Rationed Fertility: Theory and Evidence

We analyze the effect of exogenous changes in fertility on child quality both at and off the unrestricted optimal fertility level in a general model with rationed fertility. Besides the price and substitution effects analyzed in the literature, we show that a desired fertility change, representing a shift towards the optimal level, induces a positive income effect, while a forced fertility change, representing a shift away from the optimal level, induces a negative income effect. To empirically test the theory, we combine a natural experiment, i.e., twins, with a policy change, i.e., One-child Policy and find results that are consistent with the theoretical implications of our model. Our paper provides a theory of rationed fertility that reconciles recent empirical literature on the heterogeneous fertility effects on child quality, and advances our understanding of how population control policy affects human capital investment and economic development.