Staff Paper
ECONOMIC ANALYSIS APPROACHES TO POTATO-BASED INTEGRATED CROP SYSTEMS: ISSUES AND METHODS Ricardo Labarta , Scott M. Swinton, J. Roy Black, Sieglinde Snapp & Richard Leep
Staff Paper 2002-32
December, 2002
Department of Agricultural Economics MICHIGAN STATE UNIVERSITY East Lansing, Michigan 48824 MSU is an Affirmative Action/Equal Opportunity Institution
ECONOMIC ANALYSIS APPROACHES TO POTATO-BASED INTEGRATED CROP SYSTEMS: ISSUES AND METHODS
Ricardo Labarta, Scott M. Swinton*, and J. Roy Black Department of Agricultural Economics
Sieglinde Snapp and Richard Leep Department of Crop and Soils Sciences
Abstract: Economic Analysis Approaches to Potato-Based Integrated Crop Systems: Issues and Methods by R. Labarta, S. M. Swinton, J. R. Black, S. Snapp and R. Leep
In response to stagnating yields and mounting pest problems, Michigan potato growers are investigating ways to bring manure and cover crops back into potato production systems. The alternative systems bring benefits and costs for monetary net returns, the variability of net returns, and environmental impacts. This paper reviews the likely yield and biological system effects of alternative potato production systems that incorporate manure and cover crops. After briefly considering research designs for gathering experimental versus farm field data, it reviews four economic analysis methods for evaluating alternative systems. All methods are illustrated with examples. First, for evaluating comparative average profitability, it reviews a) enterprise budgets, b) partial budgets, and c) break-even analysis. Second, for integrating environmental impacts into profitability analysis by using monetary measures of environmental effects, it introduces “green” budgets. Third, for evaluating efficiency trade-offs between profitability and environmental impacts, it covers trade-off frontiers. Finally, for comparing the variability of returns across systems (including for risk-averse decision makers), it introduces analysis of variance and stochastic dominance. These methods provide a basic set of tools for the economic analysis of changes in potato-based crop systems that should be adequate for most static comparisons of annual crop management practices. *Corresponding author (
[email protected]). The authors are graduate research assistant, associate professor and professor in the Dept. of Agricultural Economics and assistant professor and professor in the Department of Crop and Soil Sciences at Michigan State University, East Lansing, MI.
The authors gratefully acknowledge financial support from the U.S. Department of Agriculture under the special grant for Sustainable Agriculture: Ecological Integration of Soil, Plants, and Animals Michigan project on “Quantifying Benefits and Costs of Cover Crops in Irrigated Vegetable and Potato Systems” as well as the Integrated Food and Farming Systems (IFAFS) project on “Re-Integrating Crops and Livestock Enterprises in Three Northern States” and the Michigan Agricultural Experiment Station. They also thank Don Smucker, Mark Otto and Ben Kudwa for their kind cooperation, as well as Timothy Dalton and Tim Griffin for comments on earlier drafts. 42 pages
Copyright 8 2002 by Ricardo Labarta, Scott M. Swinton, J. Roy Black, Sieglinde Snapp, and Richard Leep. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.
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ECONOMIC ANALYSIS APPROACHES TO POTATO-BASED INTEGRATED CROP SYSTEMS: ISSUES AND METHODS SUSTAINABILITY OF MICHIGAN POTATO PRODUCTION During the early 1900’s, Michigan potato production took place on mixed crop and livestock farms in scattered plots of 15-25 acres. By 1900, Michigan’s total potato acreage was approximately 350,000 acres (Salazar and Busch, 2001). Livestock manure helped to maintain soil organic matter. Legumes and perennial grasses were commonly grown in the dairy-potato cropping programs on these small farms. In the transition to the 21st century, a dramatic consolidation has occurred. Michigan potato acreage has declined to approximately 47,000, and farms have grown much larger and more specialized. Sixty percent of the acreage involves farms at least 500 acres in size. Significant investments in specialized equipment and management skills are now required to grow and store tubers successfully. An unforeseen consequence of specialization has been the tendency towards greatly reduced diversity of crops grown in rotation with potatoes, and limited use of manure and other soil amendments. Potatoes are frequently grown every other year in Central Michigan, rather than at four-year or greater intervals. The combined effect of continuous potato production with limited return of residues, and heavy equipment, has tended to reduce soil quality and increase pest levels. Declines of soil quality are reflected in the frequent need to fumigate, in order to reduce pest problems. Tillage requirements have increased in response to soil crusting and inconsistent drainage and water holding patterns across a field. Slight reductions in yield have also occurred that cannot be overcome through increasing rates of fertilizer application and other inputs. Less efficient nitrogen use in potato systems, particularly where soil quality has declined, creates the potential for environmental problems associated with nitrogen leaching and volatilization. All of these factors have contributed to renewed interest by potato producers in reintegration of their crop enterprises with livestock production operations. In addition, larger dairy and livestock producers are also looking for additional acreage to deposit animal manure and grow more forages for animal feed. One way forward being explored in Michigan is through cross-farm agreements. Informal contracts between potato growers and dairy operators facilitate land-swapping arrangements that broaden potato rotations to include forages. The availability of animal manure could help to re-build soil quality on potato ground. At the same time, application of manure to potato farms spreads out the land area on which manure is applied, reducing potential leaching and runoff into local waters. In order to determine whether the potential environmental and soil quality benefits can be realized, biological research is being undertaken. If and when these benefits can be documented, then farmers’ interest in integrating potato-based crop systems with livestock operations will depend on the balance of costs against those benefits. Defined broadly, those costs and benefits include not only average monetary values, but also the degree of variability and environmental impacts (Roberts and Swinton, 1996). Objectives The goal of this paper is to outline possible economic analysis approaches for the comparison of alternative potato-based crop systems. Of particular interest are alternative crop rotations 4
(including forage cover crops) and the incorporation of animal manure. While most of the costs of these systems are direct cash costs to the farmer, many of the environmental benefits either range beyond the farm or else are realized by the farm only gradually over time. A careful economic analysis must therefore proceed from an inventory of the environmental effects to economic methods for evaluating both non-market and marketed benefits and costs. The three steps necessary to identify suitable economic analysis approaches represent the objectives of this paper: 1) Characterize environmental effects of the alternative systems, including crop rotations, forage cover crops, and manure use; 2) Identify economic benefits and costs associated with each system; 3) Associate potential analytical methods with the specific types of benefits and costs identified for the alternative crop systems.
I. Potential Environmental Effects from Integrated Potato Systems Highlights of potato production that affect sustainability Potatoes are Michigan’s leading produce commodity (Michigan Department of Agriculture 2001). But intensive production practices have raised concerns about sustainability among growers and agronomists, as well as concerns about environmental consequences among water quality specialists. The main environmental effects of potato production are summarized as follows: Frequent potato planting can lead to declining yield At 47,000 harvested acres, potatoes represent less than one percent of Michigan’s total field crop acreage. In total value of production, potatoes rank fifth in the state (Table 1). However, in value of production per acre, they jump to first place compared with Michigan’s other major field crops (Figure 1). The high value of the potatoes encourages growers to seek high yields and short crop rotations. But these two goals can be incompatible when frequent planting leads to declining yield (Honeycutt et al., 1996). Soil compaction from heavy machinery One possible contribution to declining yields is soil compaction from heavy equipment, particularly where soils are fine-textured. Despite the high capital cost, specialized machinery for potato planting and harvest is necessary and cost-effective, given the considerable labor savings for this labor-intensive crop. Heavy machinery now dominates potato production throughout North America, leading to soil compaction in many cases.
