## 4. Estimates and Interpretation

Table 2 summarizes the pertinent implications of the estimates (fully presented in the appendix) for the basic nonlinear estimates in Panel A and for the comparison between the nonlinear and the linear estimates in Panel B. The theoretical derivation in Section 2 assumes that the population is homogeneous. This assumption is relaxed for the empirical implementation. Initially we therefore calculate individual-level direct and total effects for each woman in the sample, assuming she interacts with a population having a distribution of characteristics as do the remaining women in the sample. We then average over these individual-level effects and obtain the (overall) direct and total effects. These (overall) direct and total effects are reported in Tables 2. They measure the average direct and total increases in the probability of ever using family planning for all women in the sample resulting from a small increase in program effort x. The specific equations to calculate these effects are extensions of the respective equations in Section 2 and are reported in the Appendix.

The first three columns in Table 2 gives the results for the KDHS 1989, KDHS 1993, and KDICP 1994/5 data sets on the basis of cluster (village) based measures of interaction. The last column reports the results for the KDICP 1994/5 data using reported networks. For each of the two dependent variables there are eight sets of estimates - one for the nonlinear logistic model and one for the linear probability model for each of the four columns. In tables A2 and A3 in the appendix we additionally provide the corresponding results that are obtained from an alternative measure of family planning effort based on the distance to the nearest family planning clinic (KDHS 1989 and 1993 only).

Multiple equilibria: We first consider whether the estimates for the logistic model imply that there is more than one stable equilibrium after the effects of a family planning innovation have worked their way through the population, an interesting possibility with policy implications that we discussed above. We find that in these data there is only one equilibrium level of ever used family planning [Note 8]. Our estimates thus imply that Nyanza is not stuck in a low-level Malthusian equilibrium with another high contraceptive use stable equilibrium that is attainable if there were a large enough program effort. This, then, suggests that a large but transitory program effort would not have the effect of shifting women in this province rapidly to a sustainable high-contraceptive-use and low-fertility equilibrium. Persistent changes in program effort are necessary to affect the equilibrium and therefore long-term levels of contraceptive use and desires to stop childbearing.

Equilibrium levels: The equilibrium levels are of interest because, as noted, they represent the levels of use at which there is no incentive for systematic change (though there may be transitory fluctuations around them) as long as program efforts are sustained at a given level. At an equilibrium, individual probabilities of contraceptive use equal the network partners' average probability of use. Row A1 gives the estimated equilibrium levels (ye) for the nonlinear model. These estimated equilibrium levels for the nonlinear models are slightly below the observed levels. The estimated equilibrium levels for the linear model are slightly higher (row B1) and are basically at the sample means.

Direct program effects, without and with social interactions: The estimated direct effects from a marginal increase in program effort are given both for a specification with no social interactions and a specification with social interactions (rows A2 and A3). All the estimates indicate that the failure to include social interactions would result in substantial upward biases in the estimated direct program effects. These overestimates are considerable - in the nonlinear models by from 33 to 148% for the effect of how program efforts change the level of ever used family planning (row A6). The linear model produces estimates of direct program effects that are higher than the nonlinear model in the KDICP data, but lower than the nonlinear model in the KDHS data (rows B2 and B3). Moreover, the direct effect with and without social interaction for the KDICP data differ relatively little depending on whether village averages or network averages are used to measure social interaction, although the bias caused by ignoring social interactions in the direct program effect is lower when individual-level measures of social interaction are used.

Total program effects with social interactions: The total program effects with social interactions in the nonlinear model have a marginal effect on the probability of having ever used family planning in the range of 0.14 to 0.20 (row A4). These estimates imply that social interactions amplify the direct program effects on the propensity to ever use family planning considerably, ranging from 21 to 75% (row A7). The estimates for the total program effort in the KDICP data differ relatively little between the two measures of social interaction, while the social network-based estimates yield the lower social multiplier. Similar to our estimates of direct program effects, the linear model estimates of the total program effect are less than the nonlinear model estimates for the KDHS data (by -4.2 to -16.1%), but tend to be greater for the KDICP (with a range from 0.7 to 33.7%, row B4).

In the linear model, the total program effect does not depend on individual characteristics. In the nonlinear model, however, subpopulations with different levels of contraceptive use can be subject to different multiplier effects and also total effects. Since the education level is a significant determinant of having used family planning, we provide in Panel C of Table 2 the total effect separately for women with low and high education. The results clearly demonstrate that both the total effect and the social multiplier are higher-sometimes substantially so-- for the high education subpopulation with a higher overall propensity of ever using family planning.

Effect of increasing the impact of social interactions: Table 2 present two effects of intensifying social interaction that measure the change in the total program effect (row A5) and in the social multiplier effect (row A8) that are caused by increasing the `strength'-or parameter a or - of social interaction (see note 5 for the respective formal derivations). The estimates for the nonlinear model indicate that the effects of intensifying social interaction on the total effect are negative, while the effect of `more' social interaction on the social multiplier effect is positive. Intensified social interaction therefore reduces the total effect that results from program efforts, but since it also reduces the direct effect, the social multiplier defined as the ratio of total to direct effect slightly increases. While the results therefore do not classify social interaction as status-quo enforcing (which is defined as a negative effect of intensifying social interaction on the social multiplier), `more' social interaction would still be undesirable from a program standpoint because the total effects resulting from program efforts would decrease as a consequence of this intensified social interaction. Thus, any assumption that increasing the impact of social interactions must accelerate diffusion make it easier for family planning programs to achieve changes in the prevalence of contraceptive use is not supported by our preferred nonlinear estimates. The linear estimates, as noted, imply a positive effect of increasing social interaction on both the social multiplier and the total program effect, and the linear estimates thus suggest the opposite effect of intensifying interaction on the total effect as compared to the nonlinear estimates (so the signs are negative in row B5).

 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 http://www.demographic-research.org/Volumes/Vol3/7