Abstract
This paper analyses the cost-effectiveness of agri-environmental auctions that solicit two-dimensional bids consisting of conservation activity and compensation payment. Taking a self-selecting contract schedule as a benchmark, an optimally designed auction has the potential to reduce government expenditure significantly. However, the relative cost-effectiveness of a multi-dimensional auction is determined by the bid scoring system and farmers' expectations of the maximum acceptable bid score. The article elaborates conditions for a bid scoring rule that optimises cost-effectiveness and tests how benefits of an auction approach may be eroded if farmers' expectations of the maximum acceptable bid score diverge from the level consistent with this optimum.
1. Introduction
There are two important trends affecting agri-environmental policy in the European Union (EU). On the one hand, the rising importance of environmental considerations has led to an increasing demand for the implementation of agri-environmental programmes. On the other hand, budgetary constraints have set limits to the spending on agri-environmental policy. In the light of budgetary constraints, policy makers face the challenge of searching for cost-effective ways to address agri-environmental concerns.
The common practice of most EU agri-environmental programmes has been to offer fixed payments for environmentally friendly management practices. An alternative approach to enhancing the cost-effectiveness of public expenses would be to auction agri-environmental contracts. The most prominent example of auctioning agri-environmental contracts is the Conservation Reserve Program (CRP) in the United States (US), which was established with the Food Security Act of 1985 (Reichelderfer and Boggess, 1988). Other examples are the US Environmental Quality Incentive Program (EQIP) in its design prior to the 2002 Farm Bill, the Australian BushTender Trial and EcoTender Trial, as well as various European pilot projects (Stoneham et al., 2003; Latacz-Lohmann and Schilizzi, 2005).
Empirical studies have demonstrated that cost reductions through conservation auctions can be substantial, though the scale of savings depends crucially on the specific auction design (Stoneham et al., 2003; Schilizzi and Latacz-Lohmann, 2007). Economic theory suggests that public expenses could also be reduced if a well-designed scheme of differentiated contracts, based on the principles of mechanism design, was offered (Wu and Babcock, 1995, 1996; Moxey et al., 1999; Glebe, 2006). The objective of the present study is to compare the cost-effectiveness of an agri-environmental auction with that of a self-selecting contract menu. In this context, we will analyse how the economic performance of an auction approach is determined by the bid scoring rule and farmers' expectations on the maximum acceptable bid score.
The analysis assumes a principal–agent relationship in which the government (principal) pays farmers (agents) for conducting conservation measures on their land. Since costs associated with conservation measures are specific to land characteristics and management techniques, farmers are considered to have an informational advantage over the government. The study will analyse how the adverse selection problem, which may result from the information asymmetry, can be best dealt with by using either a bidding or a self-selection mechanism. The analysis of the self-selection mechanism draws on the study of Wu and Babcock (1996), while the bidding mechanism is based on an extended version of the auction model introduced by Latacz-Lohmann and van der Hamsvoort (1997).
The remainder of the article is structured as follows: after reviewing the literature on contract and auction theory, Section 3 presents a conceptual framework of a voluntary agri-environmental programme dealing with endogenous environmental effects. In Sections 4 and 5 we analyse the cost-effectiveness of a self-selecting contract schedule and compare it with that of an optimal auction design. Section 6 demonstrates how budgetary costs of a multi-dimensional auction are determined by the bid scoring rule. Section 7 conducts a sensitivity analysis to demonstrate how the potential cost saving of an auction approach may be affected as farmers' expectations regarding the maximum acceptable bid score vary. The article ends with a discussion of the main findings.
2. Principles of contract and auction theory
2.1. Contract theory
Contract theory analyses conditions for an optimal contractual arrangement ensuring that agents voluntarily select the contract designed for them. Reducing the programme outlay by offering incentive-compatible contracts requires at least one other selection parameter besides the payment level. Applying a self-selection mechanism in the context of agri-environmental policy is therefore only meaningful if farmers are offered a choice between different management practices.
