What Drives Marginal Abatement Costs of Greenhouse Gases on Dairy Farms? A Meta-modelling Approach

What Drives Marginal AbatementCosts of Greenhouse Gases on DairyFarms? A Meta-modelling Approach

Bernd Lengers, Wolfgang Britz and Karin Holm-Muller1

(Original submitted April 2013, revision received July 2013, accepted October2013.)

Abstract

This paper examines the relationships between the marginal abatement costs(MAC) of greenhouse gas (GHG) emissions on dairy farms and factors such asherd size, milk yield and available farm labour, on the one hand, and prices, GHGindicators and GHG reduction levels, on the other. A two-stage Heckman proce-dure is used to estimate these relationships from a systematically designed set ofsimulations with a highly detailed mixed integer bio-economic farm-level model.The resulting meta-models are then used to analyse how MAC vary across farm-level conditions and GHG measures. We nd that simpler GHG indicators lead tosignicantly higher MAC, and that MAC strongly increase beyond a 15% emis-sion reduction, depending on farm attributes and the chosen indicator. MACdecrease rapidly with increasing farm size, but the eect levels o beyond a herdsize of 40 cows. As expected, the main factors driving gross margins per dairy cowalso signicantly inuence mitigation costs. Our results indicate high variability ofMAC on real life farms. In contrast to time consuming simulations with the com-plex mixed integer bio-economic programming model, the meta-models allow thedistribution of MAC in a farm population to be eciently derived and thus couldbe used to upscale to regional or sector level.

Keywords: Dairy farms; greenhouse gas indicators; Latin-Hypercube sampling;marginal abatement costs; meta-modelling.

JEL classifications: Q12, Q52, C34, C99.

1Bernd Lengers is a Research Assistant at the Institute of Food and Resource Economics, Uni-versity of Bonn, Germany. E-mail: [email protected] for correspondence. Wolf-

gang Britz is a Researcher and Karin Holm-Muller is Professor at the same Institute. Theresearch is funded by a grant of the German Science Foundation (DFG) with the referencenumber HO 3780/2-1. The authors thank anonymous referees for their comments on an earlier

version of this paper.

Journal of Agricultural Economics, Vol. 65, No. 3, 2014, 579599doi: 10.1111/1477-9552.12057

2014 The Agricultural Economics Society

1. Introduction

The mitigation of greenhouse gases (GHGs) from agricultural production processes isbroadly discussed from a political and a scientic viewpoint, both with regard toabatement costs (AC) (Anvec, 2011; DeCara and Vermont, 2011) and whether andhow to incorporate agriculture into GHG reduction eorts (e.g. Ramilan et al.,2011). Any decision on policy instruments and potential reduction levels requiresknowledge about possible abatement options, abatement potentials and, in particular,related abatement costs. For political purposes, knowledge about the marginal abate-ment costs (MAC) is of high relevance as these costs determine the mitigation poten-tial under each price-based GHG mitigation policy. Farmers will only mitigate GHGsas long as MAC for GHGs are below the CO2-equivalent prices.Various studies (see section 2) are available regarding possible abatement strategies

and potential GHG savings from agriculture, oering a wider range of MAC esti-mates. However, these are hard to generalise as they depend on factors not systemati-cally controlled for, such as exogenous assumptions on prices, farm characteristics,the model or estimation structure or the GHG indicator used. A GHG indicator isnecessary as an accounting scheme for GHG quantication, since direct measure-ments are not possible on farms. Published meta-analyses on MAC by Vermont andDeCara (2010) as well as Kuik et al. (2009) only investigate dierences in methodo-logical approaches and assumptions. To our knowledge, no study exists which system-atically analyses drivers of dierences in MAC and thus farm income changesprovoked by GHG-related policy instruments. Yet this is certainly a signicant aspectof the policy debate about inclusion of agriculture in emission reduction eorts. Wedevelop and illustrate a methodology for meta-analyses and apply it to dairy farmconditions in a larger German region to provide an analysis of these issues.The evidence, for example from Lengers and Britz (2012), about dierences in

MAC between farms and the necessity of GHG reduction policies to use GHG indica-tors (Scheele et al., 1993, p. 298), gives rise to two major questions. (1) Which are themost important farm characteristics impacting MAC and what are their quantitativeeects? and (2) What is the relationship between the applied GHG indicator and otherdrivers such as prices and MAC?Answering these questions requires a set of farm-level observations of MAC with su-

cient variation in key factors, but time and cost considerations exclude real-life experi-ments for a reasonable group of existing farms. But even simulating abatement strategieswith a computer model for a larger set of farms can be a time consuming exercise. Wetherefore conduct a representative sample of what-if simulations following DOE-principles (design of experiments: Kleijnen, 1999, 2005) with the single farm modelDAIRYDYN, a highly detailed bio-economicmodel for specialised dairy farms. The focuson dairy farms is motivated by their high share in German agricultural GHG emissions.From these simulation results we derive meta-models for a simple and a rather

detailed GHG indicator which allow us to analyse the relationships between MACand key factors such as predened characteristics of dairy farms, prices and GHGreduction level. The meta-models summarise the behaviour of the underlying, morecomplex simulation model and show how MAC depend on these factors and theapplied GHG indicator over the range of varying circumstances of real farms. Ourndings complement the existing literature which typically provides results either forselected single farms only, or at a rather high aggregation level of larger administra-tive regions, but cannot give farm-specic information on what drives MAC.


