The top 1% of taxpayers would likely avoid about $5 trillion in taxes over the next decade unless the IRS improves its enforcement, according to a new analysis.

A research paper by Lawrence Summers, a former Treasury Secretary, and finance professor Natasha Sarin found that lax enforcement by the Internal Revenue Service has led to hundreds of billions of dollars a year in uncollected taxes from the wealthy, which could reach trillions over the next decade.

Summers — a vocal opponent of the wealth taxes being proposed by Democratic presidential candidates Sens. Elizabeth Warren and Bernie Sanders — contends that one way to start making the tax system more fair and progressive without raising rates would be to plug the holes in collection.

The "tax gap" — the difference between the amount due to the IRS each year and the amount collected — grew to just under $400 billion in 2013, according to the IRS. Summers and Sarin estimate based on current income and IRS trends, the tax would total $7.5 trillion over a 10-year period from 2020 through 2029.

"The sheer magnitude of the tax gap suggests that there is substantial revenue-raising potential from shrinking it through well-targeted enforcement measures," they write in the paper.

The main reason for the large and growing gap is declining enforcement by the IRS, especially of the wealthy. In 2011, 12% of millionaires were audited by the IRS. Now it's 3%.

Budget cuts to the IRS have reduced the number of auditors. With the IRS enforcement budget slashed by 25% since 2011, the IRS has fewer auditors than at any point since World War II, according to Summers and Sarin.

The top 1% account for about 70% of underreporting, they found, and the wealthier the taxpayer the more likely they are to underreport. The paper found that those making between $200,000 and $400,000 underreport about 4.5% of their real taxable income, while those making more than $10 million underreport 14% of their income.

Summers and Sarin concede that the tax gap can never shrink to zero. But they argue that a $100 billion investment in IRS enforcement, better IRS technology, more targeted audits of the wealthy and other measures could bring $1.1 trillion in revenue over 10 years. That would be far more revenue than Summers estimates from a wealth tax.

"We hope to emphasize that the revenue significance of decisions about the scale of the IRS is comparable to the revenue significance of much of the debate about changes in tax provisions," he and Sarin wrote.