Methods
To detect long-term trends in demographic rates and measure their sensitivity to sorghum prices, we make use of discrete-time event-history analysis. Specifically, we use regression methods for limited dependent variables.
As described below, the type of regression depended on the dependent variable. To detect trends and sensitivity to prices, we included as right-hand side variables interactions between year and region, as well as between logged low sorghum prices and region.13 The logged prices are base 1.1, so that coefficients represent the effects of a 10% change in prices. We do not include main effects of year and price, so for each there are a total of four interactions, one for each region. Coefficients on these termsare accordingly specific to each region, and do not measure slopes relative to the slope for an omitted reference category.
For each of three demographic events, mortality, fertility, and nuptiality, we estimate three models. We estimate one model over the entire period for which demographic data are available and price results are interpretable: 1780—1888. We also divide this period into two halves and estimate separate models for each to examine whether there were changes between periods in trends in rates and their sensitivity to price. We expect that if the last half of the nineteenth century was one of declining living standards, especially in the less commercial northern and central regions, rising mortality or falling fertility and nuptiality would be more apparent there than for the period as a whole. We also expect that if increasing commercialization in southern Liaoning during the last half of the nineteenth century led to improvements in living standards, mortality there may have fallen, nuptiality or fertility may have increased, or rates in general may have become less sensitive to prices.
In the case of nuptiality, the dependent variable is a dichotomous indicator of whether or not a man marries for the first time in the next three years. We only include observations of men who have not yet married. Instead of logistic regression, we use complementary log—log regression.14 In this case, the coefficient for an interaction between year and region measures the average annual change in the chances of marrying in the next three years for men in the specified region. Similarly, the coefficient for an interaction between logged price and region measures the effect of a 10% increase in low sorghum prices in the region. Because we expect the men who married early, at the modal ages, and late to have differed in terms of what affected whether or not they would marry in a particular time interval, we carry out separate analyses for the age ranges 6—15 sui, 16—25 sui, and 26—40 sui^
For mortality, the dependent variable is a dichotomous indicator of whether or not an individual dies in the next three years. Again, we use complementary log—log regression. We carry out separate analyses for the age ranges 2—15, 16—55, and 56—75 sui because the determinants of mortality differed between childhood, adulthood, and old age. For the youngest age group, we only analyse male mortality because only a few of the state farm systems had appreciable numbers of daughters recorded. For adulthood and old age, we carried out analyses by each sex.16
For fertility, the dependent variable is a count of the number of births attributed to a married woman in a year. Since the dependent variable is a count, we use Poisson regression. Whereas the analyses of mortality and nuptiality made use of triennial observations, the analysis of fertility makes use of a specially constructed file of annual observations described in the section on data. We accounted for variation by age in the probability of having a birth by inclusion of a fifth-order orthogonal polynomial and interactions between its terms and the region indicators, though to save space we do not present the estimated coefficients.
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