E. Barandiaran writes in the comments:

Tyler, I hope that tomorrow (7/14) you read this comment about Arnold Kling's challenge to BC: define money that meets two requirements. Please tell AK that his two requirements were the same that Milton F. argued for the QT of M to make sense –but as anyone familiar with the history of Milton's version knows, he failed miserably. I'm still waiting your definition of money.

Arnold Kling writes:

So my challenge for Bryan (and for the rest of the profession, because I am the one who is out on a limb on this) is to come up with a definition of money that satisfies two criteria. First, your monetary aggregate is correlated with nominal GDP in a reliable way (with "reliable" including that if you were to target it, the relationship would not fall apart). Second, the Fed controls that monetary aggregate reasonably closely.

No definition of money fits Arnold's challenge (though Bryan argues for the monetary base) and I'm not going to offer a single definition of money, period.  I see money first as a medium of account and then as an option on purchasing goods and services.  As an option, "money" is more like "credit cards" than many economists might find comfortable, but so be it.  No single number very well summarizes the quantity or outstanding value of the money supply, properly understood to include the option value of lines of credit but also the option value of currency and bank reserves.  (Bill Barnett promotes "divisia indices," which I view as a nice try to a hard-to-solve problem.)

That said, a large, exogenous shift in the money supply will raise the general level of prices.  There is overwhelming evidence for that proposition (check out my macro Principles text with Alex, for one good chart, or visit Zimbabwe).  If some mix of currency, bank reserves, and useful lines of credit go up, prices will go up too, in very rough proportion, no matter what the exact measure of the money supply should be.

A lot of the better criticisms of the quantity theory play off of whether "money" is exogenous in the first place.  Many of the points of these critics are well-taken, but still a properly specified exogenous boost in the money supply will bring the traditional quantity theory result.  You just don't have to see that exogenous shift as the only relevant scenario for all real world monetary economics.

I see this post as "a lot of words."  I'm not saying much, I am just trying to limit how much other people's words confuse you.

On the quantity theory, I recommend reading and studying Arthur Marget's A Theory of Prices, especially volume II.  Marget was a penetrating thinker who understood his chosen topics better than anyone else and who was very good at pulling out the deep truths in apparently simple propositions.  I think of him as the Scott Sumner of his day, minus a blog.

George Loewenstein and Peter Ubel say yes.  Often there is no nudge-based free lunch and we need a straightforward relative price shift:

Behavioral economics should complement, not substitute for, more substantive economic interventions. If traditional economics suggests that we should have a larger price difference between sugar-free and sugared drinks, behavioral economics could suggest whether consumers would respond better to a subsidy on unsweetened drinks or a tax on sugary drinks.

But that’s the most it can do. For all of its insights, behavioral economics alone is not a viable alternative to the kinds of far-reaching policies we need to tackle our nation’s challenges.

There is much more here, hat tip to Mark Thoma.  Loewenstein, of course, is one of the pioneers of…behavioral economics.  (If you're wondering, I don't agree with a number of their examples, but I do agree with their overall point.)

I am happy to see Paul Krugman address the question.  He writes:

So why not forget about open-market operations, and just drop the stuff
from helicopters? Well, remember that at this point cash and short-term
bonds are equivalent. So a helicopter drop is just like a temporary
lump-sum tax cut. And we would expect people to save much or most of
such a tax cut – all of it, if you believe in full Ricardian
equivalence.

I hold a different opinion for two reasons.  First, cash and short-term bonds may be near-substitutes but they are not literally, strictly equivalent.  The nominal rate on T-bills is not exactly zero and furthermore you can't use a T-bill for every retail purchase.  The demand curve for real cash need slope down only slightly for a quantity theory result to hold.  After everyone spends the new cash balances, and prices rise, people end up with the quantity of real balances which they initially desired.  These equilibria have "knife-edge" properties, where "identical to T-Bills" and "nearly identical to T-Bills" do not bring the same results.  Tsiang showed this in a very good JMCB article on Friedman's optimum quantity of money, in the early 1970s and you might regard it as implicit in Bewley's Econometrica article on Friedman.

Second, after a helicopter drop no one need expect future taxes to be raised to retire the money (although maybe a sufficiently credible government could create such an expectation).  So there is no Ricardian motive to save the new cash, as Brad DeLong points out.  Indeed, if you think there is some chance that others will spend the money, raising the price level, you will want to spend your new cash soon, so as to preserve its value against forthcoming price inflation.  The resulting game-theoretic equilibrium, applying dominant strategies, again leads to higher prices, higher aggregate demand, and the desired quantity of real cash balances held.

Those are not the only possible cases (see the work of Fischer Black) but I take them to be the most sensible default cases.  Both indicate that a helicopter drop of cash will work fine in boosting aggregate demand.

The most likely scenario for no positive AD effect is simply that the helicopter drop is so small that no one expects a price level rise and thus no one expects an inflationary tax on the new cash, people (for bounded rationality reasons) treat the new cash as a transfer purely to themselves, the precautionary motive for saving is strong, and so the new money is simply held.  A larger helicopter drop should overcome that inertia, if need be.

Maybe these arguments are incorrect but they date from a consensus established in the mid- to late 1960s and early 1970s, much of it springing from Patinkin's book on money and the subsequent discussions thereof.  Krugman suggests this perspective is wrong, but he hasn't yet given me — or others — a reason to budge from it.

In May 2010, DNA
Consultants began offering a test called the Neanderthal Index.  Priced at USD $90.00, the test
purports to “estimate how much Neanderthal is in your ancestry.” 

There is much more here.