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Diffusion in Sociological Analysis

ALBERTO PALLONI

OBJECTIVES

There are a number of very lucid, thorough, and authoritative reviews about the nature and applications of theories and models of diffusion in sociology (see, for example, Rogers, 1962, 1973, 1988, 1995; Valente, 1995). However, this literature is neither geared to deal with problems in the explanation of demographic phenomena nor does it indicate how to take advantage of new developments in economic and social network theories and methodological innovations for the study of dynamic processes. This paper is designed to fill this gap. In particular, I have four interrelated goals:

  1. To identify the backbone of diffusion models and theories in sociology, and to show that recent formulations and applications require robust, well-specified theories about social systems and about the positions that individuals exposed to diffusion occupy within the social structure;

  2. To illustrate recent applications of diffusion models and theories in two key areas of sociology, social movements and social organizations;

  3. To define conditions (“identification conditions”) for testing new hypotheses and conjectures that invoke diffusion processes. These conditions are strict, are difficult to satisfy, and have implications for issues ranging from data collection to selection of estimation procedures. I argue that unless these conditions are met, we will not be able to identify

Alberto Palloni is professor of sociology at the University of Wisconsin, Madison.



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Diffusion Processes and Fertility Transition: Selected Perspectives 3 Diffusion in Sociological Analysis ALBERTO PALLONI OBJECTIVES There are a number of very lucid, thorough, and authoritative reviews about the nature and applications of theories and models of diffusion in sociology (see, for example, Rogers, 1962, 1973, 1988, 1995; Valente, 1995). However, this literature is neither geared to deal with problems in the explanation of demographic phenomena nor does it indicate how to take advantage of new developments in economic and social network theories and methodological innovations for the study of dynamic processes. This paper is designed to fill this gap. In particular, I have four interrelated goals: To identify the backbone of diffusion models and theories in sociology, and to show that recent formulations and applications require robust, well-specified theories about social systems and about the positions that individuals exposed to diffusion occupy within the social structure; To illustrate recent applications of diffusion models and theories in two key areas of sociology, social movements and social organizations; To define conditions (“identification conditions”) for testing new hypotheses and conjectures that invoke diffusion processes. These conditions are strict, are difficult to satisfy, and have implications for issues ranging from data collection to selection of estimation procedures. I argue that unless these conditions are met, we will not be able to identify Alberto Palloni is professor of sociology at the University of Wisconsin, Madison.

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Diffusion Processes and Fertility Transition: Selected Perspectives diffusion processes from among other processes producing similar observable outcomes. To argue that until very recently at least, applications of diffusion models in demography have not taken advantage of innovations identified in goal 1, and have not adhered to the formal conditions identified in goal 3. Thus, these applications are unlikely to be of much help to improve our understanding of demographic phenomena. The organization of the paper is as follows: the first sections deal with goals 1 and 2, respectively, middle sections focus on goal 3, the next section discusses material related to goal 4 and, the last section contains a summary and concluding remarks. THE BASIC MODEL OF DIFFUSION IN SOCIOLOGY In this section I show that sociological theories of diffusion have evolved from fairly simple propositions regarding average or aggregate behavior into complex formulations about how individuals define preferences and make decisions to realize those preferences. In this section I argue that in order to be analytically useful, diffusion models require theorizing about social structures, about the positions that individuals occupy in them, about individual decision-making processes that accompany adoption of a behavior, and about the constraints these individuals face. I conclude that it is unilluminating to confront diffusion theories with competing explanations that regard behaviors as responsive to “structural” factors, such as socioeconomic positions or social class membership, as if diffusion processes did not require or could proceed independently of structural factors that characterize the environment where individuals act and where behaviors take place. Similarly, it is misleading to cast diffusion models or theories against alternative ones on the grounds that the latter are usually erected on a foundation of assumptions about rational actors and well-defined decision-making processes, as if diffusion processes did not require making assumptions about preferences, costs, and a rational calculus. Well-defined diffusion hypotheses and models must be built on assumptions about social and economic conditions that constrain individual actors’ preferences and resources, and rely on these assumptions no less than alternative hypotheses and models often pitted against them. This is not to say that diffusion models or theories do not have a specificity of their own. They do, and it will be the task of the next sections to identify what this specificity is. In the end, however, my message is somewhat pessimistic because the conditions for identification of a diffusion process from observables are fairly hard to meet, much harder than what is normally implied in traditional applications of diffusion theories and models to sociological and demographic analyses.

