macroresilience

resilience, not stability

Helicopter Drops Do Not Imply Higher Inflation

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I am a strong advocate of helicopter drops as the primary and first-choice tool of macroeconomic stabilisation. There is increasing debate about helicopter drops but almost everyone assumes that helicopter money is just another way to generate higher inflation. Those who fear inflation see helicopter drops as irresponsible and those who seek more inflation see helicopter drops as irrelevant and equivalent to asset purchases by the central bank. Both these views are wrong – helicopter drops can be implemented without any change in inflation so long as interest rates are hiked to counteract the inflationary impact of helicopter money. Let me take a simple example to illustrate how – if the UK government were to send a sum of £500 to each British resident and financed this transfer via monetary financing from the Bank of England, the Bank of England in turn could simply hike the base rate till the inflationary impact of the helicopter drop was negated.

Even if helicopter drops did lead to higher inflation, the inflation target does not matter in a world of interest-bearing money. Holders of money and holders of bonds only care about real interest rates. If helicopter drops result in inflation going up from 3% to 5% and interest rates going from 0.50% to 2.50%, then money-holders are no better or worse off.

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Written by Ashwin Parameswaran

February 14th, 2013 at 6:06 pm

Posted in Monetary Policy

37 Responses to 'Helicopter Drops Do Not Imply Higher Inflation'

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  1. But how can one raise the price (interest rate) and supply (quantity) simultaneously?

    Or is the argument that these sterilized helicopter drops don’t change the equilibrium quantity of money? Or that they raise quantity but lower velocity? In which case what are they doing?

    It’s all very unclear.

    polymath

    14 Feb 13 at 7:09 pm

  2. Yup, good point. Just pay IOR and the CB can control quantity and the short rate independently. But with two instruments shouldn’t they have two targets? It would make sense to me to use helicopter drops to target consumer credit conditions and the policy rate for inflation. I think this would create incentives to better avoid bubble lending, since creditors would know that any resulting crash would result in a wealth transfer to debtors. Also, rather than exiting a recession by using lower rates in order to try to drive releveraging, we’d actually deleverage troubled balance sheets.

    You could also target inequality directly instead of credit, via the helicopter drop. That doesn’t seem right to me for the simple reason that issues of equity should be settled democratically, via fiscal policy and regulation. Dysfunctional credit conditions, on the other hand, are unequivocally an impediment to market efficiency and are therefore reasonably the domain of the central bank.

    A decent relevant framework for analysing this problem is Eggertsson Krugman (2010) which clearly showed that you need fiscal transfers as well as interest rate fiscal policy to get efficient outcomes when some agents are credit constrained. It’s not a surprising result since every efficiency result that’s ever been produced depends on all all agents having equal and unlimited access to credit.

    K

    14 Feb 13 at 7:22 pm

  3. polymath – when the CB pays interest on reserves, it can control quantity and the base rate independently.

    K – Interesting point on how this may avoid bubble lending.

    There’s obviously a debate to be had on the appropriate mix of monetary policy instruments and targets. In a world where interest rates are still subject to the zero bound, is it not worthwhile to use heli-drops to target inflation as well? I’m not really in favour of targeting inequality thru heli-drops – send the same amount of money to everybody. But having this option will also allow the CB/govt to allow some bubbles to burst, allow banks to fail without having to bail them out etc safe in the knowledge that they can counter the possibility of a deflationary collapse with heli-drops. This alone should reduce inequality significantly across cycles.

    Ashwin

    14 Feb 13 at 8:14 pm

  4. Ashwin,

    “In a world where interest rates are still subject to the zero bound, is it not worthwhile to use heli-drops to target inflation as well?”

    Yes. But the big shocks that take us to the ZLB seem to be credit/balance sheet shocks. If we target a 5% nominal rate under normal conditions there are very few real shocks that can lower the natural rate by 5% as far as I can tell. But EK (2010) finds an optimal mix of both that is definitely affected by the existence of the ZLB. So you are right that you can’t exclusively assign fiscal policy to non-output gap measures. But I suspect that if you deal with financial crises, the rest *could* (not necessarily should) for the most part be solved with interest rates.

    “I’m not really in favour of targeting inequality thru heli-drops – send the same amount of money to everybody.”

    But even if you send the same amount to everyone you are reducing inequality. Anyways, my point was irrelevant. It has no impact on the top end of the distribution. Monetary policy really can’t directly do much about *that* kind of inequality.

