Impact of Direct Subsidies before and after the CAP’92

Reform – A Critical Analysis for Spain

August 11, 2005

Abstract

The economic effect of the introduction of direct subsidies of the CAP’92 reform isanalyzed in this paper using semi parametric and non-parametric methods. The esti-mated models explain the impact of the direct payments on efficiency and environmentaladaptation for animal orientated farms before and after the reform. We also study therelationship with other factors such as economic size. We use large samples of indi-vidual farms with joint animal and vegetal production in Spain, which are of specialinterest due to their relevance for Mediterranean forest and grazing land preservation.Using non parametric methods we do not restrict the production functions of the farms,e.g. when calculating effects on efficiency. Even though the direct payments increasedsharply after the CAP’92, in general, the new direct payment system turns out to beinsufficient to offset the fact that less environmentally friendly farms remain much more“efficient,” i.e. profitable for the farmer. Contrarily, after the CAP’92 reform, the sub-sidy schedule was even more correlated with farm size than before, which we find to becounterproductive.1

Keywords: Common Agricultural Policy, subsidies, efficiency, non-parametric meth-ods, natural resources, environmental economics.

1This research was supported by the Spanish “Direccion General de Investigacion del Ministerio de Ciencia

y Tecnologıa”, number BEC2001-1121, and SEJ2004-04583/ECON.

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1 Introduction and Motivation

The purpose of this paper is to study the effects of Direct Payments on factors such asefficiency before and after the CAP reform of 1992 (CAP’92). In particular we will lookat the impact on the efficiency of environmentally friendly, or in our case, animal adapted,farms.

Given the increasing role that direct payments will play in the future distribution of resourcesto support the farmers of the European Union, a quantitative framework to measure thedegree to which programs are biased either against or in favor of farm efficiency is highlyrelevant. The introduction of direct payments (DP), reinforced strongly by the CAP’92,was expected to have an important impact on efficiency as well as on the environmentaladaptation of farms.

For the preservation of large extensions of forest and grasslands in Spain the key farms arethose oriented to animal production partially based on their own (including rented) land’svegetal output. In fact, the Mediterranean forest and the traditional techniques of livestockraising are frequently close to ecological farming. Under the CAP, especially after the ’92reform, there was a potential contradiction between several policy targets: interventionprice reduction and a rise in the environmental adaptation of farms and improvement ofefficiency. We explore the ex-post effects on farms using a data-set of a representative sampleof individual holdings. Farm technologies allow for shifting between different proportionsof animal and vegetal products. The production frontier and efficiency index for each typeof farm are identified using DEA (Data Envelope Analysis) techniques. We address thedifferential impact of direct payments on relative efficiency differentiating the effects byfarm size and different levels of environmentally friendly adaptations.

One of our key results shows that, on average, absolute direct payments generally tend toincrease efficiency (in monetary terms) but not productivity (in physical terms). However,in most of the cases the mean efficiency decreases as the percentage of direct payments rises.So the CAP’03 idea of modulation or capping of direct subsidies in the future will potentiallyincrease the efficiency of the public expenses on DP.

For our purposes it is important to point out that the typical holdings with vegetal andanimal production can collect DP from several programs. We are interested in those types offarms because of their potential for cross-compliance. In fact, this type of land managementprovides important opportunities for a trade off between environment preservation and gainsin efficiency using intensive techniques. The most obvious alternatives are the choice in theproportions of animal nutrients cropped or grazed on the farm versus feedstuff providedby the industry. There is also the choice between traditional and specialized (intensive)livestock breeds. Note that the spread of epidemics is often strongly related to the ratio ofland per animal units. So for example the mad cow outbreak is a result of industrial feeding.

The current (i.e. the 2003) CAP reform is, in many ways, a step ahead on the basicprinciples and tools introduced in the CAP’92 reform to control over-production by reducingintervention price and DP to compensate farmers for their income losses.

Efficiency and environmental adaptation have become key issues in new European agricul-

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tural policy. The agreement of the Council of Ministers in June 2003 (Mid-Term Reviewof the Common Agricultural Politic [CAP MTR]), means a step towards the decouplingof income from prices and helps in reaching an agreement in the WTO. Additionally, CAPMTR introduces a modulation of the direct payment (e.g., limiting direct payments by size).In view of the new CAP reform (in force since 2005) it would be interesting to look back andstudy the effects of the previous reform CAP’92, especially regarding those aspects tackledby the recent reform.

The first step of the recent CAP reform was to introduce direct payments and cut theintervention price while trying to reduce intervention stocks. Just to give an idea of theimportance of DP: currently, due to the CAP, 4.50 million farmers benefit from subsidiesof 24.8 billion Euros at the EU 15 level. Part of that goes to Spain where 4.89 thousandbeneficiaries received 2.98 billion Euros. On average, the farms in Spain receive fewer inDP per holding than the average EU farm. Note also that so far, the allocation of directspending among farmers has been known to be unequal in two ways: First, the bulk ofdirect income support is concentrated in a few beneficiaries. For example, the Commissionacknowledges that in the 2000-01 financial year, only 12.2% of beneficiaries received 69.21%of all payments in 14 EU2 states. In the case of Spain, 9.3% of beneficiaries received 59.18%of all payments and 18.43% of the Spanish farmers received 75.86 per cent of DP. This ismainly due to the direct or indirect link of direct payments to economic size. Second, thedistribution of direct aid payments among animal type and / or crop is very asymmetricaland is spread over several regulations. The most important action under which farmersreceive income is the set-aside program and animal premiums. As a result, the percentage ofpayments which were directed towards arable crops and livestock in the year 2000 amountedto 92.71 and 79.78% of all payments in the EU and Spain respectively. With the informationavailable as to the distribution of direct income payments by crops, it is easy to contrastthe asymmetries on the distribution for Spain: under livestock premiums 185.4 thousandbeneficiaries received 974 million Euros while for arable crops 373.9 thousand of beneficiariesreceived 2.013 million Euros.

Surprisingly few empirical studies are available to contrast whether the CAP’92 incrementsin direct payments were followed by a rise in efficiency or environmental adaptation, orwether they have decreased the asymmetry between large and small holdings. Critics evenforecasted a negative incentive to improve productivity. Our aim is to analyze the distortionsin efficiency due to CAP subsidies before and after the CAP’92, and ascertain whether thedirect payments that farmers received actually resulted in more environmentally friendlyfarming. We also address the issue of the relationship between efficiency and size as it istheoretically unclear whether subsidies allow inefficient holdings to survive or help them tocatch up the production frontier. A second (hypothetical) scenario (calculating efficiencywithout direct payments) allows us to compare whether (before and after the CAP’92) directsubsidies helped farms to reach the efficiency frontier.

