Debt and utility come alive!

As promised, here is an interactive Excel spreadsheet showing how utility changes in a debt-financing scenario versus the laissez faire case. Read my previous post to get a sense of the motivation.

The spreadsheet is based on Bob Murphy's initial table, albeit with some slight changes. Perhaps most importantly, I assume that old people may now earn less than young people (where the Old:Young income ratio is determined by the parameter "a"). And we can obviously vary all other parameters as desired.

As we can see, it is ultimately the combination of variables and parameters -- say nothing of the assumptions used within this simple model -- that determine whether people are better off as a result of deficit financing and transfers. E.g. All else equal, a lower "a" will mean that government is able to transfer more from Old Al to Young Bob in the first period (i.e. higher "t"), whilst not lowering the utilities of future generations. Indeed, "t" is the most interesting parameter from my perspective since this is the one that Government must decide on when all the others are given exogenously.

For a more specific example, plug in the following values: r = 100%, g = 500%, a = 0.5 and t = 3. Clearly these large growth rates are absurd, but they serve to illustrate how subsequent generations can actually suffer a relative loss in utility if GDP growth ("g") is significantly higher than the interest rate ("r"). As I explained in my previous post, this is because I am assuming a diminishing marginal utility (DMU) function. However, you can offset things by now plugging in a = 0.2. This gives you an idea of how important the interplay between our parameters is.

I'd obviously encourage you to play around with things and see how your results change. As an added bonus, I've included a formula (in the light blue cell) that works out the maximum transfer for maintaining a neutral effect on utility, when we assume that utility is logarithmic.[*]



Please feel free to share and adapt as you wish. Of course, a pointer towards the original source would not go amiss.

THOUGHT FOR THE DAY: Relative to the non-intervention case, government deficits may or may not have negative consequences for the utilities of future generations... Like everything else in life, it depends on our starting assumptions. I sense that this might not be the definitive answer that some of you were hoping for, but so be it. That said, I'd suggest that plausible values for our parameters would be r = g = 3% and a = 0.75. In this case, one notes that government in our simple model could actually improve utilities quite easily by using deficit finance. (In the logarithmic utility case, they can transfer anything up to 25 units and still yield an improvement in the utility levels of future generations.)

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[*] The formula is based on equating the laissez faire and deficit utilities:

ln(X) + ln(aX) = ln(X - t) + ln[(1 + g)aX + (1 + r)]

Taking exponents and a bit of algebra allows us to solve for t:

t = [1/(1 +r)] * X [(1 +r) - a(1 + g)]

The plot thickens in the debt debate

Since joining this debate, I have consistently argued that deficit financing is no less sustainable than taxation if economic growth is at least equal to the interest rate (i.e. g >= r). The models that I have discussed so far always seemed to assume that the reverse was true, so it was completely unsurprising that future generations ran into trouble in these scenarios at some point. It was an inevitable outcome of the design.

As a corollary of this, I also assumed that individual's utility would not be adversely affected if g >= r. To be sure, some important qualifications need to be made here. Most notably, in economics we typically assume that people have diminishing marginal utility (DMU) with respect to consumption. This effectively means that they value losses higher than equivalent gains at any given income level. (If I have 100 apples, then I would lose more utility from having three apples taken away from me, than I would gain in utility if someone gave me three apples.) Of course, this is why we generally think it is better to tax rich people and give that money to poor people, rather than the other way around. 

In this case, deficit financing would improve individual utilities if it meant transferring money (or apples) from a young generation that was wealthier than the old generation.[*] The relatively poor old generation would value the gain in apples more than the rich younger generation would value their loss. And, of course, it certainly seems reasonable to assume that old people will be earning less direct income than young people at any moment in time (due to retirement, etc). This is at least a standard assumption in the OLG literature to the best of my knowledge. I tried to make these points more explicitly in this comment to Nick Rowe... 

However, I had something of an epiphany walking home from the pub last night. (Two epiphanies if you include the realisation that I really should have brought an umbrella with me.):

What if high GDP growth is actually bad for individual utility when a government is using deficit financing? More specifically, what if g > r is the very thing that causes the utilities of future generations (at some point) to fall relative to what they would have been under the laissez faire scenario? This may seem pretty counter-intuitive -- at least it was to me until last night -- but the reasoning is actually pretty simple. Again, it comes back to our old friend: diminishing marginal utility (DMU).

If g exceeds r then at some point a "poor" old generation will be relatively more well off next to their "rich" young selves. Economic growth will outstrip the relative increase in bond repayments. In this case, DMU kicks in such that the transfer from young to old becomes a net "loss"... at least relative to non-intervention scenario. 

