Oct. 7 (Bloomberg) — Job openings in the climbed to a 13-year high in August as employers gained confidence about the outlook for demand in the world's biggest economy.   The number of positions waiting to be filled rose to 4.84 million in August, the most since January 2001, from a revised 4.61 million the prior month, the Labor Department reported today in Washington. Hiring and firings cooled, while fewer people quit their jobs.   The upswing in openings adds to signs of sustained progress in the labor market. The figures form part of a package of data Federal Reserve Chair Janet Yellen and her colleagues use to measure the labor market's health, which will help determine when the central bank will to begin to raise its benchmark interest rate in 2015.   "It reinforces the view that the labor market is improving," Sal Guatieri, senior economist at BMO Capital Markets in Toronto, said before the report. "It's making progress, reflecting an economy that seems to have pretty good momentum."   The median forecast in a Bloomberg survey of economists called for 4.7 million openings after a previously reported 4.67 million in July.

With assistance from Chris Middleton in Washington.