Abstract: Taking the self-selection rather than a stochastic process of children's accompanying migration into account, this paper uses the China Migrants Dynamic Survey(CMDS) data in 2013 to examine the effect of children's accompanying migration on their parents' wage with Endogenous Switching Regression Model(ESRM), which would reduce endogeneity of self-selection. There are some new findings. First, self-selection factors affect family decision-making, and children have self-selection as they migrate. Second, quite different from popular judgment, children's accompanying migration would restrain their parents' wage rate significantly. It will underestimate the negative effect of children's accompanying migration without considering the self-selection. Third, the wage effect of children's accompanying migration has the gender heterogeneity of “father benefit, mother damage” by reducing mothers' wage by 8% while promoting fathers' wage by 2%. Working time, working stability, health level as well as consuming level can help to explain the gender heterogeneity of wage effect. Happiness from children's migration and family gathering cost mothers' wage, and social gender identity still plays a key role in gender heterogeneous wage effect. This paper suggests that the government should create convenient conditions for the migration of workers' children, further improve the policies for the migration of children, reduce the costs of migration to offset or exceed the wage effect of reduction, and increase the happiness and social integration of rural migrant workers' families. The service policy of rural migrants with the family as a unit must include gender factors in the public policy category in the top-level design, and pay attention to the policy supply of gender equality.

Key words: children's accompanying migration, income of rural migrant workers, gender heterogeneity, self-selection, social gender identity