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Diffusion Processes and Fertility Transition: Selected Perspectives Diffusion Explanations and Structural Explanations “Structural” explanations of behavioral changes seek their cause in the alteration of preferences and opportunities that result from either changes in positions that individuals occupy (individual social mobility) or from reshuffling of resources associated with a given social position (structural social mobility or redistribution of wealth). Diffusion explanations or models, on the other hand, attempt to identify a cascading mechanism that leads to cumulative adoption of behaviors by some individuals, even while their social position, or the resources associated with them, changes only trivially or remains unaltered. In diffusion models, the behavior “spreads” and is adopted by individuals irrespective of their socioeconomic positions, even among those whose social or economic positions are hypothetically associated with cost-benefit calculations that do not necessarily require the new behavior. Adopting the new behavior occurs as a result of reevaluation of one’s own choices in light of other people’s behavior, not as a strategic response or accommodation to a realignment of resources associated with one’s social position in the social system. To use the terminology Coleman (1990) coined for the study of collective behavior, diffusion models are built on the central idea that individuals transfer partial or total control of their own behavior to others. As I will show later, this requires a decision process as complicated (or uncomplicated) as the ones that are normally associated with structural explanations. Diffusion processes do not always involve adoption of new behaviors. In fact, they may include abandonment of a recently adopted behavior or resistance to change. For example, it has been observed that, contrary to expectations, class-based political alignments do not always take hold at a pace that is commensurate with advances of industrialization. Instead, traditional political allegiances, based on language or ethnic identities, may remain dominant long after industrialization has created the structural conditions for class-based politics. This type of phenomenon has been studied widely in political sociology to understand the stubborn persistence of nonclass-based allegiances and ethnic enclaves (Hechter, 1975). In these cases observed individual political behavior (voting behavior) is at odds with what is expected by virtue of an individual’s position or ranking in the social system. Failure of individuals to act according to class positions—an expectation derived from a “structuralist” explanation of political behavior—occurs as a result of adherence to practices that were consistent with positions occupied prior to the social and economic transformations that accompanied industrialization. What is diffused or adopted here is the individual resistance to act according to class-based principles (the new behavior), and the reinforcement of tradi-

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Diffusion Processes and Fertility Transition: Selected Perspectives tional political alignments (the old behavior). If political sociologists were able to gather information on collective protests against British rule, rather than just on voting patterns, they would observe waves of protests extending across and confined within the boundaries of the British fringe, much as they observe waves of protests in the United States during the 1960s (Myers, 1997). Similarly, we know all too well that fertility decline in Europe did not always follow a trajectory consistent with social and economic transformations that accompanied industrialization. Instead, the course of the decline revealed a marked tendency to proceed along or be halted by ethnic, language, and religious boundaries. The resulting geographic and territorial clustering of fertility levels and patterns has been construed as evidence against a structural explanation of fertility decline, and as support for the hypothesis that fertility changes were strongly associated with ideational or cultural changes and diffusion mechanisms.1 The existence of strong clustering of fertility levels along cultural lines could be evidence of either diffusion of a new behavior (adoption of contraception and a low fertility norm) in areas with lower than expected fertility (structural changes), or of resistance to the new behavior (rejection of birth control and adherence to a high fertility norm) in areas with higher than expected fertility. The foregoing examples share two features. The first is that in both cases we establish a contrast between an explanation that infers an expected behavior from a reading of individual socioeconomic positions (the structuralist explanation) with an alternative explanation that infers a pattern of expected behavior from the likely adherence of actors to ethnic, religious, or cultural prescriptions or beliefs shared by others in the same community, including individuals belonging to different social classes or occupying different socioeconomic positions. In the latter case, the likelihood of adherence to prescriptions increases as a function of others’ adherence to it (or others’ resistance to the novel behavior). The definition of what is included in “others” is and must be a key element of the theory, as should the identification of the mechanisms that reproduce efficiently adherence to prescriptions and beliefs. The second common feature shared by these two examples is that the structuralist or socioeconomic explanation and the diffusion explanation offered to account for the phenomena rest on the idea that individuals are decision makers, acting in uncertain environments; sorting through limited information on prices, utilities, constraints, and potential outcomes of alternative behaviors; elucidating their own preferences; and ultimately taking some course of action. But, whereas investigators are normally careful to produce a thorough definition of the decision process associated with the structuralist explanation, they all too often fail to specify the

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Diffusion Processes and Fertility Transition: Selected Perspectives decision-making process associated with diffusion, to the point that this appears, in many instances, as a result of passive contagion and the irrational or at least a-rational adoption of a behavior. This is a situation not unlike the one found until recently in the study of collective actions that could be explained only through recourse to the irrationality of actors (Coleman, 1990). The exceptions to this lack of attention to decision-making processes embedded within diffusion are precisely the most recent studies and formulations of diffusion processes in sociology, economics, and demography (Montgomery and Chung, 1994; Montgomery and Casterline, 1993; Valente, 1995; Marsden and Friedkin, 1993; Burt, 1987). Lack of theoretical specificity is not the only problem we face as we try to identify diffusion processes. In fact, most of the evidence produced in sociology and demography to distinguish between explanations based on diffusion arguments from those attributing the primary role to socioeconomic or structural changes is carved out of aggregate, not individual, data. Because the individual adoption process is never defined, the aggregate process is also ill conditioned: there is rarely a way to determine what kind of aggregate evidence one would expect when the individual adoption process is left unspecified. This leads to the very generalized practice of using residual evidence or, equivalently, to infer the validity of a diffusionist explanation from the failure of the structural explanation: the explanatory power assigned to the diffusion argument is always directly proportional to the magnitude of the inconsistency between observed outcomes and those expected from a competing structural explanation. Handling only aggregate and residual evidence leads to the central problem in this literature—both in sociology or demography— namely, the inability to identify the key process from observables. The Elements of an Explanation Based on Diffusion Processes A classic definition of diffusion is the following: “(Diffusion) is the process by which an innovation is communicated through certain channels over time among the members of a social system. It is a special type of communication, in that the messages are concerned with new ideas” (Rogers, 1983:19). There are a number of essential elements contained in this definition: the innovation, the population of potential adopters, those who adopt, and the mechanisms through which adopters and potential adopters communicate with each other. The classical problem in diffusion models is to understand who adopts the innovation, and how fast they do so. Thus, Rogers (1995) distinguishes different types of adopters depending on how early during the adoption process occurs. To these groups one could add a category including those who never adopt, much as in social mobility we recognize movers and stayers. Delays in adoption or resis-

