The evolution of 4-2-1 family structure in China: a simulation based on multistate family structure tables

The 4-2-1 family structure has become more prevalent with the rise of only-child families, yet it remains understudied. Using 2020 census data, probability theory, and life table methods, this paper constructs multistate family structure tables to analyse the survival probabilities, expected durations, and elapsed durations of the 4-2-1 family and its 29 evolved configurations over the family life cycle. We identify 13 family structures with higher survival probabilities. The survival probability of the 4-2-1 structure declines almost linearly as members die, gradually evolving into other structures, whose survival probabilities first increase and then decrease with the child’s age. Lower-probability families are primarily Shidu families, where the parental and offspring generations die before grandparents. The four grandparents have an expected duration of approximately 17 years. Younger parental age at childbirth is associated with higher survival probabilities of the 4-2-1 structure, while older parental age advances the peak survival of the 3-2-1 structure.