Before reading this, you may want to check out Part 1 and Part 2 of this multi-part post.
Okay, I've described some settings where the taxes versus regulation choice may arise for addressing the problems with financial institutions that triggered the 2008 financial collapse. Mick Keen's paper offers a very interesting, if somewhat tersely described, initial analysis of how to think about the issue. (A more technical companion paper with a formal model makes the underlying analysis clearer, but may not be available on-line.) It addresses what I call the "cash in the strongbox" issue, but potentially could be deployed on the other regulatory issues as well.
If you check out Figure 1 on p. 18 of the paper, you will see something that looks a bit like supply and demand curves. But the horizontal axis is the amount of regulatory capital that a bank maintains (in my rendition, the percentage of its cash that remains in the strongbox). The vertical axis is the marginal cost or benefit - as the case may be - that would be derived from the next dollar of increased cash in the strong box. The Figure has two lines. The downward sloping one is marginal external benefit (MEB) - the marginal benefit to everyone else, as cash in the strongbox increases, of having yet another dollar in there. It slopes downward because each dollar helps a bit less than the one before, as the amount of cash hand (and thus the demand from one's depositors that can readily be satisfied) increases. The upward sloping one is private marginal cost (PMC) - the marginal cost to the banker for each additional dollar in the strongbox.
A bit more on the determinants of PMC: though not stated in the paper, I think of it as equaling r - b, where r is the expected return the banker could have earned by investing that dollar instead of keeping it in the strongbox, and b is the benefit to the banker of making a disastrous bank run less likely by having something in there. Since bankers, in the model (and in reality) don't want bank runs (even if they don't dislike them enough), r - b is negative where cash in the strongbox stands at zero. Thus, even absent regulation, they'd keep something there (although only the amount shown by the point where PMC crosses the horizontal axis).
PMC is downward sloping for two possible reasons. First, as noted in the paper, each dollar does less at the margin to reduce the prospects of a bank run than the dollar before it. Thus, PMC is downward-sloping for exactly the same reason that MEB is upward sloping (and opposite in direction because we are drawing it as a negative cost, rather than as a positive benefit). Second, perhaps the banker has a range of investment opportunities that he ranks from best to worst. Leaving aside the risk issue for the moment, he ranks them from the opportunity with the highest r to that with the lowest r. So the first dollar in the strongbox only deprives him of his least-favorite investment opportunity, among those for which he otherwise potentially had enough cash. But as additional dollars are taken out of his sweaty hands and placed in the strongbox, increasingly appealing investment opportunities, with ever-higher r's, start evaporating. So PMC is upward because, as the amount of cash in the strongbox increases, r gets higher and b gets lower for each additional dollar. So the marginal cost to the banker of keeping more cash in the strongbox turns positive and then keeps rising.
The socially optimal amount of cash required to stay in the strongbox is shown by the point where PMC and MEB cross. Require less, and the banker is investing dollars that yield less expected benefit to him than the expected cost that is being imposed on everyone else. Require more, and he is losing the use of cash that would have benefited him more than the cost being imposed on others. The optimal risk of a bank run, of course, is not zero, given that this would require effectively shutting down the financial sector (by banning all bank loans) and with it most of the economy.
With perfect information, you can get to this point (as Figure 1 shows) either by simply mandating the right amount of cash in the strongbox, or by relatively subsidizing such cash, such as by taxing everything that comes out of the strongbox. If the strongbox subsidy (i.e., the avoided tax) is set just right, you get the right amount of regulatory capital.
So this is a lot like, say, the carbon tax versus permits question, where you can get the same result, which with perfect information is right in either case, either by setting the carbon tax exactly right or by issuing exactly the right amount of permits. Obviously, the point of greater interest is what to do once you realize that you don't have perfect information - a point that may hold even more strongly in the bank regulatory than the carbon tax setting. (This is not to minimize the extreme difficulties presented both by alternative climate models and by the difficulty of evaluating the human welfare cost of a given set of climate changes - but at least the carbon tax setting is conceptually a bit clearer.)
