Arts and recreation services was the third fastest-growing of the 20 Tasmanian sectors measured in the Australian Bureau of Statistics' gross state product figures for 2018-19.

It increased its gross value added by 5.9 per cent, well ahead of the overall statewide annual growth of 3.6 per cent and behind only construction and healthcare and social assistance.

"I don't need any convincing that the arts has got a key role to play in the future economic circumstances of this state," Mr Gutwein said.

Asked if he saw the government taking a bolder approach to arts and recreation services sector funding, Mr Gutwein said: "I have long been convinced of the economic benefit and also the social benefit that can flow from the arts community."

"We've got the obvious key driver in MONA, but run a festival, run an event, run an arts show and people will turn up, people will spend money and people will engage with their communities."

The arts and recreation sector's annual gross value added increased by 15.1 per cent to $343 million in the five years to 2018-19, compared to 12 per cent growth for all sectors combined

The sector also appeared to have been growing jobs.

The ABS estimated total compensation of employees increased from $79 million in 2013-14 to $109 million in 2018-19.

The bureau defines arts and recreation services as "units mainly engaged in the preservation and exhibition of objects and sites of historical, cultural or educational interest; the production of original artistic works and/or participation in live performances, events, or exhibits intended for public viewing and the operation of facilities or the provision of services that enable patrons to participate in sporting or recreational activities, or to pursue amusement interests".