EU data... 2 2.2 Taking trends out of revenues... 3 2.3 Expected versus observed variances... 4 3 Results... 4 3.1 Defining a measurement of fit in the calibration step... 4 3.2 Actual results... 5 4 Summary... 5 References... 6
EV-Analysis for Germany 1 Introduction and layout of the study Risk analysis has a long-standing tradition in agricultural sector modeling (see e.g. HAZELL & NORTON 1986). Agricultural production faces two interlinked main sources of risk: 1. yield risk mainly due to uncertainties of the production processes (weather, diseases, etc.) 2. market risk due to price uncertainties, partly related to yield risk. For this study, the following approach is used: Let l denote the level of production activities, y yields and p prices, r revenues and c production costs per activity unit. Based on the PMP formulation (1) with linear revenues r and a non-linear cost c(l) function in the objective - in the following a quadratic cost function with a constant parameter is used - under linear constraints, a risk neutral decision maker would maximize expected revenues - expected costs under linear technological constraints: (1) [ c l ] max E l' r ( ) l s. t. Al b If production quantities for the analyzed region have an impact on price determination, the expected revenue is not the product of two independent stochastic variables. For down-sloping demand curves, years with high yields show low prices and vice versa. As Hazell & Norton suggest, the EV-analysis (2) is carried out by adding the covariances of the per-activity revenues cov[y p] = cov[r] weighted with an risk aversion coefficient θ. For simplicity, we assume in the following that there is no risk in costs, leading to the following model based on (1): (2) [ ] max l' E r c( l) 05θ. l'cov( r) l l s. t. Al b From a theoretical point of view, the underlying utility function of the EV-model has no specific appeal compared to alternative formulations. However, in order to integrate the model into a quadratic programming framework as planned for the PMP objective of CAPRI, the EV-model is optimal because θ cov(r) can be simply added to the matrix of quadratic terms. Hence, if cross-cost effects are included in the PMP terms, there is no real computational drawback by enriching a QP based on PMPs with an EV-risk formulation. The main objective of this case study is to analyze the relation between a classical EV-analysis and the PMP approach in sector modeling. The study was partly triggered by a paper of PARIS 1 sent to the authors as a follow-up of the discussion at the CAPRI-meeting in Reggio Emilia in spring 1997 and the presentation of and discussions with J.M. Boussard at the CAPRI-meeting in Montpellier, autumn 1997. Whereas the risk aversion coefficient θ could be evaluated in micro applications in cooperation with decision makers, its value was often used as an instrument of model calibration in macro applications (HAZELL & NORTON, 1986, p.237 f) where today the PMP-methodology offers a more straightforward way of calibration. Additionally, as for PMPs, the introduction 1 Q. Paris: CAPRI Meeting Follow-Up (Reggio Emilia) of a paper presented at the CAPRI Workshop in Reggio Emilia, Italy, May 1997. June 1997
2 of a quadratic term in the objective leads to a smoother response in the model in simulation runs and to interior solutions. Because the principal mathematical layout of an EV-analysis and a PMP-approach with an quadratic objective function are identical, the integration of an EV-analysis into the current CAPRI layout is straightforward. The main questions are: does an EV-approach contribute to the explanation of observed production activity levels? does an EV-approach lead to a more realistic simulation behavior of the model? Some points in relation to the contribution of Prof. Boussard during the CAPRI meeting in Montpellier: Price variances on markets are due to a number of effects. For agricultural markets in the EU, the CAP certainly plays a major rule. From the view point of an individual decision maker, however, his expected future prices and their expected variances matter - independently from the underlying source. Under a regime of administered prices, variances may be lower but still matter. The argument that there is no price risk because CAP guarantees a minimum price is weak because if market prices can rise above the floor, expected prices will be higher then the floor and there remains the risk that realized prices will be lower then expected ones - a scenario that might become relevant for the cereal markets in CAPRI simulations. However, it may be a real challenge to model the effect of different policy options not only on average prices, but also on variances prices. 2 Data base 2.1 SPEL-EU data As generally in the CAPRI project, we use EUROSTAT statistics as available in the SPEL-EU data base. For the purpose of this case study for Germany, the covariances of the revenues were based on national data from this data base. Germany was chosen by the authors not only because they are more familiar with German agricultural production, but for a relatively secure quality of the regionalized data at this state of the project. National data are available annually from 1975 to 1995 for about 50 different products. The model was calibrated for a three year average around 1993 for regionalized data from the CAPRI data base which is consistent to the national data from the SPEL-EU data base. The use of these data is however subject to certain peculiarities of the underlying data generation process. Revenues calculated from the Economic Accounts for Agriculture (EAA) and production statistics in the case of animals are both based on calendar-year values but plant production statistics are based on crop year data. In the latter case, specific assumptions are used in the SPEL base model to distribute the physical positions of the farm-balance sheet (sales, human consumption on farm and stock changes) matching the EAA value of the two adjacent crop years to a certain calendar year. Hence, the resulting unit value "PRIC" is derived for crops from the annual EAA position and a weighted average of physical positions of two crop years. On top, depending on the Member State, specific EAA positions are only available at an aggregate level and are broken down to derive positions for the individual outputs based on price statistics.
