Evolution of Learning in Technology Adoption: The case of the U.S. Soybean Seed Industry

This paper examines how the evolution of learning affects technology adoption. We use a sequential adoption model that accounts for differences between forward-looking adopters, who consider future impacts of their learning, and myopic adopters, who only consider past learning. We apply the analysis to three panels of U.S. soybean farmers representing different stages of the genetically modified (GM) seed technology diffusion path. We show that uncertainty is considerably reduced over time due to increased learning efficiency. Our results indicate that a forward-looking model fits the early adopters and early majority stages better, while both models perform equally well in the laggard stage. JEL classification D83, Q31, Q33, Q16


Introduction
New technology diffusion and adoption are two sides of the same coin-with "diffusion" referring to the rate at which a new technology spreads among all potential users and "adoption" describing an individual user's decision to try or not to experiment with new technology. Researchers in the fields of sociology, anthropology, education, social networks, and communications have extensively studied the technology diffusion path [1]. The S-shaped path -broken down into "early adopters", "early majority", "late majority", and "laggard" stages -is commonly observed in many cases and is a wellknown result of these studies. Following [1][2], "early adopters" and "early majority" are defined as the stages where the number of new adopters increases but with different trends: faster and slowly, respectively; and "late majority" and "laggards" are the stages where the number of new adopter decreases, also with the different trend: slowly and faster, respectively [1][2][3][4][5]. Economists, on the other hand, have studied adoption decisions-developing models that identify, examine, and characterize the various factors that may influence a user's technology adoption decisions [6]. In this literature, binary choice models, wherein users choose to adopt a new technology or choose not to adopt [7][8][9][10], are distinguished from sequential adoption models, wherein users initially and partially adopt a technology, and then adjust adoption practices in later years [11,12]. Some researchers model myopic adoption behavior with immediate utility maximization only [13][14][15], while others model forward-looking behavior where adopters maximize utility over a planning horizon [16][17][18].  To understand GM soybean seed adoption decisions, our work joins a growing literature that examines behavioral explanations for sequential adoption of new technologies under uncertainty and learning [11,19,[20][21][22]. Following previous studies, we hypothesize two sequential models with Bayesian learning in which farmers initially update believes about GM seed profitability after observing noisy signals from their own and neighbors' experience. We follow [22] to specify and estimate (i) a "myopic" model in which farmers adopt technology at a rate that provides the highest current expected utility, and (ii) a "forward-looking" model in which farmers recognize that current technology choices will affect their future information sets.
However, our work extends the modeling and analysis presented in [22]. By looking at farmers' adoption decisions in different stages of the diffusion path, we obtain insights about the evolution of learning and uncertainty. We apply our analysis to three distinct panels of soybean farmers in the U.S. for three time periods : 1996 -2001, 2001 -2006, and 2006 -2009. We did not include the 2010 -2014 time period, because the market reached saturation starting in 2010. Following [3,4] 's definition of different  diffusion stages, we label the 1996 -2001 period the "early majority" stage, the 2001 -2006 period the "late majority" stage, and the 2006 -2009 period the "laggard" stage. Concretely, we fit a polynomial specification to the adoption path and determine the stage categories by examining the sign of the first and second-order of the rate of changes in adoption increments. These periods correspond to adoption rates changing from zero adoption to 75%, then from 75% to 95%, and finally stable at around 95%.
Our results suggest that uncertainty about profit reduces significantly after farmers experiment with the new seed technology for a number of years. This decrease is attributed to less noisy signals from their own and neighbors' experiences, which, in turn, is associated with an increase in learning efficiency. We also find that the "forwardlooking" sequential model outperforms the "myopic" model in generating the observed

