Optimal Population Path Fitting for Flawed Vital Statistics and Censuses

Optimal Marriage Fitting for Imperfect Statistics

“…This is no longer true for migration, for spouses are likely to migrate together. As a matter of fact, numerically, [1] found male and female net migration rates close to each other. There is no accurate way to compute a civil-status specific migration rate in the absence of deaths by age and by civil status, as in our case study of southern Russia 1863-1916.…”

“…. , 45-50, over 50; 7 for married women-the eighth class is deduced from the equality of the sum of married men with the sum of married women-; 8 age classes for widows and divorced, 8 for widowers and divorced-the age class sizes of spinsters and bachelors are deduced by subtraction from the known sizes of their age groups given in [1]; and 13 additional controls for program (9) applied to the initial civil-status specific age pyramid. At each year of the period [0, T ], program (9) involves again 13 parameters for the age correspondence between the married of the current year.…”

“…For the sake of consistency, we take the same example as in [1] of district Khopyorskii, in the Don Army Territory (Voisko Donskoe), in southern Russia, from 1863 to 1916, to illustrate the results of the model. The 1897 census is the only one giving the age distributions by civil status during the period.…”

“…For each year of the period 1863-1916, the probabilities of dying, the fertility overall index, net migration rates, and the population by age and sex come from the reconstruction of the population by confession and by district done in [1]. We assume that mortality and migration are independent of civil status: apart from the fact that no statistics informs us about a difference, introducing differences is of second-order importance in a society experiencing a high mortality.…”

“…We assume that mortality and migration are independent of civil status: apart from the fact that no statistics informs us about a difference, introducing differences is of second-order importance in a society experiencing a high mortality. So, ∀a, μ (j ) t, a) for j = f, m in system (1). Mortality of the couple means the death of one of the spouses.…”