US housing starts bounced back in August after tumbling a month earlier, illustrating uneven residential construction as builders weigh inventory levels against brighter demand prospects tied to falling borrowing costs. Beginning home construction increased 9.6% last month to a 1.36 million annualized rate, the fastest since April, according to government figures released Wednesday. The median estimate of economists surveyed by Bloomberg called for a 1.32 million rate. The report showed overall building permits, a gauge of future construction, rose 5% to a 1.48 million annualized rate, while single-family authorizations increased to a four-month high. New construction of single-family homes increased nearly 16% to an annualized 992,000 pace, the first monthly advance since February. Starts of multifamily projects declined for the first time since May. Builders are awaiting a sustained pickup in demand to help work down an inventory of unsold homes that’s hovering near the highest level since 2008.