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Diffusion Processes and Fertility Transition: Selected Perspectives tance to adopt are explained by inadequate information or by uncertainty about the results or outcomes associated with the innovation. As the process advances and more individuals adopt, and as the outcomes of adoption by others become observable, more individuals’ resistance to adoption crumbles as the information is enriched and their uncertainty about risks, costs, and benefits diminish. Although later in the paper I will introduce a more complex notion of diffusion, in the remainder of this section I will focus on the classic definition just given. I will use it as a reference to identify elements of a diffusion process that should be important in model building but that many applications overlook. The simplicity of the classic definition is deceiving, for it contains explicitly or implicitly a number of key elements that are important to identify at the outset. First, diffusion occurs through an individual decision-making process in which there are costs and benefits (and implicitly preferences) associated with adoption (or its obverse, resistance to adoption), as well as information and ignorance about prices, costs, outcomes, and alternatives. In their influential work on cultural transmission, Cavalli-Sforza and Feldman (1981) stress the importance of decision making as the factor that distinguishes cultural from biological evolution. Whereas the latter is driven by natural selection (or genetic drift), the former is characterized by the influence of individual decision making that may reinforce or offset the pressures of natural selection: “In cultural evolution, however, there is in addition [to natural selection] a second mode of selection, which is the result of the capacity of decision making” (Cavalli-Sforza and Feldman, 1981:10). Diffusion only occurs because individuals decide to adopt after observing others do so, and after updating their information by including observed outcomes associated with others’ adoption into their own decision-making process. There may be a variable number of stages in this decision-making process (Rogers, 1983), but what is important is that its core is an individual who is making cost-benefit calculations under uncertainty about whether to join others in adopting a behavior or, alternatively, resisting. A diffusion model rests on assumptions and imageries not dissimilar to the ones that prevail when, for example, we refer to individuals changing their fertility behavior as a result of socioeconomic changes that affect them (the so-called demand theories of fertility). The vast majority of applications of diffusion models in both demography and sociology neglect this very simple tenet of diffusion models: adopters and nonadopters are rational decision makers and adoption is the outcome of a rational decision-making process. These issues have been confronted head-on in only a handful of applications. For example, in a recent study Montgomery and Casterline (1996) define three distinctive elements of a diffusion process—social learning, social influence, and institutional con-

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Diffusion Processes and Fertility Transition: Selected Perspectives straints—which operate to determine and shape individual decision making about adoption of behaviors. Similarly, Erbring and Young (1979) and Marsden and Friedkin (1993) carefully elaborate on the types of social relations that are relevant for processes whereby behaviors of one individual are affected by consideration of behaviors of other individuals belonging to the same group or social system. Coleman’s (1990) study of collective action and those involving or generating trust reveal the fundamental elements of the decision-making process on which every diffusion process depends. Even in the study of organizations and organizational diffusion (DiMaggio and Powell, 1991), there is explicit consideration of actors who imitate organizational features adopted by successful organizations as a device to minimize uncertainty. Second, given conditions defining their preferences and opportunities, individual decision makers may be more or less resistant both to adopt innovations and, if they adopt, more or less reluctant to jettison the innovation from the menu of practices and behaviors they normally employ. That is, after one accounts for all elements entering in the decision to adopt or to resist, there might be individuals who are more (less) risk averse and adopt more (less) easily than others. These will be forerunners (laggards) in the diffusion process (Rogers, 1983). As stated by Cavalli-Sforza and Feldman (1981:39), “It seems very likely, a priori, that there is variation between individuals in their capacity both to learn of an innovation and to decide for adoption. Many factors contribute to such variation, including social and economic stratification, geographic conditions such as means of transportation, availability of communication networks, and, last but not least, individual differences in the behavioral characteristics that govern both awareness and eventual adoption.” This acknowledges that after accounting for a number of social and economic factors, we are likely to face the existence of “unmeasured heterogeneity” or the inability to include all elements that contribute to the individual’s decision regarding the innovation. It is a concept analogous to frailty in the analysis of mortality and induces the same empirical patterns: as individuals who are more resistant to adopting become a larger fraction of the pool of nonadopters, the overall risk of adoption will tend to decrease. But this is not a reflection of a risk profile of adoption that decreases over time. Rather, it is an artifact of the changing composition of the pool of nonadopters as the process progresses over time. To my knowledge, the traditional literature on diffusion processes in sociology or demography has not addressed the problem created by the unmeasured resistance to adoption, except insofar as the study of forerunners and the conditions that determine their appearance is indeed a way to identify factors influencing unmeasured resistance.2 In general, however, we neglect the issue altogether. This practice is explained by one of two factors: either the assump-

