Does fertility affect woman's labor force participation in low- and middle-income settings? Findings from a Bayesian nonparametric analysis

Estimating the causal effect of fertility on women's employment is challenging because fertility and labor decisions are jointly determined. The difficulty is amplified in low- and middle-income countries, where longitudinal data are scarce. In this study, we propose a novel approach to estimating the causal effect of fertility on employment using widely available Demographic and Health Survey (DHS) observational data. Using infecundity as an instrument for family size, our approach combines principal stratification with Bayesian Additive Regression Trees to flexibly account for covariate-dependent instrument validity, work with count-valued intermediate variables, and produce estimates of causal effects and effect heterogeneity, i.e., how effects vary with covariates in the survey population. We apply the approach to DHS data from Nigeria, Senegal, and Kenya. We find in the survey sample and general population that an additional child significantly reduces employment among women in Nigeria but has no clear average effect in Senegal or Kenya. Across all three countries, however, there is strong evidence of effect heterogeneity: younger, less-educated women experience large employment penalties, while older or more advantaged women are largely unaffected. Robustness checks confirm that these findings are not sensitive to key modeling assumptions. While limitations remain due to the cross-sectional nature of the DHS data, our results illustrate how flexible non-parametric models can uncover important effect variation.