SPEL provides per activity revenues in current prices in the row "PROV". These revenues are calculated from yields and unit value prices ("UVAL"). The latter are a weighted average of the unit value of EAA ("PRIC") and the unit value for intra-sectoral transactions ("PRIN") which is either set in fixed proportion to "UVAL" or based on price statistics. Due to difficulties mentioned above, the per activity revenues can be denoted as "semi-official" data. As generally in the CAPRI project, we rely on the original SPEL data as far as possible. For details concerning the data generation process in the SPEL-EU base model, see: W. WOLF, SPEL System Methodological documentation (Rev. 1) Vol.1 : Basics, BS, SFSS; Luxembourg: Office for Official Publications of the European Communities, 1995. Generally, the use of national data may underestimate the regional variance in revenues, both due to higher yield and price variances in smaller regional units compared to the average of the sector. Along with this study, sources for regional prices will be evaluated. 3 2.2 Taking trends out of revenues The individual time series are not stationary due to the underlying trends in yields and nominal prices. HAZELL & NORTON suggest to de-trend both elements separately. In a first approach, both yields and prices were de-trended by calculating independent linear trends. The approach can be criticised for several reasons: First of all, one may argue that not the yields are stochastic, but climatic conditions and diseases, factors affecting more than one crop activity at the same time. Hence, the error term across the trend functions should show some general pattern and a SUR regression might be a better choice. A possibly more critical problem is the existence of yield effects on prices via the market mechanism. The solution here would lie in a rather complex system estimation. We stuck to our simple approach not only for technical reasons 2 and a restricted time budget. From a theoretical view point, not observed variances should be employed, but expected ones. As with price expectation, without on-farm data collection, not much can be deduced from theory or statistical data concerning the real "risk expectation" farmers. Our - from an econometric view point - simple de-trending procedures might be already much too refined to actually describe how decision makers on the farm perceive risk. In order to arrive at de-trended time series, the residuals from the trend regression were added to the trend value for our base year b (3): (3) x = a + bt + e t t t * x = x + e t b t The latter was used to account for the fact that, for example, with a continuos increase in yields, the covariances of the revenues would cp. increase over time, since (4) y p = E( y) E( p) + E( y) e + E( p) e t t pt yt The de-trended yields y* and prices p* for the products i where then used to calculated detrended revenues r* for each activity j: j (5) r = y * p * t i it it Based on the these time series of de-trended values, a variance-covariance matrix of per activity revenues was calculated. 2 For simplicity, we calculated the trends in GAMS. Switching to a more elaborated econometric approach would mean to put another software to work.