580 Bernd Lengers, Wolfgang Britz and Karin Holm-Muller

The organisation of the paper is as follows: Section 2 briey discusses available litera-ture, including reported ranges of MAC. In the Material and Methods section, we rstgive an overview about our methodology, before we briey outline DAIRYDYN andpresent the dierent GHG indicators for which MAC will be investigated. Next, we dis-cuss the set up of our experiments single farm simulation runs which cover relevantdairy production systems in North Rhine-Westphalia, Germany, based on an ecientspace lling sampling procedure recognising conditioning factor correlations. Subse-quently, we discuss the estimation of the meta-models for two dierent GHG indicatorsanalysed based on a Heckman two-stage selection procedure. The statistical estimatordelivers both test statistics and error terms for the given sample and shows its validityregarding the sampling background. Simulations with the meta-models are used topresent the main ndings in the results section before we summarise and conclude.

2. Literature Overview

Various studies are available regarding possible abatement strategies and potentialGHG savings from agriculture (e.g. Olesen et al., 2004, 2006; Flachowsky and Brade,2007; Smith et al., 2008; Niggli et al., 2009), and related abatement and marginalabatement costs. Whereas MAC are generally dened as the costs required to abatean additional unit of GHG, the approaches to quantify them dier considerably. Thestudies concerning MAC can be broadly categorised in three groups (Vermont andDeCara, 2010). The rst group uses so-called engineering models (e.g. Weiske andMichel, 2007; Moran et al., 2011) which rank existing abatement options according totheir abatement potential by increasing per unit abatement costs. Interactions betweenthe options are typically not recognised.The second group uses aggregate programming models (e.g. CAPRI by Perez,

2006; AROPAj by DeCara and Jayet, 2000) for farm type groups or regions coveringthe EU, often with less engineering detail. The sole or combined use of equilibriummodels, such as with CAPRI by Perez (2006) or with a global CGE framework inGolub et al. (2009), allows consideration of price feedback and further market inter-actions. Equilibrium model approaches tend to nd higher MACs compared toengineering models for two reasons. Firstly, induced output price increases raiseMAC further, and secondly, these models typically do not consider all low-cost abate-ment options analysed in engineering models.The third group, which comes close to our approach, are supply side models with a

rich technology description (e.g. DeCara et al., 2005; Durandeau et al., 2010; Rami-lan et al., 2011; Lengers and Britz, 2012). These studies in most cases only concernspecic regions or single farm types. While typically considering the abatementoptions also covered by engineering approaches, they optimise the farms plan underan emission ceiling or a given CO2 permit price. This allows the simultaneous intro-duction of several abatement options while recognising their potential interactions.Studies with supply-side models tend to nd the lowest MAC of the three groups.Compared to engineering models on the one hand, the prot maximal ranking andcombination of abatement options lowers their MAC estimates. On the other hand,supply-side models typically also consider low-cost abatement options not covered bymore aggregate approaches. However, the lower MAC found by supply-side modelsare also the outcome of neglecting induced output price increases.In a recent review of agricultural MAC derived by dierent approaches, Vermont

and DeCara (2010) found a high variability in estimated MAC between 0.19 and


What Drives Marginal Abatement Costs of GHGs on Dairy Farms? 581

535.80 ton1 CO2-equ. for abatement rates of 068% of baseline emissions, and alsoshow large dierences in MAC for the same percentage GHG reductions (Vermontand DeCara, 2010, pp. 13831384). They conclude that the observed variability inMAC estimates is rooted to a large extent in what type of approach is used, as statedabove. More generally, Barker et al. (2002) and Kuik et al. (2009) show that MACderived by simulation models depend on their structural characteristics and furtherassumptions such as the emission baseline used and the relevant time interval foremission quantication. Lengers et al. (2013a) stress again the inuence of the chosenabatement level, and, in addition, together with Lengers and Britz (2012) highlight theimportance of the GHG indicator for the estimated MAC, a point often neglected inother studies. They argue that the chosen abatement strategies and consequentlyMAC strongly depend on the GHG indicator as farmers can only be expected toadopt abatement options which are credited. Besides that, an economic perspectivesuggests that MAC should clearly depend on prices of input and output and furthercharacteristics of the farms investigated, points often neglected in existing studies.

3. Material and Methods

3.1. Overview on methodology

The literature review suggests that single farm approaches are best suited to reect dif-ferences related to farm attributes and GHG indicator choice as they depict the com-plex bio-physical and bio-economic processes in agricultural production in sucientdetail. However, ndings for a specic single farm are dicult to generalise to moregeneral farm types or regions (Stoker, 1993), the level of interest for policy decisions.Conducting simulations to cover the distribution of relevant factors in the farm popu-lation can consume time and resources. For example, simulating MAC for just 70dairy farms over a 15-year planning horizon with the DAIRYDYN model used inLengers et al. (2013a) took more than 3 days with an 8-core processor. Runtime con-siderations are thus important as they restrict the number of possible experiments(Bouzaher et al., 1993, p. 3; Carriquiry et al., 1998). Meta-modelling seems thus invit-ing as it can replace time consuming simulations using a complex computer modelwith a far simpler one, helping to overcome computational restrictions. A meta-modelapproximates the output (response) of the more complex model using standard statis-tical techniques on model results from representative variations of factors in theunderlying complex model. It identies the most important factors for model resultsand leads to a simpler functional form with fewer input variables (factors) (Carriquiryet al., 1998, p. 507). A meta-model thus quanties major inputoutput (I/O) relation-ships embedded in the structure of the more complex model (Kleijnen, 2008) and cantherefore improve our understanding of real-life systems (Bouzaher et al., 1993, p. 3).Consequently, the rst step in the development of a meta-model is the generation of

a set of model results. In order to account for the interactions of dierent factors2

such as farm attributes, prices and indicator choice on MAC, we construct a larger setof simulations where factor levels are systematically and simultaneously3 varied, also

