Direct and Indirect Economic Incentives to Mitigate Nitrogen Surpluses: A Sensitivity Analysis

The reduction of nitrogen (N) surplus is an ongoing topic in the agri-environmental policies of many countries in the developed world. The introduction of N balance estimation in agricultural sector models is therefore pertinent and requires an interdisciplinary approach. We extended the agent-based agricultural sector model SWISSland with an N farm gate balance estimation to pre-evaluate the introduction of a levy on N inputs, particularly a levy on fertilizer and imported concentrates, on N surplus reduction in the Swiss agriculture. The model was based on the Swiss farm accountancy data network (FADN) for 3,000 farms. The model’s ability to represent theNbalancewas assessedby conducting a structured full factorial sensitivity analysis. The sensitivity analysis revealed the possibility to switch to organic farming and the hectare based payments for ensuring food security as key parameters with the largest influence on themodelled N surplus. The evaluation of N input levy scenarios suggested that an introduction of a tax of 800% of N price will reduce the N surplus by 10% indicating a price elasticity of -0.03. The sensitivity analysis and the results from the levy scenarios suggest that indirect instruments, such as optimizing the direct payments scheme, should be considered rather than direct instruments for an e ective N surpluses mitigation in Swiss agriculture.


Introduction
. Agriculture is an important contributor to nitrogen (N) pollution (Sutton et al. ). In many Western European countries, policies such as command and control instruments or economic incentives to reduce N emissions are under discussion (Jayet & Petsakos ). The latter have the advantage of higher cost e iciency, but raise more questions about their actual impacts. Therefore, the introduction of economic incentives requires a thorough ex ante analysis of potential incentive-based instruments, for which bio-economic models are appropriate. .
In order to estimate the e ects of economic incentives on the environment, these models need to be e ectively linked to environmental indicators (e.g., N surplus, net GHG emissions, nitrate leaching). An o en used indicator is the N balance at farm level, which is represented by a subtraction of N inputs from N outputs of a farm. One of the advantages of N balance is the consideration of various N losses through all pathways such as nitrate and dissolved organic N leaching, ammonia and nitrous oxide emissions, as well as N gas losses by denitrification and thus its ability to reveal N use ine iciencies (Oenema et al. ). N farm gate balances can be calculated at farm scale (Mamardashvili et al. ) or at sectoral scale (Spiess ). Some bio-economic models integrate N balances (Jayet & Petsakos ), yield functions (Ramilan et al. ) or they link their economic model with a biogeochemical model to evaluate environmental impact (Merel et al. ). Some bio-economic models consider only one farm activity (Finger ; Feinerman & Komen ; Bourgeois et al. ), whereas other models include several animal and plant production activities (Vibart et al. ; Happe et al. ). .
Switching to an agricultural policy of multifunctionality, the Swiss government formulated ambitious agri-environmental goals(BAFU & BLW ). These goals have been reached to some extent, but in the case of N emissions little progress has been recorded and the N surpluses remains at a level of kg* ha -(Spiess ). Consequently, the Swiss government is considering strategies to further reduce N emissions from agriculture (Ricklin ).
. The SWISSland model (German acronym for Swiss structural change information system) (Möhring et al. ) is an agent-based agri-economic sector model providing a realistic description of the Swiss agriculture systems. Although, the model accounts for di erent management activities, its ability to assess the environmental impact of adopted measured is yet limited. .
In the present study, we evaluated the e ectiveness and e iciency of di erent N policies such as an N input levy or an input tax in mitigating N surpluses at the farm scale. Therefore, we integrated an N farm gate balance that represents all losses of N in the whole farm system in the model SWISSland. To evaluate the model's ability to assess the N surplus, we conducted a structured full factorial sensitivity analysis and investigated how sensitive the modelled N surplus was with respect to selected parameter. In the end, we applied the model SWISSland for three levy scenarios on N content of fertilizers and imported concentrates and evaluated their e ectiveness. .
