4.1. Sensitivity Analysis of Agent-Based Model
 To assess the agent-based model, a sensitivity analysis is conducted to evaluate the behaviors of selected output variables in response to changes in 18 selected sets of input variables. Admittedly, such an approach does not prove the realism of the model, but, in the absence of empirical data, it is a common means of establishing model plausibility [e.g., Forrester and Senge, 1980; Miller, 1974].
 The sensitivity analysis is carried out by changing one set of input variables at a time and running the agent-based model each time for the resulting combination of input variables. The simulations are carried out for the simulation period 1985–2000 for a population of 26% bold–74% cautious farmers. The farmers adapt and interact as described in section 3.4. The sensitivity analysis is carried out to simulate the effects of the 18 sets of input variables in Table 1 on four output variables, namely the fractions of the Salt Creek watershed in corn, soybeans, miscanthus, conservation tillage, and enrolled in carbon trading averaged over time. (Although the agent-based model allows farmers to convert cropland to uncultivated grass for the purpose of producing carbon offsets, the fraction of watershed in uncultivated grass is not of concern since for all scenarios examined here and below, the fraction of the watershed in uncultivated grass is negligible (<1%).) To do so, the 18 sets of input variables are perturbed one set at a time from their “base” values by −50% to +50% and the resulting values of the four output variables recorded.
Table 1. 18 Sets of Input Variables Perturbed in the Sensitivity Analysis of the Agent-Based Model
|Set Number||Description of Input Variables in Set|
|1||Time series of corn prices and farmers' initial expectations of them|
|2||Time series of soybean prices and farmers' initial expectations of them|
|3||Time series of miscanthus prices and farmers' initial expectations of them|
|4||Time series of carbon allowance prices and farmers' initial expectations of them|
|5||Time series of fertilizer prices and farmers' initial expectations of them|
|6||Time series of corn production costs and farmers' initial expectations of them|
|7||Time series of soybean production costs and farmers' initial expectations of them|
|8||Time series of miscanthus production costs and farmers' initial expectations of them|
|9||Costs of converting existing equipment for conservation tillage and farmers' initial expectations of them|
|10||Savings in crop production from conservation tillage and farmers' initial expectations of them|
|11||Farmers' risk aversions|
|12||Farmers' time discount factors used in the valuation of the time value of money|
|13||Farmers' initial standard deviations of miscanthus production costs and prices|
|14||Farmers' initial standard deviations of conservation tillage costs and savings|
|15||Farmers' initial standard deviations of carbon allowance prices|
|16||Time series of corn yields and farmers' initial expectations of them|
|17||Time series of soybean yields and farmers' initial expectations of them|
|18||Time series of miscanthus yields and farmers' initial expectations of them|
Table 2. Average Annual Nitrate Load (103 t N/yr) at the Salt Creek Watershed Outlet From 1985–2000a
|1985 Carbon Price ($/t CO2e)||MPRb = 0||MPRb = 0.4||MPRb = 0.5|
 For the most part, the base values are set according to historical values. However, historical data are unavailable for miscanthus and carbon allowance prices. Therefore, base values for the former are set at 0.4 of the average of corn and soybean prices. Base values for the latter are constructed from a forecast of future prices by Pew Center on Global Climate Change , and are set at $17/t CO2e in 1985 and rising steadily to $40/t CO2e in 2000.
 Figure 5 reports the results of the sensitivity analysis. From the sensitivity analysis, the most influential factors affecting a farmer's crop decisions are crop prices, production costs, and yields. This is in line with intuition, as well as the literature [Schnitkey and Batts, 2011]. Additionally, the output variables change in directions according to intuition. For example, the fractions of land in crops are positively correlated to crop prices and yields, but negatively correlated to production costs. Similarly, the fraction of land in conservation tillage (and with it, the fraction of land enrolled in carbon trading) increases with potential cost savings and also with carbon allowance prices, but decreases with the costs of converting existing equipment. Moreover, the fractions of land in miscanthus and conservation tillage, with which farmers are assumed to have no prior experience at the start of the simulation period, decrease with the farmers' initial uncertainties of associated prices, costs, and savings.