To study these questions, we decided to concentrate on only one country to guarantee certain2The 15 old Member States except Greece, for which no published data is available. Figures account for

the directs aids pay to farmers under the Reg. (EC) 1259/1999. Commission, MEMO/02/198 and AGRI

63569/2002

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homogeneity and reduce the variance. Note that the CAP is the same in all of the EU, soa single country can be interpreted as a case study for the impact of the CAP reform onefficiency. We decided to choose Spain for its large size (in surface its 7.2 millions of Ha ofgrazing lands and 3.4 millions of hectares of cultivated lands), export oriented agriculture(more than 55% of exports over the total output), with 37.9% of its agricultural outputin livestock raising in 2001 (MAPA, 2004 Anuario de Estadıstica Agraria 2003), and alsobecause of the availability of large data samples for each type of animal farming. It would berather difficult for us to do this study for Germany, for example, due to its policy of extremedata protection. In 2001 Spain accounted for 14.32% of the vegetal output and 11.08% ofanimal output of the EU15 (Eurostat, 2003. European Economic Accounts. SEC-95).

Therefore, the aim of this paper is to analyze the impact on efficiency of the sharp incrementof DP introduced by the CAP’92 reform. The way of modelling is not neutral to the results,for example, several papers assume functional forms that implicitly accept the existence ofconstant returns to scale or no limits for the scope of technical change. For our analysiswe always use non- or semi parametric methods when (mis-)specifications could provokeserious disturbances in our conclusions. This greatly increases the econometric effort as wellas the variance of our results but avoids any controversy as to the influence of subjectivemodelling.

The implications of this work are important for the future application of the recently ap-proved CAP Reform 2003 on an historical basis. Applying the CAP reform on “historicalbases” means translating the unequal distribution of subsidies throughout intervention pricesand direct subsidies into a single payment to each farm. Results can potentially be trans-lated into promoting the wrong type of farming, as in past years, for example, the conversionof price support into direct payments based on the previous year’s level of protection. Thuspotential implications of efficiency will affect agricultural competitiveness and have to becarefully analyzed.

The rest of the paper is organized as follows. In the next section we introduce the dataand methods we will use for our study. After that we dedicate a large section to thepresentation of the numerical results and their interpretations. Finally, we conclude. Sometechnical details of the procedures are given in the appendix of this article.

2 Data and Procedure

We use the Spanish sample data from the Farm Accounting Data Network (FADN) from1991-92 to 1999 and 2000 by type of animal farming with positive plant production. Thesame FADN survey provides detailed information on input expenditures by farm. For theselected farms, livestock production (meat and animal products) is always greater thanplant output (fodder, field crop, grain cereals, vineyards, potatoes, industrial crops, plants,fruits, dried pulses, olive groves and others) to ensure that we only include farms orientedto livestock raising. Plant production however is always positive in the selected sampleto ensure that the production function remains homogenous by type of animal farming.We only want to include farms with similar production functions, e.g. oriented to animal

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production, but also with the possibility of harvesting plant products for re-use on thefarm or for sale. We consider that farms with no-land (not even rented land) have a non-comparable production function and will therefore be excluded. For technical reasons whenusing DEA (Data Envelopment Analysis) the identification of an efficiency frontier is onlypossible if the individual production function of the farms is similar. Finally, as we areinterested in the impact on efficiency at a farm level, instead of using aggregated data wegathered individual farm accounting data that include any kind of direct payment received.

The producer level of direct support is measured by the total amount of direct paymentsin farm accounts; size by European Size Units (ESU), and livestock unit equivalents peragricultural utilized area (LU/AUA) as a proxy for measuring how environmentally friendlythe farm is, see discussion in the Introduction. In contrast, the output efficiency cannot bedirectly observed and will have to be calculated in a first step by DEA, see also Section 6.1.

Technical efficiency (or simply, efficiency) is measured using an index calculated with DEA,and again in a no subsidies “second scenario” by calculating an index ignoring the directpayments for each individual farm (for details see Section 6.1). The no direct subsidiesscenario efficiency index measures the level of efficiency distortion on the economic behaviorof the holding because under CAP there is a trade off between the choice of agriculturalproductions with a high level of subsidies, or other non-subsidized outputs. This allows us tocompare relative efficiency, with direct subsidies included in the efficiency index, to the casewhen the subsidies are eliminated in the so called “second scenario” efficiency calculations.We always assume the current prices for inputs and outputs. In the following we always referto EW (which corresponds more to productivity) when speaking of efficiency without directpayments, and to EDP (which includes “crop subsidies”) when speaking of conventionalefficiency.

The EW index measures the level of efficiency distortion on the economic behavior of theholding because under CAP it is possible to “crop subsidies” under certain conditions.Under the current multifunction farming, on top of the income for selling on the market,farmers qualify for rewards to compensate market failures by pricing positive externalities.In fact the farmer incurs an opportunity cost of not meeting the conditions to receive DP(e.g. minimum land per livestock head) when deciding the multi-product combination. As aresult of the complex regulation of products it is impossible to derive conclusions empiricallyabout the effect of the individual multi-product holdings on efficiency using aggregate data.

This leads us to calculate individual changes in relative efficiency by type of animal farmingwhen introducing compensations for positive externalities. The samples by type of animalfarming are used to calculate efficiency before and after CAP’92. This process can also bereferred to as the “natural experiment”. This experiment tracks the first time that directpayments by area and livestock units were introduced to check whether the CAP reformhad promoted efficiency and environmentally friendly practices. Moreover, we check howmuch economic size mattered when receiving subsidies before and after CAP’92.

We repeat efficiency calculations for two years before and two years after CAP’92, to testfor the influence of random weather variability (e.g. pasture availability). Furthermore, thesample is divided into type of animal farming (cattle farming, pig farming, and sheep and

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goat) as these farms are neither uniform in the treatment by CAP nor in the productionprocess. We did all calculations separately for each year.

Summarizing: All the above mentioned calculations were carried out for 1991, 1992, 1999and 2000 for cattle, pig, and sheep and goat farms. In Tables 1 and 2 the number of farmsthat are used for all the calculations are summarized, separated by year and animal type.