Learning models
In this section, we describe the "myopic" and "forward-looking" sequential learning models following [22] in the context of GM soybean seed technology adoption. Detailed derivations can be found in [22].
where > 0 is the discount factor and is the utility of farmer i at time .
The Bellman equation is: where is the information set of farmer at time , and is a set representing the parameter space to be defined in the model. Equation (2) of information she will have in the following time period. Therefore, we define farmers with immediate expected utility maximizers (where = 0) the "myopic" ones, and those with expected utility maximizers over a planning horizon (where > 0) the "forwardlooking" ones.
We assume that the distribution functions of profits for both seed technologies are unknown to farmers. Following [22], we construct farmer i's expected utility at time t as a function of the mean and variance of the total profits from planting the two types of seeds: , where the subscript "g" denotes the GM seed type, and the subscript "c" denotes the conventional seed type. Farmer learning about GM seed profitability, and hence the adoption process for both myopic and forward-looking farmers, can be developed accordingly (refer to the appendix for details).
The current payoff at time for farmer is: where The derivation of the mean ( ) and variance of the total profits ( ) can be found in the appendix, or in [22]. As defined earlier, is farmer i's adoption rate of the GM seed technology in her farmland with total acreage at time t. We use to measure farmer 's degree of risk aversion, which is assumed to be inversely related to the acreage . The parameter represents the mean profit of planting conventional seed per plot, which is common to all farmers, while is the upper bound of the plot level profit difference between planting GM seed and conventional seed. Additionally, measures the rate of dissipation of such profit difference along with adoption. Factors affecting the variance of the total profits include adoption rate , total acreage , the current belief of GM profit variance , the profit variance of conventional seeds , and the time invariant GM profit variance .
Equation (3) suggests that farmer's utility function is determined by the choice variable (adoption rate ) and the information set , given the remaining parameter space . In our model, the information set consists of factors that affect current expected utilities and/or the probability distribution of the future expected utilities (i.e. , and ). The parameter space set include parameters used to define the variance of conventional seed profitability, the risk aversion measurement, the mean profits of planting conventional seeds and the mean profit differences between conventional seeds and GM seeds, the time invariant GM profit variance (which can be obtained by learning from own experience), a parameter measuring the variance in learning of GM profitability from neighbors , and the white noise added to the variance of the conventional seed profitability .

Data
For our empirical analysis, we use U.S. farm-level soybean seed purchase data collected by dmrkynetec, St. Louis, MO (dmrk). Data are obtained from annual surveys on a  [26]. All adoption data follow a similar pattern, suggesting that farmers in our samples do not differ from those in the population at large in terms of adoption behavior over time. We believe learning from neighbors is valuable if neighbors face similar agroclimatic conditions. Therefore, we use CRD as a proxy for local market. This aligns with common practice in the empirical literature, in which the neighborhood effect is based on geographical proximity [11,23,24]. We construct the CRD adoption rate using the dmrk population data. Thus, while is measured by individual farmer's total soybean acreage in year t, -is calculated by the average soybean acreage for other farmers in the CRD in that year. We also include both linear and quadratic forms of latitude and longitude of the center of the county where each farmer is located. This captures spatial heterogeneity in farming systems and agro-climatic conditions (e.g. temperature, rainfall volume, and daylight length).

Estimation
In the empirical application, we apply the structural models discussed in the Methods-Learning Models section to each panel of farmers described in Methods-Data section. For each model, we use the Nelder-Mead simplex method to minimize the simulated generalized method of moments (GMM) objective function. More precisely, we search for the set of parameters that minimize a weighted distance between the optimal (predicted) adoption path and the observed adoption path (see [22] for details). The instruments used to facilitate the estimation are presented in the next section.

The "myopic" model
Myopic farmers choose the adoption rate that gives the highest current period expected utility. They maximize the value function defined in equation (1), with discount factor set to = 0 and utility function as specified in equation (3): The first order condition gives: , where is the parameter space as defined before; and the second-order condition holds.
To compute the predicted adopted path for each farmer in each panel following equation (4) (1), with discount factor > 0 and utility function defined in equation (3): To compute the predicted adoption path, we make the following assumptions: The transition probabilities: We rewrite and as and because we focus on farmers with relatively stable farm size over time. Thus, the information set can be reduced to . Following [11] we write the transition rules for all these variables in Markovian form (see [22], section 4.2.1 for details).