4 2.3 Expected versus observed variances Perhaps the major problem of aggregate risk analysis is the difference between "observed risk measurement", i.e. variances and co-variances deduced from statistics, and the correctly aggregated expected risk of the individual decision makers. The problem has several dimensions: 1. It is well known that variances in yields are averaged out by regional aggregation. Therefore, the variances in yields at farm level may be significantly higher then the ones deduced from national statistics. Because the resulting error may vary with the specific product, the problem cannot be adequately addressed by simply raising the risk coefficient. 2. Little is known about how expectations are formed. The problem is already severe in all applications where only means do matter, e.g. an estimation of production quantities from expected prices. Here, we face the problem to describe expectations for revenue (co)variances of individual activities that are linked through markets influenced by agricultural policy. 3. Depending on the production program of the individual farm, decision makers usually do not face the full covariance matrix. Economically, the increase of expected revenue due to scale effects dominates in many cases the decrease in risk by choosing a diversified production structure. This is especially true for highly specialised branches, e.g. eggs and poultry production. This means that risk matters for the general investment decision, i.e. long-term decisions, but not as much for the yearly determination of the production program. 3 Results 3.1 Defining a measurement of fit in the calibration step One main problem in evaluating the effect of introducing a new model element is to define an appropriate measurement for its explanatory power. Under "classical" applications, usually deviations between a base-year run and observed base year values could be used. If we integrate a new element in an existing PMP-framework, however, the deviations are always zero for the calibrated production activity levels which are of interest here. Hence, we have to look out for another effect to measure, the most natural one being the value of the duals on the calibration constraints. By varying the risk aversion coefficient θ, changes in the duals of the calibration constraints λ will occur. However, the raw information from such a sensitivity analysis is a cube of λ values over regions, production alternatives and different values of θ. In order to condense the information and to judge if the model is calibrating "better" for a specific value of θ, a "goodness of fit" measure must be defined by choosing a weighting scheme. Due to the fact that the duals can be interpreted as measuring deviations between observed and non-observed cost elements in the objective function, we use specified production costs as the denominator. The weights of the individual activities are then simply their activity levels: (6) F = i, r l abs( λ ) i, r l c i, r ir i, r ir
We should keep in mind that the levels l are kept at the observed base year level and that the related costs c are known. The measurement F shows the relation between the sum of the absolute non-observed cost elements and the sum of the observed cost values in the objective function. An introduction of the risk approach is said to improve the calibration - or to generally contribute to the explanation of observed activity levels - if F is getting smaller. Thus, for each region the deviations between our objective function (including a specific risk formulation) from the true marginals λ for each activity are first weighted with the activity levels. In order to allow a comparison across regions, the resulting sum is divided by total production cost c t per activity as defined in the SPEL-data base multiplied with the corresponding activity levels. The indicator shows something like "not covered marginals" in relation to accounting costs from EAA. If we combine (2) and (6), we already gain some insight on the effects of an introduction of an EV-Analysis into the PMP design. Differentiating the objective function in (2) with respect to the levels l leads to: (7) [ ] E r c' ( l) θl' cov( r) Since both l - the activities levels set to the base year value - and r - observed revenues - are vector of constants, l' cov(r) is again a vector independent from the model solution with fixed elements for the individual activities. Changing the risk aversion coefficient θ stepwise by certain percentages will hence add for each activity a specific, increasing fixed (positive or negative) linear term to its gradient. As long as the basis does not change (which doesn't happen in the calibration run), the duals λ will be changed by the same amount for each activity. Positive effects of an EV-element in the objective could be expected if l' cov(r) shows higher values for activities with a high positive dual if the EV-element is not introduced, e.g. if pork production has a high risk, the deviation between observed costs and calibrated ones should be relatively high. 5 3.2 Actual results The model was run for all 45 NUTS II regions for Germany. The results were put in a regression analysis to judge if the risk aversion coefficient has a significant influence on the goodness of fit. The results obtained for Germany on NUTS II level are very disappointing. An improvement of (6) can be reached with very small risk-coefficients (around 0.01) only, hence, the integration of the risk approach into the modelling framework at this stage of the model specification does not yield an important contribution to the explanation of observed activity levels and consequently does not significantly influence the simulation behaviour of the model. 4 Summary The results from this case-study do not look very promising. The duals of the calibration constraints could not be lowered significantly by changing the risk aversion coefficient. Very small positive effects could be reached with small risk aversion coefficients, only. Difficulties may arise from:
6 The underlying data generation process which may create variances quite different from the ones observed at farm level. A severe aggregation problem. Errors in the expectation model However, the difficulties mentioned above could only be overcome by strenuous data mining and a lot of additional assumptions. Due to the fact, that other elements in the objective function are still unknown, it does not seem very rational to invest currently further efforts in a risk approach. At a later stage of the modelling process, however, it might be worthwhile to rerun the analysis based on the existing programs to see whether changes in the model specification changes the results of the risk approach. However, the case-study had one useful outcome already: the definition of a goodness of fit measure which helps to evaluate the effect of changes in the model specification. References HAZELL, P.B.R. & R.D. NORTON [1986], Mathematical Programming for Economic Analysis in Agriculture, London/New York: Macmillan Q. PARIS: CAPRI Meeting Follow-Up (Reggio Emilia) of a paper presented at the CAPRI Workshop in Reggio Emilia, Italy, May 1997. June 1997
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 97-09 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? 97-10: Patrick Gaffney; A Projection of Irish Agricultural Structure Using Markov Chain Analysis 97-11: P.Nasuelli, G.Palladino, M.Setti, C.Zanasi, G.Zucchi; A bottom-up approach for the CAPRI project 97-12: P.Nasuelli, G.Palladino, M.Setti, C.Zanasi, G.Zucchi; FEED MODULE: Requirements functions and Restriction factors