    I do think it’s worth trying to flesh out exactly what you’d like to target, though. As you say, you could do unlimited helicopter drops without inflation if you just raise the short rate appropriately. So how much inflation-neutral heli-drops should you do? Eventually you are surely just using fiscal policy to favour consumption and crowd out investment. What does the economy look like in the limit of extreme heli-drops equilibrated by high rates? Is there something good there? Certainly more equality. But assuming you don’t want to go there, what *is* it that we are targeting with our dual instruments? Inflation is one thing, but what’s the other?

    The way I see it, it seems possible that you are causing a big dead weight loss if your inflation-neutral heli-drop is raising the real rate more than it is reducing credit spreads for the bulk of consumers. I.e. you should be trying to reduce, not increase market lending rates. This is why I think you might want to use your heli-drop to influence credit spreads, or rather minimize all-in consumer lending rates. And leave short rate policy for inflation (except near the ZLB).

    “But having this option will also allow the CB/govt to allow some bubbles to burst, allow banks to fail without having to bail them out etc safe in the knowledge that they can counter the possibility of a deflationary collapse with heli-drops. This alone should reduce inequality significantly across cycles.”

    Agreed. But would the collapse ever even occur if the CB continuously heli-drops to constrained consumers (everyone equally, of course, but those are the relevant balance sheets) to keep demand on target? Also, by backstopping consumers, do you backstop consumer lending? Is that dangerous? How do banks fail systematically if consumers keep paying?

    These are not rhetorical questions, BTW – I haven’t thought it through yet. As you know, I’m not a big fan of the current monetary set up, and I’m moderately suspicious that instabilities can be fixed efficiently via heli-drops.

    K

    15 Feb 13 at 3:41 pm

  5. One more way to think about it…

    We’ve been ignoring the impact of heli-drops on government debt. So long as the real rate is below the growth rate, we don’t have to put government debt in the utility function at all, since we never have to pay it off (in fact the economy is “dynamically inefficient”: we might *gain* utility by adding government debt). But if you do *a lot* of inflation controlled heli-drops (ICHD), the real rate rises and growth drops.  If we had NGDP futures then it would make sense to use ICHDs to control the spread between forward interest rates and forward NGDP, just to make sure we are keeping the economy just on the right side of dynamically inefficient. Anyways, I don’t think this goal would be very inconsistent with trying to lower all-in borrowing costs.

    Maybe we should think of this as LBOing the government. The government is sitting on cash (super low borrowing costs) and refusing to do anything with it. So we lever them up and pay a big dividend to the owners (citizens) who have plenty of good use for the cash, thereby restoring the dynamically efficient amount of leverage. Are MMTers really just “barbarians at the gates” of government? Maybe we should have put Mitt Romney in charge!

    K

    15 Feb 13 at 4:12 pm

  6. Might work in the US. Probably more problematic in the UK or small open economies.

    “Holders of money and holders of bonds only care about real interest rates” The marginal tax rate may have a significant impact as the nominal interest rate is taxed; saw this in the 70s.

    jt

    15 Feb 13 at 5:35 pm

  7. K – Thanks for the comments! A lot for me to chew on.

    Firstly, yes there is a discussion to be had on all the issues you raised and it is a discussion we need to have. The immediate trigger for this post was the fact that so many people seem to think that these “ICHDs” are literally impossible and/or incoherent.

    You say “if you deal with financial crises, the rest *could* (not necessarily should) for the most part be solved with interest rates.” I tend to agree.
    Let me try and explain my thinking on heli-drops. I see them largely as a temporary medicine, the use of which has been made necessary by the monetary and banking mismanagement of the last 30 years. If we’d been willing to live with a few minor recessions and banking/market failures during this period, we almost certainly wouldn’t be where we are. Even in 2008/2009 if we’d had the courage to use heli-drops instead of propping up the TBTF banks, we’d be better off now.

    Your point on inequality is obviously correct and yes I meant it in the sense that the amounts involved in the heli-drop aren’t really going to matter to the 1%.

    You said “it seems possible that you are causing a big dead weight loss if your inflation-neutral heli-drop is raising the real rate more than it is reducing credit spreads for the bulk of consumers”
    The way I see the current environment – the market and the financial sector are out of the woods, credit spreads and financing conditions for most large firms and others with access to the bond market are back to normal. But financing conditions for small businesses and households are still constrained. In my opinion, the loss from raising the bank rate will be far exceeded by the improvement in the household balance sheet from the heli-drop itself. Households and small businesses are anyway paying a far higher credit spread today than they were not just pre-crisis during the bubble but even in more normal times.