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Water quality risks from excess nutrients Most Michigan potatoes are grown under irrigation in sandy loam or loamy sand soils, which are low in native fertility and moderately acid. Because potatoes require large quantities of nutrients, fertilizer use for irrigated potato production is usually high (Rosen, 1991). The potato plant’s shallow root system contributes to its high fertilizer demand. Nitrogen fertilizer application levels up to 300 lb N/acre or more have led to significant leaching losses into water supplies, ammonia losses to the atmosphere, and nitrification.(Christenson, et al., 1992; Lang et al, 19990) High levels of phosphorus and potassium fertilizers (up to 110 lb/acre of P2O5 and 380 of K2O) are also typical, because potatoes use soil phosphorus inefficiently and sandy soils do not hold large reservoirs of potassium (Lang, et al., 1999; Vitosh, 1990; Westermann et al., 1994). Fertilizer rates in excess of crop demand can lead to excess phosphorus and potassium fertilizers appearing in surface runoff water. The combination of heavy agro-chemical use over permeable soils with low water holding capacity can create serious water quality hazards (Wright, 1991). Soil fumigants kill beneficial soil microbes and contaminate water Potato early dying (PED) is a serious disease complex that causes plants to collapse and die prior to full maturity. It is associated with the combined infection of root lesion nematodes Pratylenchus spp. and the soil-borne fungus Verticillium dahliae (Wicks and and Harding, 1996). In severely infested fields, if growers do not fumigate the soils, tuber yields will be reduced. Some studies have documented losses of over 100 cwt/ac (MDA 2000). Moreover, once fields are infested, these organisms are difficult to eradicate, although in soils with higher levels of organic matter the impact of verticillium wilt may be ameliorated, as shown in a survey of 100 Idaho potato fields (Davis et al., 2001). In Michigan periodic fumigation is important for yield protection (MDA, 2000), particularly in shorter rotations. Unfortunately, fumigation kills not only the PED disease complex, but also other beneficial soil microbial life, and microbial populations take time to recover. Fumigants are costly to growers, toxic, and often leachable into water supplies.
II. Benefits and Costs from Integrated Cropping Systems with Focus on Potatoes Although the general benefits and costs of cover crops, rotation systems and the use of manure have received considerable attention in the literature, few studies have focused specifically on potato-based cropping systems. In this section, we summarize the benefits and costs – both private and social – associated with more “integrated” systems of potato production. Because farmers are often expected to bear the costs of their production practices, yet they may not realize all of the benefits, we divide discussion of the environmental benefits and costs between those external and internal to farm. Benefits external to the farm Some socially desirable benefits occur largely off the farm. systems may reduce soil erosion and nitrate runoff (Table 2).
For example, integrated cropping
The search for alternative cropping systems that abate the effect of soil erosion have produced promising results. Creamer et al. (1997) found that 13 cover crop mixtures (mainly legumes) 6
achieved 30% ground cover one month after planting and showed a high above ground biomass accumulation, which could reduce soil erosion potential. Torbet et al. (1996) found the potential for soil erosion control with the use of crimson clover and rye. Finally, Tanaka et al. (1997) reported a four-year experiment where field pea and tangier flat pea were introduced in a wheatfallow rotation. This study found that both legumes provided adequate dry matter production and surface cover to control soil erosion. Earlier Foltz et al. (1993) compared a corn-soybean rotation with a corn-alfalfa one. Using the EPIC biophysical model to simulate erosion effects between the two systems, they found that alfalfa provided greater soil erosion control. Although the environmental benefits of potato based systems have not been well investigated, some survey results from potato farmers are instructive. In a survey of Western New York vegetable and potato growers, 25% of those interviewed recognized the positive effect in soil erosion control from most of the cover crops they use (Stivers-Young and Tucker, 1999). Similar results were obtained in surveys of Michigan potato growers, where 40% and 45% of respondents reported using winter cover crops to reduce soil and wind erosion (Leep et al., 1995; Snapp et al., 2001). Nitrate leaching and agro-chemical surface runoffs are two important environmental effects that reach beyond farm boundaries. However few studies dwell upon potato-based systems. But reviewing the presence of both effects in other cropping systems that have less chemical use, can offer indicative information about potential nitrate leaching and chemical runoffs of potato systems. Jackson et al. (1993) found substantial reductions in soil nitrate leaching through the use of oilseed radish, rye and other legumes as a winter cover crop in lettuce systems. Foltz et al. (1993) used the CREAMS (Chemical, Runoff and Erosion from Agricultural Management Systems) model to simulate the chemical runoff in corn-soybean and corn-alfalfa rotations, finding that alfalfa was associated with reduced runoff of metolachlor and bentazon. In another study, Vyn et al. (1999) tested the nitrate leaching risk when establishing cover crops in corn systems. They found that annual ryegrass could reduce nitrate leaching. Apparent reduction in nitrate leaching losses has been observed with use of winter rye in Michigan field crop systems (Kinyangi et al., 2001). Benefits internal to the farm As listed in Table 2, benefits internal to the farm include are diverse. Some environmental benefits do not pass farm boundaries, but others share their effects between the farm and the landscape. However as the primary effects go to the farm, we consider these benefits as internal to farm. The increase of crop yields is the most direct expected benefit that cover crops and animal manure produce. The contribution of legume and manure to soil fertility have been well documented. Examples for this environmental benefit are the contribution of red clover and crimson clover to corn and barley yields (Torbet et al., 1996; Vyn et al., 1999), the positive effect of berseem clover in corn-soybean-oats rotation (Ghaffarzadeh, 1997) and experiments with legume green manures (Sweeney and Moyer, 1994). In potato systems, legume cover crops have been shown to supply 20 to 240 lb N per acre to a subsequent potato crop (Griffin and Hesterman, 1991; Honeycutt et al., 1996).