In Section , we describe the SWISSland model and the extension of the N balance estimation. In Section , we present the sensitivity analysis results. In Section , the results of the N input levy are presented and discussed. Finally, further implications and conclusions are drawn in Section .

Model Description
Model SWISSland . We extended the agent-based agri-economic sector model SWISSland (Möhring et al. ) with an estimation of an N farm gate balance in order to analyse the e ects of a levy on N content of concentrates and fertilizer on N farm gate surpluses in the Swiss agricultural sector. The model optimizes for the farm income under the restriction of land endowment and was developed to obtain a realistic description of the Swiss agriculture systems in order to support policy decisions (Möhring et al. ). An ODD (Overview Design Concepts and Details) -protocol of the model is provided by Zimmermann et al. ( ).
. The data used for the representation of the di erent agents was based on the Swiss farm accountancy data network (FADN) averages from to (herea er referred to as base year) for about , farms across the whole Swiss agricultural area. This database provides information on workforce availability, costs as well as the revenues from prices and direct payments for about crop and animal production activities (e.g., milk, wheat). The model therefore accounts for di erent management options (Möhring et al. ). The FADN data set was considered to be insu iciently representative of the whole Swiss agricultural situation, due to overrepresentation of certain farm types such as dairy farms, and underrepresentation of other farm types such as farms with sheep, goats and horses. To correct for this in the model development, the farm types that were underrepresented were replicated and some of the farms from the overrepresented types were omitted. Additionally, di erent upscaling factors were applied to every farm type to achieve a representative result for the whole sector (Zimmermann et al. ). .
Within given restrictions such as land endowment and limitations on animal stocking, the agents behaved rationally and maximized their farm income Z (Equation ). A positive mathematical programming (PMP) approach was used to simulate the farm behaviour based on the observed preferences in the past (Möhring et al. ).
The farm income results from the revenues from farm activities i (p i : price, x i : production quantities) and direct payments minus the costs of farm activities (d i ). The quadratic cost term was a symmetric and positive (semi-) definite matrix and was represented by Q ii . The model was calibrated to observed production levels in the base year in order to avoid overspecialization in prediction years. Qii is defined as follows (Equation ): where ρ ii represented the supply elasticity. Due to the lack of specific data this value usually is set to one. The parameter x i + took the observed production levels in the base year into account.
. The model shows income trends at farm and sectoral scale as well as structural change and its consequences on land use, livestock population and prices. Prices were determined by a partial equilibrium model (market module). The agents were clustered in spatial community structures, which allow agents to quit the agricultural sector and lease their land to neighbouring agents (Möhring et al. ).

N balances .
There are several types of N balances: farm gate, soil surface and soil balance. The farm gate balance accounts for all N inputs that enter the farm and all N outputs in plant and animal products that leave the farm. By contrast, the soil surface N balance considers only N inputs to the soil and N removed by plants. Lastly, the soil N balance tracks individual soil processes (Oenema et al. ). The advantages of the N farm gate balance is the ease of calculation as it does not account for the processes within the farm and the consideration of the N losses in both animal and plant production (see Figure ). However, it has the disadvantage of not locating the surplus generated on the farm, and the individual pathways of N losses are therefore not detectable (Oenema et al. ). The "Suisse-Bilanz" (Amaudruz et al. ), which is part of the Swiss cross-compliance scheme, is a combination of a farm gate and a soil surface balance, as it accounts for the applied N fertilizer including the farmyard manure that must not exceed the plant N requirements by more than %. This scheme already includes a certain level of N losses in the animal house and on the field. .
