HAPPY NEW YEAR. A new fiscal year began on Oct. 1. Fiscal 1980, with its federal budget, is now ended. That budget is worth a retrospective glance. Its deficit will be around $61 billion -- more than twice the deficit calculated when the budget was first published by President Carter in January 1979.

The chief reason for that enormous swelling of the deficit is, simply, inflation. The common wisdom holds that inflation cuts deficits, because taxes rise faster than spending. But the recession that began last winter disrupted that mechanism. It held down tax revenues much more effectively than -- to the economists' dismay -- the inflation rate. It's true that budget deficits -- under some circumstances -- increase inflation. But in fiscal 1980 the inflation increased the deficit, suggesting an ominous circularity.

The one significant change in spending policy over that year was the president's decision to increase the money for defense. Defense got about $133 billion, about $75 billion more than the original estimate. But a lot of that increase went into inflation -- above all, the higher costs of gasoline. Defense spending actually turned out to be a smaller proportion of the 1980 budget than the president had proposed.

The largest unexpected increase was in interest payments on the federal debt. Inflation also expanded all of the federal benefits, like Social Security, that by law rise automatically with the price level. Indexing pensions is a decent and generous policy. But in a time when incomes don't rise as fast as the inflation rate, the effect is to increase the share that goes to the federal budget and the federal benefits.

When Mr. Carter took office, the budget was about 22 percent of the gross national product, a high level in historical terms. He promised to get it down to 21 percent by fiscal 1981. It's hard to say what that 1981 figure may turn out to be. But in the year just ended, it was 23 percent, the highest since World War II.

Even that number is an understatement. The government is sliding into the bad old habit of off-budget spending. Counting off-budget spending of $15 billion, total federal spending in fiscal 1980 was 23.6 percent of GNP and the deficit was a ringing $76 billion.

Those numbers were not the result of deliberate policy. They were produced by a peculiar combination of circumstances -- high inflation and recession together -- which, everyone hopes, will not be repeated next year. But the 1980 budget contains lessons that need to be taken seriously.

First lesson: At high inflation rates, the budget swells automatically to preempt the money that both presidential candidates want to put into defense. Second lesson: With the present inflation, the budget can only be balanced through large tax increases. The next administration, and its budget-makers, can't say that they haven't been warned.