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Soil nitrogen mineralization potential increases over time in field crop systems with the integration of legumes or manure. This mineralization can support reduced use of fertilizer to maintain the same yield levels (Jones et al., 1998). Crop yield increase due to use of animal manure is also documented, including in potato based systems (Motavalli et al., 1989; Porter et al., 1999). Soil physical properties take a number of years to be observed, but occur with consistent manure application in potato systems (Porter et al, 1999). Weeds pose an important problem to potato producers. If integrated practices can lower weed pressure, this can reduce herbicide use and bring economic savings as well. Several studies have demonstrated that the use of cover crops and crop rotations can limit the effect of weeds, although manure application can be associated with enhanced weed pressure as well as suppression, depending upon the manure source and quality. Cover crops control weeds through competition, allelopathy, soil environmental changes, physical effect, and through maintaining surface residues (Creamer et al., 1996). Stivers-Young (1998) found that oilseed radish and mustards can suppress weeds. She concluded that annual winter weed suppression was probably the result of both competition in the fall and light interception by the residue in spring. Similar levels of cover-crop mediated suppression was found in processing tomato systems (Creamer et al., 1996). In a “Potato Ecosystem Project,” Gallandt et al. (1998) interseeded red clover in a barley crop rotated with potatoes. Weed biomass was reduced 77% and 72% respectively in year 3 and year 4 of the experiment, compared to systems without interseeded red clover. Cover crop suppression of weeds was reported as a benefit by 15% of vegetable and potato growers surveyed in New York (StiversYoung and Tucker, 1999), and by less than 5% of potato growers surveyed in Michigan (Snapp et al., 2001). Eghball et al. (1996) reported that composting manure reduces weed seed viability, and in the absence of composting, weed pressure was higher with some manure sources. Manure use tended to increase weed germination and weed control requirements in a long-term ecosystem potato experiment in Maine (Gallandt et al., 1998). Breaking disease and pest cycles is another environmental effect provided by integrated cropping systems, internal to farm but with important benefits to resources external to farm. The presence of diseases and pests has led potato growers to an increasing use of insecticides and fungicides (Padgitt, 2001). It also has caused a profit reduction for the higher input investment level. The use of cover crops and crop rotations could potentially provide this kind of benefit, as evaluated by several studies. Incorporation of an alfalfa rotation reduced Rhizoctonia solani infection in potatoes by 50%, while simultaneously providing 50 lb N per acre fertilizer equivalent to enhance yields (Honeycutt et al., 1996). Lazarus and White (1984) described a chemical-use reduction through the use of rye in different cropping systems that include potatoes, cauliflower, beets and beans. In another study Christenson et al. (1991) conducted a five-year experiment to evaluate different crop rotations. One of their most important findings was that longer rotations with alfalfa, beans and sugar beets provide important benefits in managing diseases and pests. Nematode control, and the potential to reduce fumigation frequency, has been observed with some brassica cover 8
crops (Porter et al., 1998), and three year alfalfa rotations with potatoes compared to shorter rotations (Bird, 1999).The use of animal manure can also provide benefits in the control of diseases and insects. Eghball (2000) reported that composted manure can kill pathogens. Manure had variable effects, but poultry manure was associated with reduced verticillium wilt in potato systems in Ontario farmer fields (Conn and Lazarovits, 1999). Over the long-term, if manure inputs build soil organic matter, this may contribute to lower incidence of verticillium wilt as observed in a recent survey of 100 potato fields in southeastern Idaho (Davis et al, 2001). Costs external to the farm Integrated cropping systems bring costs as well as benefits to the farm and the environment. Like benefits, costs can be divided into categories that are internal and external to farm. Research on the environmental effects of integrated cropping systems has identified some potentially negative effects if manure or cover crops are mismanaged. Examples include high levels of nitrogen leaching or volatilization, phosphorus accumulation in the topsoil, and increased nutrient runoff (Table 3). Although Foltz et al. (1993) showed important environmental benefits from the use of cover crops, they also found an incremental increase in chemical runoffs as a negative effect. They estimated a significant presence of atrazine and alachlor in topsoil after corn-alfalfa rotation (which may have resulted from their herbicide choice rather than the crop rotation). The application of manure has raised concerns about the accumulation of phosphorus in the topsoil and runoff to streams and rivers. Eghball et al. (1996) conducted a long-term experiment to study the effect of high rates of manure application on crops and soils. They found that phosphorus (P) from manure moved deeper in the soil, comparing with a chemical fertilizer. They also pointed out that this P movement may reach the groundwater, especially in areas with shallow water tables. Sharpley (1996) also indicated the risk of phosphorus accumulation in soil surface and its runoffs, from high rates of manure application. In Michigan, the Generally Approved Agricultural Management Practices (GAAMPs) now recommend that P content of both manure and soil be determined by soil test laboratories before application of manure. Costs internal to the farm Slow soil warming that delays crop planting can be a direct cost of growing winter cover crops or a forage rotation. Stivers-Young and Tucker (1999) found that cover crops of clover, wheat and rye slowed soil warming on potato and vegetable farms in New York. A slow rate nitrogen release from cover crop residues, and the difficulty of accurately estimating the level of nutrient availability from residue mineralization are related problems with cover crop rotations. Initial nitrogen immobilization has been found after winter cereal crops are incorporated (Griffin and Hesterman, 1991; Vyn et al., 1999) and manure is applied (Motavalli, et al., 1989). Animal manure application could have potentially negative effects on quality of crop products within the farm, as shown by application of high rates of manure to potato, which apparently increased the incidence of potato tuber rots (Porter et al., 1999).
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Potential benefits to monitor in experimentation with manure and cover crops The literature review above indicated that monitoring the following characteristics should help to document benefits from more integrated systems: 1) Need to fumigate to control plant parasitic nematodes and verticilium wilt 2) Improvements in potato storage life, and ability to maintain potato tuber quality for chip frying (gravity, bruise potential, sugar profile and chip frying color during storage) 3) Yield increase 4) Nutrient efficiency: a) Input/output budgets indicate enhanced yield output per nutrient input b) Soil nitrogen mineralization potential pool increased, decrease in soil inorganic nitrogen (leachable) at harvest 5) Increase in duration and quantity of soil cover (months with living crop cover, amount of high quality residues from crops and cover crops) 6) Effects on soil quality properties: a) Bulk density (a decrease indicates soil compaction is lower) b) Aggregate stability (increase is associated with reduced crusting and tillage requirements, enhanced soil aeration) c) Water retention properties (increase in soil water holding capacity will improve irrigation efficiency).
