The key government index designed to foretell changes in the performance of the economy rebounded in December, the government reported yesterday, holstering predictions by economists that the recovery would continue at a moderate pace.

The Commerce Department's index of leading economic indicators rose a robust 0.7 percent, the agency announced - up from a revised 0.1 percent rise in November. It was the sixth month in a row that the index has posted a gain.

The rebound was regarded as moderately encouraging. Preliminary estimates had shown the index declining by 0.2 percent in November - a dip that might have proved worrisome had it continued for several months. Late-breaking data, however, converted it to a small rise.

Courtenay M. Slater, the department's chief economist, said the increase was "consistent with our view" that the economy would be performing well during the first half of 1978 following a drainoff of business in ventories late last year.

However, Slater noted that except during outright turning-points in the business cycle, month-to-month changes in the leading indicators index are not really a very valuable guide to the economy's performance.

For example, the fact that the index increases more sharply does not necessarily mean that the economy will grow more rapidly. Nor does a decline of one or two months' duration by itself signal an economic slump.

The reason stems in part from the makeup of the indext. Some of the measure's components comprise elements such as stock prices which may have performed badly for short-term reasons that have little to do with the pace of economic activity.

"My own feeling is that the index is not very useful," Slater said.

Yesterday's report showed five of the 10 indicators now available for December contributed to the rise last month - vendor performance, changes in sensitive prices, contracts and orders for plant and equipment in 1972 dollars, money balance in 1972 dollars, and new orders.

Four others declined - the length of the average work week, change in total liquid assets, stock prices and building permits. The tenth, the layoff rate for workers, remained unchanged.

The new figures brought the index to 135.3 per cent of its 1967 average.