In recent years Brian Gottlob has noticed a trend around his home in Dover: more out-of-state banks, particularly from Maine, opening branches in NH.

Gottlob, who is the director of the state’s Economic and Labor Market Information Bureau, wasn’t surprised. Compared to the rest of New England and the country, NH has a strong economy, he says, fueled by a well-educated population and thriving business community.

That makes …