′91 ′92 ′99 ′00

sheep and goat 391 373 553 679cattle 2230 1787 1435 1543pig farming 126 161 255 249

Table 1: Number of farms used for all our calculations.

in absolute numbers in percentages′91 ′92 ′99 ′00 ′91 ′92 ′99 ′00

sheep and goat 82 35 0 0 21.0 9.4 0.0 0.0cattle 1373 1198 439 230 61.6 67.0 30.6 14.9pig farming 72 66 22 17 57.1 41.0 8.6 6.8

Table 2: Number of farms used for all our calculations not receiving direct payments.

Our DEA-model to calculate efficiency of production with two outputs and five inputs is asfollows:

OUTPUTS pbveg plant outputpbanim animal output

INPUTS capital capital, especially buildings and machinerycostsg fodder and other animal linked inputscosts inputs crop linked (fertilizer, agro-chemicals, seeds, water

and other crop specific inputs, fuels and lubricants)salary wagesland Agricultural Utilized Area of farm aggregate adjusted for quality

(thus including pasture and agricultural land adjusted for quality)nDP shadow price; the costs for producing without Direct Payments.

The shadow price (nDP) is calculated from direct payments including premium with anegative sign, therefore the notation “nDP”. In fact, in the DEA, any variable can beshifted by a constant without changing the results. Therefore, by taking the subsidies withnegative signs for each farm, and then adding the highest subsidies paid in that year, we geta number that gives us the costs to be paid for not producing in a subsidized way. Directpayments include any amount of of cash received under the CAP or national regulation

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and not linked to an amount of production (e.g. set aside payments, livestock premia, etc.)Capital input includes machinery, transport equipment and structures (not dwellings). Forsimplicity all animals are treated as variable stock. Land is considered as a separate inputvariable. Land area is adjusted by quality. This means that we calculated the value of input“land” by

land value = saureg * psaureg + sausec * psausec ,

where saureg: Agricultural Utilized Area (AUA) irrigated (Ha.); sausec: AUA non-irrigated(Ha.); psaureg: price AUA irrigated by region (Euros/Ha); psausec: price AUA non-irrigatedby region (Euros/Ha).

In the Appendix we give a brief introduction to the DEA method explaining in detail itsexact definition and indicating how it is calculated in practice. We conclude with threeremarks that can now be better understood:

As animal and plant outputs cannot be easily substituted, we must not aggregate them, butinstead consider the calculation of efficiency as a two dimensional output problem.

Including shadow prices representing the costs paid for not producing in a subsidized man-ner can also be understood as including direct payments as negative inputs. There are tworeasons then why we preferred not to consider them as a third output: First, many farmshave zero subsidies and would thus form a non-interpretable hyper-plane in the DEA; fur-thermore, the production factors considered do not produce our subsidies, so there is noreasonable argument for allowing them to appear on the left hand side of the productionfunction. The second reason is that in DEA, including a variable as output or as negativeinput will give the same interpretation for the efficiency.

It could be discussed whether more input variables should be aggregated for a non-parametricanalysis such as DEA, in order to get stronger results with respect to larger differences inthe resulting efficiency index for example. However, this question is nothing more than adiscussion of the bias dilemma – variance trade off: more aggregating leads to more biasbut less variance and vice versa. We have opted here for high resolution, in other words,high variance, small bias. Thus, since we always conduct non-parametric analysis with highresolution level, none of our results will suffer errors due to possible misspecification.

Once the efficiency index is calculated, we use the efficiency results to analyze the changescaused by the CAP’92 reform by different methods (correlations and semi parametric re-gression) .

As the policy faces different targets simultaneously such as productivity, cross compliance,and small farm protection, we need more sophisticated instruments to contrast these objec-tives.

More specifically, we use two regression models to study the level of compatibility betweendifferent targets of the new CAP, including environmental adaptation and competitivenessat the farm level. The objective is to quantify the impact on efficiency when the CAP’92

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increased the direct payments. Our model has efficiency as the dependent variable and theexplicative variable is environmental adaptation, filtering out the regional and size effects:

E = g[ln(EF ), ln(ESU)] + βT R + e , (1)

where E is first efficiency EDP , then productivity EW . EF indicates the environmentallyfriendly degree proxy measure, ESU is the European Size Unit, and R is a vector of dummyvariables for agricultural region divided into North, Center, Northeast, South and East.As we analyze the subsidies policy here, for a fair evaluation we have to choose the samemeasure that is applied by the European Community (i.e. Livestock Units per AgriculturalUtilized Area, i.e. LU/UAA).3 The LU/UAA is used in the European regulation and isgenerally considered a good proxy of the environmental performance of the farm, see alsoremarks in the Introduction. Note that the smaller the EF, the more “environmentallyfriendly” the farm. In the next section it will be seen how the comparison of these tworegressions (i.e. one with EDP , one with EW ) helps us to better understand the impact ofsubsidy policy in practice.

The function g : <2 → < is not specified further because the impact of ln(EF ) andln(ESU) turned out to be nonlinear and to have (strong) interaction. Finally, the “error”term e stands for the not further specified heterogeneity. As g(·, ·) is non-parametric, wecould have directly used the co-variates ESU and EF in the model (1). The logarithm ,therefore, does not impose any model specification here. This variable transformation is onlydue to smoothing necessities, see Appendix. The Appendix also explains in detail how theestimates of the function g(·) respectively β, presented in the next section, were calculated.

3 Empirical Results, Interpretation and Comments

We first of all calculate the efficiency with and without DP respectively with the aid of DEAas described in the previous section. These results will be used below for almost all of ourfurther conclusions relating efficiency with different economic and policy factors. In thissense it is mainly an auxiliary step. As a byproduct, based on these results we are also ableto check the effect of certain agricultural extension programs on efficiency.

In order to address the question “what are the subsidies related to in practice?” we mustfirst clarify the question of modelling. As we are interested in both absolute and relativemean increases, we have calculated all the following correlations and their p− values:

corr(DP, EW ), corr(ln(1 + DP ), EW )

corr(DP, ESU), corr(DP, ln(ESU)), corr(ln(1 + DP ), ln(ESU)), corr(ln(1 + DP ), ESU)

corr(DP, EF ), corr(ln(1 + DP ), EF ), corr(ln(1 + DP ), ln(EF )), corr(ln(1 + DP ), EF )

It is clear that when efficiency is calculated including DP, it will then be (positively) re-lated with DP. Therefore we considered here only EW , efficiency calculated without DP.

