Will the CDS really reflect well what Hart and Zingales say it will?

Hart and Zingales write:

In our mechanism, when the CDS [Credit Default Swap] price rises above a critical value (indicating that the institution has reached an unacceptable threshold of weakness), the regulator would force the LFI [Large Financial Institution] to issue equity until the CDS price and risk of failure back down. If the LFI fails to do this within a predetermined period of time, the regulator will take over.

But what about this criticism:

The CDS may be a poor measure of the large financial institution's probability of failure absent government assistance, because the market will price the CDS to include the substantial likelihood that the government will pump in taxpayer money if the large financial institution (LFI) would otherwise go under.

Even if the LFI were being run in an extremely risky way (because management was taking advantage of the "heads I win, tails you lose" taxpayer backup likelihood), the CDS could still be very low priced, if the market knows the government is likely to bail the LFI out.

Even if the LFI would almost surely go bankrupt without government assistance, the CDS might not be particularly low priced if investors think it hardly matters; the tax payers will almost surely give the LFI billions to keep it from bankruptcy.

If instead you had a highly skilled team of regulators, with complete authority to see any and all of the LFI's records, they might be able to – using high-level, flexible, ultra-high-dimensional intelligence, not just simple mathematical formulas – estimate the probability of default much better than from the price of the CDS, if the CDS's signal is extremely blunted and noisy from investor perceptions of the probability of a government bailout to the tune of billions, tens of billions, or even hundreds of billions. I should make very clear, though, that I do support having some strong smart "objective" limits on shadow banks, of any size, LFI or SFI, things like leverage limits. Clearly we've seen that Republican regulators, or "regulators" can't be trusted with complete discretion.

I've looked through Hart and Zingales' working paper on this. Although I haven't read it very patiently and carefully, word for word, as I like to for academic papers, what I found that responds to my criticism is this:

Our mechanism is similar in spirit to the “market-based” regulation underlying Basel 2. The main difference, however, is that we rely on market prices and not on credit rating agencies...Would our mechanism have worked better?...In answering this question, it is important to appreciate that the CDS prices are endogenous with respect to the default rule we choose. On the one hand, this endogeneity implies that there is no guarantee that CDS prices will perform in the same way as in the past under our proposed rule. On the other hand, the continuous government interventions, which led to the rescue of Bear Stearns, AIG, Citigroup, and Bank of America, have certainly affected the reliability of CDS prices as an indicator of the probability of financial insolvency. To minimize this latter effect we look at CDS prices before 10/14/2008 (i.e., the Paulson rescue of all the major US Banks). (pages 17-18)

But this appears suspect, at least in claims (or implied claims) about how well their idea would work in the short run (as well as perhaps the medium run, and perhaps for decades). Because their idea would be put into effect after the information in the CDS became less reliable due to the government bailouts of Bear Stearns, AIG, etc. That's the world we're living in now, one where investors saw in 2008-9 a demonstration of the great lengths the government would go to to keep LFI's from failing, especially when they are so interlinked. This may strongly increase investors' confidence that the government would do it again in the future.

The authors claim that their CDS idea would work well only by looking at CDS prices in the world before the recent spate of hundreds of billions of dollars of bailouts.

So, I have my doubts about this. I'm not sure how accurate CDS's will be, and how overfitted the rule for using them that Hart and Zingales devised might be to past data, especially pre-recent-crisis past data. If their rule is used at all, it might be best to use it as a guide for flexible, intelligent, skilled regulators, who would have the final say, on a case by case basis, after going deep into the books of the LFI. In addition, it may easily be best to greatly limit the choices of LFIs of the kind of difficult to price, complicated assets and liabilities that H&Z say are a reason for using the CDS as a measure of default probability.

Update, 4/15/10: I added the line in the sixth paragraph, 'I should make clear, though, that I do support having some strong smart "objective" limits on shadow banks, of any size, LFI or SFI, things like leverage limits. Clearly we've seen that Republican regulators, or "regulators" can't be trusted with complete discretion.'