The Reproduction of Intelligence attempts to quanitfy this effect:

Although a negative relationship between fertility and education has been described consistently in most countries of the world, less is known about the relationship between intelligence and reproductive outcomes. Also the paths through which intelligence influences reproductive outcomes are uncertain. The present study uses the NLSY79 to analyze the relationship of intelligence measured in 1980 with the number of children reported in 2004, when the respondents were between 39 and 47 years old. Intelligence is negatively related to the number of children, with partial correlations (age controlled) of −.156, −.069, −.235 and −.028 for White females, White males, Black females and Black males, respectively. This effect is related mainly to the g-factor. It is mediated in part by education and income, and to a lesser extent by the more “liberal” gender attitudes of more intelligent people. In the absence of migration and with constant environment, genetic selection would reduce the average IQ of the US population by about .8 points per generation.