PETERBOROUGH, N.H. — A 168-year-old company in New Hampshire known for its handwoven, hardwood baskets is closing its factory and stopping production, partly because of an insect pest that has been destroying ash trees. The Peterboro Basket Company has been in business since 1854. The company said in a recent announcement that the baskets “are principally made of U.S.-grown Appalachian White Ash, the same wood used in ax handles and baseball bats. “For some years the Emerald Ash Borer beetle has reduced the availability of the wood used to make the baskets,” it said.