NEW YORK—Wall Street brushed off more bad economic news Tuesday to finish with a moderate advance that left broad stock indexes at their highest levels in two months.

Stocks gained after stumbling in the early going because of mixed readings on the service sector, factory orders and pending home sales. While investors expected the data would show further deterioration, they were hoping the pace of the declines would slow. The market is eager for signs that the U.S. recession will end this year.

Stocks recovered in midafternoon trading after the Federal Reserve released ...

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