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The oil price plunge has been touted as a global growth elixir, but so far the impact on the economy has been subtle and it's unclear when that will change.
"Local fuel prices have almost fully adjusted to lower crude oil prices," Goldman Sachs said in a note last week after tracking data from 24 countries. But it expects the stimulus impact on the economy won't be straightforward, depending on whether low prices are perceived as likely to persist and government policy responses.
"Income gains of households might not necessarily translate into significant spending rises," it said, adding that corporate gains would likely be reflected more slowly.
Read More Why oil decline could get ugly again
For companies, "the price pass-through mechanism is quite complex, with oil windfalls spread out to dividends, wages, and retained earnings, not necessarily spilled over directly to consumers via lower retail prices," Goldman said. "The use of oil is also quite diverse, entailing transportation, feedstock, and energy and a significant part of final goods are exported, with any spillover of windfalls going overseas."
What spending boost?
These factors appear to be playing out in the U.S. economy.
Households there don't appear to be spending the oil largesse just yet, Paul Dales, an economist at Capital Economics, said in a note Monday.
Real disposable income in the U.S. rose by 0.5 percent on month in both November and December, but "these extra funds, however, have not made it into the cash registers in the shopping malls or the bars and restaurants on Main Street," Dale said, adding households are saving, not spending their windfall.
Indeed, U.S. households in January bought 6 percent more gasoline than a year-earlier, but they spent $120 billion less doing it. The windfall appears to have gone to savings as the savings rate in January rose to a two-year high of 5.5 percent, Dale noted. Brent oil prices for April delivery are trading around $56.88 a barrel, off the lows under $49 touched in January, but they remain sharply down from their level over $115 a barrel in mid-June of last year.
"Households just want to make sure that lower gasoline prices are here to stay," Dale said. "Assuming that gasoline prices stay close to current levels, as we expect, then it is only a matter of time before real consumption rises more rapidly."
Elsewhere, spending is on the rise
In other regions globally, however, Capital Economics noted that households are starting to loosen the purse strings.
"Household spending has picked up sharply in response to the collapse in oil prices," it said in a separate note last week. "In January, the growth rate of underlying retail sales in advanced economies reached its highest level since 2006," Capital Economics said. "Even consumers in the euro zone are participating in the upturn, though Japanese households are not. Business surveys suggest that broader economic activity has also rebounded."
With the cost of motor fuel in major developed economies down by an average of 30 percent compared with last summer, consumers in the four largest advanced economies should see around $250 billion annually get freed up for other spending, Capital Economics said.
Uneven growth recovery
But while Capital Economics sees signs the oil savings will spur economic growth ahead, the economic recovery is "highly uneven" globally.
"The threat of deflation continues to hang over the euro-zone while Japan is yet to get back to its pre-tax-hike levels of consumption or gross domestic product (GDP)," Capital Economics said, citing data showing economic growth slipped to 2.4 percent in the last quarter of 2014.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter