This study is intended to examine (l)whether the value of son-for example, old age security and succession of family lineage- causing son preference in the traditional society can be explained at the individual level, (2)whether women without son in the son preference country continue her childbearing until having at least one son or give up the desire of having a son at a certain level. To accomplish these purposes, the 1974 Korean National Fertility Survey data are analyzed by the quadratic hazard models controlling unobserved heterogeneity. Unlike ordinary regression model, even omitted variables that affect hazard rates and are uncorrelated with the included independent variables can distort the parameter estimates in the hazard model. Therefore the nonparametric maximum likelihood estimator(NPMLE) of a mixing distribution developed by Heckman and Singer is used to control unobserved heterogeneity. Based on the statistical result in this study, the value of son causing son preference is determined at the societal level, not at the individual level. And Korean women without a son did not continue endlessly childbearing during child bearing ages until having a son. In general, they gave up the desire having a son when she had born six daughters continuously. Thus, 30-40 years ago, the number of daughters that women without a son giving up the desire of son was six, which is about the level of total fertility rate during 1960s. In these days, we can often see many women who have only two or three daughters and do not any son. This means that the level of giving up the desire of son, which is one factor representing the strength of son preference, becomes lower. If the strength of son preference did not become much weaker, then the fertility rates in Korea could not reach the below replacement level.