WASHINGTON- U.S. homebuilding unexpectedly fell in September amid persistent shortages of inputs and labor that are crimping the housing market and overall economic activity.

Housing starts dropped 1.6% to a seasonally adjusted annual rate of 1.555 million units last month, the Commerce Department said on Tuesday. Data for August was revised down to a rate of 1.580 million units from the previously reported 1.615 million units.

Economists polled by Reuters had forecast starts would rise to a rate of 1.620 million units.

Permits for future homebuilding declined 7.7% to a rate of 1.589 million units last month.

Though lumber prices have tumbled in recent months, the lower prices have yet to filter through to builders. Building materials, like windows and electric breaker boxes, are in short supply. The supply chain has been strained by the COVID-19 pandemic's upending of labor market dynamics, which has pushed up prices across all segments of the economy.

Starts have declined from the 1.725 million unit-pace level scaled in March, which was more than a 14-1/2-year high. There is a huge backlog of houses authorized for construction but not yet started.

A survey from the National Association of Home Builders on Monday showed confidence among single-family homebuilders rising further in October, but noted that "builders continue to grapple with ongoing supply chain disruptions and labor shortages that are delaying completion times."

The housing market was boosted early in the coronavirus pandemic by an exodus from cities to suburbs and other low-density locations as Americans sought more spacious accommodations for home offices and online schooling. That tailwind is ebbing as workers return to offices and schools reopened for in-person learning, thanks to COVID-19 vaccinations.

High inflation is also lifting mortgage rates. The 30-year fixed mortgage rate rose to an average of 3.05 last week from 2.99% in the prior week, according to data from mortgage giant Freddie Mac.

Though still low by historical standards, rising borrowing costs could make homeownership less affordable for some first-time buyers. House prices notched record double-digit growth on an annual basis in July.

(Reporting by Lucia Mutikani Editing by Paul Simao) ((Lucia.Mutikani@thomsonreuters.com; 1 202 898 8315; Reuters Messaging: lucia.mutikani.thomsonreuters.com@reuters.net))