III. Monitoring of Systems to Be Analyzed Which analytical approaches best suit a comparison of conventional to alternative management systems depends in part on whether the data are experimental or not. Experimental data offer strong controls over non-treatment effects, resulting in robust statistical comparisons. Nonexperimental data tend to require larger sample sizes due to the wider range of factors besides the treatment effect that may affect outcomes. Either way, the foundation of sound economic analysis is the careful recording of data of economic interest. The term “of economic interest” here has a broad meaning, for it includes all those factors that affect the costs and benefits inventoried above. Hence, for alternative potato-based crop systems, variables of economic interest will include not just input costs and value of crop yield, but also invisible costs such as labor time and the range of environmental outcomes from these systems. Likewise, “economic interest” embraces not only mean values of variables, but also higner statistical moments, measuring dispersion and skewness that influence the riskiness of outcomes. Monitoring of variables in controlled experiments and paired comparisons Controlled experiments offer the best means to isolate a treatment effect (such as potato yield and quality response to manure application) from a baseline “control” system. However, controlled experiments of dynamic systems can be slow to generate results on the dynamic processes affecting soil quality and associated potato yield and quality
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Comparison of paired farm fields The monitoring of existing potato fields under integrated vs. non-integrated management offers an opportunity to observe the dynamic effects of these systems over time. The chief design challenges are 1) to choose field pairs that minimize the number of non-treatment effects, and 2) to obtain a sample size that will permit useful statistical inferences. 1 While field monitoring involves more uncontrolled variables than do experiments, the number of non-treatment effects can be limited via judicious selection of paired fields. A useful paired comparison might focus on manure application into a current potato cropping system. The first step in such a study would be to identify pairs of fields with and without a history of manure application. The target fields should have a short (2-year) rotation of chip potatoes and corn. Given the fields to be compared, a key decision is what to hold constant and what to compare between both treatments. In order to focus on differences in outcomes associated with cover crop and manure use, it is desirable to keep constant across the paired fields: 1) Chipping potato variety, 2) Field management (as much as possible), 3) Crop rotation 4) Soil type (texture), 5) Maturity/harvest period (implying similar planting date) If possible, paired fields should be located near one another. The key outcome variables to be monitored are those that affect profitability, environmental impacts, and the sustainability of productive land: 1) Potato yield 2) Potato tuber quality, including a) Internal tuber defects, specific gravity, bruise potential b) Potato chip color (changes over time) c) Storability (changes in sugar over time), 3) Soil quality (chemical and physical characteristics) a) Physical measures (% water-stable soil aggregates, bulk density, water holding capacity) b) Total organic matter carbon and active organic matter (i.e., light/large fraction C) c) Nitrogen (total N, nitrogen mineralization potential, soil inorganic N after harvest) d) Water infiltration rate e) Soil phosphorus status f) Soil pH 4) Agrochemical use a) Fumigation b) Fertilizer c) Nutrient efficiency ( Input/output budgets indicate yield output per nutrient input)
1 Note that it may be quite difficult to identify suitable pairs of working farm fields. Farmers’ natural propensity to seek the most successful crop management practices given current knowledge available and market price expectations often limits the variety of practices in use within a limited geographic area. However, the consequences of failing to obtain suitable pairs are to be forced to base analysis upon much weaker nonparametric statistics or anecdotal arguments (Roberts and Swinton, 1995).
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5) Irrigation efficiency (estimated from water holding capacity) 6) Farmer perceptions of both production process and resultant potato marketing attributes. Note that profitability effects can be calculated from elements 1, 2, 4 and 5 above. Given the desired characteristics of paired fields, the next step is to ensure a sample size appropriate for meaningful statistical inference. See Appendix 1 for a review of methods for determining sample size for meaningful inferences from paired comparisons.
IV. Plan for Economic Analysis Economic analysis is one key class of evaluation criteria for potato-based integrated systems. With data from controlled experiments and/or paired field comparisons, a range of analytical approaches is possible. Desirable choices will depend upon analytical goals and resources available. The focus here is on methods that require limited resources, assuming that most effort will be devoted to the biological side of potato systems evaluation. Budgeting Budgeting approaches can compare the average economic performance of different alternative cropping systems. Four budgeting methods are suggested to compare the benefits and costs of potato-based systems under integrated and non-integrated management. They include 1) single enterprise budgets, 2) partial budgets of profitability effects from making changes, 3) break-even budgets for the minimum change required in order to obtain net gains, 4) “green” budgets that incorporate environmental values. Enterprise budgets for individual crop and system enterprises The main objective of enterprise budgets is to determine the profitability of each potato-based cropping system and assess the gross return to fixed cost in each case. For this purpose we first should elaborate enterprise budgets for each component crop in a rotation (e.g., potato, corn, wheat, alfalfa). On that basis, it is possible to build enterprise budgets for any cropping system by combining individual crop budgets with other components of integrated potato management into “system enterprise budgets”. For each enterprise budget we need to calculate the gross revenue and the total variable cost. The gross revenue is the result of multiplying an average crop market price times the average yield of the same crop. The yields for the average calculation must come from the experiments and the paired field comparisons (rather than from the standard published values used in the pro forma examples included here). In the cropping system case, the gross revenue should include the price of each crop considered in the system and the yield that each crop obtains under an integrated or non-integrated management. Where a component crop may produce more than one quality grade of product, the gross revenues should include different product quality categories with corresponding prices and percentages of the total output (e.g., Swinton and Scorsone, 1997).
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The variable costs are the costs incurred only if production takes place. Typical variable costs included: - Seed - Chemical inputs - Equipment repairs - Other inputs (i.e. fuel, oil, lube) - Labor - Marketing - Other costs that vary with yield (i.e., harvest, transport, drying) The last step is to calculate the net return to fixed factors2 (NRTF) that each crop and cropping system produces. This measure is the difference between the gross revenue and the total variable cost. The NRTF measures returns above such fixed costs as capital depreciation, interest, maintenance, taxes, insurance, and management. NRTF is generally suitable for comparison across annual crop systems that do not differ significantly in their requirements for capital investment and management skills. Examples of pro forma enterprise budgets for potato-corn and potato-alfalfa 2-year rotations are shown in Tables 4a and 4b. Partial budgets for system comparisons between groups of enterprises This technique has been used largely when comparing two or more similar production systems. Usually the comparison is between a benchmark cropping system and one or more alternatives. All systems under comparison must face the same production conditions, the same fixed cost and only vary in explicitly specified components. The classic partial budget includes two main sections (Kay and Edwards, 1994). The Reductions to Income section includes the added costs and reduced revenues caused by shifting to the alternative option. All extra costs for adopting the new system and the losses for leaving the traditional system are tallied in this section. The second section is the Gains to Income, where added revenues and decreased costs counterbalance the reductions to income. This second section includes all the direct gains from adopting the alternative system as well as the cost reductions due to leaving the “base” system. The bottom line is the Net Change in Income, which subtracts the total reductions to income from the total gains to income. If the time horizon of the analysis is greater than one year the Net Change in Income can be divided by the number of years of the time horizon to yield a Net Annual Change. Table 5 illustrates a pro forma partial budget for a change from a potato-corn to a potato-alfalfa 2-year rotation, based on the enterprise budget data from Tables 4a and 4b. The key requirement for using the partial budget method is to identify carefully all the changes (positive and negative) produced by shifting from a traditional cropping system to a proposed alternative. Changes that could be a substitution, an inclusion, or an exclusion should be valued and incorporated as a reduction to income or as a gain to income.