The principles of incentive-compatible contracts (Laffont and Martimort, 2002) were developed by Mirrlees (1971), Groves (1973), Green and Laffont (1977), Dasgupta et al. (1979), Myerson (1979), Guesnerie and Laffont (1984) and others. Building upon mechanism design theory, the standard approach is to analyse how information from informed agents can be transferred to an uninformed principal who has full bargaining power in contracting (Salanié, 2005). By offering different contracts, the agents' choice will reveal information about their respective adverse selection parameter. A crucial element is to design a menu of contracts ensuring that agents will find it optimal to reveal their adverse selection parameter. This condition is referred to as the incentive compatibility constraint (Laffont and Tirole, 1993). To be acceptable, a contract must also satisfy the agents' participation constraints, implying that by contracting, agents get at least their reservation payoff.
Contract theory was previously applied to agri-environmental policy by Smith (1995) who investigated how mechanism design may reduce the programme outlay of the CRP and by Smith and Tomasi (1995) who analysed the influence of transaction costs on the optimality conditions of an input tax. Further studies related to agri-environmental issues were conducted by Wu and Babcock (1995, 1996), Moxey et al. (1999) and Glebe (2006). The authors developed optimality conditions for a self-selecting contract menu aiming at the reduction of agricultural inputs. While Wu and Babcock (1995) and Moxey et al. (1999) differentiated two land types, a continuum of type was considered by Wu and Babcock (1996).
The present analysis of the optimal menu of agri-environmental contracts draws on the study of Wu and Babcock (1996), which developed criteria for the selection of an optimal input and payment schedule in dependency of land quality that they considered to be a continuous selection parameter. Since the authors assumed pollution abatement levels and payments to be endogenously determined by deadweight costs of tax increases, the calculation of optimal payment and input levels was rather complex. To facilitate comparison between a self-selecting contract menu and an auction mechanism, the present study will employ a modified model. We will consider a cost-minimisation problem, based on an exogenously given environmental target function.
2.2. Auction theory
Auction theory pursues a different route when dealing with adverse selection problems. The principle is to induce agents to reveal their adverse selection parameter through competitive bidding (Latacz-Lohmann and Schilizzi, 2005). An agri-environmental auction represents a procurement auction since it deals with an auctioneer (government) buying environmental improvements from bidders (farmers). The centrepiece of auction theory is the Revenue Equivalence Theorem (RET), which was introduced by Vickrey (1961, 1962) and generalised by Myerson (1981) and Riley and Samuelson (1981). It suggests that all major auction designs will lead to the same expected revenues for the auctioneer. Since the RET is based on a set of rather restrictive assumptions, numerous studies analysing the effects of relaxing these assumptions have evolved over recent decades. A comprehensive literature review on auction theory was conducted by McAfee and McMillan (1987), Milgrom (1985), Wilson (1992) and Klemperer (1999, 2000).
The bulk of the literature on auction theory is based on game-theoretic models that are often constrained by analytical tractability (Rothkopf and Harstad, 1994; Klemperer, 2002). Moreover, the bidding for agri-environmental contracts violates some of the benchmark assumptions underlying the RET since it is associated with bidder asymmetry and involves the supply of multiple units of environmental benefits (Cason et al., 2003). The Nash-equilibrium optimal bid of a multi-unit procurement auction can be calculated if bidders offer a single unit each (Schilizzi and Latacz-Lohmann, 2005). However, when dealing with auctions where bidders offer multiple units each, the computation of equilibrium bidding strategies becomes extremely complicated (Nautz, 1995). This may explain why most auction theory has dealt with the sale of a single indivisible unit, whereas the literature on multi-unit auctions of divisible units has not been much developed (Tenorio, 1997; Klemperer, 1999).
The agri-environmental policy set-up considered in this study allows farmers participating in an agri-environmental auction to offer multiple units of environmental benefit. When dealing with multi-dimensional auctions in which only a single bid is accepted (e.g. Hansen, 1988; Che, 1993), economic efficiency is achieved if the auctioneer announces his true utility function as the scoring rule (Milgrom, 2000). The present article differs from those studies since it considers procurement auctions in which multiple bids are accepted and bidders have the option of offering price/quality combinations of their own choice. To the author's best knowledge, there has been no research formally analysing the optimal bid scoring rule relevant for such agri-environmental auctions.
