More than 2 million American children have vanished -- vaporized, it seems, by the tax code.

It began in 1988 when Congress, as part of a welfare reform package, began requiring parents who take a special tax credit for child care expenses to identify their day care providers. There was widespread suspicion that many providers were not reporting the income they were getting for their services.

The identification requirement went into effect in 1989.

Now the Internal Revenue Service has found a dramatic decline in the number of tax returns claiming the tax credit. After years of fairly steady increases, peaking at 8.7 million in 1988, the number plunged to 6 million in 1989. The value of the credit to taxpayers dropped from $3.7 billion in 1988 to $2.5 billion in 1989.

At the same time, the number of child care providers skyrocketed from 262,000 in 1988 to 431,000 in 1989, a roughly 65 percent increase. The IRS has not calculated the revenue gain, but it is likely to be substantial.

The IRS has not finished studying the numbers, nor has it decided what to do about them. But a spokesman said that while there are legitimate explanations for part of the decline, the agency is assuming that at least some of the disappearing children were fictitious.

He noted that this is the second mass disappearance of dependents following a change in reporting rules. In 1987 -- when the law began demanding the Social Security number of anyone over age 5 (now it is age 2) claimed by a taxpayer as a dependent -- some 6 million "dependents" disappeared from the tax rolls.

That resulted in a revenue gain to the government of $2.8 billion in 1987 alone, the IRS spokesman said.

Besides fictitious children, the spokesman said, there are probably parents who decided to continue with an under-the-table arrangement -- in which the provider does not report the income -- and forget the tax credit.

"We will probably be taking a look at some of these areas, especially first-time {day care income} filers. . . ," the IRS official said. "We'll probably be contacting those individuals to see if they had income from child care in previous years or was this in fact their first year" in business.

And the agency will likely "be looking at returns where they stopped claiming the child care credit" to find out whether they might be using an off-the-books provider or conversely whether they were truly eligible for the benefit in the past.

Plainly, not all the children who have gone off the rolls did so because their parents or day care people were cheating.

Former IRS commissioner Lawrence Gibbs, asked about the numbers, said that while they suggest plenty of taxpayers "are making less than honest errors," others may well be genuinely confused by the system.

Gibbs noted that in a pilot program in Boston designed to increase the accuracy of IRS telephone advice, the agency was startled at how difficult it is to sort out the dependency rules.

Also, a number of children outgrow day care each year and in other cases their parents make different but perfectly legal arrangements, the IRS spokesman said.

On top of that, changes in the law have restricted eligibility for the tax credit while making the program less attractive to certain parents.

For example, until 1988, children up to age 15 could qualify; now the limit is 13.

At the same time, Congress eliminated the practice of piggybacking the tax credit on another child care benefit known as a dependent care account. Under the latter benefit, which is offered by employers, pre-tax money is deducted from a worker's pay and placed into an account that the worker can draw on to pay child care costs.

Not all employers offer this plan, but parents who have the choice usually find it a better deal and drop the tax credit.