Figure 5. Results of the sensitivity analysis of the 18 sets of input variables defined in Table 1 for four output variables. The time averages of the fractions of the Salt Creek watershed in corn (solid line), soybeans (solid gray line), miscanthus (dashed line) and conservation tillage (dashed gray line), or enrolled in carbon trading (dotted line).
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 To assess the agent-based model further, a second set of simulations is carried out to evaluate farmers' aggregate behavior for different assumptions of the proportions of bold and cautious farmers, and with and without farmer interactions. The simulations are run for the same simulation period, and with the same values of input price, cost, yield, and weather variables as for the sensitivity analysis described above. Figure 6 presents the results. Figure 6 compares the aggregates of farmers' crop and BMP decisions for five populations of farmers. In the first population, the entire population is 100% bold (0% cautious) and, in the second through the fifth, the percentages are 74% (26%), 50% (50%), 26% (74%), and 0% (100%), respectively. The results are presented as time series of fractions of the watershed in corn, soybeans, miscanthus, conservation tillage, and enrolled in carbon trading.
Figure 6. Time-aggregates of farmers' crop and BMP decisions for different populations of farmers without and with interactions when miscanthus price is set at 0.4 of the average of corn and soybean prices, and carbon allowance price set to the $17/t CO2e in 1985 scenario. The farmer populations consist of farmers with perfect foresight (solid gray line), farmers that are stationary (with zero adaptation of forecasts) (dashed line), 100% bold farmers (squares), 26% cautious–74% bold farmers (open diamonds), 50% cautious–50% bold farmers (open inverted triangles), 74% cautious–26% bold farmers (open circles), and 100% cautious farmers (solid triangles).
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 Figure 6 also compares the results when the farmers interact and share information with neighbors and when they do not. For comparison, Figure 6 presents predictions for a population of farmers with perfect foresight and another population of 26% bold–74% cautious farmers with zero adaptation of forecasts. For the farmers with perfect foresight, risk aversion and the bold-cautious distinction do not apply as there is no uncertainty of future prices, costs, yields, and weather, and therefore, no Bayesian adaptation of forecasts and no aversion to risk. As for the farmers with zero adaptation, their perceptions of future conditions do not change with new observations and are stationary at their initial values. For farmers with zero adaptation of forecasts, the definitions of bold and cautious still apply (in terms of risk aversion) even though there is no Bayesian updating, but there is still uncertainty, and therefore the potential for aversion to risk.
 The results in Figure 6 agree with intuition. Take, for example, the farmers' adoption of miscanthus cultivation, which is considered in this study as a new practice with which the farmers have no prior experience at the start of the simulation period. In general, the farmer populations that are interacting and with a higher proportion of bold farmers tend to adopt miscanthus cultivation quicker. Bold farmers, who are more risk tolerant, are more willing to adopt miscanthus cultivation. And, as they interact with their neighbors, who may be cautious and therefore, more risk averse, their neighbors' uncertainty about miscanthus cultivation is gradually reduced until it reaches a point where they too are willing to adopt it. In this manner, miscanthus cultivation is propagated from one farmer to the next, eventually to include the entire population. The same pattern can be observed for conservation tillage and carbon trading. As shown in Figure 6, the farmers' uptakes of the three new practices all follow an S-shape pattern, which is consistent with predictions of the Bass model of new product diffusion [Bass, 1969].
 A closer look at the individual decisions of the farmers (not shown here) reveals that when adopting miscanthus cultivation or conservation tillage for the first time, the farmers (whether bold or cautious) tend to do so first on one (out of three) plot of land, usually the marginal plot, which is the smallest and which has a higher flood frequency (which affects corn and soybean yields but not miscanthus yield). After some time, they will plant miscanthus on a second plot of land, and finally on the third plot. Due to their risk aversion, most of the farmers are not willing to commit all their land at once to the new practices but will do so only after they have gained some experience and reduced their uncertainties. This pattern is consistent with observations and discussions in the literature [e.g., Tisdell, 2000; Scherr, 1995].