In the light of the complexities linked to game-theoretic auction models, we follow Latacz-Lohmann and van der Hamsvoort (1996, 1997) by modelling bidders' expectations of the highest acceptable bid as an exogenous variable. While Latacz-Lohmann and van der Hamsvoort (1997) dealt with one-dimensional bids, we extend their analysis by considering an auctioneer who chooses bids on the basis of financial offers and environmental benefits associated with programme participation. Environmental programme benefits are considered to be endogenous to conservation measures. To ensure that optimal conservation activity levels are chosen, farmers are given full information on the bid ranking system. The study does not examine whether withholding information on the bid scoring system may enhance the cost-effectiveness of auctions, as suggested by Cason et al. (2003) based on a laboratory study of repeated auctions. In contrast, the present study deals with a one-shot auction and therefore does not need to capture potential learning effects of repeated auctions (Hailu and Schilizzi, 2004).
3. The modelling framework
Consider a principal–agent relationship in which farmers are paid for participating in a voluntary agri-environmental scheme. The government tries to minimise payments by reducing the information rent that farmers can receive due to their informational advantage over the government. Information asymmetry arises due to the fact that the government only understands the range and distribution of different types of land quality and their associated production technologies, but has no knowledge of site-specific production conditions. The quality of a particular hectare of land is given by the index a, which may represent its specific soil, hydrological and biological characteristics. Since changes in natural conditions are smooth, a will be distributed as a continuous variable; land participating in the programme ranges from the worst quality a to the best land type ā, according to a land quality density function f(a).1
The physical agricultural output (q) that can be harvested per hectare is determined by site-specific characteristics (a) in combination with management practices. The latter are modelled by an input index x, which may combine the use of environmentally harmful inputs such as fertiliser or pesticides. We assume that agricultural output increases as a and x increase (qx(x, a) = ∂q(x, a)/∂x > 0; qa(x, a) = ∂q(x, a)/∂a > 0), while the marginal product of input use is declining (qxx(·) = ∂qx(·)/∂x < 0). The social value of environmental degradation (z) linked to input use is also determined by site-specific characteristics (zx(x, a) = ∂z(x, a)/∂x ≥ 0). Given that the leaching of groundwater pollutants and health problems increase more than proportionately as the intensity of agro-chemical input use increases (Kolpin, 1997; Yiridoe et al., 1997; Watson et al., 2000), we assume the environmental cost function to be convex (zxx(·) = ∂zx(·)/∂x ≥ 0). Both the production and the environmental functions are assumed to be twice differentiable.
If transaction costs, moral hazard problems (Ozanne et al., 2001) or political interests were taken into account (Glebe and Salhofer, 2007), governments might target input schedules that do not follow the rule of equating marginal profits and marginal environmental costs. Nevertheless, the results of the subsequent analysis will remain unaffected as long as targeted input levels are higher for better quality land (∂xs(a)/∂a > 0). The latter implies that farmers with lower compliance costs face stricter environmental restrictions. It guarantees that an incentive-compatible contract schedule based on mechanism design is superior to a fixed payment scheme.2 If the government aimed at higher input levels for lower quality land (∂xs(a)/∂a < 0), the subsequent analysis would be redundant, since the environmental target could neither be achieved by offering a contract menu nor by implementing a multi-dimensional auction.
Imposing stricter environmental restrictions on farmers with lower compliance costs applies to a wide range of agri-environmental programmes in which the input intensity on agricultural land is reduced. Examples are programmes restricting the use of agro-chemicals, as commonly applied in the EU (Diakosavvas, 2003). However, the domain of agri-environmental programmes dealt with in the subsequent analysis is not restricted to working land. It may also apply to conservation measures on fallow land, given that environmental benefits associated with these measures are positively correlated with farmers' costs of programme participation. On the other hand, the analysis will not apply to schemes in which the environmental performance of programme participation is not systematically (or not positively) linked to the level of farmers' compliance costs.