2 The NRTF is also referred to as “return over variable costs” (Marra, 1996) or simply “gross margin.”
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Break-even Analysis Break-even analysis is appropriate when considering marginal shifts of acreage from one crop system to another (Hilker et al., 1987). This method compares a “defender” crop or system (e.g., a conventional system) to a “challenger” crop or system (e.g., an alternative system). Like enterprise budgets, break-even analysis is also based on the calculation of the net return to fixed resources (NRTF), the difference between gross revenues and variable costs. The NRTF for the defender system measures the opportunity cost of the earnings sacrificed in replacing one crop or system by another. The break-even method can answer two questions: 1) Break-even price: Given the yields per acre and the variable cost per acre of two crops and the price of one of them, what would the price of the second crop have to be to generate the same return to fixed cost as generated by the first crop? 2) Break-even yield: Given prices and variable cost of two crops and the yield of one of them, what would the yield of the second crop have to be in order to generate the same return to fixed costs as generated by the first crop? As potato-based alternative integrated systems are typically more costly than the conventional potato-corn rotation, their appeal hinges on finding higher benefits. Given that potato growers have little influence over potato prices, the break-even yield can identify a practical target to make the higher cost systems economically competitive. The break-even condition or critical point is reached when the defender NRTF equals the challenger NRTF (NRTFch = NRTFdf). The allocated cost in the challenger system has two components. The first depends directly on the level of yields of the product under evaluation (i.e. hauling, sorting, storage). The second component is a cost that varies from the defender technology but it is independent of the changes in yield. We can represent the allocated costs as: AC = C0 +C1Y where: AC = Allocated Costs C0 = Cost independent of the yield C1 = Cost dependent on the level of yield Y = Yield The first application of the method is for systems (defender and challenger) that do not change the crop used (e.g., manure application). In this situation the important changes are produced through differences in the allocated costs of the two systems. In this case the break-even yield is calculated as:
∆Yield= (Allocated costsch – allocated costsdf) /(P- C1)
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The second application is used when the challenger and defender systems differ in some of the crop revenues considered. In this case, the defender NRTF measures the “loss” (opportunity cost) of giving up the NRTF from the defender system. This break-even yield is calculated by:
∆Yield= (Allocated costsch + NRTFdf) /(P- C1) A sensitivity analysis with different yield and price scenarios can be useful. Table 7 illustrates a break-even analysis for the potato yield gain required in order for the 2-year potato-alfalfa rotation to match the net returns from a potato-corn rotation. “Green” budget method Green budgeting can complement any of the budgeting approaches above. This procedure allows incorporating the environmental effects that a crop or cropping system may generate. In practice the green budget typically begins with an enterprise budget to which environmental benefits and costs are added. Although adding lines to an enterprise budget is easy enough, identifying suitable values for environmental services lack market prices presents a challenge. A large literature exists on methods of non-market valuation, including methods based on hypothetical contingent markets, environmental characteristics embodied in marketed goods and services, consumer expenditures to avert health risks, and other approaches (see, e.g., Braden and Kolstad, 1991; Freeman, 1993; Bergstrom et al., 2001). The first step to build a green budget is to identify each environmental benefit or cost for any cropping system being evaluated. Information from experimental plots or paired comparison fields can be the base for this calculation. The second step is to select an adequate non-market value for that environmental effect. Environmental values of different impacts may be based on different valuation methods. Values may be drawn from the literature with appropriate adjustments in order to avoid the high cost of primary research into valuation of non-market environmental services. The literature on “benefit transfer” examines conditions under which environmental values from the literature may be applied under different conditions than those for which they were originally estimated (e.g., Vandenberg et al., 2001). Appendix 2 illustrates the use of benefit transfer to develop an environmental cost value for nitrate leaching for use in a “green” enterprise budget. Once incorporated in an enterprise budget, the environmental values permit a new net return to fixed factors (NRTF) adjusted for specified environmental impacts. Table 7 illustrates a green budget template based on the potato-corn rotation.
PROFITABILITY-ENVIRONMENTAL TRADEOFF FRONTIERS Monetary values for environmental impacts may seem subjective or may simply be unavailable. An alternative way to incorporate environmental effects into an economic analysis of profitability is to evaluate the tradeoff between profits and environmental impacts. Trade-off frontiers allow evaluation of two distinct objectives using the concept of efficiency.
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Expected Benefits
Expected benefits
The efficiency criterion assumes that given a choice among alternatives with the same level of risk, the farmer would choose the most profitable option; conversely, among different alternatives with the same level of profits, the farmer would choose the least risky (Bouzaher et al., 1992). A set of these efficient strategies makes up the “efficient frontier” of alternatives that cannot be improved upon without a tradeoff. Figure a) shows an example of an efficient tradeoff frontier. Any point along the curve represents an efficient point, and any point above the line is less efficient considering the same level of either expected benefit or level of risk. For example, points A and B offer the same level of expected benefit, but point A is more efficient because it provides a lower level of risk. Likewise, points C and D face the same level of risk, but point C is more efficient because it allows a higher level of expected benefits. Policy changes may affect the profitability impacts of these tradeoffs. Similarly, technological innovation may change the shape of the tradeoff frontier (Swinton and Casey, 1999).
Measures of dispersion for risk analysis Agricultural production is subject to many sources of random variability. Analysis of variance provides a method for separating certain sources of statistical variability in order to determine whether there exist significant differences in some treatment effect (such as conventional versus alternative crop system). Stochastic dominance is a nonparametric method for comparing entire probability distributions based on stated preference criteria. These methods are discussed below. Analysis of Variance The budgeting methods above are useful for synthetic analysis of means or scenarios. They do not, however, permit insights about variability in outcomes. Analysis of variance (ANOVA) is a classic method to analyze the variation in response variables and assign portions of this variation to the independent variables considered. The objective of the ANOVA is to locate the important independent variables and determine how they affect the response variable (Wackerly et al., 16
1996). In controlled experiments, the key independent variables are treatment effects and block effects. In uncontrolled studies, the independent variables typically include many variables that are expected to condition the effects of the treatment variables of research interest. The variance is the expected distance from any variable to its mean (Wooldridge, 2000). This measure is calculated dividing the sum of squared deviations from the mean of a variable by n-1 (where n is the sample size). Using the method of least squares we can minimize the variability of the dependent variables by making the sum of squared deviations as small as possible. This sum of square deviation is also known as the total sum square of the dependent variable and can be divided in the sum of squared deviations due to each independent variable and the unassigned sum of squared error (SSE). In order to determine the importance of any independent variable, we need a comparison between the sum of squares due to each independent variable and the SSE. This is possible using an F-test, which evaluates the null hypothesis that the independent variable has no effect. In our case we will apply this procedure to two key variables 1) net returns to system, and 2) environmental benefits. In both cases, the analysis of variance will follow the same procedure. Our interest is to test the difference between net returns in a conventional system and the net returns in an alternative integrated system (or the difference in both systems about environmental benefits). Following previous notation we are interested in comparing the means of two populations µ1 and µ2, assuming equal variances. Considering equal sample size among any comparison (n1 = n2), the relevant F-statistic becomes: F= (SST/1)/(SSE/(2n1-2)) with 1 and 2n1-2 degrees of freedom, where SST =(n1/2)*(Y1 – Y2)2 and SSE = Σ(n1-1)Si2 where Y1 and Y2 are the sample means of the two populations sampled and Si2 is the estimator of the common variance. A large F statistic implies rejection of the null hypothesis that the conventional system population has a larger mean than the other. Hence the rejection area for a one-tailed test with significance level α is F > Fα, where Fα is the critical value of F corresponding to α. We use synthetic gross revenue data from three potato-based systems to illustrate the analysis of variance calculations. We calculated 9 different gross revenue values for each of three two-year alternative rotations that include: 1) a potato-corn rotation 2) a potato-alfalfa rotation with hay harvested, and 3) a potato-alfalfa-rotation with no hay harvest. The raw data and the results of the ANOVA procedure are summarized in Tables 8 and 9. For ease of interpretation, treatment means are compared using the least significant difference (LSD) criterion, which assumes that the same standard error applies to comparisons across all treatment pairs. The results show that significant differences are only present between the two systems that include alfalfa, not between the potato-corn and the alfalfa systems.
