Beginning this month, the world's largest economy is doing something it hasn't done in 40 years: shipping supplies of U.S. crude oil to international markets. So will globally traded domestic crude translate into higher gas prices at home?

"Absolutely," said Tyson Slocum, energy director at the Washington-based consumer advocacy group, Public Citizen. Despite oil prices slumping to their lowest levels in 12 years, Slocum told CNBC's "On the Money" that he expects the "(oil) market will tighten later this year."

He's far from the only one who thinks that way. Last week, Goldman Sachs said in a research note that it expects oil to rebound back above $40 by midyear.

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And Slocum's remarks echo the concerns voiced by supporters of the four decade law that prohibited U.S. oil sales abroad, who have argued that exporting crude would limit domestic supplies, thereby driving up prices.

Slocum, however, said "we're not going to see the impact right away, because both the domestic and international oil market is saturated with excess oil and storage."

During the height of the 1970's oil crisis, President Gerald Ford and Congress banned US crude oil exports. That rule was in place until President Obama signed a bill less than a month ago that abolished the ban.

With the sales block lifted, Slocum says, American oil producers will no longer be "burdened by having to only sell their oil to US refiners."

Slocum says producers will be "free to move very large volumes of US-made oil out of the United States," and that oil sales to Europe and China have already begun. He says "that will accelerate and what that's going to do is raise U.S. benchmark oil prices, which in turn is going to increase the price at the pump."

Helima Croft, global head of commodities strategy at RBC Capital Markets, disagrees. The Wall Street analyst said that "more oil on the global market means potentially lower prices, so the consumer should benefit."

Croft's assessment dovetailed with organizations like the American Petroleum Institute, the oil and gas lobby, which has argued for years that lifting the ban would gradually curb energy prices.

The analyst did agree that the impact won't be felt "right away." With the world crude oil supply so high, she says "this is not going to make a difference until we have a recovery in U.S. prices and also U.S. production coming back."

She told CNBC lifting the export ban underscored the U.S.'s commitment to free trade, and called the 40 year-old ban an "antiquated relic of the OPEC oil embargo era."

Croft also is calling the new rules a "great thing for U.S. producers, since the global market "gives an outlet" for their U.S. crude oil.

The key to the increase in U.S. crude production has been the impact of fracking, or hydraulic fracturing. The controversial drilling technique extracts oil and natural gas using a high-pressure fluid mixture injected into shale rocks, and has helped lead to a resurgence in domestic energy production. Meanwhile, conservationists disdain the practice's environmental effects.

Yet the U.S. oil boom has shaken up the global energy order, and sent crude prices reeling. Last week, U.S. and Brent crude closed at multi-year lows below $30 a barrel. The bear market has sent prices down by more than 20 percent, the worse two-week decline since the 2008 financial crisis.

Public Citizen's Slocum says when oil was going "gangbusters, we had $80 and $100 a barrel" prices. At that time, oil producing states, like North Dakota and Texas, were "flying high" with budget surpluses and jobs. With oil prices plummeting, he said, "we're seeing economic disruption in those states."

Beyond economic policy, Croft thinks the export ban will help foreign policy—especially dealing with OPEC countries in the Middle East upon which the US had relied for decades.

"The broader story," says Croft, "and why I think it is important to keep US production going … is it does mean in the end we're less dependent on these countries."

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Croft, who spent four years as a senior economic analyst at the Central Intelligence Agency, cites the national security benefits to the US's new strength in the global oil export market.

"After 9/11, we were very concerned in the US government with access to energy in places like Nigeria, because we never thought we'd have US production," she said. "So we can have a different foreign policy relationship with these governments than we might have had, because we have this abundant resource in U.S."

On the Money airs on CNBC Saturday at 5:30 am ET, or check listings for air times in local markets.