Edmund Chattoe and Nigel Gilbert

Centre for Research on Simulation in the Social Sciences (CRESS)

Department of Sociology

University of Surrey

Guildford, GU2 5XH

United Kingdom

{E.Chattoe | N.Gilbert}@surrey.ac.uk

5th September 1997

PLEASE NOTE THIS IS AN INTERNAL WORKING PAPER FOR DISCUSSION ONLY. IT WAS PREPARED FOR THE IMAGES MEETING IN DOLOMIEU, 1997. PLEASE DO NOT QUOTE WITHOUT CONSULTING ONE OF THE AUTHORS.

This paper describes the literature on the diffusion of innovations and applies it to the task of modelling the AEM adoption decision of farmers. The paper discusses various limitations of the traditional theory of innovation diffusion and whether it is appropriate to compare the two processes. It concludes by sketching out three sorts of analysis that might be done using readily available data as a precursor to the interview and questionnaire stage. The role of simulation in investigating useful formal results is also considered.

The task of the Surrey group for M1 has been to make suggestions about the modelling of the dynamics of farmer adoption, initially somewhat independent of the farmer decision models being presented by the ENS team. In order to do that, we have reverted to the most basic view of the dynamics possible which is that it simply consists of a graph of the number of farmers who have adopted any given measure at particular times after its initial announcement. It was this very aggregated view which suggested the parallel with innovation diffusion, a field with a respectable pedigree in which much work has already been done. However, as the development of this idea in subsequent sections will hopefully show, this view is also an effective way of making use of the data that we are liable to be able to access or collect. In addition, the basic innovation diffusion insight can be progressively sharpened within the same framework. This will be useful if the preliminary, highly simplified models do not prove effective or if it is possible to extend the range of data available at a later stage.

One of the most "robust" findings of the economic theory of innovation diffusion is that shifts from one technology or product to another follow a sigmoid curve. This result has been obtained in many different industries, for different countries and times (Parker 1978, Mansfield et al. 1977, Mansfield 1979).

There are a number of possible explanations for this process:

The adoption of new technologies is a process purely based on imitation, so that the probability of adoption is a function of the number of people who have already adopted. This "pure" theory, at least in its noiseless form, is actually incoherent, since it does not explain how the first person comes to adopt the technology. (Apart from the obvious, but rather implausible addition of noise so that people can adopt "by mistake", we might modify this model by seeing innovators as those who have "deviant" adoption functions, that is, relax the assumption of a homogenous adoption functions. While most individuals will tend to adopt as an increasing function of proportion adopted, there may be those who adopt in a decreasing function. Fanatical innovators may even have a "Star Trek" function - to boldly go where no man has gone before - losing interest completely even in fields with only one other adopter.)

It is clear that this model takes no account of either the determinants of social influence (Latané and Nowak 1997) and spatial or social networks. The adoption function is a function of raw numbers or proportions not of the identities and properties of the people concerned. It will be necessary to establish whether this can be used as a workable first approximation. In addition to tractability, it has the important merit that the data required is available. By contrast, general data on spatial location and social networks may be highly problematic to collect. It may however be possible to project from a limited sample, if, for example, farmers tend to imitate farmers of another particular observable type rather than just some farmers. The findings of Latané and Nowak (1997) may be relevant here, that it is the existence of difference that matters and not its precise nature. In the following sections, we will discuss the progressive refinement of the conceptual framework in more detail.

The adoption decision involves the estimation of certain variables of a decision model which are initially uncertain, for example, how much a new harvesting technique will increase wheat yields. Initial guesses may be provided by domain knowledge, by advertising and so forth, and these will differ from person to person. Individuals will also differ in the pay back they expect from innovation. An innovator can be defined as someone who is either prepared to accept a very low additional pay back before proceeding or who has, for whatever reason, a belief that the gains are very high and the losses very low, which amounts to the same thing. (Farmers may even innovate in their own individual circumstances, they might be better not to.) As the innovators proceed to adopt the new technology, two additional processes occur. Firstly, the distribution of costs and benefits becomes much better known through new data provided by the outcomes to adopters. As a result non adopters may reconsider their non adoption decisions based on previous beliefs. Secondly, the technologies themselves are not completely fixed as is often assumed and there may be reductions in costs and increases in benefits, though learning-by-doing (Arrow 1962) and so on. The net result of both of these processes is that more people will adopt. It may even be possible to explain the sigmoid adoption curve by a sort of information theory argument (Lazarus 1996) combined with assumptions about the distributions of beliefs. The first piece of "real" data about the process, provided by the outcome for the first adopter, generates the maximum amount of additional information and thus encourages the most people to reconsider. Each additional adoption provides progressively less information about the distribution of costs and benefits. It is clear that this theory subsumes the first since, in addition to solving the conceptual problem of the first adopter, one technique by which individuals may save effort is to use the number of adopters as a "shorthand" for increased knowledge about the distribution of costs and benefits. This is certainly true at the extremes. Early adopters are most likely to do the calculations for themselves while very late adopters can be almost certain that imitation is a "safe" strategy. (This is the distinction between behavioural and cognitive or phenotypic and genotypic imitation in evolutionary modelling.)

The adoption decision curve is to some extent an artefact of the representation and subsidiary assumptions. In the first place, it appears to be regarded as part of the definition of an innovation that at least some people will definitely find it better than the current technology. As such, there is no outflow process with people reverting to the previous technology. Explanations address the various reasons why people may take time to discover which technology is better, but not the assumption that new is ultimately better. (There are problems in trying to identify "potential" technologies which never even reached the point of minimal adoption before everyone lost interest. There is therefore a sample bias towards situations where the dominant technology is obvious with hindsight.) In the model above there is no reason why we should not equally expect to find "over-enthusiastic" adopters (for example C5 owners) reverting to previous technologies, since they also have an opportunity to revise their expectations of costs and benefits. (This revision on the basis of others experience may be independent of own experience data. For example, we would expect a dramatic shift away from a comfortable car which sometimes blew up, not just a shift by those who had been blown up.) Because of the "no outflow" assumption and the cumulative nature of diffusion graphs, it is necessary that the graph must begin at 0 percent adoption and end up at 100 percent eventually even with random switching. Given this situation, the demonstration that adoption is logistic (especially when estimating with two free parameters) rather than linear or merely "sloppy" becomes rather less dramatic as a finding. (In fact, the shape of the curve may reveal something about the validity of the "pure imitation" assumption relative to other possibilities.) Furthermore, for a wide range of different non-pathological adoption functions, something like a logistic curve is enforced by the additional assumption of a fixed eligible population. This is easiest to see in the case of the simple imitation model, where, after the mysterious initial adoption, the rate of adoption continues to accelerate until it comes up against a shortage of eligible adopters. (There is an obvious analogy here with ecological populations.)

The no outflow assumption raises three other important issues. Firstly, there may be a risk of self-selection in the micro sample of people involved in a particular adoption decision as well as the macro sample of innovation curves collected. People will probably be loathe to respond to questionnaires if they have adopted a new technology and reverted, particular after a highly negative outcome. Secondly, it is clear that in the long run at least, the no outflow assumption must fail. If nothing else, today’s dominant innovation is almost certain to be tomorrow’s fading star. There has been far less work on peaking and declining technologies, which might in some respects prove more interesting, though see Marchetti (1980, 1985). Thirdly, it seems behaviourally plausible that imitation of outflow decisions might be weighted more heavily than that for inflow decisions, for example because the distribution of costs and benefits for the prevailing technology is already very well known. This makes the absence of significant outflows even more surprising.

The simplest view of the dynamics of farmer AEM adoption, independent of the mental model of the farmer and the physical description of the farm is as the diffusion of an "innovation", a shift from the old "technology" where the farm plan did not include the AEM payments, to the new one where it does.

