Only about a quarter of U.S. stocks are owned by people who pay taxes on their gains, down from more than 80 percent in the 1960s, according to new analysis.

That shift, outlined in a paper done for the nonpartisan group Tax Analysts, means the government is collecting far less revenue from stock market gains than it used to. As a result, any potential changes in the capital gains tax may not have as great an impact on government revenue as many might expect.

Hillary Clinton has called for an increase in the top tax rate for capital gains. Meanwhile, some Republicans have called for lowering the capital gains rate, contending it represents "double taxation" of corporate earnings.

"Understanding the erosion of the taxable shareholder base is critical for determining how best to tax corporate earnings — and capital more generally," according to the report.