The single farm optimization model, which determines the production decisions of the agents, required an N balance estimation that would assess the consequences of the measures adopted. The model was therefore extended by the calculation of the N farm gate balance and the restrictions embraced in the "Suisse-Bilanz". The farm N inputs and outputs were estimated for every agent included in the analysis based on the prices of farm inputs/outputs, their quantities and N content (Flisch et al. ). The N fertilizer input of all crop production activities was estimated based on the expenses for N fertilizer derived from the FADN data set. The fertilizer cost per farm distributed between crop production activities was based on the fertilizer recommendations for Switzerland (Agridea ). This methodology led to an underestimation of the amount of fertilizer use by % in comparison with reported values from (Swiss Farmers Union ) in the base year. Therefore, the final fertiliser use has been corrected by this figure. Concentrate inputs for animal production activities were estimated and distributed in a similar manner using typical feed mixtures and their N contents (Agridea ). For N inputs by atmospheric deposition, an average value representative of Swiss conditions of kg N hawas used (Jan et al. ). For inputs by biological fixation, typical values depending on pasture intensity were chosen (Boller et al. ). Overall, the modelled N surplus was underestimated by % in comparison with literature data (Spiess ).
. The model constraints on the farmyard manure and N fertilizers were set up according to the "Suisse-Bilanz" as follows: The "Suisse-Bilanz" sets limits for N fertilizer use and farmyard manure N and thus animal numbers depending on N requirements of plant cultures and the plant-available N content of the farmyard manure. The plantavailable N must not exceed the plants' requirements by more than % (Equation ).The "Suisse-Bilanz" scheme has di erent correction factors to account for di erent slurry types and also allows farmyard manure shipments. However, since information on farmyard manure shipments and the slurry types used on the farms was not available in the FADN-data set, we assumed that all farms comply with the requirements of the crosscompliance scheme and thus the amount of N that exceeded the requirement was corrected accordingly for the forecast years. . Figure presents various options available to the agents to reduce their modelled N farm gate surplus in the model. Option to are implemented in the model constraints, while option is defined by a Bayesian Network. Option allows agents to reduce the amount of applied fertilizers for the main crop activities by or %. We modelled the N fertilizer intensity reduction impact on crop production using input-yield functions for cereals, maize, potatoes, sugar beet and rape seed (Möhring et al. ). A % reduction in N fertilizer corresponds to extensive production as defined in a current agri-environmental program for Swiss farms and consequently this reduction is concomitantly associated with receiving direct payments for extensive production (extenso). In milk production, option allows to optimize the concentrate inputs. A reduction in concentrate inputs below % of the feed ratio leads to receiving direct payments from the Grassland-based Milk and Meat Production (GbMMP) program o ered by the Swiss Federation. In addition to this, the agents are able to change their cultivation patterns (option ) or animal stocking (option ). In option , the agents have the possibility to transform their farming practices from conventional to organic. This decision option is modelled using the Bayesian network embedded in the SWISSland organic module. The probability to change to organic production is determined by the farmer's income and age, the farm size, animal stocking and the working force requirements. The organic module estimates the farmer income based on higher prices for organic products, di erent costs for farm activities, takes into account higher direct payments and also lower yields. A change to organic production reduces the agent's N input from fertilizers and possibly their concentrate use, but it also reduces their N outputs due to lower yields. The farm has to stay at least three years in the organic option, as only a er three years, they receive the full price for organic products (Möhring et al. ).
Figure : SWISSland agents options to reduce nitrogen inputs. Option to are implemented in the model constraints, while option is defined by a Bayesian Network (details in Section . ).

Sensitivity of the N Surplus Per Area with Respect to Selected Model Parameters
Sensitivity analysis approach . We conducted a sensitivity analysis in order to a) to investigate how the modelled N surplus per area (kg N ha -) responds to systematic variation in the management options adopted by the agents in order to reduce the N  surplus; b) to identify which decision options have a small or large influence on the modelled N surplus; c) to detect interaction e ects between selected management options. .
There are several approaches to determine how sensitive the model output is with respect to the model factors (i.e., model parameters or inputs). One commonly used way is "One factor at a time". This approach is the most intuitive. However, since it varies one model factor at a time, while the other factors are fixed, it does not take into account interactions between the factors (Saltelli & Annoni ). For our analysis we decided to implement a global sensitivity method that is not too computationally demanding, but still reveals interaction e ects between selected factors. The variance of N surplus was studied with respect to selected model factors at a restricted number of levels within their uncertainty intervals using a full factorial design and analysis of variance (ANOVA) (Wallach et al. ). Sensitivity analysis help to identify the parameters that influence the uncertainty of the model output (Troost & Berger ). .