Given the description of innovation diffusion above, an important question is whether it is appropriate to model the adoption of AEMs by farmers in this way. This raises a number of issues:

The first test, which is empirical, can be performed extremely easily. Do the adoption curves for particular AEMs look anything like sigmoid innovation diffusion curves? This is an extremely weak condition, for the reasons outlined above, but is also a good way of seeing whether it is worth proceeding in this direction without too much additional investment of effort.

The assumption of a fixed constituency. Is it true that the number of farmers eligible for a given AEM remains more or less constant over its lifetime? Note that this assumption is only required to encourage sigmoid adoption, it may not be required for other kinds of adoption profiles which are nonetheless regular. (There seems to be little theoretical work which relaxes the assumption of fixed constituency. It would be interesting to investigate this further.) We have already discussed the possibility that farmers tend to adopt if the AEM will pay them to do what they are already doing. A much more positive possibility is that non adopters may modify their practices to the extent that they become eligible for the AEM after a certain time. (This might not be unambiguously desirable though. It might be better to let your barn fall into ruin and get money to rebuild it than to spend your own money on running repairs!)

The assumption of no outflow. In this case, the structure of the AEM, at least in the UK, works in favour of an innovation diffusion model, since once farmers have entered the scheme, they are committed for a considerable period. Since AEMs have not so far been running for that long, the possibilities for outflow and its effects on subsequent inflow may actually be rather small. (Nevertheless, it would be interesting to investigate the effects of relaxing this assumption in various ways.)

The assumption of a single innovation. Again, there may be some support for this assumption in the institutional arrangements of the AEMs, since different sources of funding are often mutually exclusive. Nevertheless, it does seem to be the case that a rolling program of "new", "upgraded" and "overlapping" AEMs, certainly in Italy, would make it worthwhile to do some modelling of situations with overlapping or sequential innovations. Such modelling might also be useful for representing what happens in the adoption of a "single" innovation when the multiple interlocking components of the new and old processes may cause shifts in costs and benefits with experience.

Prima facie, it might seem inappropriate to model AEM adoption as a technological diffusion process simply because it seems rather different in nature. However, by unpacking the features of the innovation diffusion model described in the first section, it becomes clear that the differences are not so great as they might at first appear. If we consider decision-makers with a model of the current process and the innovative process, there are a number of components which are common to the two processes. This model goes some way to explaining the generality of sigmoid adoption curves since it does not rely on the assumption of a particular model but the assumption that models exist and differ. (We are assuming for the moment that models differ in parameters. It may be necessary to start assuming that they differ systematically.)

In both cases agents differ in their beliefs about the costs and benefits of the new system, due to different information, different models and different preferences. (In fact they may also differ in their knowledge and competence connected with operating the current system, but this issue is often assumed away. Perhaps a case can be made for looking at relative costs, but this is only easy to justify when the new technology is dominant and this is somewhat implausible. For most "mixed blessing" technologies, relative aggregate costs may not be a useful indicator.)

In both cases, adopters provide an additional source of information about the costs and benefits of adoption.

In both cases, the costs and benefits are not "free floating" but are actually opportunity costs which rely on an underlying structure of time, labour and technology constraints. Both farms and factories are exercises in complex scheduling. (Many examples are provided even in casual discussions with farmers from the three countries.) Adoption decisions will reflect the compatibility of AEM measures with this structure of opportunity costs in an activity plan. (Some examples are provided by the incompatibility of maximum nitrate use with support payments on nitrate reduction in Italy and refusal to adopt measures which require land to be left fallow at times of maximum usage in Scotland.)

