The U.S. super-rich are still avoiding taxes a lot more than investigators had hoped, despite a crackdown on tax havens, according to a study.

More than one-fifth of the top one percent of U.S. wealthy are reporting too little income to the Internal Revenue Service, according to a study released by the National Bureau of Economic Research on Monday and co-authored by the IRS’ researchers as well as academic economists including Gabriel Zucman.

The study comes roughly 15 years after U.S. prosecutors, lawmakers, and tax investigators began cracking down on havens and in particular Swiss offshore accounts. The cull has extracted billions in fines and lost tax income from private banks in Switzerland, which has since softened its banking secrecy laws and begun data-swapping with allies.

Sophisticated Schemes

The study found that U.S. investigators are still poor at rooting out tax income hidden in so-called S-corporations, no subject to certain types of tax, or other partnerships. It looked at taxpayers who had come forward between 2009 and 2012 with foreign bank accounts.

Of the 21 percent of wealthy who under-report, 6 percent represent sophisticated schemes of evasion that audits normally don’t detect, according to the study, authored by John Guyton, Patrick Langetieg, Daniel Reck, Max Risch, and Zucman. The results were first reported by «The Wall Street Journal» (behind paywall) on Monday.

«We stress that our estimates are likely to be conservative with regard to the overall amount of evasion at the top,» the authors wrote. They noted that it seems likely the wealthy are evading tax with similarly sophisticated schemes.

Largest Recorded U.S. Fraud

These include abusing syndicated conservation easements, micro-captive insurance schemes, private inurement in tax-exempt organizations, and offshore trusts. «Many of these strategies involve pass-through businesses or other entities controlled by the taxpayer,» the study said. The IRS doesn't list tax havens, but Switzerland has figured prominently in its investigations.

The report comes several months after the largest case of U.S. tax evasion emerges around Robert Brockman, a Texas-based software billionaire who is accused of hiding as as much as $2 billion from the IRS thanks to a complicated tangle of offshore entities, some tied to Switzerland. 

Swiss Banks Settle Probes

Just ten days ago, Zurich's oldest private bank agreed to pay $22 million to U.S. officials in order to settle a more than decade-old probe into helping Americans hide their wealth in offshore Swiss accounts. This now leaves just Pictet as the last Swiss wealth manager still on the hook for criminal charges with U.S. prosecutors.

UBS settled with U.S. prosecutors in 2009 for $780 million. This marked the beginning of a more than ten-year pursuit of other Swiss private banks, which culminated in a record $2.5 billion total penalty against Credit Suisse.