The sensitivity analysis was conducted in several runs and the structured full factorial design was applied to three selected factors at a time. The influence of each factor was studied at two to three restricted levels, depending on the model factor variability. This approach resulted in * * model scenarios for each phase of the sensitivity analysis, as we studied one dichotomous parameter in combinations with parameters at low, medium and high levels. The full factorial design analysis allows detection of some interaction e ects at lower computational cost than the sensitivity analysis based on Monte Carlo or Latin hypercube sampling of the uncertainty intervals.
. Selected factors were assumed to influence the farmer's decision to reduce their N input (see Table ). The SWISSland organic module allows agents to convert to organic farming, whereas the intensity reduction and the milk yield function provide opportunities to reduce intensity levels. The PMP elasticities (ρ ii , see equ ) influence the changes in the animal stocking and land use. Direct payments and prices a ect all decisions, as they influence the revenues and costs of various farm activities. The price levels were chosen based on observed maximum and minimum prices of the products in the last ten years.
. The most sensitive factor and also the interactive e ects between the factors were determined using an analysis of variance (ANOVA) in R so ware package (R Core Team ). For this reason we calculated the mean of N surplus per ha of the region weighted by each agent's area. The most sensitive parameter identified in the previous run of the sensitivity analysis was included in the following run along with two new additional factors. .
For the sensitivity analysis, we ran the model with only one spatial community in order to further reduce the JASSS, ( ) , http://jasss.soc.surrey.ac.uk/ / / .html Doi: . /jasss. computational cost of the simulations from the base year (average from -) to . The spatial community characterized by agents in the base year represented the ratio between organic and integrated production farms and the proportion of valley, hill and mountain farms as well as the proportion of dairy farms in the whole model SWISSland. As a consequence of applying only one spatial community, the market module could not be used and prices were given exogenously for the sensitivity runs.

Result and discussion
. In the first sensitivity run, modelled N surplus showed similar patterns in response to the systematic variation in PMP elasticities of land use, the input reduction level of N fertilizer, and the option of converting to organic farming (see Figure a)). The average modelled N surplus on the national scale decreased from . kg N hain the base year to . to . kg N hain the last year of the study ( ). Figure : Nitrogen surplus in response to the variation of a) the PMP-factor land elasticity (LE, status quo (sq) for LE = ), the intensity reduction (IR, status quo (sq) for IR = . ) level of the fertilizer input and the option of switching to organic (OM) b) the PMP-factor for animal stocking (animal elasticity, AE,status quo (sq) for AE = ), the milk yield function level of the concentrate input (MY), and the option of switching to organic farming parameters (OM). c) the systematic variation of the milk price (MP,status quo (sq) for MP = . ), the wheat price (WP, status quo (sq) for WP = ) and the option of switching to organic (OM) parameters. d) the price for N (N-P,status quo (sq) for N-P = . ), the option of switching to organic farming (OM) and the payments for ensuring food security (PEFS,status quo (sq) for PEFS = ) parameters. Sq refers to the status quo level of the parameters. The sensitivity analysis shows the mean squares of the analysis of variance (ANOVA) .
The most sensitive parameter for the modelled N surplus, i.e., the parameter that explains the highest variability in the modelled N surplus, was the organic module. The organic module increased the number of organic farms by about % on average ( Figure Apendix). The higher number of organic farms and their lower N surplus per area lead to a lower modelled N surplus per ha on average. The input reduction level of N fertilizer only a ected a small number of agents (i.e., arable farms), particularly farms with a high proportion of arable area. As the PMP elasticity of land use showed only negligible e ects on the distribution of grassland and open arable land, it a ected the modelled N surplus very little.

.