By choosing a constrained budget-cost-minimisation problem, we make allowance for the assumption that the environmental target is exogenous. If, instead, the decision problem were specified by social welfare maximisation, the optimal input schedule would be determined by the choice of the policy instrument and its inherent payment level. Taking into account administration and transaction costs linked to tax increases, a welfare maximising policy involving low governmental expenses would pursue more ambitious environmental goals than would a costlier programme. The most cost-effective measure following our approach is, therefore, the policy instrument (auction versus self-selection) that maximises social welfare. While both approaches (budget-cost-minimisation and welfare maximisation) lead to the same ranking of optimal agri-environmental policy instruments, the advantage of the problem specification pursued here is to simplify the algebraic analysis.4
To facilitate the analysis, we also consider that farmers have no reservation utility, implying that they will sign up to a conservation contract even if their net return is zero. Relaxing this assumption would not alter the results of the subsequent analysis, since a positive reservation utility affects the self-selection and the bidding mechanism in the same way.
4. Analysis of a self-selecting contract schedule
Building upon the principal–agent relationship introduced in the previous section, we will analyse the relative cost-effectiveness of an optimal self-selecting contractual arrangement. As discussed above, the government knows only the range of farmers' compliance cost structures (πx(a)), but is unable to attribute compliance costs to individual farmers. Under a discriminating policy, the principal (government) offers a menu of contracts, each of which specifies an input constraint and the respective compensation payment. A self-selecting contract schedule offers the scheme {[x(a), s(a)]; a ≤ a ≤ ā} where x(a) is the input quota on type a land and s(a) is the government payment per hectare.
The intuition of an optimal self-selecting contract schedule can be easily derived from Figure 1. If the government decided to offer only two contracts for the land types a and ā, type ā farmers should be paid at least area CDF in order deliberately to reduce the input level from xp(ā) (profit maximising level) to the targeted level xs(ā). Analogously, the minimum compensation payment for type a farmers for reducing inputs from xp(ā) to xp(a) is given by area AEG (participation constraint). However, given type a farmers' informational advantage over the government, they may realise an information rent of area CDEB if they sign up for the alternative contract (input quota xs(ā), payment CDF). Incentive compatibility requires therefore that the input quota xs(a) should be linked to a minimum payment equal to area ABCDG.
The cost-effective contract schedule for the two-land-type case implies that the additional payment when moving from the input quota xs(ā) to xs(a) is equal to area ABFG (Figure 1). From this we can intuitively derive that an optimum contract schedule for the whole range of land types [a, ā] (continuum land-type case) should offer a payment equal to area CDF for keeping the input quota xs(ā), while marginal payments for lower input quotas should follow the environmental target function gx(x). The payment for the strictest input quota xs(a) would be subsequently equal to area ACDG.
5. Cost-effectiveness of an agri-environmental auction
Next, we analyse the cost-effectiveness of an auction mechanism in comparison to that of the self-selecting contract schedule of the previous section. While the bidding model introduced by Latacz-Lohmann and van der Hamsvoort (1997) considered a unilateral input quota, we extend their framework by allowing bidders to propose input levels of their own choosing. This is needed if the government wants to achieve higher input levels for better land quality (∂xs(a)/∂a > 0) with a single auction.
Equation (17) demonstrates that proposed payments depend crucially on farmers' expectations about the range and probability distribution of the critical bid index. Since bidders would not accept a negative net return, proposed payments will not be lower than the costs associated with programme participation.
If farmers' expected maximal acceptable index score (Ī) is equal to I2 (see Figure 3), the government can achieve its aim of minimising the budget cost. If Ī < I2, land type ā farmers will have no incentive to participate in the auction, implying that the environmental target cannot be reached. The condition Ī ≥ I2 thereby ensures that all farmers will have an incentive to participate in the auction. Since proposed payments will tend to be higher when the expected index cap is higher, expectations given by Ī = I2 ensure that the environmental target is achieved with the smallest programme outlays.