An activity plan is simply an ordered set of activities which the farmer would like to carry out. The range of possible plans is heavily constrained by the fact that many activities have pre-requisites and consequences. You can’t harvest wheat you haven’t planted and you can’t fill the barn with late potatoes until you have sold the early wheat. Because of the wide range of constraints, which also take into account weather conditions, time and money limitations on the farm household and physical processes, there is considerably more cognitive effort and risk entailed by redesigning the whole plan from the ground up rather than making incremental changes and improvements. The complexity and non-separability of the problem also means that the success of small changes is easier to determine. Examples are provided by growing a small additional crop which can be planted and harvested at times which might otherwise be slack, or swopping pairs of activities, harvesting two weeks later and planting the next crop two weeks earlier while leaving everything else unchanged. The unwillingness of farmers to change may be partly explained by the time it takes to "evolve" activity plans of an appropriate quality. Although in some cases, it may be possible to "buy" your way out of these constraints, for example purchasing silage to compensate for the loss of a field, it should not be assumed that all the constraints involved have a cash equivalent. (Market niches themselves imply a model standard enough to generate significant returns, maybe only three farmers face one particular problem.)

Farmers will be pre-filtering AEMs according to perceived compatibility with current practice, in the "worst" cases, getting money for doing nothing or having nothing to do with AEMs which appear to be incoherent or fundamentally incompatible with their farming practice. They may then go on to assess the AEM(s) in more detail once past the filter. There are two subsidiary issues here. Firstly, why are policy-makers so much more interested in changes than in end states? Why is it acceptable to pay a farmer to go organic, but not to be organic, even to pay them for having changed in the past? One obvious suggestion is that it is cheaper! Another is that in a rational choice world, it can be assumed that all those who have not changed, will not, without a change of financial circumstances. Changing information and attitudes are not considered. Secondly, it may be at least as worthwhile to consider the agronomistic design of AEMs than the financial or policy side (Mazzeto and Vaccaroni 1997). For a given policy objective, more ponds say, it may be better to find a "technical fix" for farmers dislike of ponds as places where animals founder, than to try increasing the payment for ponds or making them part of a compulsory package with other more desirable measures. (Again this refers to the separable and disembodied nature of economistic preferences. Farmers don’t just dislike ponds qua ponds, but because they connect to other aspects of the farm plan. It is possible that these interlocking effects in the farm plan will make the whole system non-linear, introducing thresholds (Granovetter 1978), so that incremental changes in payments are an ineffective policy tool. One task of simulation may be to investigate the emergent patterns of behaviour resulting from highly constrained activity plans.) This becomes much clearer when we think about opportunity costs rather than costs. Tentatively, the negotiation process which farmers in Scotland undergo to design their farm plans, through farm advisors who are both trusted and knowledgeable about farming may explain the apparently high effectiveness in Scotland. This negotiation allows the payments to be reconciled to farming practice in an effective way. It also concentrates on "uncontroversial" goals like "more fences" while allowing some latitude in how this goal is to be achieved. Several Scottish farmers appeared to distinguish the advisors opinions from those of "theorists" from environmental agencies or universities. In Italy and France, there appears to be more of a split between those whose advice you trust, like other farmers, and those with certain sorts of technical knowledge.)

Provided that we accept that there is something worth pursuing in the parallel between innovation diffusion and the adoption of AEMs, it is possible to develop these models at a number of levels of detail and sophistication:

Such models have the advantage that they rely on the most basic data of all, the number of adopters for each AEM and the time when they adopted. Unfortunately, not only is such a prediction model theoretically trivial but it suffers from two serious limitations. Firstly, it can only be used on AEMs that are already in place which limits its application as a useful policy tool dramatically. Secondly, even though it might be possible to justify this technique as relevant to policy sufficiently early in the existence of an AEM, this is precisely the time when prediction will be subject to maximum error. If we assume constant measurement error and a sigmoid diffusion curve, the very flat section of the graph directly after the introduction of the AEM will make estimation of the "curve" parameter very inaccurate. (This problem is well known to epidemiologists and has beset recent attempts to project the spread of HIV and the eventual severity of CJD, although with the additional difficulty that there is also no known "time zero" for these diffusion processes, since existence of the diseases almost certainly precedes the possibility of accurate diagnosis.)

