LATELY, one has been able to detect in the murmurs of the economics commentariat the faint hope that Europe may have solved its problems. On the heels of nearly €500 billion in initial lending through the European Central Bank's new long-term refinancing operation, borrowing costs have been coming down—dramatically so for short-term debt and meaningfully so for some long-term debt. It is truly worth asking whether or not a corner has been turned. To do that, it is probably worth taking a step back and looking at the nature of the crisis as a whole. This is going to be a bit lengthy, so I'm putting the rest of the discussion below the jump.

Begin by focusing on a single economy: Italy's. An economy like Italy's can and will be able to mobilise a total amount of real resources now and in the future. These resources include the stock of total Italian wealth and the flow of current and expected future output. All of this adds up to what we might call Italy's total potential payouts.

This pool of total potential payouts is promised to holders of a broad set of implicit and explicit claims. Lots of people and institutions, many of them Italian, have an assumed claim on much of this pool in the form of expected real income. Another portion of this pool represents claims in the form of expected government outlays: public payrolls, benefits expenditures, and so on. Italy has also sold lots of claims on this pool to foreign individuals, banks, and institutions. Holders of Italian government debt, in other words, have a claim on a portion of future Italian output. On the one hand you have the pool of potential payouts, and on the other you have total claims on that pool.

Over the past decade, since the introduction of the euro, three big trends developed in the nature of these sums. First, in some cases total claims rose. Second, in nearly every case the distribution of claims shifted such that the share of foreign claims on the pool of payouts rose significantly. Cross-border claims within the euro zone rose substantially over the past decade. And third, expectations of the size of the pool of payouts rose steadily, then underwent a sharp reversal in the wake of the financial crisis.

Following on the heels of this reversal, a situation developed in which a number of claimholders began to suspect that the amount of claims on the pool of payouts significantly outstripped the contents of the pool itself. This raised the possibility that some holders of claims might not receive the full value of the payout to which they believed themselves entitled. And this made many holders of claims nervous, since they had quite often taken on obligations of their own against the expected payout of their claims.

Claimholders then reacted rationally. On the one hand, they tried to deleverage in an attempt to make sure that their own imbalance of payments doesn't result in a damaging insolvency. And on the other hand, they tried to move to the front of the claimholder line in order to ensure that however the Italian state's shortfall is addressed, they receive as close to the full value of their claim as possible. In particular, holders of tradable claims sought to sell their claims while prices were favourable. This process drove down the prices of such claims and drove up yields. Individuals would only accept new claims on potential Italian payouts if offered compensation for the risk of an eventual haircut: higher interest rates. Of course, these moves raised Italian borrowing costs, increasing the likelihood that other claimholders would get stiffed.

As it happened, Italy wasn't the first economy in the crosshairs. The yawning gap between potential payouts and claims first became apparent in Greece. The situation in Greece, and then Ireland and Portugal, became contagious, however, for a couple of reasons. First, as investors learned more about Greece's difficulties, they may have come to assume that they were also underestimating weaknesses in similar economies. Second, investors learned from the policy response to the Greek gap, and what they learned reduced confidence in the euro zone's ability to make claimholders elsewhere whole. And third, investors saw the possibility of direct contagion—financial and economic trouble in Greece, Ireland, and Portugal was likely to contribute directly to financial and economic difficulty in Spain and Italy, via bank finances, trade, and other channels. Greece's troubles inevitably sucked in other euro-zone members.

The question is: how can a large gap between potential payouts and claims be addressed? Well, one option is to increase the size of the pool of potential payouts. This could be accomplished through a direct transfer; countries with total potential payouts that exceed claims—surplus countries—could simply give deficit countries the money to meet their obligations. Another option is to raise expectations of the future flow of GDP. A country can only do that in the short term, however, if there are supply- or demand-side constraints holding growth below its potential and which can be eliminated (otherwise, a country can only increase growth by pushing out the production frontier through enhanced technological capability). Italy would seem to be afflicted by both constraints. It could undertake sweeping reforms in order to raise potential supply. The demand-side constraints are more binding. Fiscal expansion could raise potential payouts but would also increase the number of claims. Monetary policy is set in Frankfurt. Critically for Italy, external demand appears to be falling. It will be very difficult for Italy to increase its potential payouts in the short term.

Adjustments can also be made to the size of outstanding claims. There are a few different ways to do this. Italy could reduce claims that take the form of expected government outlays. If the government says it will ever after pay out less in benefits—by cutting pensions, for instance—then a larger share of the pool of payouts is available to meet other claims. Italy could reduce claims by cutting expected real income through higher taxes. The trouble with achieving balance through these methods is that these payouts show up on both sides of the ledger; they represent claims, but those claims are then spent and show up as GDP. Reducing one reduces the other, which makes it difficult to meet the economy's obligations unless more income can be derived from external sources, as from selling production abroad. Now, that's basically just a way of reframing the initial problem: Italy's consumption outstripped its production in an unsustainable fashion. To make ends meet, Italy must consume much less and sell much more and use the difference to pay off claims.