In the second sensitivity run, the values of modelled N surplus for ranged from . to . kg N haon average, while varying the PMP elasticity of animal stocking, milk yield function and the option of changing to organic farming (Figure b)). Similarly to the first sensitivity run, the organic module was the most influential parameter for the modelled N surplus. The number of animals was restricted by factors other than the PMPfactor for animal stocking, such as housing capacities and limits on animal stocking. Therefore, the influence of the PMP-factor for animal stocking on modelled N surplus was negligible. Similarly, the variation of the milk yield function level of concentrate input a ected only the N e iciency of milk production, with very minor e ects on the modelled N surplus. .
The third sensitivity run led to an average N surplus ranging from . to . kg N ha -. In this run, prices of milk and wheat were varied in combination with the organic module (Figure c)). Again, the organic module parameters variation had the highest influence on the N surplus as a single parameter. Despite this, some of the variance of N surplus was explained by the interaction of milk price and wheat price as the variation in the product prices influenced the distribution of open arable land and grassland. .
In the fourth sensitivity run, the organic module again had the highest influence on the average modelled N surplus in comparison with the direct payment for ensuring food security and the price of a kilogram of N ( Figure  d)). The observed model response with respect to the selected parameters was highest in the fourth sensitivity run; however, the modelled N surplus ranged only from . to . kg N haon average. A reduction in payments for ensuring food security caused a cultivation of ecological compensatory areas as a result of receiving lower payments. The price for N had only a small e ect on N surplus.

.
Unexpectedly, the sensitivity analysis showed only small responses of the modelled N surplus to systematic variation in the selected model parameters. The levels of the selected parameters were assumed to cover the maximum and minimum feasible values. Therefore, the possible reasons for the low sensitivity of modelled N surplus to selected parameters are: a) the N surplus is a result of many complex calculations and might be influenced by many parameters and biophysical and management restrictions embedded in the model. Based on our prior knowledge of the model, we assumed that all selected model parameters have an influence and thus have an e ect on N surplus. However, there are also other influencing parameters in the model that have a rather indirect e ect on N surplus. E.g., in addition to the organic module that was highly sensitive and its e ect was expected, we found that the parameter ensuring food security payments influenced N surplus more than expected; b) the modelled agents within the spatial community react di erently in response to variation in the individual parameter values, but at the regional scale the modelled N surpluses do not change that much. This was supported by the observation that the influence of individual farms' decisions on the average modelled N surplus is much higher when only a subsample of farms is considered compared to the analysis when all farms are included (i.e., , farms, data not shown). .
The option of switching to organic farming and payments for ensuring food security were identified as key parameters with the largest influence on the modelled N surplus. The lower N surplus was observed for scenarios with the organic module ON in all four runs. In the first run, the scenario with the intensity reduction at the intermediate position reduced the N surplus the most. The second run was mainly influenced by the organic module. In the third run, a high milk price and a low wheat price led to a low N surplus on average. High payments for ensuring food security increased the N surplus. This is surprising, as the payments for food security were expected to bu er the model response.

Model Response to a Levy on N in Fertilizers and Imported Concentrates
Levy scenarios . To model an N input levy, we extended the cost function of the model. Based on the estimated N content of fertilizer and concentrates, we added the levy to the fertilizer and feeding costs and ran the model for years from to . The agents' levy costs were extrapolated to the sectoral scale and divided by the total utilized land area. The tax revenues were equally paid back to the agents based on the agent's land area in the following modelling year in order to lower the impact of the levy on the farm income. This has been recommended by Rougoor et al. ( ) to prevent the reduction of competitiveness of the agricultural sector. In this way, farmers with low N inputs per area, profited from the levy, while farmers with high N inputs per area had to bear higher costs. .
We evaluated the impact of four levy scenarios on N surplus reduction: ) the reference scenario representative of the current agricultural policy (AP -); ) Basis scenario with the levy equal to CHF per kg N , which is about % of the N price); ) Basis scenario with the levy equal to CHF per kg N ( % of the N price) and lastly ) Basis scenario with levy equal to CHF per kg N ( % of the N price). In each scenario, the levy was reimbursed to the sector based on the agent's land area and the levy rose continually up to the final level of the levy from to .