We now compare bidders' proposed financial bids with the payment level of the self-selecting mechanism, based on the assumption of expectations (Ī = I2), which are optimal given the government's cost-minimising objective. A comparison between the bidding (equation (17)) and the self-selection mechanism (equation (10)) can be conducted on an equal footing, since both approaches lead to the same input schedule. Note that payments linked to an optimal self-selecting schedule (s(x) curve in Figure 2) correspond to proposed payments aiming at the index level I2 (s(x) = b|I=I2) (Figure 3). This is because land type ā farmers would propose payments equal to their costs in order to reach the index level I2, while the slope of the iso-index curve b|I = I2 (equation (18)) is the same as that of an optimal self-selecting payment schedule (equation (7)). Since we can derive from equation (12) that financial bids (b) will be lower than the payment levels at which the expected probability of bid acceptance is zero (b < b|Ī = I2), we conclude that proposed payments of an auction mechanism will be lower than that of a self-selecting contract schedule (b < s(x)).
If we consider that farmers expect the maximum acceptable bid to exceed the level consistent with cost-minimisation (Ī > I2), proposed payments will increase as Ī increases. An auction approach may therefore lead to higher programme outlays than a self-selection mechanism, if expectations about the maximum acceptable bid index are sufficiently high. We conclude that the cost-saving potential of an auction approach can only be exploited if farmers' expectations coincide with this ‘optimal’ level.
6. Analysis of an optimal scoring system
Having demonstrated that an auction approach has the potential to reduce programme outlays when compared with a self-selecting contract schedule, this section analyses the conditions for an optimal scoring system. We maintain the assumption that the maximum expected index cap Ī is at the level consistent with being able to reach the lowest budget cost ((b|Ī) = s(x)). In the following section, we then test how sensitive the programme outlays of an agri-environmental auction are to departures from this level of Ī.
The suggestion that the information rent is exactly halved is an artefact of the assumption that the expected bid cap is uniformly distributed and that the scoring system is additively separable (equation (19)). Figure 4 illustrates how optimal proposed payments (b) are determined by the bid scoring system (shape of the iso-index curves) and farmers' expectations on the critical bid index. An additively separable scoring system (equation (19)) induces optimal price–quality combinations (tangent points of iso-index and iso-net-return curves) for land quality ã to be located on the vertical line (quadrant 2). Consequently, when moving upwards on the line
, the net return (Π(ã))) will increase proportionally as the payment level b increases (quadrant 3). If I increases proportionally with b (quadrant 1) while the expected critical index is uniformly distributed (linear relationship between I and P(I ≤ I*)) (quadrant 4), there will be a linear relationship between P(I ≤ I*)) and Π(ã) (quadrant 5). Let the expected net return (product of P(I ≤ I*)) and Π(ã)) be maximised at point C, so that the associated proposed payment (b0*) will be exactly between A and B (equation (23)).
Figure 4 illustrates how the financial bid is affected by farmers' expectations. If their expected distribution function of the critical scoring index is convex rather than linear, the relationship between P(I ≤ I*)) and Π(a) is also convex. As a result, the bid that maximises the expected net return (point D) will be lower than that of the benchmark scenario (b1* < b0*), so that the information rent could even be reduced by more than 50 per cent. Analogously, bids will be higher if the expected distribution function is concave rather than linear.
Next, we consider scoring systems where optimal input quotas depend on financial bids. Figure 5 demonstrates that the cost-effectiveness of an auction can be enhanced if a scoring system induces farmers to offer higher input quotas as they increase their financial bids. However, the challenge of such a bid scoring system will be to induce farmers to propose the input quotas that are targeted by the government. The scoring system I** may lead to lower programme outlays (b** < b*) than the additively separable scoring system I* (equation (19)), since the line connecting efficient points for land type ã farmers (line ) is negatively sloped (quadrant 2). Figure 5 illustrates that the scoring system I** will affect the relationship between I and b (quadrant 1) as well as between Π(a) and b (quadrant 3), which will shift the line relating P(I ≤ I* and Π(ã)) (quadrant 5). The financial bid that maximises the expected net return (point F) linked to the scoring system I** might be lower than that of the additively separable scoring rule.8 However, this is not guaranteed and depends on the curvature of the relationships between I and b as well as between Π(a) and b.
