Bayesian reconstruction of two-sex populations by age: estimating sex ratios at birth and sex ratios of mortality

The original version of Bayesian reconstruction, which is a method for estimating age-specific fertility, mortality, migration and population counts of the recent past with uncertainty, produced estimates for female-only populations. Here we show how two-sex populations can be similarly reconstructed and probabilistic estimates of various sex ratio quantities obtained. We demonstrate the method by reconstructing the populations of India from 1971 to 2001, Thailand from 1960 to 2000 and Laos from 1985 to 2005. We found evidence that, in India, the sex ratio at birth exceeded its conventional upper limit of 1.06, and, further, increased over the period of study, with posterior probability above 0.9. In addition, almost uniquely, we found evidence that life expectancy at birth, e(0), was lower for females than for males in India (posterior probability for 1971-1976 equal to 0.79), although there was strong evidence for a reversal of the gap through to 2001. In both Thailand and Laos, we found strong evidence for the more usual result that e(0) was greater for females and, in Thailand, that the difference increased over the period of study.