President Reagan's idea of income tax indexing is simplicity itself: adjust rates each year so that inflation does not push taxpayers into higher brackets. To get some sense of how indexing actually works, we can look at Minnesota, the state that has tested it most.

In usually Democratic Minnesota, the Republicans swept the 1978 elections. One of the first things Gov. Albert Quie and the new legislature did was to index state income taxes. That lowered taxes for 1979-82 by $1.2 billion. The state then could not pay for the services it intended to provide. Because Minnesota's constitution requires a balanced budget, taxes had to be raised in five special sessions of the legislature by a total of $1 billion.

This experience leaves in shambles the following arguments for indexation:

* Indexing automatically adjusts tax rates to changes in the economy. Minnesota's continuing fiscal crises suggest there is no such thing as putting a tax system on autopilot.

* Indexing holds down state spending. Republicans claim the state would have spent the $1.2 billion that indexing cut from revenues. But the fact is that the political force behind spending was strong enough to make legislators pass more than $1 billion of tax increases. Gov. Quie himself rejected proposals for further budget cuts, which would have closed down parks, hospitals and prisons, cut aid to local government and school districts and reduced property tax relief.

* Indexing is a fair, neutral way to hold down taxes. Minnesota has already had to change once the index it used--it overstated inflation. Any index of inflation will, sooner or later, be inaccurate; and inflation affects different taxpayers differently.

* Indexing forces decisions on taxes to be made openly. But in Minnesota no one ever proposed what actually happened: a replacement of more than $500 million in progressive income tax revenues with revenues from "temporary" regressive sales taxes. To make up for the revenue shortfall that followed indexing, Minnesota postponed $600 million of spending from one fiscal year to the next--hardly an example of frank and open fiscal policy.

* Indexing builds a political constituency to hold down government spending. Gov. Quie, his popularity way down, announced in January he would not seek reelection; the Democrats are heavy favorites in November's election. True, the Democrats do not attack indexing explicitly. But they are eyeing Iowa's plan, in which indexing comes into effect only when the state treasury has a surplus.

Minnesota is not the federal government, and any one state's experience is at most only suggestive of what federal indexing would mean. But the Minnesota experience does illumine severe problems inherent in the nature of indexing. Certainly indexing is no quick fix.