17
Stochastic Dominance Stochastic dominance is a method for ranking alternative cumulative probability distributions for decision makers whose risk preferences fit into a broad class. Thus a comparison among alternatives must be made at every specific point along the distributions. Economic analysis often employs net return as the outcome variable of interest (Gebremedhin et al., 1998; Hardaker et al., 1997). First-degree stochastic dominance (FSD) builds from the assumption that a decision maker prefers more of the attribute (e.g., net return) to less. This assumption is the least restrictive in that it fits all classes of risk preference. Results are based on the pairwise comparison of cumulative probability distributions. In conventional terms, a challenger system with a cumulative distribution F(x) is preferred to (dominates) a defender system with cumulative distribution G(x) if and only if F(x) ≤ G(x) for all x. When paired data are available, it is possible to take differences to calculate FSD. The procedure starts by calculating the annual NRTF for each experimental plot. In a balanced experimental design where pairwise comparisons are possible, the next step is to compute differences of net returns between all pair-wise combinations of cropping systems (i.e. two-year potato-corn rotation vs. two year potato-alfalfa rotation, etc). A cropping system A dominates a cropping system B if the differences in the net returns are all positive when the differences computed by subtracting the net returns of system B from that of system A (Gebremedhin et al., 1998). In other words, when comparing net returns distributions from two different cropping systems, we need to pair each observation ai (system A) with each observation bi (system B). The difference for all pairwise comparisons (ai -bi) should be all positive if System A dominates and all negative if system B dominates. When there is any change of signs in these differences, we cannot claim that one system dominates the other. Second-degree stochastic dominance (SSD) is a more discriminating method tht applies to all risk-averse decision makers (Hardaker et al. 1997, King and Robison 1984). Again assuming the availability of paired comparison data, the dominance decision rule in SSD states that a challenger system A is preferred to (dominates) a defender system B if and only if
∑ ∑b k
i =1
ai ≥
k
i =1
i
∀i, k (k = 1 to N )
Using the synthetic gross revenue distributions from the three potato based systems presented in Table 8, we illustrate these two methods of risk efficiency analysis. As a first step, , we order the gross revenues from smallest to largest to form cumulative distributions (Table 10a and 10b). For FSD, differences between gross revenues across rotations are taken for individual observation pairs. For SSD, cumulative differences between rotations are calculated at each pair of observations. Comparing the cumulative distributions of the three systems (Table 10a and Graph 2) both the potato-corn system and the potato-alfalfa with hay harvest dominate the potato-alfalfa system without hay harvest under FSD. This means that at every point, the gross revenues of the first two systems are superior to the potato-alfalfa system without hay harvest. However, using FSD 18
we cannot rank the first two systems. Using SSD (Table 10b) we observe that the cumulative difference between the gross revenues from the potato-corn rotation and the potato-alfalfa with hay harvest are always positive. This implies that despite some individual observations where revenue from the potato-alfalfa system exceeded the potato-corn rotation, the cumulative value is always superior for the potato-corn rotation, making it the dominant system under the SSD criterion that applies to risk-averse decision makers.
CONCLUSION
The methods presented here provide a basic set of tools for the economic analysis of changes in annual crop systems. They are appropriate for static comparisons of annual crop management practices when there are no important underlying dynamic effects. The illustrated applications of these methods are intended as examples only, and not as primary research results. Likewise, space constraints did not permit examination of the subtleties of the methods introduced, all of which can be explored in greater detail by consulting the cited references. Innovations in the potato-based crop systems discussed in the opening literature review suggest the potential for productivity and environmental benefits. These economic analysis tools can be applied to evaluating whether those benefits are worth the costs incurred to obtain them.
19
TABLE 1. AVERAGE PRODUCTION VALUE AMONG MAIN FIELD CROPS IN MICHIGAN (19962000)
Crops
Acres harvested
Rank
Barley
22,000
9
2,080,000
1
309,000
Value of Production (thousands of $) 2,128
Rank
Value per Acre
Rank
9
100
8
504,488
1
240
5
5
94,094
6
300
3
78,000
7
7,382
8
90
9
47,000
8
94,868
5
2,020
1
1,882,000
2
308,976
3
160
6
Sugar beets
163,800
6
104,050
4
640
2
Winter wheat
558,000
4
85,867
7
150
7
1,280,000
3
341,010
2
270
4
Corn Dry beans Oats POTATOES
Soybeans
Dry hay
Source: MDA (2001).
20
Table 2. Benefits from integrated crop systems on and off farm as cited in literature.
Integrated practices
cropping On-farm benefits
Off-farm benefits Reduces pollution of ground and surface water
Increases crop yields Reduces N losses
Manure Application
Reduces fertilizer
requirement
for
Improves soil structure Improves soil carbon status Improves soil water holding capacity, irrigation efficiency
Cover Crop/Rotation
Kills pathogens Increases crop yields
Reduces soil erosion
Suppresses weeds
Prevents wind erosion
Breaks disease and pest cycles
Reduces nitrate leaching and surface runoff
Reduces leaching Reduces soil compaction Improves soil structure Improves soil carbon status Reduces fertilizer
requirement
for
21
Table 3. Costs from integrated crop systems on and off-farm as cited in literature.
Integrated cropping On-farm costs practices Manure Application Increases tuber incidence
Off-farm costs
decay Causes nitrogen leaching and volatilization (if surface applied rather Increases weed pressure than injected) Accumulates P in surface (if surface applied rather than injected) Increases fertilizer runoff
Cover Crop/Rotation
Competes for water and Increases nitrate percolation nutrients Limits soil warming Limits soil N mineralization early in season
22
TABLE 4A. SYSTEM ENTERPRISE BUDGET: EXAMPLE FOR A 2-YEAR POTATO-CORN ROTATION Units Potato Corn System Marketable yield cwt or bu/ac 315.00 200.00 Marketable price $/cwt or bu 6.85 2.10 GROSS REVENUE $/ac 2157.75 420.00 2577.75 COSTS*
$/ac
Seed Fertilizer Herbicides Insecticides Other chemical Irrigation Drying Fuel, Oil, Lube Repairs Utilities Marketing Trucking Others NRTF**
808.80 158.00 102.20 40.80 150.00 12.00
316.89 38.25 87.20 29.25
27.00 50.00 9.49 30.00 5.50 10.00 30.00
68.60 83.00 41.00 100.00 53.20 $/ac
1348.95
103.11
1125.69 196.25 189.40 70.05 150.00 12.00 27.00 50.00 78.09 113.00 46.50 110.00 30.00 53.20 1452.06
* Source: Individual crop enterprise budgets (Nott et al., 1995) ** Net Return To Fixed Resources
23
TABLE 4B. SYSTEM ENTERPRISE BUDGET: EXAMPLE OF A 2-YEAR POTATO-ALFALFA ROTATION. Units cwt or bu/ac $/cwt or bu $/ac
Potato 346.50 6.85 2373.53
COSTS* Seed Fertilizer Herbicides Insecticides1 Other chemical Irrigation Drying Fuel, Oil, Lube Repairs Utilities Marketing Trucking Others
$/ac
798.30 158.00 91.70 40.80 150.00 12.00
174.75 48.00 55.20
68.60 83.00 41.00 100.00
24.15 35.90 1.50
92.75 118.90 42.50 100.00
53.20
2.00
55.20
NRTF**
$/ac
1575.23
-174.75
1400.48
Marketable yield Marketable price GROSS REVENUE
Alfalfa 0.00 0.00
8.00
System 346.50 6.85 2373.53 973.05 206.00 146.90 40.80 158.00 12.00
* Source: Individual crop enterprise budgets (Nott et al., 1995). ** Net Return To Fixed Resources 1 Note that rotation with alfalfa could reduce the need for fumigation, thus reducing potato insecticide costs in the potato-alfalfa system. The data presented here are not experimental, and are intended only to illustrate budgeting methods. Basic Assumptions: Potato yields increases 10% after an alfalfa rotation. Alfalfa generates no direct revenues (only indirect fertility benefits as a cover crop). Nitrogen credit is 42 lb/acre (Mahler and Hemanda, 1993), valued at 0.25 $/lb. (Note that this value is a conservative estimate compared with 150 lb/ac by Griffin and Hesterman [1991] and 100 lb/ac from Vitosh [1990], based on a 100% alfalfa stand.)