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Diffusion Processes and Fertility Transition: Selected Perspectives tion is made that all relevant factors were well measured (including those affecting awareness and propensity to adopt), or the focus of attention is on aggregate patterns of adoption. It is only recently, mainly through the influential work of Granovetter (1978) and Valente (1995), that the concept of individual (or group) thresholds has been introduced as a way to handle the problem, but still without deriving the full consequences for model testing. Later I will provide an interpretation, by no means unique, of unmeasured resistance to adoption. Equally important for the successful progression of diffusion are processes that may undermine continued practice of the new behavior. To the extent that these acquire some dominance, individuals are more likely to abandon the new practice or behavior some time after adoption. Despite the fact that this is a rather key part of a diffusion process, it is rarely mentioned and almost never explicitly modeled or studied.3 Third, the decision-making process underlying adoption of new behaviors occurs within a social structure composed of formal and informal elements. Individuals occupy positions within these social structures, perform certain roles, and are connected formally and informally to a number of other individuals within them through relations of authority, functional rapports, respect, and trust. They adhere to values and norms that shape preferences, constrain the field of feasible behaviors, and alter the information they may receive about prices, utilities, and ultimately about what others are doing. Despite the fact that often it is difficult to tell so from actual empirical research involving diffusion models, diffusion processes are affected by the social structure of systems within which they are occurring. Social structures determine the content and shape of the repertoire of feasible behaviors (“Is the behavior within the realm of conscious choice?”), individual’s preferences (“Is the behavior advantageous at all?”), and individual’s resources (“Can individuals adopt at low costs?”). The questions within quotes describe Coale’s well-known desiderata for fertility change (Coale, 1973; see also Lesthaeghe and Vanderhoeft, this volume) and could be utilized equally well by an explanation resting on diffusion as an alternative mechanism involving adjustment to structural changes. I will elaborate on this in later sections. The importance of social structure appears to weigh more heavily when the diffusion process is suspected to be under the control of internal sources rather than external sources of diffusion. However, even the idea that external sources of diffusion have an impact independent of individuals’ position in the social structure is acceptable only as a tool to render the algebra of models tractable, but it is woefully inadequate for analytic purposes. Some of the best original work on diffusion processes emphasizes that social diffusion is an analytically sterile construct if not cast against a social structure: “It is as unthinkable to study diffusion

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Diffusion Processes and Fertility Transition: Selected Perspectives without some knowledge of the social structure in which potential adopters are located as it is to study blood circulation without adequate knowledge of the structure of veins and arteries” (Katz, 1961; cited in Rogers, 1983:25). Similarly, in their influential study on use of hybrid corn among farmers in two Iowa communities, Ryan and Gross (1943) argue that it is the social structure that may explain the delay with which certain technologies are adopted. They reason that, if all individuals act as rational actors, adoption of an advantageous technological innovation must occur instantaneously and simultaneously. Delays and lags in the process and the emergence of laggards in the population of potential adopters can only be explained by institutional constraints and by sociocultural and psychological factors that influence the diffusion process. In this case, social structure is taken to be an obstacle rather than a facilitator. Structure accounts for the slow progress of diffusion rather than diffusion undermining the constraints fabricated by social structures. Although emphasis on the importance of social structure for diffusion processes is hardly new, and even despite the fact that there are good examples demonstrating careful attention to social structure (Rogers and Kincaid, 1981; Coleman et al., 1966; Burt, 1987), it has seldom been systematically incorporated into actual empirical research. It is only recently that sociologists interested in diffusion have begun to pay close attention to it and accounting for it explicitly in the formulation of models. In a recent paper, Strang and Soule (1997:1) make the point that while diffusion studies inquire about how practices spread, they also “provide an opportunity to locate and document the social structure, where we consider how patterns of apparent influence reflect durable social relations.” Furthermore, because these models involve individual decision making subjected to constraints imposed by a social structure, they may”… verge on the one hand towards models of individual choice, since diffusion models often treat the adopter as a reflective decision maker… [or] verge on the other [hand] towards a broader class of contextual and environmental processes, where conditions outside the actor shape behavior” (Strang and Soule, 1997:2). Fourth, once innovations are adopted, they could be abandoned and replaced by other technology, instruments, or behaviors. Thus, in addition to understanding who adopts and how fast they do so, models of diffusion should specify the obverse process, the persistent use of the innovation. This aspect of a diffusion process is of importance in applications to social behaviors that are inherently reversible or unstable. For example, participation in mass protests usually involves increased risk of participation followed by increased risk of withdrawal from the pool of protesters. Withdrawal from protest is as much a diffusion process as is participation in it (Myers, 1997), and could be triggered and encouraged