. The average surpluses were calculated with the assumption that the inputs of mineral N fertilizer derived from the FADN data set were underestimated by % in the base year in comparison with the data from the Swiss farmer's association (Swiss Farmers Union ). The surplus was corrected by a factor . to match the values reported for the Swiss agricultural sector (Spiess ). Due to a lack of data on inputs of concentrates, no further corrections were conducted.  Arable farms -. -.
-.  Table : Gross margin per kg N input for di erent production activities estimated based on farm accountancy data network (FADN) (Hoop & Schmid ). Mean refers to the mean contribution margin in / , the lower and higher % refer to the % with the highest contribution margin and with the lowest contribution margin, respectively.

Result and discussion .
Increasing N price by % (Scenario basis ) led to a reduction of modelled sectoral N surplus on average by . %; with an eight times higher N price (Scenario basis ) the reduction was . % (Figure , Table ). The reduction was mainly achieved by a reduction in N fertilizer use, while the use of concentrates was barely a ected by a higher N price. There are three reasons for this. Firstly, feed concentrates for roughage-consuming animals have a low N content (i.e., . -. %). Consequently, increasing N price by % led to a lower price increase for concentrates (a % price increase per kg) than for N fertilizer (a % price increase per kg). Secondly, the reduction of concentrate input in milk production is mainly driven by payments for grassland-based milk and meat production in the reference and the N input levy scenarios. Therefore, a further N input levy did not reduce concentrate input in milk production significantly. Thirdly, the gross margin for the main animal production activities is much higher than the gross margin for crop production activities. The income loss when reducing animal stocking is therefore much higher in comparison with decreasing N input in crop production. Animal stocking even increased under the levy scenario of or CHF, as a result of the income loss compensation.
Figure : N surplus reduction from to . Basis , Basis and Basis scenarios refer to a level of the N input levy equal to CHF, CHF and CHF, respectively .
The response to the N input levy di ered between farm types (Table ). For arable farms, the average N surplus was reduced by % with a levy of CHF. For pig and poultry farms, the N surplus with an N input levy was higher than in the reference scenario. The increase in farm activities with higher gross margins and normally higher N surplus was also reported by (Jayet & Petsakos ). In Table , presents the estimated relative contribution margin of di erent farm activities. It shows that for some farms, a levy have to be quite high in order to induce a switch to another activity. Thus, a uniform N input levy can lead to unintended responses in some agents. .
Average farm income rose under all levy scenarios due to a higher number of exits of farm activities, especially for farms that already had low incomes. If they produced intensively, they were not profiting from the reimbursement of the levy, but faced higher costs. Under all levy scenarios, these farms had a higher risk of stopping their farming activities. The levy led to a decrease in open arable area and simultaneously in an increase in grassland and crops used for animal feeding. Under Basis scenario, the increasing grassland area was lower than the increase in animal numbers. Under all other levy scenarios, the decrease in animal numbers was lower than grassland extensions.
. The price elasticity for fertilizer use estimated by the model was -. . Price elasticity has been reported as crucial for the e iciency of a tax (Finger ). In the present study, the estimated price elasticity was very low in comparison with previously published results. For example, (Rougoor et al. ) in an econometric study reported price elasticities ranging from -. to -. . Similarly, in other modelling studies authors reported price elasticity ranging from -. to . (Finger ; Merel et al. ; Jayet & Petsakos ; Berntsen et al. ). The di erence to other models could be a result of PMP modeling. Buysse et al. ( ) recommended a normative mathematical programming that is more prone to abrupt changes, rather than PMP for the simulation of new policies. However, this could not explain the di erence between our results and other studies such as Merel et al. ( ), who also used a PMP model and achieved an elasticity of . . One possible explanation can be that our model is mainly represented by dairy farms ( %) with low fertilizer inputs that did not show a strong response to the levy on N inputs, whereas the model of Merel et al. ( ) is a regional model representing an intensive cropping system in California. Arable farms tend to respond more e ectively to a levy, as shown in our results (see Table ). .