24
Table 5. Partial budget: Change from a potato-corn rotation to a potato-alfalfa rotation (2year rotations per acre). Reduction to Income ($/ac) ADDED COST Alfalfa Seed 48.00 Alfalfa establishment 126.75
Gains To Income ($/ac) ADDED REVENUES Potato Yield gain 215.78
REDUCED REVENUES No corn yield 103.11
Decreased Cost N fertilizer Savings
Total Reductions (A) 277.86 Net Change in income (B-A) -51.58 Net Annual Change -25.79
Total Gains (B)
10.50 226.28
BASIC ASSUMPTIONS Potato yields increases by 10% due to alfalfa rotation. Nitrogen credit of alfalfa is 42 lb per acre (47 kg/ha).
25
Table 6. Break-even yield analysis: Change from a potato-corn rotation to a potato-alfalfa rotation (2-year rotations per acre) Defender System ($/ac) NRTF** (OPPORTUNITY COST) 103.11 Corn net return 103.11
Challenger System ($/ac) Allocated Cost 163.75 Nitrogen credit -10.50 Alfalfa seed 48.00 Alfalfa establishment 126.25
BREAK-EVEN POTATO YIELD GAIN = 42 CWT/AC (P = $6.85 and C1 = $0.49 / cwt)
** NET RETURN TO FIXED RESOURCES BASIC ASSUMPTIONS BREAK-EVEN POTATO YIELD GAIN = (NRTFDE + ALLOCATED COSTCH) / (P-C1), WHERE P = POTATO PRICE PER HUNDREDWEIGHT (CWT) = $6.85 / CWT C1 = UNIT COSTS THAT VARY WITH YIELD PER CWT = (MARKETING + OTHERS) / YIELDDE = (100+53.20) / 315 = $0.49 / cwt
26
Table 7. Green enterprise budgets: Example of 2-year rotation budgets with environmental cost charged for nitrate leaching. Potato-corn Potato-alfalfa $/ac $/ac Agricultural revenue 2577.75 2373.53 Environmental revenue --Gross Revenue 2577.75 2373.53 Agricultural costs Seed Fertilizer Herbicides Insecticides Other chemical Irrigation Drying Fuel, Oil, Lube Repairs Utilities Marketing Trucking Others
1125.69 196.25 189.40 70.05 150.00 12.00 27.00 50.00 78.09 113.00 46.50 110.00 30.00 53.20
973.05 206.00 146.90 40.80 158.00 12.00 --92.75 118.90 42.50 100.00 -55.20
157.60
123.60
Total Costs
1283.29
1096.65
NRTF***
1294.46
1276.88
Environmental costs Nitrate leaching**
* Source: Tables 4a & 4b and Appendix 2. ** See calculations in Appendix 2. Assumes no leaching from alfalfa crop. *** Net Return to Fixed Resources
27
Table 8: Nine-year gross revenues for three potato based systems
Years of rotation 80-81 82-83 84-85 86-87 88-89 90-91 92-93 94-95 96-97
Potato-corn 1824 1591 1846 1909 1994 2119 2191 2282 1948
Potato-alfalfa 1 1584 1455 1724 1830 1910 2048 2112 2105 1815
Potato-alfalfa 2 1835 1708 1891 2029 2138 2423 2427 2400 2072
1 The grower cannot harvest and sell the hay 2 The grower can harvest and sell the hay
TABLE 9: ANALYSIS OF VARIANCES OF GROSS RETURNS FOR THREE POTATO BASED SYSTEMS
LSD
Mean Standard Difference Error
Sig
(I) Treatm (J) Treatm 1 2 124.56 111.792 .276 3 -135.44 111.792 .237 2 1 -124.56 111.792 .276 3 -260.00* 111.792 .029 3 1 135.44 111.792 .237 2 260.00* 111.792 .029 *The mean difference is significant at the 0.05 level
C.I Lower Bound -106.17 -366.17 -355.28 -490.73 -95.28 29.27
C.I Upper Bound 355.28 95.28 106.17 -29.27 366.17 490.73
28
Table 10a: First degree stochastic dominance in potato-corn and potato-alfalfa rotations systems. Potato-corn $/ acre (System C)
PotatoAlfalfa (no hay harvest) $/ acre (System A1)
PotatoAlfalfa (with hay harvest) $/ acre (System A2)
Gross revenue difference between A1 and C
Gross revenue difference between A2 and C
Gross revenue difference between A2 and A1
1591 1824 1846 1909 1948 1994 2119 2191 2282
1455 1584 1724 1815 1830 1910 2048 2105 2112
1575 1735 1835 1863 1907 1965 2208 2235 2236
-136 -240 -122 -94 -118 -84 -71 -86 -170
-16 -89 -11 \-46 -41 -29 89 44 -46
120 151 111 48 77 55 160 130 124
Basic Assumptions Defender system: 2-years potato-corn rotation Alternative 1: 2 years potato-alfalfa rotation (with no hay harvesting) Alternative 2: 2 years potato-alfalfa rotation (With hay harvesting) Alternative 1 increases potato yield after an alfalfa rotation in 10%, due the nitrogen contribution Alternative 2, does not increase potato production but generates profits from dry hay harvest Potato and Corn price and yields come from Michigan statistics (MDA 2001) Alfalfa yields and price come from Minnesota and National Statistics (USDA, 2001)
Table 10.b. Second degree stochastic dominance analysis for potato-based systems (based on Table 10a). Cumulative difference between system A1 and C -136 -376 -498 -592 -710 -794 -865 -951 -1121
Cumulative difference between system A2 and C -16 -105 -116 -162 -203 -232 -143 -99 -145
Cumulative difference between system A2 and A1 120 271 382 430 507 562 722 852 976
29
Figure 1: Share of chemical input in annual operating cost per acre, nine field crops, USA, 2000.