This is not an easy or frictionless process, however, particularly when many closely linked trading partners are all doing the same thing. If Italy reduces its claims by cutting domestic outlays and raising taxes and there is no corresponding increase in external surplus, then the result is just a painful wash. Cuts to claims impair the pool of payouts, generating unemployment without much reducing the gap between the two amounts because the external surplus is slow to materialise. It's slow to materialise, in part, because there are nominal wage rigidities in the downward direction. Wages must adjust downward to make it profitable to hire unemployed Italians at current productivities, and this is a slow process.

There are other ways to reduce the value of claims. One straightforward means to do so is through default; Italy could simply say that those who bought claims on future Italian payouts were suckers and will not be receiving what they thought they would receive. This might seem like a decent option for Italy. Its budget is close to running a primary surplus. The fact that creditors would lock Italy out of markets after a default isn't that big a deal, since Italy only needs to borrow to pay interest on existing debt. But in fact, it would be very bad for Italy. Many important institutions, including banks, have used their claims on the Italian government to secure funding. If those claims were suddenly made much less valuable, those institutions might be made insolvent, which would lead to an economic and financial disaster.

Another option has historically been more appealing. The government could address the imbalance between potential payouts and claims by writing down the value of claims across the board. By creating more of the unit of exchange it reduces the real value of all claims denominated in that unit of exchange. The real value of personal incomes is reduced slightly. The real value of promised pensions is reduced slightly (assuming those pensions aren't automatically adjusted to take into account such an eventuality). The real value of payouts to claimholders is reduced slightly. No contracts are abrogated, and since most domestic debtors will have the real value of both their claims and obligations reduced, cascading insolvency isn't an issue. There is a limit to the extent to which this strategy can be used, since private parties will soon begin building this decline in the value of the unit of exchange into their calculations, and will ask to be compensated in new contracts so that real values are unaffected. But, if the decline in the value of the unit of exchange is faster than any corresponding rise in nominal wages (and nominal wage increases aren't that likely while unemployment is high), then the real downward wage adjustment can occur fairly quickly. Production for external markets is likely to replace depleted domestic demand faster, and so Italy will be able to adjust more quickly since its efforts to shrink domestic consumption won't result in the idling of willing labour.

The trouble, of course, is that Italy's government no longer has the ability to produce the unit of exchange. It outsourced that task to the European Central Bank. And the ECB is unlikely to indulge Italy in its desire to reduce its obligations in this manner for two reasons. First, reducing the real value of Italy's debt through inflation is not at all part of its mandate; on the contrary, it is explicitly charged with maintaining the value of the unit of exchange. And secondly, the effort to use inflation in this fashion wouldn't just affect Italy. It would also reduce the real value of claims all across the euro zone.

At its heart, the crisis is about the perception that claims on total potential payouts across much of the euro zone are greater than the pool of potential payouts. Until this disparity is reconciled, the crisis will fester.

So, what has the euro zone done to reconcile these claims? Well, it has pushed the countries now targeted by markets to reduce government spending and raise taxes. Given the discussion above, we'd expect this strategy to fix the problem only slowly and painfully, if at all. And indeed, the economies going this route have been thrown into recession and are falling short of targeted deficit reduction. There has been some discussion of direct transfers (remember the Marshall Plan for Greece?). Any direct transfers are likely to remain too small to make much of a difference, both because such transfers are very unpopular and because large transfers might threaten to move surplus countries into the markets' crosshairs.

What about the EFSF and the ESM—the emergency funding vehicles that are supposed to buy claims on payouts from troubled economies when panic threatens to force a default? Well, if these funds were big enough to credibly commit to buying any claims suffering a panic-induced fall in prices, then that commitment could hold down borrowing costs. This practice would protect any economy who found itself in the claims-bigger-than-payouts situation thanks solely to panic-induced increases in borrowing costs. And this could potentially create a firewall around insolvent economies, the collective gaps of which might be small enough to be dealt with by the other available mechanisms. For instance, if the EFSF managed to eliminate the panic-premium on Spanish and Italian debt and thereby shifted them back into solvency, then the gaps for Greece, Ireland, and Portugal might be small enough to address through austerity and direct transfers (more likely from the German government to German banks after a Greek default than from the German government to Greeks).

What if it seems unlikely that eliminating the panic-premium alone will return troubled economies to solvency? Or what if these funds can't make that kind of commitment, due to insufficient size or government opposition? Then they can only help to close the claim gap to the extent that they represent direct transfers (perhaps by agreeing to forgive any debt they buy) or by facilitating a large enough flow in new money from the ECB to reduce the real value of claims through inflation. Right now, none of these seem like real options for the EFSF or ESM. They will remain small, with limited leverage from the ECB and no remit to take losses on purchased debt.

Then we must turn to the ECB itself, and especially to the wild card it played in December in the form of its long-term refinancing operations: unlimited, low-cost lending to banks for up to three years. Could this be the solution to the crisis?

