TWO YEARS of the Reagan presidency: today is the second anniversary of the inauguration of a man in whom the radical impulse has been stronger than in any president for a generation. The effect of the experiment has been, curiously, to bring a lot of Americans back into a better relation with their government--not always, certainly, in ways that Mr. Reagan intended or that served his purpose. But that's been good for the country.

By early 1981, there had been too many years of established verities and good intentions that were getting flabby for lack of hard challenge. Citizens seemed to sense that the whole incomprehensible stucture of the federal government had been placed, by the rules of conventional politics, beyond any very rigorous examination. Mr. Reagan has certainly changed all that.

He and his budget cutters have now been through the whole catalogue of programs a couple of times, holding up each suspected offender and asking for a show of hands. Some of these programs have been chucked out. But the process has forced the country to think about public responsibilities more carefully than it had done for a long time. The idea that it was mere waste and fraud that drove the budget totals upward has been amply tested; it was a myth, and has evaporated. The debate over the social benefits is no longer in terms of some undefined, and undeserving, "them." It is clearer now to most citizens that those benefits go to just about everybody, now or later, mostly in the form of Social Security and Medicare, and are important to their own lives.

But the Reagan White House is the worst possible judge of its own achievements. What it trumpets as its triumphs are generally its great failures. There is, for example, the inflation rate.

True, it is substantially lower than it was two years ago. But nobody ever doubted that the government could force the inflation rate down by running unemployment up over 10 percent. Mr. Reagan is the exterminator who told you that he could get the rats out of your barn without using poison. Through an unfortunate miscalculation, he has burned down the barn and now stands in the ashes pointing out, with a winning smile, that the rats have departed and it is time to look to the future rather than dwelling on past misfortunes. The present unemployment rate has created a burden of misery in this country that is a matter of deep reproach to the administration. It is reasonable to argue that a recession was unavoidable, but it need not have been nearly so severe. It was aggravated not only by consistently bad policy but a flat refusal to come to terms with reality.

One of the real mysteries in current American politics is the slight impact of this tremendous unemployment rate on the last elections. It is as though a lot of voters, whatever their current anxieties, still feel that the country was living a little too well on inflation and borrowed money in the late 1970s. Perhaps, in retrospect, it will turn out that for many people the Reagan administration was the necessary and deserved corrective.

But it is also evident that the administration has reached the limits of most of the ideas that it brought to the White House two years ago. The government isn't going to get any smaller, and taxes are not going to go any lower. If the last two years have been an inevitable corrective to an era of political complaisance and easy money, the process has gone on long enough. It is still not clear that Mr. Reagan knows how to find his directions in a period in which he will not merely be reacting to the mistakes of a vulnerable predecessor.