2In DOE simulation an input variable or parameter is understood as a factor.3Only changing one factor at a time is not the accurate scientic way to analyse eects of thisfactor because single factor eects may be dierent through interaction when other factors

change simultaneously (Kleijnen, 1999).



respecting possible correlations between the variables. Simulation results are thenused to derive appropriate statistical meta-models. The systematic of the overallapproach is visualised in the following gure.

In the following, we discuss the dierent elements shown in Figure 1. The set-up ofthe experiments is clearly related to the structure of the simulation model such that werst briey present the DAIRYDYN model (section 3.2). Next, we discuss whichfactors are varied (section 3.3) and how the experiments are designed (section 3.4).Finally, we discuss the statistical estimator.

3.2. The simulation model DAIRYDYN

DAIRYDYN (Lengers and Britz, 2012) is a highly detailed, fully dynamic mixed inte-ger linear programming model (MIP) for the simulation of economically optimalfarm-level plans on specialised dairy farms, realised in GAMS (general algebraic mod-elling system). It maximises the expected net-present value over several years and dif-ferent states of nature under GHG emission ceilings related to specic GHGindicators. The model hence implements full technical and allocative eciency, whichmeans that so-called winwin abatement options which reduce emissions andsimultaneously raise farm prots are already realised in the unrestricted baseline.It takes into account investment and labour use decisions, respecting their non-

continuous character, and considers sunk costs of past investment decisions alongwith the evolving path dependencies. Specically, existing stables cannot be sold orrented out, and the resale value of machinery is assumed to be low. DAIRYDYN isbased on a detailed production-based approach, simulating farm managementdecisions and related material ows for animal husbandry, cultivation of land, feedproduction and feeding as well as manure management, partly on a monthly basis.

DAIRYDYN

Meta-Modelling

Definition of explanatory factors and related factor ranges

Design of experiments (DOE):Sampling procedure of representative single farm experiments

Execution of experiments with simulation model to derive MAC under different emission ceilings

Result matrix with MAC and explanatories

Derivation of appropriate statistical estimators

Figure 1. Analysis process



The simulation model is designed to analyse impacts of GHG emission ceilings com-pared with a baseline of an optimised farm plan without any emission ceiling. Thefully dynamic, forward-looking character of DAIRYDYN excludes a formal calibra-tion against existing observations, since the time series with the necessary detail aremissing. Instead, we rely on the combination of highly detailed information from farmmanagement handbooks (KTBL, 2010) and a rich set of constraints. However, theGHG emission inventory simulated with the model for a specic farm can be com-pared against long-term measurements (Lengers et al., 2013b).The decision variables in the simulationmodel are linked to aGHGaccountingmodule

which incorporates ve dierent Intergovernmental Panel on Climate Change (IPCC)-based GHG calculation schemes (indicators) to quantify the farm-level GHG inventory(IPCC, 2006; Lengers, 2012). These GHG indicators dier in the level of detail of requiredprocess information. In our analysis, we only use the two extreme indicators, i.e. the sim-plest (actBased) based on default per animal or per ha emission parameters (comparableto the IPCC Tier 1 approach) and the most detailed (refInd), which implements highlydetailed process information in its GHG calculation such as, for example, milk yield level,composition of the ration, type and duration ofmanure storage, synthetic and organic fer-tiliser practice andmanure coverage techniques, at a yearly and, where necessary, monthlyresolution (derived from the IPCC Tier 3 approach) (see Lengers and Britz, 2012; Lengerset al., 2013a for more detail, or Lengers, 2012 for a full description). We omit the remain-ing three intermediateGHG indicators as earlier results showed that abatement strategiesand related costs for these intermediate indicators do not dier signicantly from one orother of the two extremes (Lengers and Britz, 2012; Lengers et al., 2013a). Whereas thesimple indicator (actBased) is only sensitive to changes in activity levels (change of animalnumbers, cropping and grassland acreage decisions), the advanced indicator (refInd) alsoaccounts for changes in the intensity of management, feed composition, fertiliser practiceand manure storage types and time (Lengers, 2012). This leads to dierent abatementstrategies and associated costs under the GHG indicators, as shown by Lengers and Britz(2012) because dierent GHG mitigation options (permanent and variable ones) areaccounted by the dierent detailed indicators (see Table 1).

Table 1

GHG abatement options recognised by indicators

actBased refInd

Permanent

Manure management techniques X

Application techniques XVariable

Fodder optimization X*Breeding activities X

Intensity management XN-reduced feeding XFertiliser practice X

Area cultivated X XHerd size managment, crop growing decisions X XFeed additives/fat content X

Pasture management/ increase grazing X

Notes: *Also recognising digestibility of dierent feed components.