I'm not sure whether this is an easy point for people to digest in written form. I sense that it would be much easier to show this in mathematical terms than the long verbal description that I have given above. Nonetheless, I've actually made an Excel spreadsheet that shows that the intuition is correct. As soon as someone is able to tell me how I can upload an active Excel sheet to a blog, I'll do so. [UPDATE: Here it is.]

Make no mistake, g =? r is not the only thing that matters here. Another key issue, for example, is the ratio of old people's incomes relative to the incomes of young people. That's why I want to upload an interactive version of the spreadsheet, so that people can play with different parameter values to see how relative utilities are affected.

I don't know what this means in the context of original blogosphere debt blowout. Frankly, I'm not even particularly interested in who said what at this point. The assumptions that we've been working with are pretty far removed from many of the real-life reasons for taking on debt in any case (e.g. Debt could spur innovation or actually boost economic growth relative to the counterfactual). However, it was an interesting "theoretical" result for me. Nick Rowe may have been making a more profound point than even he realised.

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[*] Strictly speaking, what matters in this case is that any young individual (or cohort) is relatively wealthy relative to their older selves. I have more disposable income available when I am working than when I am retired.

Even more debt and inheritance (and sales)

Bob Murphy and another commentator have left some interesting observations underneath my last post. They basically want to distinguish between straight-up bequests versus the sale of bonds to the next generation. I was going to leave a response there, but figured that this may be long enough to warrant it's own post.

Bob writes:

You're right, if people in the future are literally bequeathed the bonds from the previous generation, then they are OK (holding all other bequests constant). But what if the previous generation *sells* the bonds to them? Then they're screwed.

My immediate response is to say: "Okay, but what if these young people buy bonds only to resell them to the next generation in the following period?" That seems perfectly consistent with the other assumptions of this model. Taking it for granted that this option is available to every subsequent generation, we would be in exactly the same position as we started with. i.e. This is ultimately a problem of GDP growth being lower than the interest rate... Something which everyone seems to agree upon.

As a thought experiment, however, let's consider the alternative: What if the younger generation refuse to buy the bonds off the old generation? These old timers are now stuck with bonds that they can't sell and, assuming that they decide not to leave any bequests out of spite, what happens next? Well, surely both the bonds and corresponding government debt are extinguished at the start of the next period. In this case, government no longer has a need to finance any outstanding debt burden. We are back to the laissez faire outcome for all future generations.

To be sure, in this scenario one particular generation -- (e.g.) Frank -- will be made worse off, at the same time as everyone else is fine. However, having said that, government could step in at period 6 to maintain Frank's lifetime utility. It does this by taxing Young George an eye-watering 96 apples and transferring them to Old Frank. Of course, now the government is finally at an impasse in period 7. It physically cannot tax Young Hank enough to offset (Old) George's initial losses, since 96*2 > 100 annual production. However, that is an artefact of the model set-up, where any form of debt financing is de facto unsustainable given that we have imposed a positive interest rate and zero economic growth!

The way I see it, this keeps returning to one unavoidable conclusion: The "bad" outcomes of Bob's model can all be traced back to the fact that the interest rate exceeds GDP growth. Everything else is paper fodder.

Debt and inheritance

UPDATE: Spotted an important typo in the text that I've now corrected for. I've also added a sentence or two to the paragraph before the Baker quote to hopefully make things clearer.

Believe it or, but there are people out there who haven't been following this whole government debt debate from the very beginning. (That is, whether locally financed debt can ever really be a burden to future generations since we effectively owe it to ourselves. ) After a recent link from Daniel Kuehn, I finally decided to bite the bullet and have a quick look over some posts. I may be covering very stale ground here, but please bear with me while I wade in at this very late stage.

Right, so following from Daniel's links, I've clicked through to Bob Murphy's blog. Bob is shameless about his addiction to this debt issue and apparently has infinity + 1 posts on it. I've read these two. (And didn't even make it to the comments!) 

Bob neatly summarizes his (and Nick Rowe's) position via this nifty table, which shows an OLG endowment economy with 100 apples produced in each period and a 100 percent interest rate:

Using the above, Bob claims victory over people like Dean Baker and Paul Krugman, who have ostensibly been arguing that public debt cannot make an economy poorer if it is owed to its citizens. (We can see that all the people in red colouring from period 6 onwards are worse off.)

Nonetheless, I immediately have several questions upon seeing this table, including the obvious comment that you will always run into long-run problems if the interest rate exceeds GDP growth. Nonetheless, I'll stick to my most structural observation:

All the action effectively happens in period 6 when the government switches financing schemes. (In addition to young people financing old people, those same old people are now also being used to "pay back" their younger selves.)

