An Explanation for the Increased Rate of First Marriage of the Cohort Born in the Year of the Fire Horse Using a Two Sex Model Based on the Concept of the “Encounter”

The year 1966 was the Year of the Fire Horse in the Chinese calendar. In Japan, the influence of this tradition accounts for the very low number of births in that year - approximately 3/4 of that in the previous year. Twenty-nine years later in 1995, the probability of first marriage by age for the generation born in the year is unnaturally high compared to immediately younger and older cohorts.

If we consider the population pyramid in detail, the range of ages marrying the cohort born in the Year of the Fire Horse is considerable. Therefore, in order to calculate the correct probability of first marriage it is necessary to control both male and female populations together. This requires presentation of the two-sex model (marriage function). Assuming the number of first marriages m differentiated at time t as m’, the male population as M, and the female population as F (M < F), the probability of first marriage k is k=m’/(M(1-(m/M))(1-(m/F))). The denominator then represents the number of “encounters” between males and females. Solving this differential equation permits derivation of the marriage function kt=K=(F/(F-M))-ln((M/F)((F-m(t))/(M-m(t)))). The “distortion” associated with the Year of the Fire Horse is considerably reduced when the probability of first marriage is calculated using this model.

Of course, this Year of the Fire Horse Effect is not unique, and appears whenever there are irregularities in the population pyramid. The probability of first marriage is currently decreasing in many East Asian countries. In order to clarify the causes of this phenomenon it is necessary to eliminate these effects from the original data using the two-sex model.