One important difference that I put in my notes for the session is that PMC and MEB will tend to shift together with certain changes in information. For example, if a bank run is starting to become more likely, PMC shifts downward (as shown in Figure 1), because the bankers now want to keep a bit more capital on hand. (Again, PMC = r - b, and here we've increased b.) But this should also cause MEB to shift upward, since if a bank run is more likely the expected benefit to the public of each expected dollar in the strongbox goes up. Nothing similar would be likely to hold in a pollution version of the same chart, which would be comparing the private cost to the business of carbon abatement versus the external benefit to the public of reduced global warming. The polluter is effectively entirely indifferent to contributing global warming (since his marginal effect on it will be so small), and thus would do zero abatement absent regulation or taxes.
On the other hand, PMC might also shift downward because r declines. That is, the set of available investment opportunities grows less appealing. This may not imply any change in MEB.
OK, at last on to the Weitszman analysis that the paper deploys. Weitzman shows, to put it as unintuitively as possible, that the right answer depends on the relative slope of the two lines, here MEB and PMC, in the region where we are uncertain about getting it right. But let's make that more intuitive by giving an example from an early footnote in the Weitzman paper describing a case where we may prefer quantity to price regulation. "Suppose that fulfillment of an important emergency rescue operation demands a certain number of airlplane flights. It would be inefficient to just order airline companies or branches of the military to supply a certain number of the needed aircraft, because marginal (opportunity) costs would almost certainly vary all over the place. Nevertheless, such an approach would undoubtedly be preferable to the efficient procedure of naming a price for plane services. Under profit maximization, overall output would be uncertain, with too few planes spelling disaster and too many being superfluous."
Weitzman's point is that falling just short of having enough planes would be enormously costly - it would doom the rescue operation - whereas having too many planes is simply garden-variety wasteful. Another way of putting this would be that MEB is extremely steep as we move towards having just enough planes. Plus, presumably we know enough about this point that quantity regulation would not be done entirely in the dark. So in a case like this, you may want to require at least a sufficient quantity to get past the point where you are confident that MEB is still very steep.
(By the way, we can do better still in the Weitzman example by using the equivalent of cap and trade - that is, by assigning the obligation to deploy rescue planes just as above, but permitting the obligors to pay others to perform the same services instead. In a well-functioning market, the resulting transactions would ensure that those for whom the cost of sending rescue flights was cheapest would end up being the ones who were deployed.)
Back to regulatory capital or required cash in the strongbox. This analysis arguably rationalizes using command regulation to require some minimum capital, up to the point where it is no longer clear that one is quite significantly reducing the risk of a bank run. One doesn't want to take the risk of ending up with less regulatory capital than one believes is the minimum necessary to reduce bank run risk to acceptable levels. But beyond that point, one is in the realm where taxes and regulation are both plausible players.
Keen's paper also notes the possibility that we might consider trying to create a situation where high-quality firms can buy out of some of their capital requirements, by paying an otherwise avoidable tax. This would be good sorting if the firms that elected to pay the tax were those for whom b is especially low because they are well-managed, or for whom r is especially high and hence the opportunity cost of keeping cash in the strongbox is greater. One can convert this into a tradable permits-style scenario by positing that one bank is permitted to keep less capital on hand if it pays a second bank to agree to keep more on hand (although it is unclear how much this helps, if MEB depends on per-firm rather than sector-wide capital inadequacy).
While clearly worth thinking about, the problem is that we might not end up with the right sorting. For example, suppose that the firms that opt out of having more regulatory capital are those with a fake high r - that is, one that reflects their ability to make risky "heads I win, tails you lose" bets that don't actually have a higher social return.
Still, requiring regulatory capital PLUS a tax on the stuff that leaves the strongbox is an interesting regulatory approach to consider, if it can reasonably be operationalized. Likewise, for the arguably bigger problem of financial firms making unduly risk bets, one could combine an FAT approach with Glass-Steagall style regulatory bans (although, for the latter, keep in mind that in today's world we need to worry about a wide range of "non-bank banks" that perform important financial intermediary and transaction services). And likewise as well, perhaps, for "too big to fail" issues.
All this falls depressingly short of being anywhere near a constructive and practical approach to taxing and regulating the financial sector. Not to mention that, at least in the U.S. it's pretty hard to do anything that financial firms don't like, especially if it's called a tax. It's their country, the rest of us just live in it. So we may have to wait for the next horrendous crisis, leaving aside the possibility that we'll get a U.S. government fiscal implosion first.
Still, perhaps Keen's paper offers a bit of intellectual progress, regarding how to think about these very complicated, important, and yet in a sense distressingly amorphous, issues.