This paper considers differential fertility and analyzes how the fertility of people caught in poverty disturbs their escape from poverty. For escape from poverty, it is necessary that the average human capital stock exceed certain thresholds before the ratio of the number of poor to rich people increases more rapidly than the human capital level of rich people. Thus, the escape depends on a race between the accumulation of human capital by the rich and the accumulation of children by the poor. A high initial ratio of the number of poor to rich people would imply persistent poverty.