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Diffusion Processes and Fertility Transition: Selected Perspectives by external reprisals. Discontinuation is also relevant for situations where what is at stake is the adoption of an innovation such as contraception. Contraceptive discontinuation is an obvious illustration that has become a staple of empirical studies of contraception, but so is the possibility that certain groups may adopt contraception and then abandon altogether the very ideal of family limitation. If one succeeded in providing a convincing explanation of fertility decline in Western Europe entirely based on diffusion arguments, we should also explain why the decline turned out to be irreversible. Although this seems an obvious requirement, I have seen no systematic evidence indicating that the issue has been raised, much less treated systematically (for an exception, see Kohler, 1997). Note that this is not a requirement that applies to explanations invoking adaptation to new social and economic conditions. Whenever possible and nontrivial, an ideal diffusion model ought to specify the conditions for the persistence of adoption. Fifth, the social and economic environment may be modified by the process of adoption itself, and may involve feedbacks accelerating or retarding the process. The adoption of some computer technologies, for example, becomes unavoidable once a critical mass of users has adopted because the incentive structure for all users is altered, becomes more favorable for adoption of the technology, and creates niches for the introduction of even newer technology. The adoption of operating systems for PCs proceeds in this fashion, with software production being the element that induces interdependence among consumers in the market. Similarly, changing prices of a product induced by partial adoption of a technological innovation in agriculture will alter the elements that enter into the calculus of nonadopters (Ryan and Gross, 1943; Hagerstrand, 1967). Adoption of organizational features such as civil service reform may begin to occur for reasons that have more to do with the establishment of legitimacy of the practice than with associated increases in efficiency (DiMaggio and Powell, 1991). Adoption of a practice may accelerate as organizations that have not yet adopted find it advantageous to mimic what others have done successfully as a way to sharpen their competitive edge in the new environment created by a handful of forerunners (Fligstein, 1985). DiMaggio and Powell’s “mimic processes,” whereby organizations imitate what other organizations do, refers to processes whereby the linkage between a practice and its net benefits is subject to less variability, but also to processes where the institutional environment is so changed by early adopters that adoption simply becomes more cost effective. Only the latter is an example of endogenous feedback. Similar processes may be at work in fertility behavior: forerunners who first adopt fertility control not only generate an environment with reduced uncertainty for others to follow, but may also create emulation

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Diffusion Processes and Fertility Transition: Selected Perspectives conditions. This can happen, for example, if with fewer children they are able to support higher or better educational standards and if, in the long run, this enhances their power and prestige. To the extent that this is so, nonadopters pursuing power and prestige will be better off if they imitate fertility limitation. As the process evolves, the institutional context to satisfy the demand for more and better education also evolves, thus changing the context in which fertility decision making is taking place. In the case of organizational adoption, the pool of means to attain some ends is changed by adoption of newer procedures or strategies, and so is the ranking of those that are preferred among all organizations in the field, not just those who initially adopt. In the case of fertility, the connection between fertility limitation and power and prestige via children’s education converts the adoption of contraceptive behavior from an oddity to a useful and productive behavioral strategy. In these examples taken from sociology of organizations and fertility, there is endogenous feedback since the spread of the behavior changes the elements that enter into the decision-making process of everybody, including nonadopters. Surely, there must be considerable empirical variability in the lags with which the feedback operates, and in their actual significance for individual decision makers. Thus, endogenous feedback need not be an inherent nor a uniform characteristic of all diffusion processes. But, when it is, it will alter individual probabilities of adoption for individuals who have not yet adopted at a certain time in the process.4 The combination of some of these five elements of a diffusion process may produce lightning-fast spread of innovations. By the same token, though, particular constellations of the elements may lead to excruciatingly slow adoption, to innovation processes that begin rapidly but then taper off without ever reaching near saturation, or to those that fail altogether and are then relegated to the pool of diffusion processes that we will never be able to study.5 An immediate corollary of this inherent variability is that it is not necessarily correct to infer the existence of a causal mechanism (diffusion mechanisms versus structural mechanisms) only from observation of the relative speed with which a behavioral change occurs. It is as much an error to believe that when a process of behavioral change is quick and swift it must have been due to diffusion as it is to think that no diffusion process could be responsible for slow changes. The observed rate of change in the prevalence of a behavior by itself will generally be of limited help to identify a diffusion process because the effects of the basic elements of a diffusion process may lead to outcomes that can also be produced by mechanisms not associated with diffusion at all. Rapid rates of change in a behavior in the absence of changes in structural condition may be a reflection of diffusion, but it surely should not be taken as prima facie evidence of its existence or predominance.