    You said “by backstopping consumers, do you backstop consumer lending? Is that dangerous? How do banks fail systematically if consumers keep paying?” Excellent point and I’ve debated this with others. To avoid this problem, there is no doubt that the heli-drop money must not be available to banks in case of default/bankruptcy etc. This combined with the uncertain nature of the help-drop should be sufficient to prevent this “generalised moral hazard”. Incidentally this is why I don’t support schemes such as a high universal basic income – as an ex-banker, I’m certain that banks will find some way to transform such a certain payment into increased borrowing in some manner no matter what the law says.

    You said “If we had NGDP futures then it would make sense to use ICHDs to control the spread between forward interest rates and forward NGDP, just to make sure we are keeping the economy just on the right side of dynamically inefficient.” That is an intriguing thought and one that I need to think about a lot more before I can respond.

    You said “Maybe we should think of this as LBOing the government. The government is sitting on cash (super low borrowing costs) and refusing to do anything with it. So we lever them up and pay a big dividend to the owners (citizens) who have plenty of good use for the cash, thereby restoring the dynamically efficient amount of leverage. Are MMTers really just “barbarians at the gates” of government? Maybe we should have put Mitt Romney in charge!”
    Even by your standards, that may be your best comment yet!

    Ashwin

    15 Feb 13 at 5:44 pm

  8. jt – so yes taxes matter always. On the open economy question, can you elaborate on why you think it would be less effective? The improvements to the household balance sheet should happen even in an open economy IMO. Thanks.

    Ashwin

    15 Feb 13 at 5:47 pm

  9. Ashwin,

    “In my opinion, the loss from raising the bank rate will be far exceeded by the improvement in the household balance sheet from the heli-drop itself.”

    Because household credit spreads will decline more than the real rate will rise? Or do you also consider the utility of the extra wealth? I.e. is it enough to just target lowering all-in borrowing costs or is it OK to raise all-in borrowing costs *a bit* if it’s offset by a big gain in consumer wealth? My point was that we could just task the CB with lowering all-in borrowing costs and let them ignore the utility enhancing effects of improved wealth distribution. I.e. they should only do ICHDs if credit spreads for the representative household are reduced more than real rates rise.

    “there is no doubt that the heli-drop money must not be available to banks in case of default/bankruptcy”

    Yes, good point. But I don’t agree that the same measures won’t work for a citizen’s dividend. Maybe banks will succeed in garnishing more wage income if there is a universal payment. So be it. People should learn not to deal with banks. The main thing is that you can’t be destitute just because you are unlucky or even incompetent. No matter what, what banks can or cannot lay claim to shouldn’t be an argument against a citizen’s dividend. If you can create a universal income you can also change the bankruptcy laws.

    “Thanks for the comments!”

    Thanks for the posts! I do wonder why you don’t get one tenth of the comments you deserve. In my case, I often don’t comment because I have nothing to add. I just think “yup, Ashwin is right. Again.” and it seems trite to just say that. It seems the blogs that get the most comments tend to be clever but consistently wrong about something or inflammatory. Who knows. I suspect you’d get more traffic if you tried starting off a few posts with “So and so is a moron…” Especially pick on somebody with a lot of good commenters (e.g. Steve Waldman, Nick Rowe or Brad Delong). I do think it would be great if your ideas were more at the centre of the discourse.

    K

    15 Feb 13 at 7:20 pm

  10. K – so yes I do consider the utility of the extra wealth. And I’m not sure the argument for helidrops is as robust if we ignore it.

    On universal income, I’m not against it per se. Just against the sort of high amounts that the left tends to argue for. But I’d even take that over the current mess of a system.

    On comments, I don’t really write often enough to get more comments or traffic than I do and even if I did write more often (which is an aim for 2013), I’m not really cut out to write inflammatory posts. Happy to get the few good comments/emails that I get right now!

    Ashwin

    15 Feb 13 at 7:30 pm

  11. Ashwin,

    “so yes I do consider the utility of the extra wealth.”

    If the economy is growing at 5% nominal then I suppose there is 5% or so monetary growth to be earned as seignorage for somebody. Might as well pay that to the public. But if you try to drop more money than an efficient amount in pursuit a utility optimizing wealth distribution, there will be a cost to be paid in terms of a rise in the real rate which will inefficiently favour consumption at the expense of investment. While flat payments are the right benefit, I don’t think raising the real rate is the right “tax” to effect the wealth distribution. In fact, I think it’s probably *less* efficient than a bit of surprise inflation. So if you are going to use monetary policy to effect a wealth transfer I don’t think you should control inflation.

    But I doubt that inflation is a good tax either. Wealth transfers are better financed via efficient taxation like land or externalities like carbon. Or by targeting the monopoly rents that drive profits and depress wages in the first place. Surprise inflation or high real rates are low on my list of good redistribution measures.

