Estimating the Total Fertility Rate from Multiple Imperfect Data Sources and Assessing Its Uncertainty

Leontine Alkema, University of Washington
Adrian Raftery, University of Washington
Patrick Gerland, United Nations Population Division
François Pelletier, United Nations Population Division

We develop methodology for estimating and assessing the uncertainty about the total fertility rate over time, based on imperfect estimates from different data sources. Measurement error is decomposed into bias and variance, and estimated by linear regression on data quality covariates. We estimate the total fertility rate using a local smoother and assess uncertainty using the weighted likelihood bootstrap. Based on a data set of seven West African countries we found that estimates with a recall period of more than five years tended to overestimate the total fertility rate, while direct estimates and observations from longer ago underestimated fertility. The measurement error variance was larger for observations with a one-year time span, for observations that were collected before the mid 1990s, and for one Demographic Health Survey. Cross-validation showed that taking into account differences in data quality between observations gave better calibrated confidence intervals and reduced the widths by about 40%.