WASHINGTON — U.S. home building jumped 3.8% in October, a positive sign for the overall economy as developers anticipate steady demand.

The Commerce Department said Tuesday that housing starts reached a seasonally adjusted annual rate of 1.31 million. Starts for single-family houses were up 2%, largely because of construction in the West and South. Construction of apartment buildings rose 6.8% from the prior month.

Lower mortgage rates and a healthy job market have aided the housing market in recent months, yet housing starts are still down 0.6% year-to-date as a shortage of land and high construction costs have limited building. Affordability is a problem for would-be buyers as increases in home prices have outstripped wage growth.

The average 30-year mortgage has an interest rate of 3.75%, down from 4.94% a year ago, according to mortgage buyer Freddie Mac.

Cheaper borrowing costs has fueled greater demand from buyers, but a broader shortage of homes for sale has caused prices to generally rise faster than incomes since 2012 when the market began to recover from the Great Recession.

Building permits, a measure of future construction, rose 5% in October to 1.46 million. The bulk of the gains in permits so far this year has been for apartment complexes, while permits for single-family houses has slumped 1.5%.

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