    “And I’m not sure the argument for helidrops is as robust if we ignore it.”

    Surely it isn’t, but it’s still very strong. Like you said, we would never have had deficient demand, even in 08/09, if we’d had heli-drops. And I don’t think you will get anywhere trying to convince people that central banks should have an equality target. There are better ways of addressing inequality and it’s risky to use a good policy to address the wrong goal. If you just stick to efficiency arguments you are way more likely to get your policy implemented.

    “I’m not really cut out to write inflammatory posts”

    You could still point out how wrong they are. Politely!

    K

    15 Feb 13 at 9:05 pm

  12. K

    Since the beta of growth is closer to 1 than to 0, r<g for govt bonds does not imply dynamic inefficiency at all. Fiscal equilibrium can have r<g forever, with the govt running a moderate primary deficit forever depending on the amount of govt debt investors are willing to hold on to.

    Phelps/Diamond raised it in the 60s, Tobin provided the resolution in the early 70s, almost dismissing the idea of dynamic efficiency as nothing more than a theoretical curiosity in a world with risk.

    Apart from that, great comments!

    Ritwik

    16 Feb 13 at 3:47 pm

  13. Ashwin,
    How does a helidrop work from a Fed balance sheet perspective? The Fed would credit drop-recipient deposit accounts, which is the same thing as issuing reserves (liability). Against the reserves there is no asset. Therefore the Fed would take an immediate loss. Since Fed remittances form part of fiscal projections, the loss would show as higher net spending (due to the decline in revenues) financed through bank reserves.

    My question: how does the above differ from a QE-financed payroll tax cut?

    The reason I ask is I think the payroll tax cut expiration marks the end of the only real incidence of “helidrops” we have seen since the crisis began. That is, most other net fiscal spending did little for middle class income expectations. The effects of this expiration may therefore be much larger than most currently envision.

    Diego Espinosa

    16 Feb 13 at 5:30 pm

  14. Diego – from a balance sheet perspective, helidrops are easier to implement when the payment comes from the fiscal arm and is funded by bonds bought by the central bank and kept on the CB balance sheet forever if needed. For what its worth, I’m not that obsessed with CB losses (although CBs certainly are!) for exactly this reason.

    Your point on payroll tax cuts is interesting – one reason I prefer helidrops is to make the intervention as “fair” as possible. but in a cronyist economy, payroll tax cuts will probably flow more to firms than to individuals. Of course helidrops will also probably flow back to a cronyist corporate sector and none of this solves the structural crony capitalism problem.

    Ashwin

    17 Feb 13 at 10:34 am

  15. K – “If you just stick to efficiency arguments you are way more likely to get your policy implemented.” You may well be right and I need to think a lot more about this perspective.

    And I do plan to write more regular short posts pointing out the macro-silliness I see online so let’s see how that goes!

    Ashwin

    17 Feb 13 at 10:37 am

  16. I suppose from an ‘efficiency’ perspective, a helicopter drop is predicated upon the contention that the current *natural* real rate is unnaturally low. So we wish to raise that rate w/o doing much with the market real rate, or even allowing the market real rate to increase, because we suspect that even at current real rates, the market threatens to run into financial instability/gold or land trap issues.

    If we don’t make that contention, then difficult to see why the first-best policy is not simply a higher inflation target. The helicopter drop then needs to be argued on a plank of – this is the only/best way to achieve inflation, which may be a more difficult argument to make.

    Of course, there’s the small matter of fiscal distributional neutrality/progressivity on top. Even if we place a small individual probability on each of the three reasons mentioned above, the overall case for heli drops becomes quite compelling. Which is why I’m in favour and have always been since SRW’s post many months back.

    Ritwik

    17 Feb 13 at 7:13 pm

  17. Here’s another thought that I’ve had for a while. Until the recent cuts that kicked in, the US has had an expanded deficit than pre-recession, and the Fed does hold a greater % of bonds on its balance sheet than before.

    In that sense, has the US already had a few helicopter drops? Does that explain the relatively strong aggregate performance of the economy? Is the jump in corporate profits on account of these heli drops?

    Ritwik

    17 Feb 13 at 7:25 pm

  18. […] my previous post I argued that introducing helicopter money does not imply that the inflation target must change. […]

  19. Ritwik – you said “has the US already had a few helicopter drops? Does that explain the relatively strong aggregate performance of the economy? Is the jump in corporate profits on account of these heli drops?”

