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The index of leading indicators, released Tuesday, points to improving economic conditions ahead for the United States economy. If the index is accurate, the economy will not expand too rapidly. That decreases concern that inflation will reignite and that government and private-sector borrowers will compete in a ''credit crunch.''

The Commerce Department's measuring device registered a 0.6 percent rise over November. November had dropped slightly, the only decline in 16 months of advances. Introduced in 1968 and backdated to 1948, this index, which tracks 11 different indicators, is based on a 1967 level of 100. December registered 162.9 .

That closed out 1983, a year of solid - but apparently decelerating - economic expansion. The index rose 5.9 percent in the first quarter, 4.7 percent in the second, 2.8 percent in the third, and 2 percent in the fourth.

If the leading indicators foreshadow the economy's future, two others indexes released Tuesday confirm economic strength in the recent past and in the present: ''Coincident indicators'' gained 0.6 percent in December; ''lagging indicators'' rose 0.8 percent.

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