Several government statistics released yesterday seem to confirm what many administration and private anyalysts have been saying for months: The economy will grow more slowly over the next few months and inflation will continue at an uncomfortable level.

The index of leading exonomic indicators, which is supposed to foreshadow economic conditions, declined slightly in July for the third consecutive month.

Administration economists said the 0.2 per cent decline in the Commerce Department index does not signal a recession, but confirms their prediction that the ebullient 7 per cent growth rate of the first half of the year will not continue.

If the administration is right - and most private forecasters agree with it, although a few predict recession within thenext six months to a year - the unemployment rate will continue to improve but not as fast as during the early months of 1977.

While House press secretary Jody Powell said that despite the third consecutive monthly decline in leading indicators, the administration expects "healthy growth in the months ahead."

He said that 17 times since World War II the index declined three months in a row, and on 11 of those occassions no recession followed. The latest three-month decline is smaller than any of the previous 17.

In a separate report, the Department of Labor said that a basic measure of inflation pressure - unitlabor costs - rose by a revised 7.7 per cent in the second quarter compared with 5.3 per cent in the first quarter.

The department initially reported that unit labor costs in the private economy rose a seasonally adjusted 8.2 per cent in the second quarter.

Unit labor costs measure by how much worker compensation per unit of output is rising. Unit labor costs rise, for example, when increases in wages or fringe benefits are bigger than increases in worker output.

Because wages on the average represent 75 per cent of the cost of goods and services produced in the United States, rising unit labor costs usually signal bigger inflation pressures, and declining unit labor costs (which come about when the same cost of wages and salaries is spread over more production) mean that inflation pressures are easing.

Economists warn, however, that quarterly chages in unit labor costs and productivity figures are erratic and are a far-from-perfect signal of underlying inflation trends.

While labor costs per unit of output were rising, the increase in hourly compensation rose 6.8 per cent, about half the 12.8 per cent increase of the first quarter and th smallest quarterly rise since the third quarter of 1975, the Labor Department said.

But because output growth slowed in the second quarter, productivity (output per hour worked) declined by 1.4 per cent.

The Commerce Department also reported that new orders for manufactured goods fell by $3.3 billion, or 3 per cent, in July, further indication that business expects slower growth.

Much of the decline in orders for manufactured products was due to a slowdown in orders for aircraft, according to Courtenay M. Slater, chief economist for the Department of Commerce.

She said that nearly all the economic statistics reported in recent months confirm the administration's judgment that economic growth will be slower for the next year and a half. "We have seen them all pick up in the spring, then flatten out for a while," she said.

But the statistics which signal the level of economic activity should pick up again soon, she said.

Although it was the thrid month in a row the index of leading economic indicators fell 0.2 per cent, Treasury Department consultant and Lafayette College economist Herman I. Liebling said these declines do "not presage a recession, merely a slowing down."

Of the 10 indicators available to compute the preliminary index for July, 6 declined and 4 rose. The indicators which moed adversely were the length of the average work week, the layoff rate in manufacturing, changes in sensitive prices, new orders for plant and equipment, new orders for consumer products and building permits.

The indicators which moved favorably in July were the change in cashlike assets, the number of companies reporting slower deliveries, the price of stocks and real money balances.