The simulation model generates MAC by relating marginal losses in prot tochanges in the GHG emission ceiling (for a more detailed description see Lengers andBritz, 2012, p. 131) to avoid problems with shadow prices in a mixed integer program-ming (MIP) approach. These MAC are termed net on-farm because they excludetransaction costs relating to administrative and control eorts (Lengers et al., 2013a).For the current study, we construct the MAC for the range between a 1% and 20%reduction of GHG compared to the unrestricted baseline, where the GHG reductioneorts refer to the GHGs credited by the specic indicator used in the simulation.So far, DAIRYDYN has been used by Lengers and Britz (2012) and Lengers et al.

(2013a) for the estimation of abatement strategies and related costs under dierentGHG indicators, and in a paper by Lengers et al. (2013b) to compare modeled GHGestimates with real-life long-term measurements. The rst two studies report MAC inthe range of estimates from other comparable studies, and the third shows a rathergood t for the estimated GHGs to real-life examination results of an experimentaldairy farm installation in North Rhine-Westphalia, Germany.

3.3. Explanatory factors

Keeping in mind that we want to investigate key attributes impacting MAC, two typesof factors are potential candidates for our experiments: (1) economic drivers and farmattributes for which (population) statistics are available (Bettonvil and Kleijnen, 1996;Sarndal et al., 1992 cited in Carriquiry et al., 1998, p. 507), and/or (2) factors relatingto a potential GHG reduction policy. Based on these criteria, we have chosen the fol-lowing factors (the number in parentheses indicates the factor class):

1 Number of cows (1): This factor, characterising the herd size at the starting point,gives a good indication of the size of the farm. In DAIRYDYN it determines, forexample, the initial endowment of stables, machinery and land. The farm size, viareturns-to-scale, impacts production costs and should therefore impact the MAC.

2 Milk yield (1): The average milk yield per cow in the herd indicates the intensity ofthe production system: higher milk yield increases GHG emission per cow, butdecreases emission per kg of milk produced. Besides its impact on productioncosts, the milk yield may therefore signicantly impact abatement strategies andrelated costs under dierent indicators (Lengers and Britz, 2012).

3 Age of stables (1): The older the stables are, the earlier new investments in stablesmust be made to maintain the farm. New investments will also allow for an expan-sion strategy by increasing stable sizes. The stable age also clearly impacts theshare of sunk cost over the simulation horizon if new investments are made inresponse to a GHG policy.

4 Labour productivity (1): As the amount of labour available for one cow cruciallydetermines the labour productivity of the farm, it is included for similar reasons asthe wage rate.

5 Milk price (1): The milk price predominantly impacts the revenues of the overallfarm. Higher milk prices drive up the gross margin of a single cow and thus thecost of herd size reductions or a complete farm exit. Furthermore, it determinesthe optimal intensity of milk production where the marginal costs per unit ofoutput are equal to the price.

6 Wage rate (1): The wage rate is included in our simulations to analyse the impactof the opportunity costs of labour which impact farm size reductions or a



possible exit decision of a farmer if marginal returns to on-farm labour dropbelow the wage rate in response to a GHG restriction. More generally, it impactsthe overall protability of the operation.

7 Concentrate price (1): The most important feed ingredient to control the energylevel of the ration and hence the intensity level of the cows are concentrates. Theyare an important cost factor for mitigation options based on fodder optimisationand more generally for the protability of the farm.

8 Time horizon (2): As we require a certain reduction of GHG only on average overthe full simulation period, and not in each single year, a longer simulation periodallows larger shifts of emission between years and increases the exibility of theadjustment further as investment-based mitigation measures face a longerdepreciation time. This factor is an important aspect describing the reactionscope oered to the GHG regulated farms.

9 GHG reduction level (2): The required GHG reduction which is determined by aspecic GHG ceiling will clearly impact MAC.

10 Indicator (2): Lengers and Britz (2012) as well as Lengers et al. (2013a) show thatthe indicator choice has a signicant impact on the MAC as dierent indicatorsaccount for dierent sets of abatement strategies.

We aim to generate a sample of runs with DAIRYDYN (experiments) which is rep-resentative of the dairy farm population in the German state North Rhine-Westpha-lia, a focus motivated by the importance of dairy farming in that region and gooddata availability. Ranges for the factors are taken from regional as well as country-specic statistical data sources (BMELV, 19912011, 2012; FDZ, 2013; IT.NRW,2012; KTBL, 2010; LFL, 2012; LKV-NRW, 2012; LWK-NRW, 20082012) to ensurethat the designed experiments t the actual population of dairy farms in North Rhine-Westphalia, Germany.Correlations4 between factors are derived from dierent datasets such as

BMELV (several years), FDZ (2013), KTBL (2010), p. 541, LWK-NRW (20082012) and the LKV-NRW (2012): between milk yield and herd size at 0.24***(n = 5,044) and between milk yield and labour productivity at 0.18* (n = 115),between milk price and concentrate prices of 0.76*** (n = 36), and betweenlabour intensity per cow and herd size of 0.65*** (n = 3,034). Furthermore,though there are no statistical data on this aspect, we assume that the herd sizeslightly decreases with increasing age of the buildings, implemented by a correla-tion of 0.10 between herd size and construction year of the stables. All othercorrelations are assumed to be zero.5 We assume a uniform distribution functionbetween the minimal and maximal values reported in Table 2.

