Abstract Implications of Linear and Nonlinear Models of Family Planning Diffusion with Social Interactions

1. Introduction

Most empirical studies of the diffusion of modern methods of family planning have treated family planning programs as if they only affect individuals directly [Note 1]. It is unlikely, however, that all of those who hear family planning messages on the radio or from the clinic keep quiet about what they have heard [Katz and Lazarsfeld 1955]. Indeed, exposure to messages from formal sources may stimulate conversation, perhaps especially when there is widespread uncertainty-for example, about the desirability of fewer children, the legitimacy of deliberate control of fertility in marriage, or the safety of modern methods of family planning.

If social interaction is relevant for attitudes and behavior, then family planning programs have both a direct effect on those who are in contact with the program and an indirect effect produced by social interaction [Bongaarts and Watkins 1996, Montgomery and Casterline 1993, Montgomery and Casterline 1996]. This latter, indirect effect of family planning programs leads to a social multiplier effect that implies that the total-or long term-change in family planning use exceeds the change in contraceptive prevalence that is directly attributable to program interventions. For example, in a recent household survey conducted in Nyanza Province, Kenya and described in more detail below, the majority of women who reported hearing a family planning talk in a clinic or receiving a family planning message from the radio, movies or newspapers or who were visited by a Community Based Distribution agent, said they then talked about it with others. Moreover, substantial proportions of those who had not directly been exposed to a program message nonetheless had chatted about family planning with others. Indeed, it may be that messages heard second-hand may be particularly influential and thus lead to additional increases in contraceptive use among women who were not reached or not convinced by the initial program effort. For instance, in the qualitative component of the Nyanza study, the process of transmission of information from person to person was often accompanied by an evaluation of the generic program information to suit the particular local context, and social interaction therefore augmented and modulated the information provided by the program [Watkins 1998, Watkins, Rutenberg, and Green 1995].

Because social interactions might be important in helping us to understand fertility change in developing countries, there has been a small, though rapidly growing, empirical literature that examines their possible impact [e.g., Arends-Kuenning 1997, Entwisle and Godley 1998, Kohler, Behrmann, and Watkins 2001, Montgomery and Casterline 1993, Montgomery and Casterline 1996, Montgomery and Chung 1994, Munshi and Myaux 1997]. But despite the increasing attention given by demographers to issues of social interaction, there remain fundamental problems of analysis and inference.

In this paper we consider the implications of using nonlinear models in empirical analyses of the impact of family planning programs, modulated by social interaction, on reproductive attitudes and behavior. To clarify these implications, we discuss for comparison a simple and more transparent linear model that we perceive is the basis of the intuitions of many analysts regarding the impact of social interactions on family planning adoption. Although this linear model is used in some studies [e.g., Montgomery and Casterline 1993], most studies of social interactions in the context about the adoption of contraception use nonlinear models, frequently logistic models, without extensive discussion of the implications of this choice [Arends-Kuenning 1997, Entwisle and Godley 1998, Kohler, Behrman, and Watkins 2001, Montgomery and Chung 1994, Munshi and Myaux 1997]. Although the implications of using nonlinear models might appear to be a technical issue with little consequence for the results of empirical analyses, the implications of this choice for understanding behavior and for policy may be substantial. We are unaware of any prior consideration of the implications of using nonlinear models, nor of the consequences of using linear versus a nonlinear model, in the literature on the diffusion of contraception with social interactions.

If the relation between program effort and the use of family planning is linear, there is only one stable equilibrium, i.e., the ultimate level of use of modern family planning that a population can be expected to reach after the effects of a sustained change in a family planning program have worked through the population. The extent to which social interaction multiplies program efforts is unaffected by whether the equilibrium is at a low or high level of contraceptive use. With a nonlinear model, however, there may be both low and high equilibria; in the former family planning use is low despite program effort, and in the latter it is high. In this nonlinear world, the effects of program efforts depend on whether the community targeted by the program has a low or a high level of contraceptive use. A striking implication of a nonlinear model, moreover, is that a sufficiently large change in program intensity may cause a large shift from a old, low-family-planning-use equilibrium to a new, high-level equilibrium even if the program change is transitory rather than sustained. This means that even were program efforts to subsequently diminish - due, for example, to donor fatigue or strained governmental budgets- fertility would continue to be controlled [Note 2].

Just as the form of the model has implications for evaluating the impact of intensified program efforts, the form of the model has implications for evaluating the impact of intensified social interaction. If the relation is linear, any intensified social interaction must increase the social multiplier effect, i.e., the difference between the total and direct change in family planning use that results from program interventions. It is plausible, however, that program efforts may provoke opposition. For example, where the elderly rely on their descendants for economic support, the introduction of an accessible family planning clinic may intensify opposition by parents-in-law, who worry even more that the numbers of their grandchildren - and thus the intergenerational support they hope for - might be diminished [Watkins 1998]. Moreover, researchers and other observers long have known that new users of family planning may not be satisfied: rather, they may alarm their friends by detailing the negative side effects of modern methods that they have perceived [DeClerque et al. 1986, Forthingham 1968, Rutenberg and Watkins 1997]. Although this aspect has been discussed in the literature at least since Granovetter [1973] introduced the notion of weak and strong ties [e.g., for relevant demographic discussions see Crook 1978, Bongaarts and Watkins 1996, Montgomery and Casterline 1993, Montgomery and Casterline 1996], it has not been addressed within formal analyses on the adoption of contraception. Our analyses in this paper show that if the model is nonlinear, the ambiguous effect of intensifying social interaction is represented in the theoretical framework. In a nonlinear model, intensified social interaction can increase or decrease the social multiplier effect and intensified social interaction can thus retard or enhance the diffusion of family planning after program interventions. The direction of this effect is then an empirical question, and it is no longer imposed by the formal theoretical framework as is the case with a linear model.

Section 2 presents a formal model of diffusion with social interactions, develops the implications of the nonlinearity of the model, and contrasts this model with a linear probability model. Section 3 summarizes the two data sets that we use for illustration. Section 4 presents and discusses our empirical estimates. We emphasize that we do not address completely or satisfactorily what we consider to be the central substantive issue: the impact of social networks on contraceptive use and fertility. This question raises other important methodological issues, such as the role of endogenous choices of social network partners and unobserved heterogeneities, that cannot be well addressed with the cross-sectional data we use for our estimates here. The comparisons in Section 4, nevertheless, provide insight into evaluating program effects under the maintained hypothesis that estimation problems such as unobserved heterogeneities, while they may affect each of the estimates being compared, do not affect them differentially.


Abstract Implications of Linear and Nonlinear Models of Family Planning Diffusion with Social Interactions

Empirical Assessments of Social Networks, Fertility and Family Planning Programs: Nonlinearities and their Implications
Hans-Peter Kohler, Jere R. Behrman, Susan Cotts Watkins
© 2000 Max-Planck-Gesellschaft ISSN 1435-9871