THE FEDERAL income tax system tries too hard to redistribute income from rich to poor, the theory goes, and the result is low economic growth. The Reagan administration intends to do something about that. The president's tax program, Secretary of the Treasury Regan testified the other day, is designed to "expand incentives and opportunities for socially productive efforts and saving for all taxpayers, not try to redistribute a slower and slower growing amount of total income."

The striking thing about the distribution of income in this country is that there's been hardly any visible change for more than 30 years. The country as a whole has grown much richer, but the shares of total income at the top and at the bottom are just about where they were in the late 1940s. We say that with a couple of emphatic qualifications that readers will need to keep in mind as this debate proceeds. There are many different definitions of income, and different ways to count it. American demography is changing, with families becoming smaller; that does strange things to the figures on family income. The variations in statistical treatments are far greater than the trends in any data. But in spite of all the hazards, the broad pattern is worth noting.

At the top of the scale, the income tax rates paid by the wealthiest have dropped over the past generation. In World War II a surtax took the top rate up to 90 percent. It was reimposed during the Korean War, and remained until 1963 -- that is, through the investment boom of the 1950s. It dropped to 70 percent in the middle 1960s, went up with the Vietnam surtax, and back down in 1971. The following year the top rate on earned income was lowered to the present 50 percent.

Through all of it, the share of the total income tax burden paid by the wealthiest taxpayers has been remarkably stable. As for people in the middle and at the bottom, the steady rise of the Social Security payroll taxes has weighed heavily on them. Taken all together, the taxation of personal income is somewhat less progressive today than it was when President Eisenhower came to office.

But in the intervening years, the federal government has collected increasingly large revenues, mainly from people in the top third of the ladder, and distributed them mainly among people in the bottom half. Why hasn't that changed the distribution of income more significantly? There are several hypotheses, all controversial. Perhaps there is a trend toward concentration at the top that has been offset by the tax system. But that's not clear.

It's possible to argue that there is some evidence of a faint trend toward greater equality over the past generation. But certainly there has been no shift, either in income or in taxation, sufficient to account for the sudden and drastic increase in inflation, and the stagnation of productivity, since the early 1970s. Similarly, there's a case for a tax cut. But it's hard to conclude that the administration's proposed changes in the distribution of taxes would make any very dramatic difference in the way the economy works.