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Diffusion Processes and Fertility Transition: Selected Perspectives ables measuring industrialization, urbanization, state centralization, bureaucratization, and others to predict the onset and the pace of fertility decline turns out to be modest at best. This evidence led to a more refined representation of how diffusion and resistance to diffusion may operate in societies sharply divided along linguistic and ethnic cleavages. Yet, with the exception of work by Lesthaeghe on Belgium’s fertility decline (Lesthaeghe, 1977), the contrast between the structuralist and diffusion theories is always resolved by estimating conventional linear regression models on aggregate indicators of fertility, then resorting to residual analyses as a tool to assess the degree of failure of the structuralist theory. This failure is automatically considered as a sort of reverse measure of the degree of success of the diffusion model. Thus, although most studies in the Princeton project attempted to conceptualize more precisely the process of diffusion, adding the idea of cultural and ethnic boundary and refining the conceptualization and measurement of structural conditions, the rules of inference remained quite primitive. The paradigm that characterizes the Princeton fertility project has been subsequently modified along three lines of research. The first introduces more fine-tuned analyses of the same or moderately augmented data used in the Princeton study without significantly changing the theoretical discourse (see the work by Galloway et al., 1994; Bocquet-Appel, 1997). The second line of research focuses on different measures of fertility, correctly arguing that the proper measures to test diffusion models ought to be measures of prevalence of the new behavior (contraception) that are only poorly correlated with the indirect measures of fertility normally used by demographers (Okun, 1994). Finally, the third line of research is more theoretical because it refines the conceptual scheme and brings to the forefront the discussion of the nature of mechanisms whereby individual adoption of new behaviors takes place. This occurs in reaction to overwhelming evidence of the failure of conventional, structuralist explanations of fertility changes. At the end of the 1990s, demographers had already surveyed extensive territories in addition to Western and Eastern Europe. The World Fertility Survey, the Demographic and Health Survey, and a handful of other more localized data collection undertakings produced a large amount of evidence regarding fertility decline in developing nations. In a sweeping and controversial summary of this evidence, Cleland and Wilson (1987) suggest that any version of demand theories of fertility, that is, economic theories invoking the need for structural changes in individual’s positions as a precondition for fertility changes, cannot account for the onset, pace, and geographic location of fertility declines throughout the developing world. Instead, these changes appear to be driven by ideational changes riding on the back of a diffusion process. Much the

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Diffusion Processes and Fertility Transition: Selected Perspectives same conclusion had been reached by Caldwell in some of his writings where he assigns importance to the onslaught of an ideational change (“Westernization”) that precedes and is partially independent of changes in forms of production and distribution (Caldwell, 1982). However persuasive their argumentation may be, the formulation put forward by Cleland and Wilson runs into two problems, one theoretical and the other methodological. First, there is a conceptual confusion that takes ideational changes as equivalent to diffusion processes. If fertility declines because individuals change ideas about the advantages of having children, even though their social and economic positions remain apparently the same, one cannot automatically infer the existence of a diffusion process. For this to be a proper inference, one must find evidence that the new ideas or the change of ideas are driven by imitation of others’ ideas. Second, the evidence that Cleland and Wilson use to support their claims belongs to a type we identified before as insufficient. Indeed, they examine the speed of changes in fertility and compare them with what would be expected given observed changes in structural conditions or, alternatively, they verify that the main cleavages created by fertility changes are drawn by ethnic or language distinctions. This contrast between ideational changes and demand-driven changes at the core of Cleland and Wilson and Caldwell’s formulations are reminiscent of the coarse contrast between adjustment and diffusion already contained in the older paradigm used by Carlsson. More recently, Bongaarts and Watkins (1996) review aggregate empirical evidence regarding the timing and pace of recent fertility declines. As Cleland and Wilson do, they too reach the conclusion that much of what we observe during the past twenty or thirty years is attributable to the transmission of information and ideas regarding fertility control. Their conceptualization of what is being transmitted and how it is transmitted is broader and perhaps more precise than Cleland and Wilson’s because it includes both micro-level diffusion processes (at the level of local networks and peers) as well as macro-level diffusion (global and national networks). But their inferences are based on linear shifts analysis, a device that rests on the unverified assumption that the magnitude of unexplained variance accounted for by shifts is associated with mechanisms facilitating diffusion. This may be suggestive but it is not the kind of proof we require to verify the existence of diffusion processes. Robust Theoretical Formulations The paradigm that characterizes the third stage in the history of application of diffusion processes to the study of fertility rests on three different and somewhat independent developments. In all three cases, the

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Diffusion Processes and Fertility Transition: Selected Perspectives most important contribution is the introduction of conceptual precision and ex ante identification of the mechanisms promoting (inhibiting) diffusion of new behaviors. An Integrated Theory In an attempt to grapple with the proper identification of the nature of diffusion processes and adjustment behaviors in fertility, Retherford (1985) formulates an integrated theory that contains many of the advances we singled out as necessary for a testable theory of diffusion. In particular, the author assumes a unique decision-making framework whereby behavioral adjustments (structural factors) and emulation of others’ behaviors (diffusion) may occur in tandem, the latter being more likely in highly integrated communities where psychic costs of deviant behavior are minimized. An important limitation of Retherford’s theory is that it does not contain much elaboration of mechanisms of social influence and only indirect reference to feedback mechanisms. Coale’s RWA Framework In a much-cited statement, Coale formulated three preconditions for fertility decline, “ready, willing and able” (RWA). This statement can be the basis for an alternative integrated framework. First, fertility control must be within the field of conscious choice or, equivalently, the new behavior, Bo, must be a member of the set of feasible behaviors among which the individual can choose. A necessary condition for this readiness to exist is that there should be information flowing from members of an individual’s network or from external sources of information. The idea of a new behavior must appear from somewhere. When we refer to ideational change, we seem to have in mind at least this dimension of the process. If so, and as indicated above, ideational change and diffusion should not be used as equivalent concepts because ideational changes may also depend on structural changes. The second and third conditions can be considered simultaneously because they are two parts of a model of rational decision making. Individuals must be willing to engage in the new behavior and they must be able to do so. Being willing refers to the ability to detect net benefits associated with the new behavior—what we referred to earlier as the linkage between net benefits and behavior. Being able simply refers to the accessibility to means to engage in the behavior and to the ability to bypass institutional constraints that impede the practice of the behavior. Coale’s RWA framework is agnostic regarding the nature of forces that may erode or develop support for each of the three preconditions. In particular, changes in any one of the three components could involve