    Given that any deficits, no matter how trickle-down in nature, will eventually work in a manner not too dissimilar to helidrops that is a reasonable conclusion. Having said that, I tend to think not of the US as the exceptionally strong economy but Europe as the exceptionally weak one (largely for reasons of pathological insanity!)

    Ashwin

    18 Feb 13 at 5:02 pm

  20. Ritwik,

    “Since the beta of growth is closer to 1 than to 0, r<g for govt bonds does not imply dynamic inefficiency at all"

    The Tobin paper provides lots of good reasons why r might be less than g. The reasons include anything that might induce people to care more about the near over the distant future including liquidity constrained consumers, those who are childless or for whatever reason don't care as much about the welfare of their descendants as they do about their own. But none of these in any way refute the fact that the resulting outcome is, in fact, inefficient.

    An important observation of modern portfolio theory is that if you have a large number of independent investments, a portfolio of such investments should earn the risk-free rate because you can completely eliminate all risk via diversification. This result is true in general to the extent that the individual returns satisfy the assumptions of the central limit theorem. If the expected return of that portfolio is greater than r then we have a "static" inefficiency. The contribution of the CAPM was that individual investments could not earn above r *except* to the extent that they are exposed to undiversifiable (systemic) risk factors.

    But CAPM (and all of early MPT) was a single period model. The difficulty with extending it to the multi-period setting is that if the individual periods are long enough, income in each period will be independent and so an agent that can diversify through an arbitrarily long period of time has statistically vanishing income risk. So your statement doesn't make much sense to me: the "beta" of various income sources in any given period is irrelevant. It is the correlation between different *time periods* that matters. It's very non-trivial to make infinitely lived agents demand *any* risk premium whatsoever from their investments.

    So *if* r<g (and Tobin gives us lots of good reasons to think that it might be) then government could provide any payment whatsoever to current agents and pay for it via any *arbitrarily small* annual income tax. You might argue that it is not *pareto* optimal to take anything, no matter how small, from future agents and give it to current agents. I might agree, but in that case you only have to invest a bit of the wealth transfer in order to produce any arbitrarily small improvement in g in order to make the trade pareto optimal. Sounds to me like a *massive* inefficiency no matter how you define it.

    From this perspective there is no doubt that government should borrow and spend. The only question is how much to consume and how much to invest. That depends on how much you think government should represent current versus future citizens. I think you can make a strong philosophical case that government should optimize over all citizens, present and future, which would tend to favour a large investment in education and R&D over current consumption.

    K

    18 Feb 13 at 6:13 pm

  21. Ritwik,

    “I suppose from an ‘efficiency’ perspective, a helicopter drop is predicated upon the contention that the current *natural* real rate is unnaturally low”

    Sort of. I’d say it’s predicated on very standard theory which says that you shouldn’t expect an efficient equilibrium if agents don’t all have equal access to borrowing, i.e. are unable to monetize their wealth.  Yes, that depresses the natural rate, but the inefficiency is the direct consequence of the illiquidity. Now you might be able to raise the natural rate without alleviating the ultimate cause of the inefficiency, if you could just bring back the confidence fairy. And maybe that would reignite lending. But the purpose of the heli-drop is to solve the actual consumer balance sheet problem in as direct a manner as possible.

    Now some inequality of access to credit is a necessary condition of people learning the consequences of their own bad decisions. But systemic lack of access serves disproportionately as punishment to borrowers for mistakes made by lenders. A heli-drop both restores market efficiency and inflicts a relative wealth loss on lenders, a lesson which they thoroughly deserve.

    K

    18 Feb 13 at 6:34 pm

  22. K

    I’m not sure I entirely follow/agree with what you have to say.

    The way I understand you, your argument on dynamic inefficiency is contingent upon an argument that can be distilled to :

    “For an infinitely lived agent/economy, p(undiversifiable systemic risk) tends to 0. ”

    I disagree. For an infinitely lived agent/economy, p(undiversifiable systemic risk) tends to 1.

    I suppose it’s the St. Petersburg paradox in a different form. Or perhaps I’m massively misunderstanding you.

    Ritwik

    18 Feb 13 at 6:36 pm

  23. Ritwik,

    “For an infinitely lived agent/economy, p(undiversifiable systemic risk) tends to 0. ”

    The St-Petersburg paradox says you can make a finite return with probability one if you are willing to wager an unbounded amount of capital doubling up on an unbiased coin. It’s a dumb result: if you phrase it as the limit of the expected *return/risk* (rather than dollars) after n coin flips, the result is zero. It’s not asking a relevant question.

