  The sex ratio at birth (SRB) is defined as the ratio of male to female live
births. The SRB imbalance in parts of the world over the past several decades
is a direct consequence of sex-selective abortion, driven by the co-existence
of son preference, readily available technology of prenatal sex determination,
and fertility decline. Estimation and projection of the degree of SRB imbalance
is complicated because of variability in SRB reference levels and because of
the uncertainty associated with SRB observations. We develop Bayesian
hierarchical time series mixture models for SRB estimation and scenario-based
projections for all countries from 1950 to 2100. We model the SRB regional and
national reference levels, and the fluctuation around national reference
levels. We identify countries at risk of SRB imbalances and model both (i) the
absence or presence of sex ratio transitions in such countries and, if present,
(ii) the transition process. The transition model of SRB imbalance captures
three stages (increase, stagnation and convergence back to SRB baselines). The
model identifies countries with statistical evidence of SRB inflation in a
fully Bayesian approach. The scenario-based SRB projections are based on the
sex ratio transition model with varying assumptions regarding the occurrence of
a sex ratio transition in at-risk countries. Projections are used to quantify
the future burden of missing female births due to sex-selective abortions under
different scenarios.

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