By Steve Quinn

JUNEAU, Alaska (Reuters) - A majority of Alaska residents will receive $2,072 from the state's oil wealth investment fund earnings, an annual payout set against the backdrop of a $3.5 billion to $4 billion budget deficit driven by low crude prices the last year, officials said on Monday.

Nearly 645,000 residents out of some 736,700 will receive the annual dividend from the Alaska Permanent Fund's earnings, Governor Bill Walker said at a news conference.

This year's was the highest payout in 34 years, Walker said, though the windfall only edges the 2008 amount by $3.

Alaska's Permanent Fund was established by a constitutional amendment passed by voters in 1976 that requires a portion of state oil revenues be put into a savings account to be available for the distant future, when North Slope oil fields are tapped out.

The fund's value now sits at $51 billion and produced more earnings during the most recent fiscal year than oil production did for the state, Walker told the news conference.

The annual direct payout to citizens, derived from a formula averaging the Permanent Fund earnings over a five-year period, is unique to Alaska, even though other jurisdictions have resource wealth funds.

The dividend remains an important perk of Alaska residency and a major economic infusion. It is used for college and retirement savings, big-ticket purchases, but also for significant expenses, such as fuel, that far outstrip costs in other parts of the country.

But with the state looking for new ways to boost revenue and narrow the budget deficit, economists and lawmakers are floating ideas that would cut into these checks, such as capping the dividends.

For years any discussion about tapping into the dividends was considered politically dangerous, but Alaska Governor Bill Walker, as well as economists, has said it is time to re-examine options.

"It is time to have an open and honest conversation about our finances, and how resources like the Permanent Fund can be used as an asset," Walker said.

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"The vision of the Permanent Fund was to turn a nonrenewable resource into a renewable one, and it is our job to determine how to best use and protect that gift for the benefit of all Alaskans," he said.

Checks will be sent by mail and direct deposit to bank accounts beginning on Oct. 1, according to the state.

Alaska residents must have lived in the state an entire calendar year before becoming eligible to receive the money. However, anyone born in Alaska throughout all of 2014, so a child born on Dec. 31 would be eligible.





(Reporting by Steve Quinn; Editing by Eric M. Johnson and Sandra Maler)