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Update: I just came across this fantastic post from Nick Rowe explaining why exactly fiat money isn’t a liability to the central bank.

Paul Krugman has a new, mostly-great post on the Pigou Effect. I have one pretty big quibble:

One way to say this — which Waldmann sort of says — is that even a helicopter drop of money has no effect in a world of Ricardian equivalence, since you know that the government will eventually have to tax the windfall away. Of course, you can invoke various kinds of imperfection to soften this result, but in that case it depends very much who gets the windfall and who pays the taxes, and we’re basically talking about fiscal rather than monetary policy. And it remains true that monetary expansion carried out through open-market operations does nothing at all.

Now, Krugman has said this before. Brad DeLong called him out on the fact that fortunately we don’t believe in Ricardian equivalence. But let’s say we do. Let’s say we are operating in a world of rational expectations without any ad hoc “imperfections to soften this result”. Krugman claims that a drop is effectively a lump-sum tax cut, and representative agents would save it all in expectation of future financing efforts.

A common refrain across blogosphere holds that Treasuries are effectively high-powered money at the zero lower bound. There is a cosmetic difference – redeemability – that plays in important role within the highly stylized, unrealistic, thought experiments that are representative agent models.

Fiat money is a final transaction. Even when the coupon rate is zero, the principal on the outstanding liability must be “redeemed” by the government. Therefore, outstanding government debt does not constitute net wealth in either the government’s or household’s budget constraint.

I’ve been toying with this distinction in my head for a while now, but Willem Buiter got there almost a decade ago. In this little-cited (according RePEc it has only self-citations, which is odd given the important result) paper, Buiter shows that a helicopter drop does not function as a tax cut. The result derives from the pithy, contradictory, but fair assumption that fiat monies are are an asset to the private holder but not – meaningfully – a liability to the public issuer.

Therefore, an dissonance between the household and government perception of the net present value (NPV) of terminal fiat stock results in discordant budget constraints in the model. In this sense, the issuance of money can increase the household’s budget constraint in a way open-market operations cannot, increasing consumption and transitively aggregate demand.  (For those interested, the math is presented in the previously linked paper as well as, in better font, this lecture). The so-called “real balances effect” is, for lack of a better word, real.

We don’t have to assume any sort of friction or “imperfection” that mars the elegance of the model to achieve this result, but Krugman is right: it very much is about who gets the windfall and who pays the taxes. For every liability there does not exist an asset.

Without resorting entirely to irrational expectations (what some might term, “reality”) there is a further game theoretic equilibrium in which helicopter drops have expansionary effects. Douglas Hofstadter (whose name I can never spell) coined the idea of “super-rationality”. It’s very much an unconventional proposition in the game theoretic world. But it’s very useful. Wikipedia synopsizes it as:

Superrationality is an alternative method of reasoning. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into accountbefore knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate, since this answer maximizes their payoff. Two superrational players playing this game will each walk away with $100.

Superrationality has been used to explain voting and charitable donations – where rational agents balk that their contribution will not count; but superrational agents look at the whole picture. They endogenize into their utility functions the Kantian Universal Imperative, if you will.

In this case, superrational agents note that the provision of helicopter money will not be expansionary if everyone saves their cheque, and note the Kaldor-Hicks efficient solution would be for everyone to spend the cheque, thereby increasing prices and aggregate demand.

This may be too rich an argument – in a superrational world we would not have the Paradox of Thrift, for example – but is more robust against imperfections. For example, as an approximately superrational agent who understands the approximately superrational nature of my friends, I know that they will probably spend their money (I mean they’ve been wanting that new TV for so long). I know that will create an inflationary pressure, and while I would like to save my money, I know they will decrease its value and I’d rather get there before everyone else.

I see this as a Nash Equilibrium in favor of the money-print financed tax cut.

Paul Krugman, though, is worried that accepting the existence of Pigou’s Effect undermines the cause for a liquidity trap:

What caught me in the Waldmann piece, however, was the brief discussion of the Pigou effect, which supposedly refuted the notion of a liquidity trap. The what effect? Well, Pigou claimed that even if interest rates are up against the zero lower bound, falling prices will be expansionary, because the rising real value of the monetary base will make people wealthier. This is also often taken to mean that expansionary monetary policy also works, because it increases money holdings and thereby increases wealth and hence consumption.

