The roof may have collapsed on the Bay State’s housing boom, but sales in the Back Bay and Beacon Hill so far have exceeded last years levels as prices fell slightly.

While home sales dipped statewide by 6.4% in Massachusetts to 15,381 units this year, down from 16,438 for the same period a year ago, the two downtown neighborhoods saw home sales rise, according to data from the Massachusetts Association of Realtors and the MLS Property Information Network (MLS).

Sales of single-family homes and Boston condos during the first half of this year on Beacon Hill increased to 93 units up from 63 for the same period last year, a 34% increase, according to MLS. The Back Bay saw a more modest increase of 5% as the number of units sold this year reached 197, up from 188 units a year ago.

Despite a sluggish market statewide, Beacon Hill and Back Bay remain among the most popular Boston neighborhoods.

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