The multifamily housing sector continues to improve, fed by people renting homes and the improving for-sale market, the National Association of Home Builders reported Thursday. The trade group says that its Multifamily Production Index came in at 54 out of 100, climbing three points from the prior quarter and marking its eighth consecutive quarterly improvement. The reading is the highest since the second quarter of 2005, back before the housing market took its huge dive. The quarterly index examines confidence surrounding construction of rental and for-sale units. As with the group’s single-family index, any reading over 50 indicates that more respondents think conditions are improving, with increased construction and sales potential. More Americans burned by the housing debacle are looking to rent, particularly in big cities where glitzy towers boasting amenities including resort-style pools and outdoor kitchens are springing up. And those who can afford to buy are racing to tap mortgage rates that continue hovering near record lows.