And that’s where I came in (pdf). Looking at Japan in 1998, my gut reaction was similar to those of today’s market monetarists: I was sure that the Bank of Japan could reflate the economy if it were only willing to try. IS-LM said no, but I thought this had to be missing something, basically the Pigou effect: surely if the BoJ just printed enough money, it would burn a hole in peoples’ pockets, and reflation would follow.

What Krugman wants to say, is that the liquidity trap cannot be a rational expectations equilibrium, if monetary policy can reflate the economy at the zero lower bound. In New Keynesian models, if the growth rate of money supply exceeds the nominal rate of interest on base money, a liquidity trap cannot be a rational expectations equilibrium. The natural extension of this argument is that if the central bank commits any policy of expanding the monetary base at the zero lower bound, we cannot experience a liquidity trap (as we undoubtedly are).

It’s crucial to note this argument – while relevant to rational expectations – has nothing to do with Ricardian Equivalence. In short, the government may want to do any number of things with the issuance of fiat currency – like a future contraction – but it is not required under its intertemporal budget constraint to do anything. This is fundamentally different from the issuance of bonds where the government is required to redeem the principal even at a zero coupon rate. Therefore, in the latter scenario, Ricardian Equivalence dictates that deficits are not expansionary.

The argument follows as the NPV of terminal money stock is infinite under this rule, which implies consumption exceeds the physical capacity of everything in this world. Therefore, rational agents would expect that the central bank will commit to a future contraction to keep the money stock finite. They do not know when and to what extent, but by the Laws of Nature and God are bounded from being rational.

In this world of bounded rationality, we must think of agents as Bayesian-rational rather than economic-rational. That means there is a constant process of learning where representative agents revise their beliefs that the central bank will not tighten prematurely. In fact, the existence of a liquidity trap is predicated on the prior distribution of the heterogenous agents along with their confidence that a particular move by the central bank signals future easing or tightening.

Eventually, beliefs concerning the future growth of the monetary base must (by Bayes’ Law) be equilibrated providing enough traction to escape the liquidity trap. But enough uncertainty on part of the market and mismanaged messaging on part of the central bank can sufficiently tenure the liquidity trap.

This is all a rather tortuous thought experiment. Unless one really believes that all Americans will save all of the helicopter drop, this conversation is an artifact. More importantly, a helicopter drop is essentially fiscal policy that doesn’t discredit the Keynesian position against market monetarism to begin with.

Ultimately, there is one thought experiment that trumps. Helicopter a bottomlessly large amount of funding into real projects – infrastructure, education, energy, and manufacturing. Build real things. Either we’re blessed with inflation, curtailing the ability to monetize further expansionary fiscal spending or we’ve found a free and tasty lunch. Because if we can keep printing money, buying real things, without experiencing inflation, we are unstoppable.

The little city of Macon, Georgia has a median household income of about $28,000 – barely more than half the state average. Its per capita income is one MacBook Pro more than Mexico’s, and almost a half its children are in poverty.

Far from the Federal Reserve in the Beltway, where the per capita income is almost $200,000, it is also home to what might be the most revolutionary monetary experiment in America:

Macon Money is a community-wide social game designed for the residents of Macon, Georgia. Using a new local currency with a fun twist, the game builds person to person connections throughout the community while supporting local businesses.

This was a social endeavor sponsored by the John L. and James S. Knight Foundation’s Games for Engagement Initiative. Kati London used her $65,000 in funding to back the issue of “Macon Money” bonds. They were split in two, and disbursed to random residents of this southern town. The pair would have unite and exchange the funny-money for real cash. The idea was to create new social bonds and form a strong sense of community. And to have a little fun in the process. Briefly (you can read the evaluation summary for more detail), this was a fabulous success:

  • 46% of the random sample spent Macon Money at a business new to them, and 85% had an improved perception of local shops and parks in the “target revitalization area”.
  • 20% of the matches led to further personal contact, of which 15% became “Facebook friends”
  • Almost two-thirds of all matches would have been “very unlikely” if not for Macon Money.