7. Sensitivity analysis
Having demonstrated that a bidding mechanism can reduce programme outlays relative to a self-selecting contract schedule when bidders' expectations are consistent with minimising budget cost, we now relax this assumption. This section reports a sensitivity analysis that demonstrates numerically how the cost-effectiveness of an agri-environmental auction may be eroded by alternative expectations about the maximum bid cap. The analysis is based on a hypothetical agri-environmental programme that aims to reduce the amount of fertiliser used in wheat production. The scenario is based on natural conditions and production technologies typical for Northern Europe.
We consider that differences in natural conditions such as soil or climate cause maximum yields to range from 3.9 tonnes per hectare on the poorest quality land up to 9.8 tonnes on the best land, based on standardised wheat production functions (Krayl, 1993).9 Based on an average nitrogen (N) price of €0.7/kg and a farm-level wheat price of €180 per tonnes, profit-maximising N input levels are calculated to vary between 234 and 95 kg/ha from the best to the worst quality land. For the most (least) productive land, N inputs cost therefore €0.7 × 234 = 166.6 €/ha (€0.7 × 95 = 66.5 €/ha) while wheat earns €180 × 9.8 = 1764 €/ha (€180 × 3.9 = 702 €/ha).
Given an average raw protein content of 13 per cent (Marsh, 2005), the N withdrawn by the wheat crop is estimated to be 2 per cent of the yield. Based on this estimate, we calculate that the N-surplus without environmental policy varies from 16 to 38 kg/ha from the worst to the best land. If nitrate infiltration into deeper soil layers pollutes groundwater used for drinking, a reasonable government objective would be to ensure a non-positive N balance for each land type. Given this environmental target, the government may offer a variable payment for a self-selected input quota (self-selection mechanism) or implement an agri-environmental auction. For both policies, budget costs are calculated as the sum of farmers' information rents and profits forgone (opportunity costs), based on a zero reservation utility.
The calculation considers 20 equally distributed agricultural land types. The results are summarised in Table 1. A self-selecting payment rate based on a quadratic payment function (s = α1 + α2N + α3N2) will lead to average budget costs of €103.3 per hectare. The associated per hectare opportunity costs (€21 per hectare) approximate the minimal amount required to compensate farmers for programme participation. The same input schedule and its corresponding opportunity costs can be reached if an auction based on a quadratic scoring index (I = b + α2N + α3N2) is implemented. From the perspective of the government, it would be optimal if farmers' expected maximum acceptable index score, Ī, was 393. If this is given and farmers' expected index caps are uniformly distributed, the information rent (€41.1 per hectare) could be reduced by 50 per cent compared with a self-selecting contract menu, so that budget cost could be saved by up to 40 per cent (Table 1).
