Our calculation, in a Feb. 21 editorial, showing that the top 10 U.S. banks receive a taxpayer subsidy worth $83 billion a year has generated some, um, discussion. It's a big number, and the subsidy is a big issue for the banks.

How did we get there? To recap, the largest banks can borrow money at a lower rate because creditors assume the government, on behalf of taxpayers, will rescue them in an emergency. In a 2012 study, two economists -- Kenichi Ueda of the International Monetary Fund and Beatrice Weder di Mauro of the University of Mainz -- estimated the value of that too-big-to-fail subsidy at about 0.8 percentage point. We multiplied that number by the top 10 U.S. banks' total liabilities to come up with $83 billion a year.

Some said that we shouldn't have used total liabilities in the calculation. A lot of those liabilities are customer deposits, the argument went. Since these are explicitly guaranteed by the Federal Deposit Insurance Corp., why would the subsidy apply to them?

Here's how Matt Levine, of the Dealbreaker blog, put it:

The biggest problem ... is Bloomberg’s claim that “the discount applies to all their liabilities, including bonds and customer deposits.” I can’t find any support for that in Ueda and di Mauro’s paper, which in fact says the exact opposite: that the 80bps uplift applies in the case of “issuing a five-year bond.”

And Bloomberg’s unsupported interpretation is counterintuitive. Bank deposits in the U.S. are (largely) explicitly insured by the federal government; it makes no sense that an implicit TBTF premium on top of the explicit FDIC insurance would make your deposit any safer, or make you charge a lower rate for that deposit. Also, the notion that TBTF banks are paying eighty basis points less for FDIC insured demand deposits than other banks is sort of facially absurd: if you’re getting 0.8% interest on your checking account at a little bank, let me know and I’ll move my money there. 

Naturally, we thought about this when we did the calculation. Let's deal with the "facial" aspect first. The purpose of our analysis, and the study, is to estimate the long-term value of the too-big-to-fail discount. So Levine's observation that current deposit rates are too low to allow for a 0.8 percentage point subsidy (aka 80 basis points, or bps) doesn't apply. Looking at the latest retail deposit rates doesn't do the trick, either. Interest rates fluctuate.

On the broader point, it's true that including deposits might skew the results. Problem is, so would excluding them. Just because deposits are guaranteed by the FDIC doesn't mean they're subsidy-free. Also, the guarantee doesn't cover all deposits. The threshold stood at $100,000 per account before the crisis and $250,000 after.

As it happens, two FDIC economists recently estimated the funding advantage that too-big-to-fail banks enjoy on deposits. They compared interest rates offered by small and large banks on money-market deposit accounts with balances exceeding the FDIC guarantee, from 2005 through 2010. For banks with assets greater than $100 billion, they found the deposit funding advantage to be worth 0.45 percentage point. For banks with assets greater than $200 billion -- a group that would include all the institutions involved in our calculation -- the advantage came to 1.2 percentage points.

In other words, if we want to know the full value of subsidies received by these banks, including deposits is probably going to get us closer to the right answer. And that's not even accounting for the fact that the FDIC guarantees are taxpayer-backed. Creditors would put a much smaller value -- and demand higher interest rates -- on FDIC protection if it relied solely on bank contributions to the insurance fund, with no government backing.

Oh, and we did contact one of the study's authors to clarify its implications, which were consistent with our approach.

Levine offered another criticism regarding our method of quantifying funding advantages -- our "blind use of the midpoint of the effect on funding costs." 

Here is how Ueda and di Mauro describe the funding advantage of a three-notch ratings uplift: “5-8bp for an A rated bank, 23 bp for a BBB rated bank, 61 bp for a BB rated bank, and 128 bp for a B rated bank.” Then it uses the midpoint and gets 66.5bps, which becomes 80bps for the 4-ish notches of uplift that banks get in 2009. Fine whatever.

Bloomberg applies this 80bps funding uplift to JPMorgan (Fitch holdco rating of A+), BofA (A), Citi (A), Wells Fargo (AA-), and Goldman Sachs (A). See the problem? As Ueda and di Mauro note, “government support is more ‘valuable’ at lower rating levels.” My best guess is that the paper supports about a 31bps funding uplift for those banks (equivalent to going from BBB- to A), not 80bps. 

OK, we really didn’t want to get this far down in the weeds. Our experience with such calculations has taught us that the simple approach typically gives you pretty much the same answer as the complicated approach. But here goes.

Until recently, Fitch provided an individual rating for each bank that reflected its creditworthiness without external support (meaning without government support in the case of the big U.S. banks). For the largest five U.S. banks in 2009 -- the latter period covered by the Ueda-di Mauro study -- the average individual rating, weighted by assets, was the rough equivalent of a BBB-. The weighted average long-term default rating, which includes the effect of government support, was close to AA-.

So the top banks got a too-big-to-fail boost of about 6 notches -- much larger than the average for all banks. This makes sense: Bigger, scarier institutions can be more certain of government support in an emergency, so their ratings boost should be larger. 

How much is a six-notch lift worth? Using the same scale that Ueda and di Mauro employed in their study, which is based on bond yields constructed from default data for the years 1920 to 1999, the rating gain would be worth roughly 0.50 percentage point. 

Because we're focusing on the U.S. and because the experience of the 1920s isn’t necessarily a good indicator of what will happen in the coming years, we might want to use a more relevant measure. Consider the difference between two Bank of America Merrill Lynch indexes that track the yields on actual AA and BBB bank debt in the U.S. Over the 10 years through early 2008, the average gap was 1.13 percentage points. From this perspective, our blind use of 0.8 looks conservative.

The point isn't that our critics are wrong. There's no ideal way to do the analysis. Any approach will be subject to debate. The best we can do is find the one that seems most reasonable and be transparent about it. 

Others may come up with different numbers, but the conclusion is the same: Banks get a very big subsidy from taxpayers. This subsidy distorts markets and encourages banks to become a threat to the economy.