3The aggregation of the LU is made with the standard procedure used by FADN and EUROSTAT. The

variables come from the individual accounting collected under FADN normalization. The detailed input and

output information of each farm account is fully utilized to calculate the aggregate variables that include all

production costs.

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Recall that EW can also be interpreted as “productivity”. The numerical results for thesecorrelations can be found in Tables 3 to 5 separated only by animal-type.

Cattle ’91 ’92 ’99 ’00

corr(DP, EW ) -.023* .050 .011* .135corr(ln(1 + DP ), EW ) -.158 -.059 .110 .090

corr(DP, ESU) .100 .254 .657 .616corr(ln(1 + DP ), ESU) .050 .110 .137 .106

corr(DP, ln(ESU)) .127 .209 .488 .457corr(ln(1 + DP ), ln(ESU)) .024* .085 .226 .164

corr(DP, EF ) -.012* -.115 -.127 -.181corr(ln(1 + DP ), EF ) -.129 -.305 -.386 -.326

corr(DP, ln(EF )) -.037* -.294 -.413 -.431corr(ln(1 + DP ), ln(EF )) -.079 -.166 -.185 -.196

Table 3: Correlations for Cattle farms; an asteriks means not significant at 5% level.

Pigs ’91 ’92 ’99 ’00

corr(DP,EW ) .011* -.310 -.053* -.146corr(ln(1 + DP ), EW ) -.208 -.460 -.309 -.237

corr(DP,ESU) .133* .309 .489 .168corr(ln(1 + DP ), ESU) .327 .423 .183 .046*

corr(DP, ln(ESU)) .283 .351 .343 .211corr(ln(1 + DP ), ln(ESU)) .110* .298 .119* .028

corr(DP, EF ) .301 -.196 -.089* -.143corr(ln(1 + DP ), EF ) -.136 -.414 -.432 -.472

corr(DP, ln(EF )) .140* -.461 -.257 -.421corr(ln(1 + DP ), ln(EF )) -.119* -.114* -.131 -.384

Table 4: Correlations for Pig farms; an asterisk means not significant at 5% level.

For an easier interpretation, let us briefly summarize the signs we see in the tables beforeand after the CAP reform. Looking at the pair corr(DP, EW ), corr(ln(1 + DP ), EW ) weget the following schemata

cattle pig sheep and goat

Before CAP’92 0 – 0 – 0 –After CAP’92 + + – – + –

For corr(DP, ESU), corr(ln(1+DP ), ESU), corr(DP, ln(ESU)), corr(ln(1+DP ), ln(ESU))we get the vectors of signs

cattle pig sheep and goat

Before CAP’92 + + + + + + + + + + + +After CAP’92 + + + + + + + + + + + +

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Sheep and Goat ’91 ’92 ’99 ’00

corr(DP,EW ) .034* -.048* .048* .092corr(ln(1 + DP ), EW ) -.057* -.160 -.205 -.096

corr(DP,ESU) .223 .298 .968 .973corr(ln(1 + DP ), ESU) .310 .303 .856 .830

corr(DP, ln(ESU)) .419 .450 .614 .625corr(ln(1 + DP ), ln(ESU)) .099 .159 .596 .571

corr(DP, EF ) .014* .023* -.082* -.086corr(ln(1 + DP ), EF ) -.064* -.143 -.271 -.275

corr(DP, ln(EF )) .060* .032* -.272 -.285corr(ln(1 + DP ), ln(EF )) -.072* -.090* -.127 -.130

Table 5: Correlations for sheep and goat farms; an asterisk means not significant at 5%level.

And finally, looking at corr(DP, EF ), corr(ln(1+DP ), EF ), corr(DP, ln(EF )), corr(ln(1+DP ), ln(EF )) we get the schemata of signs

cattle pig sheep and goat

Before CAP’92 – – – – 0 – 0 – + – + –After CAP’92 – – – – – – – – – – – –

As to the relation between subsidies and efficiency we find that before CAP’92 there isno positive impact of subsidies on productivity (EW ). Looking at the effect of relativesubsidy increase, the impact is even negative. Something similar happens during the periodfollowing CAP’92, except in the case of cattle farms. However, the impact of absoluteincrease of subsidies on productivity is positive for cattle, and sheep & goat, but negativefor pig farms after ’92.

Turning to the relationship between direct payments and economic size, we see that before,as well as after the CAP’92, this is always (clearly) positive. This means that no matterwhether we measure in absolute or relative terms, the policy always benefits the larger farmsmore strongly.

Finally, regarding the relationship between DP and EF (recall that the higher the EF themore intensively), we see no change of signs for cattle farms (always negative), but some forpigs, and sheep & goat farms respectively. There, along the detected signs the relationshipbetween subsidies and extensive farming has increased after CAP’92.

We now come to an interpretation of the level results which can be seen in tables 3 to 5.Again we start with the relation between DP and productivity (EW ) looking first at thelevels. Here, we hardly see any changes after the CAP’92 in any type of farm with almostall of them being close to zero. When subsidies rise in relative terms we detect significantchanges only for cattle farms. Apart from this, note that at the same time we see a positivecorrelation between subsidies and efficiency when looking at the absolute amounts; in almost

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all cases the mean efficiency decreases as the percentage of direct payments rises in. Thismeans that a combination of direct subsidies and size would be counterproductive.

So, let us look now at the relation between DP and economic size. For any modeling thecorrelation strongly increases for cattle and sheep & goat after the CAP’92, actually over90% in some cases. In other words, since the CAP’92, the level of subsidies can mainlybe related to farm size. That is not surprising since set-aside payments and animal premiaare related to the area and number of animals respectively. This is quite contradictory tothe policy’s claim of protecting small farmers. Currently, direct payment correlation withfarm size shows the level of real “modulation” of the post CAP’92 subsidies. Thus, ourresults are also congruent with the generally accepted hypothesis that direct subsidies arebasically (even if indirectly) linked to output level. So it is difficult to defend the presumabledecoupled characteristic of these aids. Moreover, our findings indicate a strong coupling ofsize and premia since CAP’92, except for pig farming.

Turning finally to the target of supporting environmentally friendly farming (in our contextof dealing with animal farms this can be translated to mean“extensive” farming), we donot find as clear a trend as we saw for economic size. Indeed, the results differ somewhatwith the modeling, see e.g. Table 4, in sign as well as in level. Therefore we will use a moresophisticated approach to deal with this problem, see the discussion of our nonparametricregression results below.