The use of curve fitting also raises another issue, the assumption that the conditions and payments for an AEM are "fixed" over its lifetime. This is equivalent to the assumption that technologies are "black boxes" which cannot be opened and that the diffusion process simply reflects a binary shift from one technology to the other. The possibility of changing the AEM in use completely vitiates the value of simple curve fitting. In this case, it obviously becomes necessary to know how adoption is influenced by the nature of the AEM and of farmers.

Despite these serious limitations, simple adoption curves, coupled with basic background information about the differences between AEMs and farm circumstances between countries may still be valuable as a preliminary study, particularly when coupled with some theoretical investigation of the effects of relaxing various assumptions in traditional models of innovation: fixed constituency, no outflow, atomic technologies. (In the UK, for example, there is quite a large sample of ESAs to compare in the adoption of different AEMs.) It may be possible to identify both tentative "causes" of differences for further investigation and "standard" patterns for AEM adoption. (Although it is true that the innovation diffusion model can be based on the assumption of some model with uncertain parameters, it is also plausible that the institutional structure within which AEMs operate may give rise to adoption curves which bear more of a "family resemblance" to each other than to, say, adoption of pieces of factory technology. This can be explained in terms of the different kinds of underlying models which may be involved. An obvious example is provided by the three year or five year contracts, which may have a visible effect when outflow again becomes possible after a certain number of years and simultaneously results in a drop in new entrants.)

Beyond attempts to predict solely on the basis of past performance of the variable to be explained, the obvious next step is to link prediction to other variables. One problem with this approach is an asymmetry in the amount of information already available about adopters and non adopters. Certainly in the UK case, the detailed farm plans provide a lot of information about the type of farm and the measures elected. By contrast, the main source of generally available farm data across the EC seems to be the FADN database, which provides regional level averages and data on some individual farms without locating them. Ideally, one would like to be in a position to "zero in" on farms with very similar environmental conditions so that one could identify the differences which made some adopters and some not. Failing this, the less satisfactory option, which is still an improvement over simple prediction, is to investigate deviations from average behaviour for adopters over time. For example, suppose the average French farm has three ponds and two stands of trees, and an AEM is introduced to make payments for preservation of water and woodland. If the first batch of farms which adopt have on average six ponds and two stands of trees, then it appears that it is the payments for pond maintenance which are deciding farmers to take part. Similarly, if only farms with no ponds joined the scheme, this would be a strong indication that the requirements on pond maintenance were highly unsatisfactory. It will also be possible to get data about whether the AEM is valuable only to farmers with a very high number of ponds or whether this reflects merely an "innovator bias" by observing what happens to the rolling average of pond numbers for later adopters.

Such an approach is obviously crude, though an improvement over simple projection, but it is important in giving a much richer quantitative set of relationships to investigate. Instead of trying to detect similarities in the shapes of sets of noisy adoption curves, one can start to identify correlations across sets of curves. For example, speeds of adoption for a particular AEM over the set of UK ESAs might be shown to divide according to the type of tenancy agreement in operation. Of course, correlation doesn’t imply causation, but such relationships may form a useful basis for detailed collection of "causal" (decision process) data in the next step.

A number of problems suggest themselves. Firstly, there is no reason why the FADN data should be necessary or sufficient to capture what is important in influencing the decisions of farmers. In the absence of additional data, there is little we can do about this. Secondly, purely average data will tell us nothing about the proportion of eligible farms, though the "sample" data on individual farms may help somewhat here. (Do farms attempt to apply and then get turned down? This sort of data could also help.) Differences between average and adopter properties are only significant when ineligible farms have been factored out. (If farms with no ponds or woods cannot join the AEM, then we would expect the average numbers of these features to be higher among adopters in any event. We don’t only have average data for adopter farms, but it is not clear how the distribution can be used without a corresponding distribution for non adopters or the population as a whole.) Finally, there are still ambiguities of motivation to be "factored out" even if "corrected" differences between average and adopter properties can be obtained. Just considering the simply case of woods and ponds, it is not clear whether a high average for ponds just represents enthusiasm for a particularly lucrative AEM payment for ponds alone or, somewhat more contortedly, a high payment for woods which is encouraging those who like ponds and have many to join to subsidise them. Another way of putting this is that the method cannot distinguish between the set of "mixtures" of motivations of the form a(woods) + b(ponds). In a sense this is irrelevant for a particular AEM, but is obviously important for design of alternative policy regimes. This last problem reflects the inevitable limitations of attempts at quantitative prediction using aggregated data.

