### Grant McDermott

Data. Economics. Environment.

# 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.