Share of chemical input in annual operating cost per acre, nine field crops, USA 2000 700 600
US $
500 400
Other operat. Cost Chemical input
300 200 100
Potato
Barley
Oats
Sorghum
Rice
Cotton
Wheat
Soybeans
Corn
0
Source: USDA, 2001.
30
Figure 2: Stochastic dominance analysis illustrated for three systems in Tables 8, 10a and 10b.
FSD and SSD for Potato based systems
Cumulative Probability Distribution
1 0.9 0.8 0.7 0.6
Pot-Corn
0.5
Pot-Alf1
0.4
Pot-Alf2
0.3 0.2 0.1 0 0
500
1000
1500
2000
2500
3000
Gross benefits ($ per acre)
31
Appendix 1: Criteria for sample size in a paired comparison
Given the desired characteristics of paired fields, the next step is to ensure a sample size appropriate for meaningful statistical inference. For the statistical analysis we will develop a pairwise comparison that is simply the difference between two means (Toohaker, 1993). Because we assume that the integrated treatment is only adoptable by farmers if it is superior to conventional practice, we use a one-sided test. For selected outcomes in the integrated treatment (i) and in the non-integrated one (n), the underlying hypothesis test is as follows: H0: Xji – Xjn ≤ 0 H1: Xji – Xjn > 0
where Xjk = mean of variable j with treatment k (k=i, n)
In this procedure we will use a paired difference t-test whose statistic is defined as: td = Xji – Xjn / (σ/n) For this statistic we are explicitly assuming a zero difference between the two population means (µi = µn) and the same for the population variance (σi2 = σn2). Hence, the standard deviation of the mean difference equals σ/n. Because the standard deviation in the denominator in the tdstatistic is divided by n, the test is highly sensitive. The minimum sample can be calculated from the above td-statistic, assuming a known variance. We used the precision method (Aczel, 1999). This method uses a known standard deviation, desirable confidence levels for the test (and associated z-values), and different acceptable margins of error. The level of confidence or power of the test is related to the probability of type II error (to accept the null hypothesis when is false). It measures the probability of correctly concluding that the true mean falls within the margin of error. The margin of error is the interval above and below the mean that the researcher defines as being no different than the mean (e.g., mean potato yield plus or minus a margin of error of 50 cwt). Combining the standard deviation, the z-value corresponding to a desired level of confidence, and the acceptable margin of error, the precision method identifies a minimum sample size by the formula: n = 2sd2z2 / margin2 Based on prior research results with Michigan potato-based systems, we developed several scenarios in Table 4 for calculating the minimum sample size in a paired comparison. For standard deviation estimates, we used the yields reported in on-farm nitrogen fertilizer trials (Vitosh, 1998). Information available was from two years of field monitoring. For each year separately, we calculated a standard deviation was 47, but combining the two years, the standard deviation rose to 50. To be conservative, we used the higher value. We assume that data from paired fields will reflect balanced information between treatments. Another important assumption is that potato yields will follow a normal distribution. Table A1.1 lists minimum
32
sample sizes by acceptable margin of error (30-50 cwt above and below mean yield) and confidence level (80, 80 and 95 percent). Given the minimum number of field pairs required, can this many suitable pairs be found among cooperating farmers? If not, it would be possible to consider a division among some farmers’ fields. Such a division is only possible statistically if each subdivision is treated as independent from the others. This means ensuring that the management of one part will not influence performance in the other part(s).3
Table A1.1. Sample size as a function of margin of error and one-sided confidence levels with known standard deviation = 50.
Margin of error 50 40 30
50 40 30 50 40 30
Level of confidence and z-value
80% 0.84
Number of pairs 2 3 4
Total sample size 4 6 8
90% 1.28
4 6 10
8 12 20
95% 1.64
6 9 16
12 18 32
Source: Aczel (1999).
3 An attempt to identify at least 8 pairs of potato fields in Michigan that met these criteria in 2002 was unsuccessful.
33
Appendix 2: Obtaining Environmental Values Using Benefit Transfer
Because estimating non-market values is costly researchers sometimes use findings of previous studies for specific environmental goods and services and under similar circumstances. This method is known as “benefit transfer”. However, in order to avoid misleading estimates it is important to document the assumptions and judgments under which the estimates are being transferred (Delavan and Epp, 2001). Poe and Bishop (2001) suggested using a damage function in order to estimate the value of environmental services and avoid incurring the high cost of original valuation research. The damage function relies on data available in previous biophysical studies and is conditioned on socio-demographic variables. This method associates different levels of damage with existing estimated values. The figure below illustrates consumer willingness to pay (WTP) to avoid nitrate exposure from drinking water at different levels of ground water contamination. The WTP estimates come from a contingent valuation survey that asked homeowner respondents how much they would be willing to pay in increased annual property taxes to avoid specified levels of nitrate exposure.
Estimated WTP for avoiding nitrate exposure $ P E R Y E A R
600 500 400 300 200 100 0 0
10
20
30
40
50
Nitrates (NO3-N) mg/l
Source: Poe and Bishop (2001), p. 62. The data illustrated cannot be used directly in crop production budgets, because the WTP values refer to consumer households’ annual WTP to avoid all nitrate exposure from groundwater. For crop budgets, relevant environmental costs need to be expressed in dollars per acre per year. In order to illustrate the conversion from consumer exposure values to values for producer mitigation, we use estimates of nitrate leaching under a potato-wheat-corn rotation in Washington State. According to Peralta-Alba et al. (2001) the potato-wheat segment of this rotation leaches on average 72.22 kg/ha (32.8 kg/acre) and the corn segment 14.64 kg/ha (6.7 kg/acre), for a total of 39.5 kg/ac over the two-year rotation.
34
For simplicity, assume that the total amount of nitrate leached per acre becomes dissolved in the total flow volume of rainfall and irrigation water that passes through a typical acre in a year. The total flow volume of water per acre in Michigan in a typical year is 916,205 gallons or 3,469,159 liters (Institute of Water Research, 1996). These figures imply a nitrate concentration in the total flow volume of 9.45 mg/l following the potato crop and 1.93 mg/l following the corn crop. Table A2.1: WTP values for selected nitrate exposure values, Wisconsin case study NO3-N (mg/l) Estimated WTP ($/yr) 2 259.45 5 312.30 10 371.05 20 453.60 Source: Poe & Bishop, 2001; Table 3.8, p. 62. If the normal ambient nitrate level equals 2 mg/l (the maximum natural nitrate level, according to Poe and Bishop [2001]), then leaching from the potato-wheat year of the rotation increases the nitrate concentration by 9.45 mg/l. Using the data in Table A2.1 (which corresponds to the previous graph), the value of increased nitrate leaching under the potato crop can be calculated as the WTP associated with the 8 mg/l increase over the ambient level (from 2 to 10 mg/l) plus 1.45/10 times the WTP increase from 10 to 20 mg/l, for a total of $123.60/yr. In the corn year of the rotation, the value of the 1.93 mg/l increased nitrate concentration in total water flow is 1.93/3 times the WTP increase from 2 to 5 mg/l, or $34.00/yr.
35
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