THE CONSUMER price index for July, when it appeared the other day, received much applause for good behavior. The inflation rate in this country is now about 5 percent a year--not terribly good, but less than half the rate in early 1981 when President Reagan took office. Since it is the one aspect of the Reagan economic program that meets its authors' hopes and promises, the administration gives it a good deal of attention. The question now, for the administration and everybody else, is whether inflation can be kept down as the economic recovery gathers momentum.

The reason for the rapid drop in inflation over the past 21/2 years is essentially the high interest rates that the Federal Reserve Board imposed for precisely that purpose. They tipped the country into a recession, longer and more arduous than anyone expected. But in recent months there have been three specific reasons for the low inflation rate, as the Congressional Budget Office observed a few days ago in its excellent review of the economy.

First, wages have been held down by high unemployment and industrial distress. In labor contracts negotiated during the first half of this year, the average initial wage change was actually negative-- that is, on average wages dropped. It was the first time in the 15 years that the goverment has been collecting these figures that they were negative. Across the whole economy, labor compensation including fringe benefits rose about 6.5 percent over the past year. But nearly half of that was offset by improved labor productivity. For the first time in six years, productivity is now rising significantly.

The second great reason for low inflation has been the drop in commodity prices--especially the price of the most important of all commodities, oil. The third reason is the very high exchange rate of the U.S. dollar. It adds to unemployment in this country, but it makes imports cheaper.

None of those three forces--wage restraint, slack commodity markets, the strong dollar--is likely to change much in the short term. But movement may begin to be visible sometime early next year. Since business profits are already rising in response to sales, labor unions are not likely to repeat this year's wage freezes and give-backs. World commodity prices have already started to move up. As for the dollar's exchange rate, it's largely set by American interest rates.

And that brings you back to the central dilemma of American policy. If interest rates aren't raised, the threat of inflation will increase again. If they are raised, they will jeopardize economic growth. Next year, as the recovery generates more upward pressure on prices, that dilemma will become increasingly painful.