 The observation that the results differ for the different farmer populations in terms of the consistency of their year-to-year decisions also agrees with intuition. Consider, in Figure 6, the time series of the fractions of the watershed in corn and soybeans. The time series for the populations with higher proportions of cautious farmers tend to be more stable with time. There are two reasons for this. First, cautious farmers are relatively slow to adjust their perceptions of prices, costs, yields, and weather with new observations, and therefore, slow to adjust their decisions too. Second, the higher levels of risk aversion ascribed to cautious farmers mean that they tend to cultivate mixed crops (as opposed to single crops) to reduce the uncertainties in their net returns. Most of the time, cautious farmers allocate roughly the same amount of land to corn as to soybeans. The results here are consistent with other studies, such as Falco and Perrings , which have found risk aversion to be a major reason for farmers to diversify their activities.
 In general, farmers in Central Illinois have been quite consistent in their crop decisions. For several decades, crop acreage patterns in that region have been fairly constant. (An exception is 2004–2008, when corn acreage showed a sudden increase in response to a growing demand for corn-based biofuels.) Perhaps it can thus be inferred that the historical behavior of real farmers tend more toward caution than boldness, and that bold farmers are a minority if they exist at all.
4.2. Example Application
 The agent-based model coupled to the hydrologic-agronomic model may be used to study farmer decisions and the environmental impact of those decisions under various assumptions of farmer adaptation of forecasts and interactions, and different scenarios of prices, costs, yields, and weather. For example, Figure 7 presents predictions of the time-average fractions of the watershed in corn, soybeans, miscanthus, conservation tillage, and enrolled in carbon trading over the simulation period 1985–2000 for multiple combinations of miscanthus and carbon allowance prices. The predictions are for the 26% bold–74% cautious population of adaptive and interacting farmers. Predictions for when they have perfect foresight and when they are stationary (i.e., when there is no adaptation of forecasts), are also provided for comparison.
Figure 7. Time-average aggregates of farmers' decisions for different scenarios of carbon prices and where the miscanthus price ratio (MPR) is 0, 0.4, and 0.5. Population of farmers with perfect foresight (open triangles), population of 26% cautious–74% bold farmers that are adaptive (solid circles), and population of 26% cautious–74% bold farmers that are stationary (with zero adaptation of forecasts) (crosses). MPR is the ratio of miscanthus price to the average of corn and soybean prices.
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 The results are for four scenarios of carbon allowance prices based on forecasts of future prices by the Pew Center on Global Climate Change . These scenarios differ in terms of their starting and ending prices but are similar in that they all show a steady rise in the price with time. In Figure 7 and below, they are identified by their starting prices in 1985, the first year of the simulation period. In the first scenario, the 1985 carbon allowance price is $13/t CO2e and in the second, third, and fourth, $17, $28, and $33/t CO2e, respectively. Note that the prices under the $17 scenario are the same as the prices used in the sensitivity analysis in section 4.1. Miscanthus price is assumed to be a fixed multiple of the average of corn and soybean prices. Here, two scenarios are examined: in the first, the ratio of miscanthus price to the average of corn and soybean prices is set at 0.4 (as assumed in section 4.1) and in the second, 0.5.
 As in Figure 6, it is apparent that different assumptions of farmers' behavioral profiles lead to very different predictions of their decisions and the environmental consequences of those decisions. For example, Figure 7 shows that when there is a positive miscanthus price, there are large differences in miscanthus acreage between farmers who are adapting their forecasts, those with perfect foresight, and those who do not adapt. The latter are very unlikely to cultivate miscanthus on a large scale. On the other hand, farmers who are adaptive are more likely to grow miscanthus if its price is favorable in relation to corn and soybean prices. Further, for a given set of prices, farmers with perfect foresight have an even greater likelihood of cultivating miscanthus. The implication of this is that a biofuel crop program (based on uncertain market prices) can succeed or fail depending on the individual behaviors of participating farmers.
 Similarly, as shown in Table 2, stream nitrate load, under the same set of prices, can be quite different between farmers with different adaptive tendencies. As before, the implication is that the success of a water quality protection program based on the cultivation of second-generation biofuel crops and/or carbon trading to stimulate conservation tillage depends on the individual behaviors of participating farmers.