Despite all these problems, the comparison of averages with the properties of adopting firms is the "minimal" instance of what can be achieved using this method. In the CAMAR and TAIR projects, Bossuet et al. appear to have used statistical techniques to sharpen the classifications of farms in a way that can only improve the possibilities of detecting useful relationships.

Although the attempt to predict adoption using other variables is clearly a step forward from mere projection, it still suffers from the limitation that it can only be applied to AEMs that are already in place. (It is not clear whether the refined technique can increase predictive accuracy in the early stages of an AEM.)

The logical next step is the attempt to move from quantitative correlation to causation through an understanding of the actual decision processes of farmers. The current intention appears to be to combine interviews and questionnaires with both adopters and non adoptors to gain additional information about possible determinants of the adoption decision and, more importantly, about possible connections between determinants which form the decision model. The results of this process will certainly inform some reconsideration of the linkages indicated by the behavioural prediction approach.

The main difficulty at this level is linking the micro-decision processes uncovered to the average or macro level data currently available. Although demonstrating that social influence is important to the adoption process provides a good argument for the official collection of social influence data, bureaucracies are seldom swayed by arguments of any sort. It is quite possible that the statistical investigations of adoption and the interviews and questionnaires themselves will suggest new sources of data or ways in which these data can be proxied by what is available. Nevertheless, it seems likely that there will be a "shortfall" between data collection resources and the amount of data required.

It is at this point that simulation of adoption processes using the Artificial Societies approach (Gilbert and Doran 1994, Gilbert and Conte 1995) may enable us to do a "sensitivity analysis" of different assumptions about decision models, plan scheduling and social networks. This will help us to focus on the data which we most need to collect. The hope is, following the suggestion of Latané and Nowak (1997), made in another context, that the existence of difference is more important to the dynamics than the exact nature of the difference. For example, the emergent properties of constrained activity plans may be almost independent of the "real" meanings of the constraints in the same way that a normal distribution emerges from a large number of random errors which may not be individually identifiable. Similarly, the existence of social influence may be far more important than the actual distribution of levels influence among individuals.

It is not really possible to go further in this paper without starting to make hypothesis about individual farmer decision-making. The next task is therefore to try and integrate the ENS findings into our very general description of the dynamics, in particular to see which theories are compatible with data which already exists or can feasibly be collected.

This content of this paper is inevitably somewhat abstract, since it attempts to make suggestions based only on the hypothesis that agents have models of the world without saying anything at all about the nature of these models. Despite this limitation, it intends to achieve three goals. Firstly, to draw out the parallels between AEM adoption and the theory of innovation diffusion in the hope that this will form a useful basis for further research. Secondly, it attempts to sketch out a progressive research strategy in which simplistic prediction gives way to more sophisticated prediction and that in turn to the construction of simulation models. Each level has the potential to direct the research that follows. At the same time it draws attention to the potential problem of available data in making the shift from sophisticated prediction using aggregate data to simulations of the adoption process using individual data. (It is suggested that this gap may be somewhat narrowed by rejecting attempts at "realistic" simulation and instead using simulation as a sensitivity analysis tool to identify the factors which are most important in adoption so that data collection and treatments can be focused on these features. (At the same time, it can be said that variables which have little effect of adoption can be regarded as "behavioural" or "institutional" constants in the sense that they may also apply in the case of previously untried AEMs. Finally, it is hoped that the framework presented is still compatible with the sort of research planned into social networks and individual farm decision making. In addition, the framework suggests an important role for the activity plan as a component of the decision making process.

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