As mentioned above, for a further analysis we need to relate the efficiency and / or produc-tivity to size, EF , and regions via a proper regression model. For this purpose we considernow

E = g[ln(EF ), ln(ESU)] + βT R + e , (2)

with E being EDP (DP included in model) or EW respectively (DP not included in model).By comparing the results of these two regressions (i.e. using two different dependent vari-ables), we will see how the CAP policy distorts the efficiency of an individual farm. Theestimation procedures applied here will be explained in detail in the Appendix.

First, let us look at the regional effects before and after CAP’92, (i.e. the estimates of theβ in regression model (2)). We divided Spain into 5 regions: North, Center, Andalusia,Ebro (along the Ebro river), and Levante. The last one has been used as a normalizingregion. Note that Andalusia could be replaced by “South”, and Levante by “East”. Ebrostands for the northeastern Spanish region including the northeastern Mediterranean coastand the Ebro river valley with a mainly Mediterranean climate that traditionally has beenconsidered to be a homogenous agricultural region. All numerical results are given in Tables6 to 9.

Before CAP’92: Surprisingly, the North was less efficient in cattle farming whereas thecenter is more efficient than other regions. In pig farms as well as with sheep and goats, allregions seem to be very close except for the ones in Levante.

After CAP’92: Surprisingly, the North and Ebro seem to be less efficient. These resultsare only insignificant for pig farming in 2000 and in 1999 when looking at EW . For cattlefarming, Levante seems to be best, though not significantly better than the center and the

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dep. var. North Center Andalusia Ebro

CattleEDP -0.0456 0.17394 -0.0293 –

0.02882 0.02889 0.03777 –EW -0.0503 0.16486 -0.0281 –

0.02790 0.02796 0.03656 –

PigEDP -0.0561 -0.0055 -0.1349 –

0.15622 0.03757 0.06438 –EW -0.0540 -0.0036 -0.1327 –

0.15644 0.03762 0.06446 –

Sheep and GoatEDP -0.4545 -0.4618 -0.4585 -0.4520

0.16941 0.16233 0.16977 0.16230EW -0.4739 -0.4722 -0.4559 -0.4703

0.16441 0.15754 0.16475 0.15751

Table 6: Estimates (upper lines) with standard error (lower lines) for the regional effects in1991. In 1991 we have neither pig nor cattle farms observed in Levante, the reference regionis Ebro, or else Levante.

south. These findings hardly change between the model with dependent variables EDP andits counterfactual opposite, using EW .

These results might intuitively surprise experts in Spanish animal farming although we mustpoint out here that in Levante we only have fewer than 10 farms in the sample, which turnedout to be technically quite advanced holdings. As we are not so much interested in analyzingthe regional differences, but only wished to correct for regional effects, this is fortunatelynot a reason for further concern.

As the functional form of g(·, ·) in model (2) is non-parametric, the results are given graphi-cally, see Figures 2 to 7 where we displayed the numerical results for g(·, ·). Note that g(·, ·)is a three dimensional graph throughout. Along our empirical results, the two regressorsln(EF ), ln(ESU) unfortunately do not enter additively. That means, as can be seen in Fig-ure 1, that it is not enough to look at the purely marginal effects of ln(EF ), and ln(ESU)respectively, because they have strong interaction. However, for ease of presentation wedecided not to show the three dimensional graphs but did present the marginal impacts ofln(EF ) (on EDP and EW ) of the median sized farms (solid line), the large farms (the upper95% quantile farms, dotted line), and the small farms (the lower 5% quantile farms, dashedline). The three resulting (2 dimensional) functions represent three slices of the three di-mensional plot. However, for a better understanding we also provide the three dimensionalplot of g(·, ·) for cattle farms in 1991, see Figure 1. In all of the graphs shown, the outer 2%

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dep. var. North Center Andalusia Ebro

CattleEDP -0.0526 0.13902 -0.0576 –

0.02871 0.02847 0.03337 –EW -0.0509 0.11145 -0.0541 –

0.02834 0.02811 0.03294 –

PigEDP -0.0837 -0.1672 -0.0170 -0.1007

0.13541 0.12468 0.14456 0.12193EW -0.0789 -0.2114 -0.0686 -0.1203

0.13201 0.12155 0.14093 0.11887

Sheep and GoatEDP -0.3565 -0.3415 -0.3350 -0.3739

0.18921 0.17782 0.18102 0.17911EW -0.3779 -0.3900 -0.3822 -0.3992

0.18341 0.17237 0.17547 0.17362

Table 7: Estimates (upper lines) with standard error (lower lines) for the regional dummiesin 1992. In 1992 we have no cattle farms observed in Levante, the reference region is Ebro,or else Levante.

are cut off (i.e. not plotted) to avoid interpreting the boundary effects.

ln EF -0.800.22

1.24

1.26 2.07 2.89

ln ESU

0.55

0.72

0.90

-0.800.22

1.24

ln EF1.262.072.89

ln ESU

0.53

0.71

0.90

Figure 1: Cattle farms in 1991, with dependent variable EDP (left), respectively EW (right).

First, let us have a look at the differences between the regression of EDP (efficiency withdirect payments) compared to regression of EW (efficiency without direct payments, also

13

dep. var. North Center Andalusia Ebro

CattleEDP -0.4617 -0.2189 -0.3761 -0.4907

0.10397 0.10400 0.11497 0.10549EW -0.4672 -0.2537 -0.3298 -0.5062

0.10214 0.10217 0.11295 0.10364

PigEDP -0.3459 -0.0607 0.08320 -0.0926

0.15810 0.04511 0.08340 0.03744EW -0.2148 -0.0158 0.12308 -0.0410

0.15722 0.04486 0.08294 0.03723

Sheep and GoatEDP -0.1201 -0.0228 -0.0901 -0.1380

0.06367 0.04137 0.05517 0.04526EW -0.1459 -0.0326 -0.0989 -0.1851

0.05864 0.03811 0.05081 0.04168

Table 8: Estimates (upper lines) with standard error (lower lines) for the regional dummiesin 1999. The reference region is Levante.

dep. var. North Center Andalusia Ebro

CattleEDP -0.4192 -0.1790 -0.3592 -0.4065

0.08852 0.08943 0.10014 0.09058EW -0.4233 -0.2001 -0.3419 -0.4030

0.08752 0.08842 0.09901 0.08955

PigEDP -0.0329 -0.0160 0.20771 -0.0460

0.11033 0.05789 0.09105 0.04707EW -0.0948 -0.0195 0.05673 -0.0431

0.10395 0.05454 0.08578 0.04434

Sheep and GoatEDP -0.1049 -0.0726 -0.2321 -0.2156

0.05082 0.03033 0.03679 0.03437EW -0.0969 -0.0667 -0.2181 -0.2632

0.04845 0.02891 0.03506 0.03276

Table 9: Estimates (upper lines) with standard error (lower lines) for the regional dummiesin 2000. The reference region is Levante.