Results
In estimation of the "forward-looking" model we chose the discount factor at .
In addition to the discount factor and the additional bias parameter b, there are another 14 parameters to be estimated as listed in Table 2. These 14 parameters are shared by the "myopic" model. The initial values for the "myopic" model for each panel of farmers follow [22] (see Table 2). We use the estimated parameters in the "myopic" model as starting values for the "forward-looking" model.  We choose 17 instruments to estimate GMM: a constant vector 1, total soybean acreage of farmer and his neighbors ( , ) plus the square terms, previous year adoption rate ( , ) and the square terms, farm characteristics (latitude and longitude of each county center where farms are located and the square terms). Although not explicitly included in our model, pricing also affects adoption decisions. As such, we add conventional and GM seed prices paid by farmer and his neighbors (computed as the average price in a given CRD).
Parameter estimates and standard errors for both "myopic" and "forwardlooking" models are presented in Table 3. Our results suggest that the "forward-looking"  Average squared root prediction errors for each particular year and each model (myopic. vs. forward-looking) are presented in Fig 3. In the following we present in more detail our findings for each panel of farmers.

Model fit
For the "early majority" (1996-2001) and the "late majority" (2001)(2002)(2003)(2004)(2005)(2006), results in Table 3 indicate that the mean square errors from the "myopic" model are larger (and more so for the early majority) than from the "forward-looking" model, suggesting that both early majority and late majority behave in the forward-looking way. Using the  Table   3 shows that both the "myopic" and "forward-looking" models fit the data equally well.
The mean square errors of the two models are close to each other. This convergence may result from a completed learning process (farmers fully understand the quality or attributes of the new GM seed) as the new technology diffusion has reached saturation.
The actual mean adoption rate is 96.90%, and this compares with the rate predicted by the "myopic" model of 96.5%, and by the "forward-looking" model of 95.75%.
The parameter (Table 3) accounts for the difference in the Bayesian belief towards profit variance of GM seeds between myopic and forward-looking farmers. The parameter's estimated value is positive and statistically significant for the "early majority" and "late majority" but not statistically significant for the "laggard" stage. This result suggests that the uncertainty about profitability of the new technology plays an important role in the first two stages along the diffusion path, yet with a declining magnitude.

Self-learning versus learning from neighbors
Learning efficiencies, from own and neighbors' experience, demonstrate different patterns along the diffusion path. We follow [11,22] to define a farmer's own-learning efficiency from planting GM seeds on plot as 0 = 1 2, and the learning efficiency from his neighbor experience as = 1 2 + 2 For the "early majority" stage (1996)(1997)(1998)(1999)(2000)(2001), Table 3 shows that the parameter 2 is positive and statistically significant, while the parameter is not significant. These results indicate noise in learning from own experience but no additional learning noise from neighbor experience. Learning efficiencies from a farmer's own experience and from his neighbors are about the same for the early majority ( ).
For the "late majority" stage (2001)(2002)(2003)(2004)(2005)(2006), however, the estimated parameters 2 and are both positive and statistically significant. Noise occurring in learning from neighbors is much louder than noise in self-learning. Consequently, the learning efficiency from a farmer's own experience is much greater than that from neighbors' experiences ( vs. ). Comparing learning efficiency patterns along the three stages on the diffusion path, it seems that farmers are cautious in the very early stage of the technology diffusion path and try to learn as much as possible from all possible sources, either own experiences or neighbors' experiences. When knowledge is accumulated, farmers tend to count more on own experiences than on neighbors' experiences. And when adoption reaches its saturation, learning seems to be complete from both sources. Note that [22] estimated soybean farmers' adoption from 2001 to 2004, which is part of our so-defined "late majority" stage. They also found that farmers have higher learning efficiency from own experience than from neighbors' experiences. Our analysis provides a more complete picture of the evolution of learning along the diffusion path.

Mean profit
The estimated parameter represents the upper bound of the profit difference between conventional and GM technologies. It is positive, suggesting potential benefits of GM ) suggest that GM technology may have advantage over conventional seeds in the southern area for early majority adopters, but the advantage seems to disappear in the later adoption stages.
Warm weather, tends to cause heavier weed infestation in southern areas, suggesting that early majority adopters are responding to severe weed infestation problems.