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Diffusion Processes and Fertility Transition: Selected Perspectives both ideational changes as well as nonideational changes, and all three of them could be affected by diffusion processes to different degrees. Coale’s integrated framework has been recently operationalized in a number of developing countries by Lesthaeghe and Vanderhoeft (this volume). They assess the status of these three conditions and estimate their influence on the onset and speed of observed fertility changes (Lesthaeghe and Vanderhoeft, this volume). The limitation of this kind of work is that, in order to test diffusion models, one needs to estimate the effects of social influences (and feedbacks) on the level and patterns of each of the three components. Only then could one assess the overall contribution of diffusion to observed fertility changes, and to estimate the relative weight of the influence of the diffusion mechanisms across the conditions contained in the RWA set. Social Learning, Feedbacks, and Institutional Constraints Finally, recent developments in model formulation and in empirical analyses have led to important improvements on two fronts. The first consists of defining explicitly an individual-based decision-making process that acknowledges the operation of social influences, and then formulating a model of such a process whose parameters are estimable from available data. Once parameters are estimated, hypothesis testing is carried out to determine if the estimates are what we would expect if social influences were indeed part and parcel of the decision-making process. The bulk of this work has been carried by a few researchers but mainly by Casterline, Montgomery, and Rosero-Bixby in various publications (Rosero-Bixby, 1991; Casterline et al., 1987; Rosero-Bixby and Casterline, 1993; Montgomery and Casterline, 1993, 1996; Montgomery and Chung, 1994). Although this work utilizes different types of models, some more data demanding than others, it derives from a unified framework (see earlier sections) that makes it comparable to other attempts to tease out social influences from observed behaviors either in organizational contexts (Erbring and Young, 1979; Marsden and Friedkin, 1993) or in social movements (Liao, 1994). One of the shortcomings of these models is that they do not specify the network dynamics in detail, although they allow simplified representation of what social influences are. In a second line of improvements, researchers focus much more rigorously on the actual configuration of networks in which adopters and nonadopters may participate. In particular, the models are formulated to understand the dynamic interplay between individual decision making and the aggregate properties of the system, notably the continuous reshuffling of network connections that take place as the diffusion process advances (Kohler, 1998; Durlauf and Walker, this volume).

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Diffusion Processes and Fertility Transition: Selected Perspectives SUMMARY AND CONCLUSIONS The main task of this paper has been to derive explicit rules for testing the existence of diffusion processes and their mechanisms or, equivalently, to formulate conditions for the empirical identification of diffusion processes. I begin by recognizing the opposition between structural and diffusion-based explanations and confirm that this contrast is pervasive in demography and sociology. Furthermore, I also verify that, in most cases, the contrast is ill posed, ill defined, and poorly resolved through empirical analyses. In particular, I suggest that the opposition between the two types of explanations tends to undermine and overlook the decision-making process that is at the root of every diffusion process. Using previous discussions and elaborations on the subject, I introduce a preliminary, minimal definition that enables identification of key elements of a diffusion process. These are decision making, resistance and thresholds, social influence, rejection, and feedbacks. Armed with this minimal definition, I undertake the task of reviewing broad areas of application of diffusion models in sociology and demography in general, and identify several stages in the history of sociological applications. I discuss recent applications in collective action and organizational theory as examples of what would be near-to-ideal conditions for model formulation and testing of diffusion processes. This review leads me to the elaboration of a much refined definition of diffusion, one that highlights what is unique to a diffusion process, namely, the salience of social influence in decision making, and three mediating mechanisms through which social influence modifies individual behavior. This leads to the formulation of a golden standard or ideal model to uniquely represent and distinguish among various mechanisms of diffusion. Finally, I state fairly precise conditions for empirical identification of such processes. The paper ends with a brief review of diffusion research in the area of fertility. This review reveals that only very recent applications and hypotheses verification meet the stricter conditions set forth in the previous section’s discussion. Paradigms used in the past are simply too loose, too unspecific, and ultimately too far removed from the golden standard to be considered as anything more than useful suggestions. The most promising areas of research are those that rest on integrated formulations, where changes via diffusion and structural adjustments are viewed as results of individual decision-making processes that include individuals’ social and economic characteristics and individuals’ ties to significant others in a set of relevant social networks. We need refinements in the identification of how individuals choose and remain members of social networks, on the nature of feedback mechanisms, and