    *But*

    If it’s a biased coin with an expected log-return of g-r then flipping it t times gives you an expected total log-return of (g-r)t. As t gets big, the realized annual return tends to g-r with probability one so long as g_i-r_i are independent and have uniformly bounded variance. I.e. the probability of getting an annual return smaller than g-r by any epsilon tends to zero as t gets large. After a finite number of steps, the probability of crossing back to a loss is *exactly* zero on many paths. And the fraction of paths for which that is true tends to 1 as t gets large.

    Since the return/risk ratio is infinite and government is infinitely lived, the government will have no trouble trouble borrowing at r for as long as it takes to win at this trade. There is simply no credit risk in lending to the government.

    Now you might reasonably ask, if these variables are independent with known mean, then what is the mean? The answer is I don’t know, but we assumed that the mean g is greater than the mean r, i.e. E[g_i-r_i]>0. That is all I need to make my case. If r begins to exceed g and this occurs at some point in the future that is not so far away that exp(gt) >> exp(rt), then we have to worry about it. But if we assume that g>r (and we did), then that is all we need to know.

    K

    18 Feb 13 at 8:47 pm

  24. “After a finite number of steps, the probability of crossing back to a loss is *exactly* zero on many paths. And the fraction of paths for which that is true tends to 1 as t gets large.”

    Thinking it over that isn’t true. What is true is that for any path in a state of profit, there is a positive probability of never even temporarily touching below zero again and as t increases that probability tends to one for a fraction of paths which also tends to one. The rest stands.

    K

    18 Feb 13 at 9:41 pm

  25. That’s a very good extrapolation from my invocation of the St. Petersburg. I had the intuition but you’re right, we should be thinking of biased coins here.

    You said:

    “..so long as g_i-r_i are independent and have uniformly bounded variance..”

    Precisely. No reason to assume either, but I can grant the first condition. I won’t grant the second.

    Also, I suppose I’m not accepting your argument because I’m not thinking of r as a generalized *rate*, but as the rate on the kind of bonds that we currently see.

    If the govt was to issue a trill perpetuity, r(trill) would immediately and always be more than expected g.

    But until we see a trill perpetuity, r<g is not dynamically inefficient.

    Ritwik

    18 Feb 13 at 11:04 pm

  26. […] To be clear, similar to Ashwin, I am in favor of “helicopter money” […]

  27. For what it’s worth:

    “What may be needed is a method of directly controlling inflation that do not interfere with free market adjustments in relative prices or rely on unemployment to keep inflation in check … Trying to control an economy in three major macroeconomic dimensions with only two instruments is like trying to fly an airplane with elevator and rudder but no ailerons…

    One possible third control measure would be a system of marketable rights to value added, (or “gross markups”) issued to firms enjoying limited liability, proportioned to the prime factors employed, such as labor and capital, with an aggregate face value corresponding to the overall market value of the output at a programmed overall price level. Firms encountering a specially favorable market could realize a higher than normal level of markups only by purchasing rights from firms less favorably situated. The market value of the rights would vary automatically so as to apply the correct downward pressure on markups to produce the desired overall price level. A suitable penalty tax would be levied on any firm found to have had value added in excess of the warrants held.”
    (Fifteen Fatal Fallacies of Financial Fundamentalism, William Vickrey, 1996.)

    Kyle

    19 Feb 13 at 2:46 am

  28. Ritwik,

    “I won’t grant the second.”

    Oh, well. There goes finance.

    But, seriously. Which part don’t you accept? No second moment at all, or just no uniform bound across time? Are you saying there is no price so high that you would sell a forward start growth-variance swap for a forward period of my choosing? Would you pay an unlimited amount for forward start growth variance?

    “I’m not thinking of r as a generalized *rate*, but as the rate on the kind of bonds that we currently see.”

    1+r is the price of 1 consumption basket now in terms of consumption baskets next year. g is the rate of increase in the output of consumption baskets (ignoring inflation in both r and g). If we define r to be anything else (trill rate or whatever) none of this conversation makes any sense whatsoever. This has nothing to do with what “we currently see.” It’s about the rate on risk-free loans of the stuff by which we measure output.

    “If the govt was to issue a trill perpetuity, r(trill) would immediately and always be more than expected g.”

    A trill is like a super-equity instrument by virtue of the fact that it lays claim to a fixed fraction of output way beyond the time period of the claims owned by current capital. Because of its extreme-beta nature, it would definitely trade at a huge discount. Which is why governments should be *buying* trills (i.e. borrowing at r and committing to taxing), not issuing them. Issuing trills would be a crime against our descendants (much like greedy sales of our finite natural resources or perpetual private ownership of land rents).

