On Tuesday, the New York Fed, through a series of research papers, said the nation’s largest banks borrow more cheaply, and take on more risks, than smaller banks and non-financial firms of all sizes, based on the belief that if anything goes wrong, the government will bail them out.

A number of other studies have reached the same conclusion, including one from the IMF and Bloomberg. Some have called for additional regulations to rein in the big bank advantage. A recent tax proposal from Republican Congressman Dave Camp calls for a too-big-to-fail tax for banks considered to be in that category. The fact that the Fed seems to be officially acknowledging too-big-to-fail will add fuel to those efforts.

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Other papers have put the too-big-to-fail benefit as high as $102 billion. Like several other similar studies, the Fed’s research — which was published by Joao Santos — examined how much less big banks have to pay to borrow than smaller banks. But Santos didn’t stop there. He also compared that to the borrowing advantage all large firms have over smaller rivals. Bigness aside, there still appears to be an advantage for being perceived as too-big-to-fail, but it’s a smaller benefit than other studies suggest.

Santos also found that the advantage isn’t shared evenly. A large chunk of the subsidies go to the firm that is viewed as the most “too-big-to-fail-y.” The Fed didn’t name names, but it did say the bank that would benefit the most would be the one with the highest rating. These days, that’s JPMorgan Chase (JPM), which has a bond rating of A. All the other big banks have a rating of either BBB or BB.

So here’s how it works out: JPMorgan saves nearly $5 billion a year. The other banks’ — Bank of America (BAC), Citigroup (C), Goldman Sachs (GS), Morgan Stanley (MS), and Wells Fargo (WFC) — TBTF discount adds up to $3.5 billion.

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At $8.5 billion a year for the six largest banks, the TBTF discount, while real, is likely much less than people think. That conclusion is backed up by another paper also released by the Fed on Tuesday. That paper found that the U.S.’s so-called shadow banking system — which includes firms like small mortgage brokers, hedge funds, and payday lenders that provide loans but are not technically banks — has actually grown faster over the past few decades than the big banks or the financial system in general. So much for that big bank advantage.

What’s more, the Fed also found that large banks — just because they are large, not because of the government’s backing — are more efficient and can offer loans and lending services at lower costs than smaller banks. So we should embrace big banks, and the bigger the better. Of course, critics say big banks don’t actually pass those savings on to consumers and instead keep them for shareholders and for their inflated bonuses.

The debate will continue.