BAGHDAD—Another crisis is percolating in Iraq beneath the onslaught of Islamic State militants: a shrinking economy and a widening fiscal deficit that politicians and analysts worry will further undermine the country’s ability to fight off the insurgents.

Iraq’s economy is set to shrink by 2.75% in 2014, the International Monetary Fund said last week, its first contraction since 2003, the year the U.S.-led invasion of the country.

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