3.4. Sampling procedure

Kleijnen (2005, p. 290) names the ranges of possible factor and value combinations insuch computer experiments the domain of admissible scenarios. Even if we dene foreach factor only a limited number of possible levels (e.g. 20, 50, 100, 200, 250 cows), itwould still be impossible to simulate all potential permutations of factor level

4Pearson correlation coecients with signicance levels of *** = 0.01, ** = 0.02, * = 0.05.5With this assumption we can also ensure that the danger of multicollinearity in sampling out-

puts is diminished.



combinations with DAIRYDYN.6 Therefore, a limited but representative set of fac-tor level combinations is selected based on DOE principles (Kleijnen, 1999). Speci-cally, we apply a Latin-hypercube sampling (LHS) method, which is more ecientthan simple random sampling (McKay et al., 1979; Iman and Conover, 1980; Imanet al., 1981, pp. 176177; Giunta et al., 2003, p. 7; Iman, 2008). LHS denes a numberof experiments which simultaneously change levels of various factors, while being rep-resentative for the full range of possible factor level permutations. Based on space ll-ing designs, LHS smoothly samples over the k-dimensional input space for a denedsize of the sample (Iman et al., 1981, p. 176; Owen, 1992, pp. 443445). It does notnecessitate a decision beforehand about for which factors a more ne-grained

Table 2

Overview of explanatory factors

Variable/attribute Name Unit Min Median Max Data source

Number of cows* nCows Head 20 135 250 IT.NRW, 2012;

LKV-NRW,2012;

Milk yield milkYield kg ECM

cow1 a15,000 8,000 11,000 LWK-NRW,

20082012;LKV-NRW,2012;

Age of stables StableAge Building yearof the stable

1995 2000 2005

Labourproductivity

WHperCow Working hourscow1 a1

30 51 72 LWK-NRW,20082012;FDZ, 2013;

Milk price milkPrice -cent kgECM1

25.97 31.205 36.44 BMELV,19912011, 2012

Wage rate wageRate hour1 6 10.5 15 LFL, 2012;LWK-NRW,2012

Price concentrate concPrice ton1 160 195 230 adapted toKTBL, 2010;LFL, 2012;LWK-NRW,

20082012Time horizon horizon Years 10 15 20GHG reduction

level

% 1 10.5 20

Notes: Prices are declared as yearly average prices.*Farms with a herd size below 20 are excluded because it is assumed that they represent pre-dominantly tethering houses; the simulation model only covers free stalls. Nevertheless, the

remaining population still represents above 92% of the whole 2012 cow population in NorthRhine-Westphalia.Values are derived from 96% of the original datasets due to exclusion of extreme values.

6All GHG reduction levels are simulated in each experiment, which leaves us with eight factors.If we would allow for ve dierent levels for each factor and simulate all combinations, we

would need to conduct 5^8~400.000 experiments.



resolution of levels is appropriate (Iman, 2008). However, standard LHS assumes zerocorrelation between the factors which may lead to invalid statistics compiled from theoutput if factors are correlated in reality (Iman and Conover, 1982, p. 331). We thusemploy a LHS procedure according to Iman and Conover (1982) which considers fac-tor correlations.We used the known correlations and factor value ranges (see section 3.3) to deter-

mine a representative sample. To do so, we employed the statistical software R (ver-sion 2.15.1) for the DOE generation, specically the LHS-package lhs_0.10 incombination with the algorithm from Iman and Conover (1982) to incorporate corre-lations. As the accuracy to which that algorithm can recover the correlation dependson the drawn sample, we performed the LHS a few thousand times for a sample size nof 200 and selected the LHS-sample with the best t between the randomised and thegiven correlation matrix (LHS runs stopped when the dierence between drawn andassumed correlation matrix did not decrease further with additional LHS runs). Thatsample size was chosen to allow running the simulations in an acceptable time, whilestill generating a suciently large sample for the econometric estimation of the MACfor the two GHG indicators.

Figure 2. Normalised scatter plot matrix of 200 LHS draws for eight factors



The histograms of the sampling outcome in the diagonal boxes in Figure 2 suggestthe desired uniform distribution over the normalised [01] factor range (cf. Wyss andJorgensen, 1998, p. 7) for each factor. The normalised scatter plots below the diagonaldepict both the space lling design as well as showing the drawn correlation betweenfactor pairs. The matching boxes across the diagonal show a satisfactory t betweenthe drawn (without parentheses) and the given (in parentheses) correlation factors.The improved LHS is hence ecient as it is space lling and shows a good t to thegiven factor correlations (the mean percentage deviation of given and drawn correla-tions of the whole random sample is 7.76%), despite a relatively low number of drawsas required by Carriquiry et al. (1998, p. 507).

3.5. Model runs

We excluded some draws with implausible factor level combinations (e.g. very highmilk yields in combination with very small herd sizes), leaving us with 155 single farmexperiments. Each experiment comprised 20 dierent optimisation runs, with increas-ing GHG reductions from 1% to 20% of the baseline emissions. The exact reductionlevel was randomised between +/ 0.5 percentage points around these reduction steps.Each experiment was conducted for the two GHG indicators, resulting in 3,100 obser-vations on MAC for each indicator.

3.6. Statistical meta-modelling

In order to quantify which factors signicantly impact MAC under the two GHGindicators and to visualise the simulations, a statistical meta-model is constructed foreach of them. These statistical response surfaces can be understood as approximationof the simulation programmes I/O transformation (Kleijnen, 1999, p. 116) in thisstudy for MAC depending on farm attributes, prices, GHG reduction levels, timehorizon and the GHG indicator applied.This requires selecting an appropriate statistical estimator. As our non-standard

LHS which accounts for factor correlations is no longer orthogonal, we therefore rsttested for multicollinearity of the randomised sample variables (not critical, the vari-ance ination factors were below 10).7

Second, a graphical analysis of results revealed that in certain experiments, farmsexit dairy production at more aggressive GHG emission ceilings. The exit decision ismainly driven by the opportunity cost of labour (returns to labour at optimal farmprogramme compared with o-farm wage) and land (a xed, but rather low land (ren-tal) price) which stays unchanged in all simulation runs), which depend in turn onfarm characteristics and prices for outputs and inputs. Once a farm has exited, itsGHG emissions will stay unchanged at zero and prots will no longer change. Hence,further tightening of the emission ceiling cannot deliver useful information on MAC.Leaving these zero observations in the sample would lead to biased results, while

excluding them would omit information (censored data) and cause a sample selectionbias8 (Heckman, 1979; Kennedy, 2008, p. 265). Therefore, we apply a two-stage

7Marquardt (1970) suggests that serious collinearity is present for VIF-values above 10.8Tobin (1958) rst showed that if censoring of the dependent variable is not considered in the

regression analysis, an ordinary least squares (OLS) estimation will produce biased estimates.



Heckman estimation procedure which in the selection equation rst estimates theprobability of exiting farming (probit-model) and in the outcome equation (OLS lin-ear regression), conditioned on the rst stage probability, the MAC. Accordingly, asstandard in the Heckman approach, the inverse Mills ratio calculated from the rststage probit-model was added as an explanatory variable to the second stage to cor-rect for the self selection bias.9 (Heckman, 1979; Kennedy, 2008, pp. 265267) Theestimation is performed with the R SampleSelection package (Toomet and Henning-sen, 2008).There is a second type of observation with zero MAC. Linear programming models

might react with a basis change and thus non-smooth reactions to changes in bindingconstraints. This behaviour is reinforced, as in DAIRYDYN, by the presence of inte-ger variables. Due to a basis change, introducing a GHG emission ceiling might leadto a higher reduction than required. In our stepwise reduction simulations, to give anexample, a 1% increase in the enforcement level could lead to a reduction in GHGs ofmore than 2%. In this case, if the next reduction is smaller than 1%, it will not requireadjustments of the farm programme. Thus, prots and abatement costs might notchange in a consecutive step for which, accordingly, the MAC become zero. Thesezero MAC observations are kept in the sample, but clearly will reduce the explainedvariance of the outcome equation, which, as a multiple linear regression model, willreact smoothly to changes in explanatory variables such as the GHG emission ceilingand cannot generate the kind of jumpy MAC curves which certain experiments mightsimulate.There is no reason to assume a priori that relationships between MAC and farm

attributes, as well as further explanatory variables such as prices should be linear, orto exclude interaction eects in the design matrix. Hence, after some tests, we rstadded the square root and the square of the reciprocal value of each factor to thedesign matrix. Similarly, we introduced interaction terms between all untransformedfactors as explanatory variables. The resulting design matrix tends to be highly co-lin-ear. Therefore, in a next step we estimated a linear regression between each explana-tory variable and all others, dropping any explanatory variable with a multiplecorrelation above 94%. Afterwards, we used a backward selection strategy, droppingany variable with a signicance level above 5% from the Heckman model.

4. Results

The selected explanatory variables with their estimated coecients for the two meta-models are shown in the Appendix (see the additional supporting information accom-panying the online version of this article). The non-linear transformations of thefactors and the presence of interaction terms render a direct interpretation of the esti-mated coecients challenging.10 In order to visualise the eect of single factors on the

9Inverse Mills ratio is added in order not to omit information of the explanatory variables of

cases censored in the selection step. An explanation of this step is also given in Giovanopoulouet al. (2011, p. 2177).10Imagine the following functional form of a meta model: MAC b0 b1x1 b21=x12 b3x1x2. In order to assess the impact of factor x1 on the estimatedMAC, one needs to consider simultaneously all terms comprising x1, i.e. @MAC

=@x1which isnot directly possible from examining the estimated coecients, as it requires consideration of

not only the non-linearities, but also the level of other factors, in the example of x2.



MAC, we therefore separately varied the value of each factor over its range (cf.Table 2), while xing all remaining factors at their median values. From there, wegenerated a set of new observations based on the transformations and interactionterms present in the estimated output equations (see Appendix S1 and S2, found inthe additional supporting information accompanying the online version of this article)for which we simulated the meta-models. This allows a graphical depiction of thedependence of MAC on changes of each factor.The resulting graphs (Figure 3) indicate that MAC dier considerably between

GHG indicators. Also, how they are aected by the dierent factors is crucially depen-dent on the GHG indicator chosen. The gures show that the simple indicator pro-vokes higher MAC in comparison with the more advanced indicator, which accountsfor more exible and low-cost abatement strategies (farm size reductions are the onlyoptions accounted for by the simple indicator as described in section 3).For all graphs, a steeper curve means a greater eect of factor level changes on the

MAC over the factor range considered in the experiments. Hence, for both GHG indi-cators the GHG reduction level (between 1% and 20%) has the highest impact. As forthe estimates under the advanced indicator (rst graph of Figure 3), MAC increasewith diminishing rates if the abatement level increases, the simple indicator inducesMAC curves which stay constant for intermediate reduction levels as the farm basi-cally shrinks proportionally (reduction of cow numbers and acreages with constantlosses of gross margins). For larger reductions above 15% under the simple indicator,the MAC increase as it becomes more likely in the sample to work half or full-timeo-farm, which leads to an increase in opportunity costs of labour as the eectivewage rate increases for half or full-time work. That nding shows the importance ofreecting indivisibilities of labour in the integer approach underlying the simulationmodel.Dierences between the GHG indicators are mostly found for low reduction levels.