And this newfangled technology not only builds social capital, but can have deep implications for expansionary government policy. Macon was basically a local injection of liquidity into a tight system (remember: low interest rates mean monetary policy has been tight). But this is a very special kind of liquidity: it can’t be used to pay taxes or debt. Now, in fairness, the “value” of this money is its parity with the dollar. And that the case, theoretically the bonds can be exchanged to a national currency then used to deleverage indebted households. This is a good thing, but doesn’t help when aggregate demand is lousy and counteracts the injection.

But what if parity conditions were relaxed and exchange rate with the dollar was governed by market forces and the Macon Mint? This policy would require three guiding conditions:

  1. Macon Money will never appreciate over parity on the dollar.
  2. Severe depreciation would be binding. That is, if Macon Money falls below any $n ∈ N, where N is a predetermined set of values (including the floor) this becomes an effective cap on its value.
  3. Some determined time after the Macon falls to F, it will no longer be guaranteed against the dollar.

This allows for free movement within discrete bands, but never the chance of significant appreciation. In fact, it’s almost inevitable Macon will only decline in value, incentivizing immediate consumption. A floor F is necessary to ensure longevity of the currency through the whole AD crisis.

But what’s the meaning of this? Depending on the industry, merchants have to pay between “2.89 and 3.20%” on transactions handled through American Express. They gladly do this because the convenience to the customer results in a sufficiently higher demand. (And for many goods the burden is likely to fall on the consumer).

Macon Money will be like that, but with a big difference. As the experiment was conceived, businesses would redeem the bonds at face value. But prices (even for funny money) are sticky in the downward direction. In the short run, the merchant can purchase things in the local community from others. There will be two things that cause Macon inflation, and hence relative depreciation to the dollar: increasing velocity and monetary base.

Here’s where we get important freedom with a small-scale currency. Lucas tells us any anticipated or rule-based increase in monetary supply would be incorporated into market expectations and hence useless. The Fed could, to some extent, overcome this by adding probabilistic factors to its policy. But this is suicide for the world’s reserve currency, where people treasure stability. For many, the dollar is a store of value.

But no one wants to save and invest in Macon! So the central authority can follow an opaque and stochastic process in minting new bonds. The only guarantee would be the floorwhich maintains temporary credibility. So we have a medium of exchange that is not a store of value!

So in this little Georgian town, if Macon was allowed to depreciate, we’d find a robust shadow economy. Instead of trading it on the dollar, people would use it as a unit of exchange with high velocity. It could be made even more sustainable by only allowing “Macon-to-dollar exchanges” on random days, this would mitigate the desire to immediately trade off the currency. Alternatively, the Macon could initially be priced less than parity, which allows a good possibility of appreciation while the currency establishes itself.

And no one would be “worried” about sell-offs because once a Macon is traded for a dollar it disappears, and the contraction of the money supply would balance prices on the exchange market. It can only be used in the community, can’t be stored in a bank, and has to be used for consumption, resulting in a marginal propensity to consume of 1.

Eventually, of course, as the Macon depreciates too significantly against the dollar, most Macons would be traded for dollars and “burned” – effectively returning to a dollar economy with rejuvenated aggregate demand. But money supply won’t totally contract. If the central bank is actually just an offshoot of the Fed, which guarantees Macons with new dollars, then the new money supply has grown by F*n, where F is the floor and n is the number of Macons traded in for dollars. (Actually, it’s greater than this considering that some would be traded at a higher exchange rate).

The trick here is creating a unit of exchange that is in the public conscious not a store of value. This gives the government broad scope to inflate that currency to spur consumption, without hurting savers. The dollar would loose some value, as the Fed guarantees an exchange rate. Today some people are saying we need 4% inflation or more to stabilize AD. This would be a cheaper way to do the same thing.

At worst, people just immediately trade the currency for dollars. This reduces to a plain monetary stimulus of the helicopter sort. On the other hand, it can support a sustained increase in money velocity, commerce, and AD recovery. And if things ever “heat up” too much the Fed can just devalue the currency. Because it came out of nowhere.