The perfect collinearity of age, period, and cohort makes it impossible to separate their effects without additional assumptions. This study compares two approaches, the Intrinsic Estimator (IE) and the hierarchical age-period-cohort model (HAPC), using data on female household headship in Iran. Data were drawn from eight waves of the Household Expenditure and Income Survey (1986–2021) and include 272979 women aged 15–89. For age, the two models converged: the probability of headship rose with age. For period, the HAPC showed a decline in headship probability from 11.4% (1986) to 7.0% (1996), followed by a mild increase to 9.8% (2021). In the IE, however, after a slight decline until 1996, the probability rose sharply from 3.5% to 12.3%. For cohort, the HAPC showed an inverted-U pattern peaking at 10.7% among women born in 1947–1956, whereas in the IE the probability declined steadily from the oldest to the youngest cohort, from 16.6% to 0.8%. Comparison tests showed that both models explain the data equally well, but when the data coding was changed, the HAPC results remained stable while the IE results changed. Therefore, for Iranian data, the HAPC is recommended as the more appropriate main model, with the IE used for sensitivity checks.