Other results
For early to mid-stage adopters (1996 -2001 and 2001 -2006), the estimated risk averse parameters 0 are positive and significant, suggesting that early majority and late majority farmers in our samples are risk averse. They are also more risk averse if their farm size is larger, as the estimated parameter 1 is negative and significant. The estimated parameters 0 , 1 are not statistically significant for model fitted for the "laggard" stage, indicating that farmers in our sample are not risk averse after 12 years of experimenting with GM soybean seed technology.
The effects of the random state variable on the variance of conventional seed profits ( 1 ) is positive and significant for the early majority (1996)(1997)(1998)(1999)(2000)(2001), indicating that these farmers perceive a higher variance about profitability of conventional seeds.
However, such patterns disappear towards the mid-and end-stage of the diffusion path, probably because farmers plant GM seeds on most of their land at this stage. We find that the "forward-looking" model fits our data better than the myopic model in the "early majority" and "late majority" stages of the adoption process, suggesting that farmers in our samples are more likely to be forward-looking in the first 12 years of experimentation with the technology. Both models perform equally well in the last adoption stage, likely due to no differences in learning between myopic and forward-looking farmers once technology adoption has reached steady state.
We also find that farmers learn both from their own and neighbors' experiences in the "early majority" and "late majority" stages, although neighborhood effect is considerably smaller in the late majority stage. In the "laggard" stage, learning is complete, resulting in minimal uncertainty from both sources. As a result, learning efficiency from own-experience and neighbor's experience improves each year, resulting in a decrease in uncertainty about profitability of GM soybean seeds over time.
It is important to recognize farmers' forward-looking behavior in "early majority" and "late majority" stages of the adoption process, and the similarity between myopic and forward-looking behavior in the "laggard" stage of the adoption process. For researchers studying technology adoption (or demand analysis of new products), our study provides guidance on how and when to choose the appropriate static or dynamic model. For early stages along the diffusion path, the dynamic model with future learning incorporated may provide a more accurate illustration of the market and demand. On the other hand, for a product in its later stages of the diffusion path, the simple static model would be appealing without loss of much insight in potential adopters' learning. Another important finding is how farmers' learning evolves over time. The fact that they switch from counting on neighbor learning to self-learning when moving along the diffusion path can serve as a source of information for policy makers or marketing firms interested in promoting the adoption of new agricultural technologies and could be extended to other market analyses. For example, it may be more effective to focus on providing training and extension support when introducing a new technology to farmers in the very early stage of the technology, and then focus more on subsidizing farmer adoption when the technology has already been in the market and adopted by certain percentage of potential users. each time period. We assume the random state variable brings additional uncertainty, thus 2 takes the form: ,where .

Farmer learning about GM seed profitability
We assume that farmers learn about the mean profitability of GM seed technology in a Bayesian fashion. Specifically, the information set of farmer at time 0, 0 consists of exogenous information (e.g., this information can come from agronomists or agricultural extension agents or from farmers' own observations of pest and weed infestation in past years and possible effectiveness of GM seeds) on the GM average profit 0 and its accuracy 2 0 . At time 1, farmer may partially experiment with GM seeds and then, using information from his field experiments and/or from neighbors, updates the information set to 1 with beliefs on both parameters 1 and 2 1 . This process continues until learning is complete. As a note, our data do not include information on the where is the upper bound of the profit difference, which is a function of farmer 's characteristics . Assume > 0 so that the mean profit difference between the two types of seeds is decreasing in .
Using equation (A3), if farmers' adoption decisions are made based on comparing mean profits only (without forward-looking) and there is independence of profits from different land plots, the mean and variance of the total profit take the following form: , . (A5) Then, the current payoff at time for farmer is: where the information set consists of all factors that affect current expected utilities and/or probability distribution of future expected utilities. It includes current belief of GM profit variance 2 , profit variance of conventional seeds 2 , and total soybean acreage . The set is the model's parameter space, defined as