Cost-effectiveness of an auction in dependency of farmers' expectations on the maximum bid score
| Budget costs | ||
|---|---|---|
| (€/ha) | % | |
| Self-selection (s(N) = 393.16 − 1.92N + 3 × 10−4N2) | 103.3 | 100 |
| Auction: [Ī;Ī] = [100;393] (Ī = 100%) | 62.2 | 60 |
| Auction: [Ī;Ī] = [100;432] (Ī = 110%) | 76.2 | 74 |
| Auction: [Ī;Ī] = [100;472] (Ī = 120%) | 90.2 | 87 |
| Auction: [Ī;Ī] = [100;511] (Ī = 130%) | 104.3 | 101 |
| Budget costs | ||
|---|---|---|
| (€/ha) | % | |
| Self-selection (s(N) = 393.16 − 1.92N + 3 × 10−4N2) | 103.3 | 100 |
| Auction: [Ī;Ī] = [100;393] (Ī = 100%) | 62.2 | 60 |
| Auction: [Ī;Ī] = [100;432] (Ī = 110%) | 76.2 | 74 |
| Auction: [Ī;Ī] = [100;472] (Ī = 120%) | 90.2 | 87 |
| Auction: [Ī;Ī] = [100;511] (Ī = 130%) | 104.3 | 101 |
Cost-effectiveness of an auction in dependency of farmers' expectations on the maximum bid score
| Budget costs | ||
|---|---|---|
| (€/ha) | % | |
| Self-selection (s(N) = 393.16 − 1.92N + 3 × 10−4N2) | 103.3 | 100 |
| Auction: [Ī;Ī] = [100;393] (Ī = 100%) | 62.2 | 60 |
| Auction: [Ī;Ī] = [100;432] (Ī = 110%) | 76.2 | 74 |
| Auction: [Ī;Ī] = [100;472] (Ī = 120%) | 90.2 | 87 |
| Auction: [Ī;Ī] = [100;511] (Ī = 130%) | 104.3 | 101 |
| Budget costs | ||
|---|---|---|
| (€/ha) | % | |
| Self-selection (s(N) = 393.16 − 1.92N + 3 × 10−4N2) | 103.3 | 100 |
| Auction: [Ī;Ī] = [100;393] (Ī = 100%) | 62.2 | 60 |
| Auction: [Ī;Ī] = [100;432] (Ī = 110%) | 76.2 | 74 |
| Auction: [Ī;Ī] = [100;472] (Ī = 120%) | 90.2 | 87 |
| Auction: [Ī;Ī] = [100;511] (Ī = 130%) | 104.3 | 101 |
If the expected maximal index score Ī increases by 10 per cent, programme outlays will increase by 23 per cent from 62.2 to 76.2 €/ha (Table 1). If farmers' expected index caps are 30 per cent above the optimal level of 393, an auction will lead to higher budget costs (104.3 €/ha) than those linked to a self-selecting contract schedule (103.3 €/ha). We conclude that potential cost-savings of an auction approach may easily be eroded if farmers' expectations diverge from the level consistent with cost-minimisation of the auction outlay.
8. Conclusions
The article has analysed to what extent a bidding approach may enhance the cost-effectiveness of voluntary agri-environmental programmes. It has also examined how two-dimensional bids should be scored when dealing with endogenous environmental programme benefits. The analysis was based on an agri-environmental policy model that allows farmers to select a conservation activity level of their own choice. The analysis demonstrates that an optimally designed auction for endogenous environmental benefits has the potential to reduce government expenditure significantly compared with a self-selecting contract schedule. However, budget cost savings may easily be eroded if farmers' expectations of the critical bid score above which bids are rejected are increasingly suboptimal.
There are several other issues affecting the cost-effectiveness of agri-environmental auctions that have not been explicitly addressed in the analysis. A crucial factor determining the relative cost-effectiveness of a bidding approach relates to transaction costs arising from programme implementation and monitoring. Transaction costs due to monitoring and enforcing compliance should not differ between auctions and self-selecting contracts if both approaches pursue the same environmental objectives. Similarly, transaction costs for bidders are unlikely to exceed those faced by farmers when they sign up for a self-selecting contract menu. In both cases, farmers need to estimate compliance costs. Rejected bids, however, also incur transaction costs, which do not arise in the case of a self-selecting contract schedule. This might be particularly relevant if the number of rejected bids is high in relation to the total number of applicants. An assessment of transaction costs of agri-environmental auctions compared with a self-selection contract scheme would therefore be needed in order to judge their overall cost-effectiveness.
The cost-effectiveness of an agri-environmental auction is also affected by farmers' risk attitude. The conceptual analysis of this article has assumed risk-neutral farmers. However, if farmers are risk-averse, they may submit lower bids than those predicted in our analysis. Moreover, a high degree of risk aversion may prevent farmers from participating in the auction, while risk-prone bidders may submit high bids that will later be rejected. Further research should therefore test how the economic performance of bidding is influenced by different distributions of farmers' risk attitudes.
