In this paper we develop and implement an econometric methodology estimating a family-specific exogenous component of life-expectancy in order to determine the responsiveness of fertility to exogenous changes in child mortality. We use a generalized waiting time regression model applied to length of life which is viewed as the output of a production process. We allow for family-specific heterogeneity in duration of life and for time-varying explanatory variables. The heterogeneity component retrieved from the production function estimation is used to estimate the impact of exogenous child mortality on a measure of fertility.