It is certainly a solution to a crisis. In recent decades, high-quality debt, and sovereign debt in particular, has become increasingly important in the operation of the shadow banking system. Many large, critical financial institutions rely on quality assets to secure the short-term funding they use to conduct much of their business. As panic has rippled through sovereign-debt markets, banks and other institutions have had a harder time using sovereign debt as collateral for short-term funding. In the fall of 2011, this was creating the conditions for a broad credit crunch. Short-term liquidity problems led to falling confidence in banks, which led to more panic over the sovereigns that back them, which led to more problems for banks. Absent some intervention, the euro zone might have faced major bank failures or chaotic sovereign defaults or both. And fears of that kind of calamity also shaped expectations for growth (and therefore for the size of the pool of potential payouts), which exacerbated the initial cause of the crisis.

The ECB has attempted to defuse this ticking time bomb. It has expanded the range of assets it will accept as collateral and offered massive amounts of liquidity to banks on easy terms. In doing so, it has greatly reduced the odds that a short-term liquidity crunch will generate a bank failure or default, and it has therefore removed one contributing factor to the problem of excessive claims over payouts. However, the initial imbalance remains. Indeed, it has likely gotten worse, since the months of uncertainty over the crisis have helped tip the euro zone into recession.

Some suspect, however, that there is more to the ECB programme than meets the eye. The ECB's goal could be to ply banks with piles of cheap liquidity which can then be used to buy up the debt of troubled economies, which can be used as collateral at the ECB. Might this offer a route to salvation?

Again, it can help address the liquidity aspect of the problem. If banks are willing borrowers of sovereign debt, then markets need not fear an inability to sell Italian debt in a pinch. Italy is still vulnerable to solvency concerns, however. And if those concerns lead to a deterioration in market perceptions of Italian debt, then banks will face a larger haircut on Italian debt they take to the ECB—it will take an ever larger pile of Italian bonds to secure a given amount of ECB funding. And so a squeeze is still possible, unless this programme can somehow be used to address the solvency question. Can it?

If we want this mechanism to work, we're ultimately left with two options. First, the ECB could allow these operations to work as a large quantitative-easing programme. If the ECB increases the size of its balance sheet through these loans and encourages banks to lend the money out, then it could help close the gap between claims and payouts in two ways. First, any resulting inflation would reduce the real value of obligations across the board. Second, QE could remove the demand-side constraint on growth represented by falling expectations for nominal output. That is, too-tight ECB policy is helping to usher the euro zone into a recession, which is making the solvency situation much worse. On a large enough scale, QE could restore NGDP to trend growth and eliminate the cyclical contribution to insolvency concerns. Right now, the big problem with this is that the ECB doesn't seem interested in raising expectations for inflation and nominal output. Much of the money created through this scheme is being parked back at the ECB as bank reserves. If the ECB wasn't willing to solve the problem through direct monetary means, it is hard to see how it might be willing to do so through indirect monetary means. Alternatively, the ECB could try to engineer a Japanese dynamic, perhaps through financial repression. If private firms and households can be coerced into savings rates like those in Japan, then the ECB might be able to engineer the digestion of insolvent economies' debts without high inflation. In this case, the ECB's machinations would simply amount to a different version of reduction in claims through erosion in real incomes. The ECB would be betting on austerity, but it would be contriving to hold down bond yields over the long period during which adjustment occurs.

What we have to conclude, then, is that Europe may have put in place a mechanism through which the crisis could be resolved, but it hasn't yet revealed what that mechanism would be, and until the mechanism is clear we should expect pressure on governments that look insolvent to increase. Unsurprisingly, the drop in long-term yields that followed the rollout of the ECB's new programmes is slowly fading. Furthermore, nothing that the ECB has done has created a new route to resolution of the crisis. The basic options—growth, austerity, inflation, and default—are unchanged. It won't be long before push comes to shove and the main European players are forced to provide more guidance as to which path (or which combination of paths) they're going to choose.

Another way to think about the dynamic is to flip it around and focus on the claimant (say, Germany) rather than the indebted party. Germany accumulated lots of claims on a pool of payouts which turned out to be much smaller than previously imagined. Germany must now decide how it wants to take its loss. It could simply take a straight haircut on the debt it holds, but that might blow up its banking system. It could accept a real decline in the value of its euros as inflation within Germany rises uncomfortably high, while the ECB adopts a level of euro-zone NGDP growth and euro-zone inflation appropriate for the euro zone as a whole. Or it could take its payment in kind, in the form of consumption of lots of Italian goods and services (including tourism to Italy). (Alternatively, it could buy lots of goods and services from some other economy, which increases its consumption of Italian goods and services in turn.) If Germany's consumers decide that they don't find such goods and services attractive at current prices, then they must recognise that they will need to choose one of the other options, or face the risk that markets will rip the euro zone apart while Italian wages slowly decline. One would think that inflation is obviously the most attractive option, but neither the Germans or the leadership at the ECB seem to agree.

Is the euro-zone crisis over? No. To keep tabs on it from now on, watch euro-zone nominal output. If it grows at a depressed pace or declines, ask who is taking big real losses. Governments are trying to force losses onto households in order to avoid a financial blow-up. But such losses are almost certainly not sustainable. The only magic wand available is a printing press. Europe will use it in a way that is obvious to all, or something will break. The ECB has brandished the wand and in doing so has temporarily calmed markets. If it is bluffing—if it won't actually wave it and aggressively—then the meltdown we all fear will occur.