For a 1% reduction the meta-model of the advanced indicator estimates MAC near0 whereas the meta-model of the simple indicator estimates MAC about 50 ton1

CO2-equ. The advanced indicator also allows for low-cost abatement options as longas the abatement potential of low-cost measures is not fully utilised. Here, during therst 15% reduction of baseline emissions, the highest increase in MAC takes place,where MAC easily double between reduction steps. This shows that cheap abatementstrategies are used rst, with however only a limited reduction potential. At thesemoderate reduction levels, the advanced GHG indicator benets from oering low-cost abatement options not credited under the simple indicator; accordingly, its MACare considerably below those induced by the simple indicator. For higher reductionlevels MAC under both indicators reach a comparable level where abatement strate-gies under both GHG indicators consist of farm size reductions. This triggers theobserved steep increase in MAC once the abatement potential of low-cost measures isfully utilised and explains the decline in abatement cost advantages under theadvanced indicator with increasing abatement level.The eect of the milk price shows that MAC are quite output price sensitive, inde-

pendent of the indicator used. This can be easily understood from the fact that over alarger range of the GHG emission reductions, abatement eorts are linked to outputreductions.The eect induced by the herd size (number of cows in initial herd) of the farms is

quite high for smaller farms below 40 cows. For larger farms, there seems to be no sig-nicant variation in MAC due to herd size variations. We interpret this nding by the



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Figure 3. MAC in ton1 CO2-equ. simulated with meta-models depending on factor levelsNote: All other factors are xed at their median; Mills-ratio from probit included.



fact that investment-based mitigation options such as manure coverage, which allowfor low-cost abatement, are not realised on small-scale farms due to economies ofscale, which however quickly level o.Higher milk yields boost economic returns per cow and also per GHG emitted and

thus provoke MAC increases under both indicators. The eect is less pronounced forthe advanced indicator (curve is less steep) for two reasons: rst, the simple indicatorassigns a default emission factor to each cow, independent of the output level, whereasthe advanced indicator also recognises the diminishing GHG emissions per kg of milkwith increasing output level per cow. It hence requires lower herd size reductionscompared with the simple indicator. Second, as the advanced indicator also accountsfor feed ration changes which lower emissions, stricter emission ceilings (hence higherGHG reduction levels) do not necessarily induce herd size reductions under theadvanced indicator, which lowers the impact of milk yield level variations on theMAC.Independent of the GHG indicator chosen, variations of the stable age (building

year of the stables) as well as the time horizon show nearly the same eect: they slightlyreduce the MAC by increasing exibility with respect to the distribution of emissionsover time, which also allows for a better timing of abatement-related investments.The wage rate, determining the opportunity costs for on-farm work, has a signi-

cant but moderately negative impact on the MAC as higher returns to o-farm workreduce the prot forgone from shrinking the farm operation.Similarly, a lower labour productivity which increases the working hours spend per

cow and year (WHperCow) reduces the MAC for both indicators (the eect is slightlysmaller under the advanced indicator). Reducing GHGs with a low labour productiv-ity releases more labour for o-farm work, which dampens income losses comparedwith more labour ecient farms.Higher concentrate prices let MAC decline somewhat under both indicators, which

is simply the opposite eect of an increased output price. The lower impact comparedwith the milk price reects the cost share of concentrates.

5. Discussion of Results

Figure 4 plots the tted values for the MAC dierence in prots in relation to dier-ence in maximal emissions of the meta-models against those simulated with theunderlying complex bio-economic model (DAIRYDYN). The reader should rst notethe thick cluster of zero MAC observations along the horizontal axis, which arerooted in basis changes in the MIP based simulation model DAIRYDYN. Theseobservations, hardly meaningful for economic analyses, are smoothed out by themeta-models.These zero observations contribute to the fact that we estimated a relatively low

adjusted R of about 0.46 and 0.47 for the meta-models of the simple and theadvanced indicators, respectively. Generally, it is hard to achieve a good t over thenon-smooth simulation behaviour of a LP or MIP with a regression model. Thereader should also be aware that, generally, the t of regression models for dierencesin dependent variables (here MAC) tend to be lower compared to level estimations(here AC). Against this background, the t of the estimated meta-models can be val-ued as acceptable as it only consists of highly signicant regressors with a signicancelevel of at least 5%.As with any type of statistical model, results are conditioned on the input data and

hence only valid for the sampling background. Whereas the direction of impacts



found for the factors can be motivated from economic theory and thus generalised,variable selection and related parameter estimates might depend on the samplingdesign and are therefore probably only representative for dairy farm conditions inNorth Rhine-Westphalia, Germany, as reected in the parameterisation and structureof DAIRYDYN.As simulation results were generated from specic assumptions about the length of

the simulation horizon and the currently observed production techniques imple-mented in the model structure of DAIRYDYN, an interesting question for furtherresearch is whether and how to reect future technical progress in farming. While it isobvious that innovations and their adaptation can change MAC (see, for example,Amir et al., 2008), it is not clear how to account systematically for that eect in aneconomic simulation with a longer time horizon.Similarly, we should emphasise that single factor eects visualised in Figure 3 are

derived by xing all other factors to their median. Clearly, the single factor MACcurves may change both with regard to their mean and slope when xing the otherfactors to dierent levels. This may reorder the ranking of the factors with regard totheir impacts on MAC. The selected curves are thus only illustrative of the statisticaldependencies expressed by, and the simulations possible with the meta-models, whileunderlining the usefulness of the meta-models for systematic analyses.