14

-1 0 1 2

ln(EF)

0.4

0.6

0.8

effi

cien

cy

-1 0 1 2ln(EF)

0.4

0.6

0.8

effi

cien

cy

-2 -1 0 1 2

ln(EF)

0.6

0.8

effi

cien

cy

-2 -1 0 1 2ln(EF)

0.6

0.8

effi

cien

cy

Figure 2: Cattle farms in 1991 (upper row) and 1992 (lower row), EDP on ln(EF ) (left),and EW on ln(EF ) (right).

-2 -1 0 1 2

ln(EF)

0.8

1

effi

cien

cy

-2 -1 0 1 2

ln(EF)

0.8

1

effi

cien

cy

-2 -1 0 1 2

ln(EF)

11.

2

effi

cien

cy

-2 -1 0 1 2

ln(EF)

11.

2

effi

cien

cy

Figure 3: Cattle farms in 1999 (upper row) and 2000 (lower row), EDP on ln(EF ) (left),and EW on ln(EF ) (right).

called productivity). Before the CAP’92 reform (Figures 2, 4, 6) we see almost no differencesbetween the two regressions, except for sheep & goat in 1991. This could be interpreted asthere being no effect of direct payments on efficiency versus productivity. In other words,

15

-4 -3 -2 -1 0 1 2 3

ln(EF)

0.8

11.

21.

4

effi

cien

cy

-4 -3 -2 -1 0 1 2 3

ln(EF)

0.8

11.

21.

4

effi

cien

cy

-4 -3 -2 -1 0 1 2 3

ln(EF)

0.8

1

effi

cien

cy

-4 -3 -2 -1 0 1 2 3

ln(EF)0.

81

effi

cien

cy

Figure 4: Pig farms in 1991 (upper row) and 1992 (lower row), EDP on ln(EF ) (left), andEW on ln(EF ) (right).

-3 -2 -1 0 1 2 3 4 5

ln(EF)

0.8

11.

2

effi

cien

cy

-3 -2 -1 0 1 2 3 4 5

ln(EF)

0.8

11.

2

effi

cien

cy

-3 -2 -1 0 1 2 3 4 5

ln(EF)

0.8

1

effi

cien

cy

-3 -2 -1 0 1 2 3 4 5

ln(EF)

0.8

1

effi

cien

cy

Figure 5: Pig farms in 1999 (upper row) and 2000 (lower row), EDP on ln(EF ) (left), andEW on ln(EF ) (right).

there was no advantage to being an environmentally friendly or a small family farm whenreceiving subsidies.

This changes with the CAP’92 reform depend on the type of animal farm. For cattle farms

16

-2 -1 0 1 2 3

ln(EF)

11.

21.

41.

6

effi

cien

cy

-2 -1 0 1 2 3

ln(EF)

11.

21.

41.

6

effi

cien

cy

-2 -1 0 1 2 3

ln(EF)

11.

21.

4

effi

cien

cy

-2 -1 0 1 2 3ln(EF)

11.

21.

4

effi

cien

cy

Figure 6: Sheep and goat farms in 1991 (upper row) and 1992 (lower row), EDP on ln(EF )(left), and EW on ln(EF ) (right).

-3 -2 -1 0 1 2

ln(EF)

0.6

0.8

1

effi

cien

cy

-3 -2 -1 0 1 2

ln(EF)

0.6

0.8

1

effi

cien

cy

-3 -2 -1 0 1 2

ln(EF)

0.8

11.

2

effi

cien

cy

-3 -2 -1 0 1 2

ln(EF)

0.8

11.

2

effi

cien

cy

Figure 7: Sheep and goat farms in 1999 (upper row) and 2000 (lower row), EDP on ln(EF )(left), and EW on ln(EF ) (right).

(Figure 3) we again obtain the same results for the two regressions, whereas for pig holdingsthe DP now favor the extensive and in particular the large holdings (compare Figure 5 leftwith right side). Since DP do not exist per pig head, this is possibly due to DP related to

17

crop and environmental issues which would explain that the large farms benefit especially.E.g. Iberian pigs grazing in the Mediterranean forest need large plots of land for grazing butare quite profitable due to the high prices their meat yields on the market. Also for sheep& goat farms, we see after the CAP’92 that now including DP in the efficiency changes theregression, see Figure 7. For any size of farm it seems that the DP especially favor farmsthat are identified as being intensive holdings.

We conclude with an animal by animal type analysis of our graphs, starting with the cattlefarms. Comparing the numerical results from before with those after the CAP’92 reformwe detect that extensive farms are not better situated (compared to intensive holdings) interms of relative efficiency levels. Also the efficiency rankings by size remain unchanged bythe ’92 reform. In any case, it is hard to make clear statements because the results varygreatly with the years (i.e. climate). Focusing only on the median farms, one might saythat after the CAP reform the efficiency difference between intensive and extensive farmshas become smaller. The scenario without direct subsidies upholds all our results.

The efficiency of the intensive pig farms is clearly above that of the environmentally friendlyfarms before, and also after the CAP reform. However, after ’92 the distance to the moreenvironmental friendly farms has also become smaller, i.e. the plotted functions have flat-tened. The scenario ignoring the subsidies when calculating the efficiency, upholds theseresults as well.

Finally, when looking at the sheep & goat we find the following. Before CAP’92 there isa clear positive impact of ln(EF ) on efficiency (both, EDP and EW ) for any size of farm,whereas this impact becomes strongly U-shaped after CAP’92. This means that extensiveholdings are now relatively better off than before. However, this statement is only true forsmall and median sized farms. Furthermore, the rankings by size changed after ’92 puttingthe small farms in a better situation than before. In any case, the large, intensive farmsremain at all times the most productive and efficient ones even though these differencesnarrowed after ’92.

