The best strategy is to prevent deflation from getting started in the first place. But what can a central bank do if deflation has set in and the policy interest rate has sunk to zero? Bernanke cited four approaches: (1) expand the balance sheet through loans or open-market purchases of assets; (2) lower long-term yields by committing to keep short-term interest rates low or by announcing a cap on government bond yields backed by unlimited willingness to purchase securities; (3) pursue monetary expansion in cooperation with fiscal stimulus; and (4) currency devaluation.
(Read more: Fed's Fisher: Liquidity is causing 'beer goggles')
For the ECB, however, the first three options pose much greater challenges than for the Federal Reserve. When the Fed wishes to expand its balance sheet or lower long-term bond yields, it can do so without taking on credit risk by purchasing Treasurys or government-backed debt. When lending to private intermediaries, the Fed can insist on high-quality collateral. Acting to support a fiscal stimulus means coordination with one executive agent (the Treasury) and one legislature (Congress).
In contrast, there is no default-free government debt in the euro area. While ECB officials have argued that quantitative easing is not off the table, they face a real problem deciding what debt to buy and how to price it. If the ECB were to purchase or accept as collateral only the lowest-risk government debt, the crisis-racked euro-area states and their banks might be unable to fund themselves. Which government bond yields could the ECB cap? To purchase without limit the debt of the region's crisis states, the ECB's Outright Monetary Transactions (OMT) program requires countries to implement a fiscal consolidation plan approved by the ECB, the European Commission, and the International Monetary Fund. In some cases, however, such a plan might require a debt write-down and a "bail-in" of existing creditors, a procedure that would exacerbate the euro-area banking crisis.
(Read more: El-Erian: This new Fed is a 'dream team')
Finally, for the ECB, cooperating with a fiscal stimulus would mean coordination with up to 18 finance ministers and legislatures. And it is doubtful that the highest-debt countries could undertake fiscal stimulus without a counterproductive loss of confidence in their consolidation efforts. Alternatively, fiscal-monetary cooperation only with the healthiest sovereigns might amplify the differences across the euro area rather than diminish them.
What about using the currency as a tool against deflation? In theory, the ECB (or the heads of state acting unanimously to create a new exchange-rate framework) could promise to cap the value of the euro versus the U.S. dollar. Under such a regime, the euro area would import over time the U.S. inflation rate and the inflation expectations that go with it. In effect, the euro-area authorities would have delegated monetary policy to the Fed, much as the Swiss National Bank, which has capped the franc versus the euro, has delegated monetary policy to the ECB. Some economists long ago proposed that Japan use this approach to exit its deflation.
In practice, however, the currency approach may be a political nonstarter even though it is probably the alternative that could be implemented most deftly. Governments long anxious to push China toward market determination of its exchange rate would be loathe to swing the other way for the two largest economies. Moreover, to make the currency policy workable, the ECB would need to be accumulating dollars rather than selling them. That means capping the euro at least slightly below its "fair value," a political no-no in the United States. These considerations probably explain why the direct currency approach has never been implemented in Japan — another large economy — despite a generation of deflation.
(Read more: This is the ECB's biggest task for 2014)
So, what is the ECB to do? Unfortunately, none of the policy options are without problems. We suspect that the currency approach would contain the long-run damage to the euro-area economy more quickly and preserve the credibility of the ECB better than the other options. Perhaps the decades of failure in Japan will have softened views about the dangers of the currency approach. In the best-case scenario, avoiding deflation in Europe may be better for U.S. trade and the U.S. economy than preserving the current framework. This is a very old argument, and sometimes it is right.
The bottom line: It's high time for the ECB to flesh out publicly — just as Ben Bernanke did a decade ago for the Fed — what tools the central bank would use to restore price stability if deflation actually set in. Doing so would anchor price stability today by reducing doubts about the ECB's willingness and ability to make sure deflation doesn't happen in the euro area.
— By Tom Cooley and Kim Schoenholtz
Tom Cooley and Kim Schoenholtz are professors at NYU Stern School of Business. Cooley is the school's former dean and has served as a research associate of the National Bureau of Economic Research and a member of the Council on Foreign Relations. Schoenholtz is a former chief global economist at Citi. Follow Stern on Twitter @NYUStern.