An Inquiry Into the Efficacy of Ricardo’s Helicopter (Wonkish with a Cherry on Top?)

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.

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3 comments
  1. Max said:

    “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.”

    I disagree that this is a fair assumption. In the first place, every central bank claims the opposite. And their claims are credible, because they hold assets sufficient to redeem their liabilities.

    • In 1920 I could redeem my currency for a dollar bill. Today meaningfully what can I get with my dollar? It’s final. You’re, I think, equivocating credibility in the way monetary economists and game theorists traditionally define the word and “credible” in the sense that Central Banks claim that they hold assets sufficient to redeem their liabilities.

      Clearly they can increase their balance sheet through QE why not random helicopter drops?

  2. Bryan Willman said:

    I think this exercise, and others like it, fails to account for at least one important aspect of reality. I would really like to encourage investigations that deal with this:

    People have cognitive limits and practical limits and great deal of uncertainty. If you give someone a “windfall” of say $100, it’s not practically possible to save that in a way that has a useful probability of making a positive material difference in the household budget very far into the future. Yet for many households, a “truly free” $100 a month or week assured for the next year could well increase their consumption and thus be reflationary. Richardian equivalence would certainly be rampant if you gave every household $100,000. And will probably be almost absent if you promise and give every household $100 a month.

    We need to stop fixating on “rational actors” who have prefect abilities to do things like make useful investments of $27.46, total calmness about the future of their own lives let alone government and society, and generally don’t exist in the first place. We should instead focus on the harried souls trying to get by on one or two low wage jobs, or working 60 hours a week a good but very demanding salaried job – those harried souls won’t do elaborate computations of future tax consequences of $100. They’ll struggle with whether to buy a nicer TV or take their spouse to a really nice dinner.

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