    “But until we see a trill perpetuity, r<g is not dynamically inefficient."

    The definition of r doesn't change just because someone issues a trill. r<g is dynamically inefficient whether trills exist or not.

    K

    19 Feb 13 at 2:58 pm

  29. K

    I would say indeterminate second moment and could choose any number of parametric distributions with a shape parameter that produces infinite variance but with a small-ish scale parameter so that the distribution itself is tractable at the time-frames that we normally make decisions of the political economy and macroeconomic management at.

    “Are you saying there is no price so high that you would sell a forward start growth-variance swap for a forward period of my choosing”

    I would, actually. And if you choose an arbitrarily distant time period, I’d accept a relatively small bid if I had an embedded option of rolling over the time period.

    “Would you pay an unlimited amount for forward start growth variance?”

    Of course not, I’d simply not trade. We’re talking systemic undiversifiable risk here. Unless you belong to a different multiverse, I wouldn’t trade.

    “1+r is the price of 1 consumption basket now in terms of consumption baskets next year”

    Of course, then r<g is dynamically inefficient. And of course, then r is not the rate of government financing. What exactly are we disagreeing about then?

    Ritwik

    19 Feb 13 at 3:46 pm

  30. Ritwik,

    Alright, I don’t actually totally disagree about tail risk. But we *did* assume that g>r. You are really threading a pretty fine needle if you want to insist that we can know the first moment but the second is undefined (and you should have told me that upfront!). What distribution, exactly, do you have in mind? I think you are violating the *spirit* of the debate.

    “And of course, then r is not the rate of government financing.”

    Why isn’t it? If government has the power to tax it can borrow at the risk free real rate. So long as government *can* borrow (and it certainly can) and r<g, it is foregoing a pareto improving trade that only it can carry out (nobody else can confiscate a fraction of future income). That's inefficient.

    K

    19 Feb 13 at 4:39 pm

  31. K

    My apologies, your incisive comments have helped me focus my objections, so that I have also distilled my critique as we went along.

    I’ve always thought that assumption of g>r was purely for the first moment, I thought that my argument around ‘the beta of growth is 1’ sort-of captured that. My current favourite resolution of the equity premium puzzle is the Barro catastrophic risk one, and that’s how I think of economic growth itself. Perhaps I should have brought that out earlier.

    I think I may have created confusion when I agreed to debate in terms of an infinitely lived agent or economy. Perhaps an infinitely lived economy is irreconcilable with the idea of catastrophic risk.

    I’m not going to suggest a specific distribution – that would be unqualified overstatement on my part. I trust that my previous clarifications ensure that I’m not violating the spirit of the debate.

    I sense that you’re thinking I’m making a case for the government not borrowing/ not borrowing more generally or currently. I’m not. I’m just saying that the statement:

    “a government should borrow until the rate of interest on its liability (assume only one kind of sovereign bond) exceeds the expected growth rate of the economy by epsilon”

    is false.

    The government is surely the only entity that can confiscate a fraction of future income. But the government is also an entity that can make its bondholders whole without confiscating a *set* fraction of aggregate future income. It can, for example, forego spending. You may say that this is equivalent to confiscating income, but it is not – spending foregone does not have to bear any relation to the *aggregate* level/rate of GDP/growth. It could do a helicopter drop on bondholders.

    g is a factor in whether/how bondholders get paid, but it does not constrain it. g is risky, r(sovereign) is not. The fiscal-financial-monetary complex of the government sets the financial numeraire, or perhaps even the term structure of financial numeraires. Consumption/income is uncertain. A government that treats the numeraire as equivalent to aggregate/average consumption has essentially foregone the act of creating a numeraire.

    r, in the sense of inter-temporal consumption equilibrium may perhaps be mirrored best – assuming financial equilibrium – by say the yield on 10 yr BAAs, or something similar.

    In a steady state, dynamically efficient economy where the government is borrowing exactly right, I’d expect r(govvies) < g < r(BAA).

    Ritwik

    19 Feb 13 at 5:21 pm

  32. Ritwik,

    No need to apologize. I’m learning lots from thinking this through too. 

    “assumption of g>r was purely for the first moment, I thought that my argument around the beta of growth is 1 sort-of captured that.”

    I don’t see the connection. You can’t compute the beta if you can’t compute the variance, no?  FWIW, Shiller says the S&P beta of trills should be about 2, i.e. about twice the duration of stocks.

    “It can, for example, forego spending.”

    How will that raise growth? The point is, if the spending increases growth by *any* amount, no matter how small, then it will be pareto improving so long as g>r going forward. Why? Because the debt has no consequences: it never has to be paid off. I don’t even really have to improve growth. I just have to now slow it. But I think it’s fair to assume that we have to pay it off within some finite time frame (however long) in which case the amount of improvement in growth sets the lower bound for the time period over which we pay it off without making anyone worse off.

    Reducing spending is senseless under our current assumptions.

    ” A government that treats the numeraire as equivalent to aggregate/average consumption has essentially foregone the act of creating a numeraire.”

    What you are describing is inflation targeting. You seem to be arguing in favour of some kind of extreme money illusion in which the choice of numeraire makes a huge difference. I’m not necessarily opposed to that, but it’s too open ended. I assumed we were sticking within relatively standard economic theory, in which the choice of numeraire is irrelevant. The reason the *real* rate is important in standard theory is that utility is assumed to be a function of *real* consumption, independent of the choice of numeraire. Not because government inflation-targets money. Anyways, I think your assumptions are carrying us into excessively open ended territory.

    “I’d expect r(govvies) < g < r(BAA)."

    Something like that, except I prefer to focus on consumer credit. But in general, if the representative household borrows at a much higher rate than government it clearly makes sense for government to lend money to the household for as long as that condition persists. If the condition is expected to persist *forever* then that loan becomes a heli-drop. So in general, the representative household's borrowing costs should be similar to government (a bit higher due to idiosyncratic risk – but systemic household balance sheet problems are just stupid). And the blended average funding cost should be similar to the growth rate at the inter-temporal equilibrium.

    K

    19 Feb 13 at 8:22 pm

  33. K

    Ahh, I see my lack of precision again confounds. By *beta* of growth, I simply mean that the factors that drive the equity risk premium will be strongly correlated with the factors that drive the *risk* premium of growth itself. That this *risk* is necessarily covariance is our current best tractable theory, but perhaps we’ll do better eventually.

    *cross fingers that I haven’t said something confounding again*

    “How will that raise growth?”

    It won’t. I’m saying that with a “prudent” government, bond holders don’t even *need* growth to be paid back, which is why we can expect r(govvies) < g in a world with income/consumption uncertainty.

    "What you are describing is inflation targeting"

    Not at all. My logic works with ANY rate of inflation. I'm presuming neither currency nor any form of 0% nominal rate money. The numeraire is simply the financial asset with the lowest real rate. My point was, a government that's pushed up its borrowing cost to the expected growth rate is essentially saying that its current fiscal stance and/or its promise to pay its bondholders in full, is ex-ante unsustainable/unbelievable. Thus, it has failed to create the financial numeraire.

    "Anyways, I think your assumptions are carrying us into excessively open ended territory"

    Again, my apologies. I had actually thought that my position would be fairly uncontroversial to a finance guy who deals in risk and uncertainty and that only economists bred on things like 'let's first derive the theory of interest in a world without certainty' would find it difficult to accept.

    I can't think of capital, interest rates or inter-temporal(and hence macroeconomic) equilibrium without thinking of risk. In fact, I'd go so far as to say that time *is* uncertainty, that the 'impatience' theory of interest is patently false, and that in a world with consumption certainty r=g and there can't possibly be unemployment. But I've found that these views have little reception the few times that I've expressed them and that I may not be particularly good at arguing for them, so usually don't bring it up.

    "Something like that, except I prefer to focus on consumer credit"

    Ok, I picked corp credit because I was operating under the standard *HH sector is net lender, corp sector is net borrower* idiom. However, given that human capital is by far the biggest component of our capital, might be better to think of the household as the investing unit.

    Ritwik

    20 Feb 13 at 12:57 am

  34. I’m feeling you totally misunderstood what I said. I’m sure you feel the same. Probably we have gone down the rabbit hole, never coming back up. Thanks for an excellent discussion!

    K

    20 Feb 13 at 3:54 am

  35. Could a sales tax tied to the rate of inflation neutralize the inflationary effects of helicopter drops? A policy tool kit incorporating a policy interest rate plus a sales tax rate variable could allow greater flexibility in dealing with the consumption/investment dynamic. Perhaps a permanent helicopter drop could be offset partially by the sales tax where increased rates could stifle investment.

    Rafael

    7 Apr 13 at 8:03 pm

  36. Rafael – That’s an easy question to answer and the answer is Yes! IMO The easiest way to reverse a helicopter drop would be some form of VAT/sales tax.

    Ashwin

    7 Apr 13 at 11:02 pm

  37. […] via taxation), an inflation- or NGDP-targeting central bank might need to impose interest rates higher than they would have imposed absent the expansion of the monetary base. Higher interest rates would exact a toll. But that toll […]

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