4 Conclusions

The results clearly show the real difficulties of the reformed CAP in reaching the objectiveof increasing the efficiency and the environmental orientation of the farms simultaneously.The introduction of direct payments was thought to be a potential source of efficiencydistortions. The results show a positive correlation between subsidies and efficiency whenlooking at the absolute amounts. However, the mean efficiency decreases or stagnates asthe percentage of direct payments rises. This holds for all type of farms, except for cattlefarms, after the CAP reform. This means that a combination of direct subsidies and sizeis counterproductive. Unfortunately, our results also clearly show that this is what thesubvention policy after CAP’92 was doing: farm size explains about 90% (or more) of thedirect payments. Note further that the strong subsidization of large farms cannot be justifiedwith their presumably high efficiency nor environmental friendliness. Neither our graphical

18

nor our numerical results confirm such a hypothesis; they may, in fact, even contradict it.4

We have found that the direct payment system introduced by CAP’92 is positive but notsufficient to correct the fact that the less environmentally friendly farms are the most effi-cient ones. The most conventional (intensive) hog holdings reach efficiency levels similar tothose of the environmentally friendly farms when accounting for direct payments (or viceversa). But the less environmentally adapted farms are still the most efficient. Nevertheless,together with the numerical results on correlations, we conclude that there is empirical evi-dence that the current direct payments system is “environmentally oriented” for all types offarms studied (a decreasing level of direct payments as the livestock units per agriculturalutilized area increases). But the empirical results, especially for sheep and goat, and cattlefarming, show that there is room for improvement of the environmental implementation ofthe CAP.

The conclusion that the direct subsidy structure (after ’92) plays a significant role in help-ing farms to preserve the natural environment under competitive conditions is empiricallysupported by our results. To further investigate this point we directly calculated differentcorrelations between subsidies and EF and tested them for significance. These results showa significant positive correlation of the direct subsidies and the proxy of adaptation to thenatural environment, i.e. direct payment negatively correlated with LU/AUA, for the lastyears over all models considered. That makes a difference with the situation before theCAP reform when we can not find a significant correlation between direct payments andenvironmental adaptation.

Economies of scale are important in the current animal farming, but we found severalexceptions: The smaller pig farms particulary perform rather well and are competitive.Also in the second scenario, looking at efficiency without subsides supports these results.We cannot make such a clear statement for cattle farming nor for sheep & goat.

Nevertheless, the small cattle farms are above the mean efficiency index. The scenario ofefficiency without direct subsidies upholds these result. That is, it reflects the shortcomingsof the managers in running the farm and solving technical problems when the economicsize increases above a certain threshold. This finding fits perfectly with the conclusions ofAlvarez and Arias (2003), who pointed out the decrease of efficiency with the farm size dueto lack of human capital. The correlation results before CAP92 reform in general showlower coefficients between direct payments and economic size. Scale economies are possiblein the present state of the art since, in general, the biggest farms obtain the highest levelsof efficiency for all animal types. This result also holds true in the second scenario (no DP).It is important to add here that the economic size impact on efficiency often interacts withthe environmental behavior, and that this impact (i.e. the one of ln(EF )) on efficiency isoften much stronger than the size effect. The result of the second scenario does not seem toreveal an impact on the efficiency of the small farms versus the medium farm.

After the reform, direct payments do not seem to positively discriminate (helping to raiserelative efficiency) by size and adaptation to the natural environment. Again, especially forpig farming, small intensive farms seem to be above the mean efficiency index and above the

4Another problem is the equity aspect of the CAP not dealt with here, see Mora and San Juan (2005).

19

biggest farms. The scenario of ignoring the subsidies when calculating the efficiency supportsthese results as well. The direct payments do not increase the efficiency of environmentallyfriendly farms compared with conventional (intensive) ones.

Summarizing, we are afraid our comparison of the situation before with that of after theCAP’92 reform of the animal farms, cannot lead us to conclude that the claimed objec-tives would have been reached; neither the small nor the more environmentally adaptedfarmers benefit from the subsidy policy whereas the large ones mainly do. This, moreoveris counterproductive. The changes we have observed for Spain due to the CAP’92 reformare marginal, although visible in some cases, concerning the claimed objectives, but strongconcerning the non-claimed objectives (e.g. linked to economic size).

5 Appendix

6 Methodologies

Even though these methodologies are not completely new, part of the readership might notbe familiar either with DEA or with nonparametric regression. Therefore we give here abrief insight in order to achieve a better understanding and interpretation of the resultspresented later.

6.1 Estimation of (Technical) Efficiency

Data envelopment analysis (DEA) is a non-parametric approach using linear programmingmethods to determine the envelopment of the DMUs (decision making units) and in thisway identifying “the best practice” for each productive unit.

Measures are calculated relative to this frontier for each individual Debreu-Farrell efficiency(see Cooper, Seiford and Tone (2000) for a comprehensive description of the methodology).The main advantage of DEA is that there is no need to specify a particular functional formfor the production frontier, though the assumption that there is no random error might beseen as a drawback.

We introduce here some basic concepts of non-parametric efficiency measurement. Letx ∈ <p and y ∈ <q

+ denote input and output vectors with which we define the following setof the feasible input-output combinations:

Ψ = {(x, y) ∈ <p+q : x can produce y}. (3)

For any y ∈ <q+ we then define the input requirement set as

X(y) = {x ∈ <p : (x, y) ∈ Ψ}, (4)

where the input efficient frontier is defined by the isoquant

δX(y) = {x ∈ X(y) : θx /∈ X(y) ∀θ < 1} . (5)

20

The corresponding Farrell input-oriented measure of technical efficiency (Farrell, 1957) isspecified as the distance function

θ(x, y) = inf{θ : θx ∈ X(y)} . (6)

So θ(x, y) defines the input technical efficiency (the maximum contraction) along a fixed rayaway from the efficient input. For example a value of θ(x, y) = 1 means that the produceris input efficient while a value of θ(x, y) < 1 indicates that the producer is input inefficientand he may reduce inputs in that proportion while maintaining the output level.5

The estimation of these concepts requires some assumptions (see Fare, Grosskopf and Lovell,1994) for both the production possibility set (mainly convexity and free disposability ofinputs and outputs) and the distance function. In any case, and under some regularityassumptions on the data generating process specified in Kneip, Park and Simar (1998),DEA allows consistent estimation of the above concepts (see Simar and Wilson (2000) andKneip, Simar and Wilson (2003) for a review of DEA statistical properties).

For a sample of n producers, the DEA estimate of the production set under the leastrestrictive returns to scale assumption (i.e. variable returns) is:

Ψ = {(x, y) ∈ <p+q : x ≥n∑

i=1

γixi, y ≤n∑

i=1

γiyi,n∑

i=1

γi = 1, ∀γi ≥ 0}, (7)

where γi is the intensity vector of firm i and it defines its best practice or benchmark firmby a linear combination of all the firms observed in the sample.