However, it seems to me that Bob's model is missing the fundamental part of Baker et al.'s argument. Clearly, "old" Frank is not being compensated for the money that he is being taxed to pay back to his "younger self". In other words, it is the switching of financing schemes that matters. As I understand the Baker et al. argument, Frank should have 86 apples' worth of bonds in period 6 that must be left to someone when he dies. No-one inherits "Old" Franks' bonds and, consequently, they can never be redeemed.

Here is Baker making this exact point:

As a country we cannot impose huge debt burdens on our children. It is impossible, at least if we are referring to government debt. The reason is simple: at one point we will all be dead. That means that the ownership of our debt will be passed on to our children.

I think that a faithful representation of the Baker and Krugman argument would include the inheritance of bonds. In this case, from Old Frank to (say) Young Hank and so on. Of course, doing so here would mean that you run into a big problem because debt now exceeds total repayment ability. (i.e. 86 rolled over to period 7 at 100% interest is 174, which is obviously more than the 100 income available in any one period.) However, this is an entirely separate  issue and again stems from the fact that this particular model assumes an interest rate of 100%, while GDP growth is zero.

As it stands, and with apologies Inigo Montoya, I'm not sure that this table means what people think it means.

Climate, economy and ladies

As a postscript to the previous entry, here's a quick story about a newspaper interview that I had last week. It was with one of the major broadsheets of the region and related to the launch of our new website.

The interview itself went pretty well, I thought. The journalist was mostly interested in discussing our aims, as well as how we perceive the public's general understanding of environmental issues from an economic perspective.

At one point, he asked the inevitable question of how I ended up in Scandinavia all the way from Cape Town. I told him that it was mostly down to my interests in these very issues. You'd be hard pressed to find a country that has a better track record of managing its natural resources than Norway. It didn't hurt that I was also lucky enough to receive some generous funding offers.[*]

However, I went on to tell him a joke that I had heard from another Southern Hemisphere expat upon arrival, which is that people like us usually find ourselves in Norway for one of two reasons: Oil or women. It was a throwaway line of course (and quite obviously a jape), and I didn't think much more of it...

I suppose it reflects my media naivete then that I was surprised[**] by the headline that ran above my interview the next day: "Climate, economy and ladies".
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[*] E.g. For those of you thinking about doing a PhD -- but can't bear the thought of scraping by on a measly tuition stipend for four/five years -- consider this: Doing a PhD in Norway is treated as a job and you are paid accordingly. That is, your salary has to be somewhat comparable with what a Master's graduate could typically earn outside of academia. Accepted PhD candidates are thus awarded a "research scholarship" which currently amounts to around US$71,000 per annum...
[**] Mind you, probably not as surprised as my (non-Norwegian) girlfriend.

Review: Surviving Progress

Apologies for the lack of posting recently. Aside from research stuff, most of my "internet" time has been spent working on the RECONOMICS HUB.[*] We have now officially gone live and will hopefully see a consistent level of posting from the various contributors in the weeks and months to come. Please free to stop by and let us know what you think... or follow us on Twitter!

My latest contribution to the blog is a review of the film Surviving Progress (produced by Martin Scorsese). To summarize, the film is long on intent and activism, but often fails to make a convincing argument. A snippet:

In another segment, the film jumps from Ronald Wright’s idea of a “progress trap” — something which certainly has merit in of itself — to claim that modern technology is at complete odds with our primitive physiology. (Wright: “We are running 21st century software, our knowledge, on hardware that hasn't been upgraded for 50,000 years.”) The language is undeniably provocative but is it necessarily meaningful? After all, our knowledge and innovations didn't occur in a vacuum. It is certainly hard to believe that any technological development can persist without bringing at least some form of benefit to its progenitors. The very strong conclusions that the film draws don’t necessarily follow from the premises that it provides.

Surviving Progress relies on a number of interviews and some of these work better than others. I was particularly unimpressed by a clip involving "geneticist/activist" David Suzuki, who is unilaterally scathing about the economics profession. (He calls conventional economics "a form of brain damage").

So, according to Suzuki, “externalities” is a collective term that economists use to explain away pesky things like the ozone layer, topsoil and biodiversity. Hmmm… 

There’s no other way to put this, so I’ll simply come out and say that Suzuki has completely mangled the concept of economic externalities. I cannot think of a single economist who subscribes to anything approaching the definition that he gives. (I’d even be surprised if anyone that has followed an ECO101 class would define an externality in this way.) Suzuki could open any introductory economics textbook and discover that an “externality” is simply some spillover cost or benefit incurred by a third party, which is not accounted for in the market price.

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[*] Resources. Energy. Climate. Economics