Estimation of stillbirth rates globally is complicated because of the paucity of reliable data from countries where most stillbirths occur. We com-piled data and developed a Bayesian hierarchical temporal sparse regression model for estimating stillbirth rates for 195 countries from 2000 to 2019. The model combines covariates with a temporal smoothing process so that estimates are data-driven in country-periods with high-quality data and deter-mined by covariates for country-periods with limited or no data. Horseshoe priors are used to encourage sparseness. The model adjusts observations with alternative stillbirth definitions and accounts for various sources of uncer-tainty. In-sample goodness of fit and out-of-sample validation results suggest that the model is reasonably well calibrated. The model is used by the UN In-teragency Group for Child Mortality Estimation to monitor the stillbirth rate for 195 countries.