Swiss farmers are less responsive to a N input levy, due to a higher level of regulation and direct payments in Swiss agriculture and as a result an increase in costs is of less importance. This is also evident from the results of the reference scenario (see Figure ). The modelled N surplus declined by % during the period from to without application of the levy on N in fertilizers and imported concentrates. This is likely a result of a new direct payment scheme introduced in Switzerland in that was already included in the reference scenario. The scheme abolished payments for animal production while increasing the payments for ecological performance (Mann & Lanz ). Also, the sensitivity analysis showed a higher influence of the direct payments than the price of N. .
Other factors that a ect the price elasticity of an environmental tax are psychological factors such as growing awareness of costs and environmental impacts of N fertilizer application as a consequence of a fertilizer tax implementation or mental accounting (Rougoor et al. ). Mental accounting could lead to adverse e ects, leading to more environmental impact since the agent has already applied some good environmental behaviour induced by the levy (Gruener & Hirschauer ). .
As model limitations, it has to be mentioned that the agents were not able to increase their N use e iciency by N reduced feeding strategies or increasing N e iciency of slurry application due to a lack of data on the implementation of such strategies in the base year. The low reduction of modelled N surplus for the pig and poultry farm types may be caused by limited options to reduce the N inputs such as the use of NP r feed in the model. In reality, N reduced feed for pigs (i.e., NP r feed) has been already used in areas with high pork production. It has been reported that NP r feed can potentially reduce total N surplus of Swiss agriculture by . % (Bracher & Spring ; Swiss Farmers Union ). Improving farmyard manure management requires investment in farmyard manure spreading equipment and farmyard manure storage facilities. This investment pays o at a levy of CHF for a reduction of % of ammonia emission (Peter et al. ). However, it could not be assumed that the investment in technologies that reduce ammonia emissions necessarily leads to a reduction in N surplus. It might happen that pollution swapping occurs and nitrous oxide emissions replace ammonia emissions (Loyon et al. ). The shipment of farmyard manure was di icult to model due to a lack of data and a low economic value of farmyard manure.

Conclusion
. The sensitivity analysis identified the possibility to switch to organic farming as a key parameter with the largest influence on the N surplus in the SWISSland model. The systematic variation in a limited fraction of parameters in the model did not lead to large responses in N surplus of the simulated agents. This could also be a consequence of the PMP cost function that favours retention of the status quo. Due to an extremely low demand elasticity of -. , the SWISSland model revealed only a small response to a levy on N in fertilizers and imported concentrates. The changes in the direct payment scheme led to a response in N surplus reduction comparable with a tax of CHF. The low response to the levy might be caused by a) the high specialisation of Swiss agriculture in dairy farming and animal production, where the losses in contribution margin in comparison with the N inputs are high and therefore agents display limited reaction to higher N prices. Some farm types even increased their N surplus as they intensify farm activities with a higher gross margin to compensate for their income loss; b) the high regulation and high direct payments which bu er Swiss agriculture. The introduction of an N input levy seems not to be e ective in achieving the Swiss agri-environmental goals. There is therefore a need to consider indirect incentives, changes in consumer behaviour by taxing food based on its environmental impact, or subsidies for low N input technologies.

Appendix A: Sensitivity analysis
Figures -show the sensitivity of response output variables such as farm income, numbers of farms, mineral fertilizer and concentrates use, the area of open arable land and grassland, the number of animals, particularly the number of cattle, pigs and poultry, and the number of organic farms, standardized by their means in the individual sensitivity phases. As the number of organic farms was low, changes in this parameter led to a higher variability in the responses of this output variables. In addition to these results, the sensitivity results provided insights into some model inconsistencies and allowed us to identify some errors in the model.