6. Summary and Conclusions

Our paper discusses the development of a statistical meta-model from simulationswith the highly detailed bio-economic single farm optimisation model DAIRYDYN,in order to systematically analyse key factors impacting marginal abatement costs forGHGs on dairy farms and to quantify their eects, in comparison between dierentGHG indicators. DAIRYDYN was parameterised and simulations conducted to yielda set of results covering the relevant range of core attributes representative of thedairy farm population in North Rhine-Westphalia, Germany. In order to keep thenecessary simulations at a manageable size, we apply a design of experimentsapproach, specically, a non-orthogonal Latin-Hypercube sampling approach whichaccounts for correlations between factors. We observed farm exits for a non-negligibleshare of simulations, which yield zero MAC for further emission enforcements.

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Figure 4. Scatter plot of tted values from meta-model against values simulated withbio-economic model ( ton1 CO2-equ.)



Therefore, the meta-model was estimated based on a Heckman two-stage procedureto avoid selection bias where the selection model depicts the probability of farm exit.Our results deliver more farm-level oriented analyses with regard to MAC and theirdriving factors compared with existing studies and hence give important insights intodierences in MAC between farms.We found the following main factors inuencing the farm level abatement costs on

dairy farms, in order of importance: the GHG reduction target (in line with ndingsfrom Kuik et al., 2009, pp. 13991400), size of the farm, milk price and milk yieldlevel. Wage level, labour productivity, concentrate prices, simulation horizon and timeof last investment in stables also impact the MAC, though at lower rates. We foundthat MAC increase quite strongly between a 1% and 5% abatement level, a clear hintof a limited potential for low-cost abatement options in dairy farming. This conclu-sion is also reached by Lengers et al. (2013a). Our ndings thus suggest that MAC dif-fer considerably between farms of dierent sizes and production intensities for thesame GHG emission target, and react quite sensitively to changes in input and outputprices. An interesting observation is the fact that MAC decrease if farms are allowedto distribute more exibly the required GHG reduction over several years, a pointalso raised by Fischer and Morgenstern (2005, p. 2). We also found that the MAC dif-fer considerably between a simple and a much more detailed GHG indicator. All theseobservations are clearly relevant for policy discussion and design as they denotehighly complex dependencies between the observed factors and farm-level MAC,which require more detailed analyses concerning the heterogeneity aspects of MAC inthe actual farm population.To conclude, our study showed signicant eects on MAC both for farm attributes

and prices, and for factors relating to policy implementation such as the GHG reduc-tion target and the chosen GHG indicator. Therefore, we complement existing meta-model analyses, which relate MAC dierences to the chosen methodologicalapproaches only, while going beyond studies at the farm level, which delivered resultsonly for selected single farms.An advantage of the derived meta-models compared with the application of the

underlying complex simulation model is their easier integration into other modellingapproaches as well as faster execution time and lower storage needs (Britz and Leip,2009, p. 267). Following the systematisation of Karplus (1983) as well as Oral andKettani (1993), the complex grey box model DAIRYDYN, which builds on detailedbio-economic causal relationships, is transformed into a far simpler black box model (aset of statistically derived functions) where the logical and also approximately numericalrelationships are maintained. These meta-models can be used for analysis and explana-tion as we have done, but also to investigate future scenarios (Kleijnen, 1995, p. 158).Hence, the meta-models derived (see the online appendix) are well suited for upscalingpurposes to regional or sectoral level from single farm or farm group observations, whilereecting highly non-linear and complex relationships between farm attributes andMAC, a point also underlined as important by Schneider and McCarl (2006, p. 285).The underlying single farm model DAIRYDYN can be used to simulate any farm

with a dairy production system matching its current structure and parameterisation(no grazing in winter, loose housing systems, rather high mechanisation level). Thus,by choosing appropriate factor boundaries and correlation terms, the combination ofthe sampling procedure and simulation runs with DAIRYDYN can be used to deriveGHG indicator dependent meta-models representative for other regions. In further



studies, such meta-models could be an important tool for analysis of distributionalaspects of GHG-related environmental policies in the actual farm population.

Supporting Information

Additional Supporting Information may be found in the online version of this article:Appendix S1. Meta-model output: probit selection equation for farm exit and OLS

outcome equation for MAC under the advanced indicatorAppendix S2. Meta-model output: probit selection equation for farm exit and OLS

outcome equation for MAC under the simple indicatorAppendix S3. Marginal eects of probit selection equation for farm exit under the

advanced indicatorAppendix S4. Marginal eects of probit selection equation for farm exit under the

simple indicator

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What Drives Marginal Abatement Costs of Greenhouse Gases on Dairy Farms? A Meta-modelling Approach

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