To be fair, the kids were all fake. The reason for this massive disappearance was due to a rules change that the IRS enacted for people declaring dependents on their tax returns. Originally, the tax return form just asked you how many dependents you had. Because there was little consequence to writing a fictitious number, and because there were major tax breaks for declaring you had kids, a large number of people lied on their returns.
In 1987, when the IRS said that people who wanted to claim dependents on their tax returns had to provide a Social Security number for each claimed children in the return. When tax returns were due, there were 7 million less kids claimed as dependents in the US. That number represented about 1 in 10 dependent children in the United States!