Finally, we want to comment on the underlying assumption that farmers are well informed about the cost structure of their farm in order to make rational decisions about the profit maximising input use. Our assumption of perfect rationality is shared with most theoretical studies in the economic literature. In practice, however, it will be difficult for most farmers to identify optimal input quotas for given prices within a self-selecting environmental programme. Estimating profit-maximising input levels becomes even more difficult, if farmers need to decide on both conservation activity levels and proposed compensation payments. We suggest empirical research in the form of experimental studies or pilot projects in order to take into account bounded rationality and to validate that the cost-saving potential of an agri-environmental auction can be realised.
Acknowledgements
The author would like to thank the ERAE's editor and anonymous referees for helpful comments and suggestions on this manuscript.
References
Appendix
Wu and Babcock (1995) analysed the conditions for a set of optimal self-selecting contracts based on a discrete number of land types, and generalised the analysis by considering a continuum of land types (Wu and Babcock, 1996). The principles of mechanism design apply in a similar fashion to both approaches. A discrete number of land types is best dealt with by offering a discrete number of contracts, whereas a continuum of land types should be offered a continuum of contracts.
Wu and Babcock (1996) demonstrated that, if a government wanted farmers with higher compliance costs to observe stricter environmental conditions (∂xs(a)/∂a < 0) over the whole range of land types, a uniform policy would be superior to any contract menu. In other words, the government would not be able to achieve its environmental goal. Analogously, the government would not be able to induce farmers with higher compliance costs to keep stricter environmental conditions by implementing a two-dimensional price–quality auction. It would thereby do better by offering a one-dimensional price auction for a uniform contract. The comparison between contract and auction theory could then be reduced to a comparison between a one-dimensional auction and a fixed payment scheme, as was done by Latacz-Lohmann and van de Hamsvoort (1996) and others.
Note that budget costs are composed of farmers' information rent and opportunity costs linked to the input restriction. Since farmers' opportunity costs are exogenously determined by the environmental target, a minimisation of information rent would lead to the same results as budget-cost minimisation.
In addition, one may argue with Hart and Latacz-Lohmann (2005) that a budget-cost-minimisation problem better reflects the decision making process of environmental policy-makers.
A formal analysis of the optimal contract menu for a continuum of land types has also been presented by Wu and Babcock (1996). The authors analysed the optimal input and payment schedule when they are endogenously determined by deadweight costs of programme outlays. Given our aim of comparing self-selection and auction mechanisms, we choose the different route of budget-cost-minimisation constrained by the exogenously given environmental target function gx(x).
The optimal payment function s(x) will be non-concave if stricter environmental restrictions are imposed on higher land qualities (∂x̂(a)/∂a >0). If this condition were not given, the optimum input schedule may involve several land types having the same input quota. In the literature on contract theory, this is referred to as ‘bunching’ or ‘pooling’ (Guesnerie and Laffont, 1984; Salanié, 2005). Since ‘bunching’ applies equally to a self-selection and an auction mechanism, it will not affect their relative cost-effectiveness and has therefore not been considered in the subsequent analysis.
To simplify the illustration, Figure 3 depicts only the bidding behaviour of land types ã and ā. Similarly, an optimal scoring index must ensure that farmers cultivating any other land type a will also choose the respective socially optimal input level xs(a).
Note that an efficient scoring index I** must ensure that land type farmers ā will deliberately propose the input quota xs(ā) (Ī** must be tangent to Π0(ā) at point G), while farmers cultivating any other land type will choose a financial bid at which the input quota xs(a) is optimal.
Measuring nitrogen (N) in kg/ha and yield (q) in ton/ha, we consider the production function qi = 16.58 + 1.421i + (0.4119 + 5.3 × 10−5 × i)N − 0.21N2/(98.5 + 8.2 × i), where i = 1, 2, … , 20.