The DEA estimates of equations (4) and (5) are then

X(y) = {x ∈ <p | (x, y) ∈ Ψ}, (8)

δX(y) = {x ∈ X(y) | θx /∈ X(y) , ∀θ < 1}, (9)

while the estimation of the Farrell technical efficiency measure (Farrell 1957) is computedby linear programming techniques as follows:

θ(xj , yj) = min{θ :n∑

i=1

γixi ≤ θxj , yj ≤n∑

i=1

γiyi ,

n∑

i=1

γi = 1 , ∀γi ≥ 0}. (10)

The analyzed firm j is technically efficient if and only if θ(xj , yj) = 1 and it is placed on theestimated frontier while a value as θ(xj , yj) < 1 means that the firm is inefficient.

6.2 Regression Analysis

As mentioned in the main text, we do not want to assume any particular functional formon g(·, ·) except that it is a smooth function, i.e. has continuous second derivatives.

5Alternatively, one could formulate (5) to (6) as an output oriented problem. However, in practice, the

interpretation is then often more complicated, in particular considering how to include direct payments in

the production function.

21

We explain the estimation of the parameters β and the asymptotic covariance of the esti-mators, as well as the estimation of the non-parametric function of g(·, ·) in a semipara-metric model of the form as described in equation (1). We assume E[e|EF,ESU,R] = 0,V ar[e] < ∞. The estimation of g(·) and β will be made in two steps: first the estimationof β and its covariance using the method of Robinson (1988), and afterwards the estimationof g(·, ·) using local linear smoothing by Ruppert and Wand (1994). For a more detailedintroduction to non- and semi-parametric modelling see also Hardle, Muller, Sperlich, andWerwatz (2004).

The basic idea is to construct an estimator that gives simply a smooth surface (or hyper-plane), e.g. in the one dimensional case a smooth line, that fits best into the point cloud ofreal observations. The smoothness of that surface can be (pre-) determined by choosing arespectively large smoothing parameter h , called bandwidth. Actually, this parameter canalso often be data driven.

First, it is important to understand that this estimator works locally, e.g. we estimate thedesired function, the hyper-plane, separately at each point we are interested in. Thereforewe need to introduce some additional notations. Consider for a moment a regression problemof the form E[Y |X = x0] = G(x0), Y ∈ < ,X, x ∈ <d with G(·) : <d → < being an unknownsmooth function. Imagine we aim to estimate G(x0) for some point x0 ∈ <d. Havingobserved {Xi, Yi}n

i=1 , this can be done by local least squares:(

G(x0)∇G(x0)

)= argmin

a0,a1

n∑

i=1

{Yi − a0 − aT

1 (Xi − x0)}2

Kh(Xi − x0) , (11)

a0 ∈ <, a1 ∈ <d and ∇G(·) being the gradient of G(·). Further, Kh(v) =∏d

j=11hK(vj

h ) is a<d → < weight function. In our calculations we chose K(v) = 15

16(1− v2)211{|v| ≤ 1}. So weused a weighted least squares estimator for linear regression that becomes a local (linear)estimator due to the weights Kh giving a lot of weight to points (Xi, Yi) where Xi is closeto x0 but zero weights to points far from x0. Consistency, asymptotic theory and propertiesare well known and studied for the multivariate case in Ruppert and Wand (1994). For ageneral introduction see Fan and Gijbels (1996).

If we eliminate the vector a1 in equation (11) and thus maximize only over a0, the mini-mizing argument is a local constant estimator of G(x0). In this case it is easy to give theexplicit formula:

G(x0) =∑n

i=1 Kh(Xi − x0)Yi∑ni=1 Kh(Xi − x0)

. (12)

As one can see, in the weighting function, the smoothing parameter h comes in: the largerthe h, and consequently the environment with positive weighting, the smoother the resultinghyper-plane (i.e. h → ∞ gives a linear function for G whereas h = 0 yields a G being theinterpolation of the Yi’s). In a context such as ours, the choice of the smoothing param-eter should be considered as degrees of freedom which would be chosen, i.e. the empiricalresearcher would allow for more flexibility or impose more smoothness on its functions. Toallow for high flexibility without increasing the variance to unreasonable levels, we chosesmoothing parameters that did not restrict the functional forms unless the plotted surfacebecame wiggly.

22

Coming back to our model (1), we will apply the local linear estimation method, i.e. equation(11), on {Wi := (ln(EFi), ln(ESUi)), (Ei − βRi)}n

i=1. The remaining question is how to getβ. The estimator of β is defined as

β = S−1R−R,R−R

SR−R,E−E (13)

where for any matrix or vector sequences Ri, Bi we set SR,B = 1n

∑ni=1 RiB

Ti and Ri =

E[Ri|Wi], Bi = E[Bi|Wi] with Bi being either Ri or Ei. We estimate the conditionalexpectations (E) via local constant smoother as defined in the equation (12). It is easyto see that the variance of β can be estimated by σ2S−1

R−R,R−Rwith σ2 being a consistent

estimator of the conditional variance of E: σ2 = V ar[E|Wi, Ri]. For more details seeRobinson (1988).

Furthermore, note that as g(·, ·) is non-parametric, we could have directly used the co-variates ESU and EF in the model (1). As mentioned above, the logarithm therefore doesnot impose any model specification here. The problem is that both variables have a ratherskewed distribution with many data-sparse areas. In contrast, ln(ESU) as well as ln(EF )look quite normal around the mode with rather short tails at the end. It is thus only forthe sake of a reasonable behavior of our smoothing techniques that we prefer to apply oursmoothing methods on the log-transformed data, see also Biedermann and Dette (2003) formore details.

In non- and semi-parametric regression, the choice of smoothness controlled via the band-width (named h in Section 6.2) and chosen by the empirical researcher, is often either notdiscussed or quite controversial. Therefore, we tried out several bandwidths and presenthere the results for those where the estimated surface starts to become smooth. In practice,for two dimensions and smooth densities as we have in this application, this provides a rea-sonable trade-off between bias and variance of the estimates. For the parametric part β ofmodel (1) it should be emphasized that the results for the (semi-) parametric estimation ofthe regional dummies turned out to be quite robust with respect to the bandwidth choice forthe non-parametric part. This is expected if for example the regional dummies are almostuncorrelated with the other covariates (ln(ESU) and ln(EF ) in our case). More details onthe methodology are available on request.

References

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