## Appendix: Calculation of direct and total effect in heterogeneous populations

The calculations of the direct and total effect reported in Table 2 assume that a woman interacts with a population having a distribution of characteristics as do the remaining women in the sample and that the program effort in the population equals the average program effort in the sample. Based on this assumption we first calculate the equilibrium level, and the individual-level direct and total effects for each woman in the sample. We then average over these individual-level effects and obtain the (overall) direct and total effects that are reported in Table 2. In this appendix we provide the specific equations that are used for these calculations.

Denote as zi the individual characteristic of women i = 1, ..., N in the sample, where N is the sample size. Moreover, denote as the average program effort in the sample, i.e., the proportion of women in the sample who have heard a family planning message on the radio. Denote as xi the specific program effect for women i, which in our estimations equals the proportion of family planning user's in woman i's village of residence.

Linear model: The parameters and re the coefficients from estimating relation {1} via a linear regression of woman i's contraceptive use on the proportion of contraceptive users in woman i's village/reference group, the program effort xi in the woman's village of residence, and the individual characteristics zi (i.e., the regression subsumes term -.5 in {1} into the constant term). The equilibrium level ye is then calculated as . The direct and total effect of changes in program effort is given respectively by and and in the linear model neither effect depends on the level or distribution of the individual characteristics zi in the data.

Nonlinear model: The parameter and are the coefficients from the estimation of relation {2} via a logistic regression of woman i's contraceptive use on the proportion of contraceptive users in woman i's village/reference group, the program effort xi in the woman's village of residence, and the individual characteristics zi (i.e., the logistic regression again subsumes the term -.5 in {2} into the constant term). The equilibrium level is then calculated iteratively and solves , that is, the equilibrium level equals the average probability that women in the sample use family planning, given that they interact with a reference group with a prevalence of ye. This definition of the equilibrium level is analogous to the definition of the equilibrium level in homogeneous populations after equation {2} above. The direct effect in Table 2 is then obtained as the average of the individual direct effects , and the total effect is calculated as the average of the individual-level total effects .

 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