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Diffusion Processes and Fertility Transition: Selected Perspectives on the existence of institutional constraints and their effects on individual choices. The most important conclusion we draw from this review, and one that should guide future efforts in the area of fertility and other social behaviors, is that the sharp divide established between processes of structural adjustment and diffusion may be a good didactic tool and part and parcel of a respectable intellectual tradition, but it is seldom an accurate way of portraying the mechanisms that shape the behaviors they are intended to explain. NOTES 1.   An important idea that I will defend later is that one should not conflate the notions of cultural or ideational explanation with the notion of diffusion. They are simply not equivalent, and many confusions could be avoided if we kept them separate. 2.   An interesting example of a case study of forerunners is Livi-Bacci’s (1986) description of apparent practices of fertility control among elites and other selected social groups in Western Europe. 3.   Potter (1998) addresses the problem explicitly, though devoting more attention to what he calls “pernicious aspects” of social interactions that end up imparting inertia in the adoption of contraceptive technology and locking populations into a restricted menu of contraceptive choices, and less attention to mechanisms of outright abandonment of an adopted practice. Sinding and Mason (1998) also addresses the problem of rejection and, finally, Kohler’s new work (Kohler, 1997) provides an opportunity for rigorous formal treatment of it. This problem has been better formalized in the literature on collective violence (Myers, 1997). 4.   See the paper by Durlauf and Walker (this volume) for a formal treatment of some aspects of the endogenous feedback mechanism. 5.   The selection issues arising from devoting overwhelming attention to diffusion processes that more or less succeed in taking hold, while neglecting those where diffusion never takes off or dies out shortly after its onset, are presumably quite important but, to my knowledge, have not been studied seriously. 6.   An important aspect of the weaknesses of these models to identify underlying processes is that researchers who employ them usually assess the fit between observed and expected outcomes by examination of cumulative occurrence (proportion of the population who has adopted, for example). It is well known that a good fit of a cumulative distribution can conceal complete failure to predict associated densities (frequencies of new adopters during a small time interval). 7.   This third mechanism is associated with a number of interesting formal and substantive problems regarding the possibility of unstable equilibria and the relation between small changes at the individual level that may translate into large changes at the aggregate level (see Durlauf and Walker, this volume). As formulated here this mechanism includes what Arthur (1989) identifies as sources of increasing returns that emerge as an adoption process gets under way. Increasing returns can occur due to coordination externalities, advantages associated with learning, and advantages associated with increased information flows. These are all sources of positive feedback. The formulation I suggest here, however, leaves the door open for the possibility that feedback also can be negative.

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Diffusion Processes and Fertility Transition: Selected Perspectives 8.   See examples of the use of spatial proximity in the previous discussion of applications to collective action and organizations. 9.   Needless to say, controlled experiments, though close to this ideal, are not close enough. 10.   For a review of processes of network formation, see Doreian and Stokman (1997). REFERENCES Aldrich, H.E. 1979 Organizations and Environments. Englewood Cliffs, NJ: Prentice-Hall. Anderson, R.M., and R.M.May 1992 Infectious Diseases of Humans. Oxford: Oxford University Press. Anselin, L. 1988 Spatial Econometrics: Methods and Models. Boston: Kluwer. Arthur, B.W. 1989 Competing technologies, increasing returns, and lock-in by historical events. Economics Journal 99:116–131. Bailey, N.T.J. 1975 The Mathematical Theory of Infectious Diseases and Its Applications. London: Charles Griffen. Bandura, A. 1986 Social Foundations of Thought and Action. Englewood Cliffs, NJ: Prentice-Hall. Bartholomew, D.J. 1982 Stochastic Models for Social Processes. New York: Wiley. Bocquet-Appel, J.-P. 1997 Diffusion Spatiale de la Contraception en Grande-Bretagne, a l’Origine de la Transition. July, Institut National d’Etudes Demographiques. Seminaire Demodynamiques. Bongaarts, J., and S.C.Watkins 1996 Social interactions and contemporary fertility transitions. Population and Development Review 22(4):639–682. Brown, L. 1981 Innovation Diffusion: A New Perspective. London: Methuen. Burt, R.S. 1987 Social contagion and innovation: Cohesion versus structural equivalence. American Journal of Sociology 92:1287–1335. Caldwell, J. 1982 Theory of Fertility Decline. New York: Academic Press. Carlsson, G. 1966 The decline of fertility: Innovation or adjustment process? Population Studies 20: 149–174. Casterline, J.B., M.R.Montgomery, and R.L.Clark 1987 Diffusion Models of Fertility Control: Are There New Insights? PSTC WP 87–06. July, Brown University. Cavalli-Sforza, L.L., and M.W.Feldman 1981 Cultural Transmission and Evolution: A Quantitative Approach. Princeton: Princeton University Press. Cleland, J., and C.Wilson 1987 Demand theories of the fertility transition: An iconoclastic view. Population Studies 41:5–30. Coale, A.J. 1973 The Demographic Transition. Liège, Belgium: Ordina.

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