Saturday, August 25, 2012

More on Nick Rowe's Model

Nick Rowe’s model seems to be all over the internet once you start to look for it; there are quite a few people who are curious about it but not yet embracing it (possibly because it implies something on the “burden of national debt” question that they find discomfiting), and others who embrace it with exceptional glee (possibly because it provides them with another reason to believe what they had already believed before they ever saw it).  

Having had a day or two to think about what he was saying in the comments to my post, I think his model does capture something that matters, but I also think it may be answering a different question than the standard one about passing the burden of national debt on to “our grandchildren”, or at least a different question than the one I have always thought of when I heard that phrase.  I said that in our conversation in the comments, where I admitted that his original post had confused me a bit because I was stuck in a comparative-accounting-period frame of reference while he was looking at a process of linked cohorts.  Professor Rowe's linguistic criticism is right: I was talking about future times, not future generations.   Fortunately, the answer is still the same: whether we are asking whether current debt can burden future times or future generations, the answer is “it depends”.   But it may depend on different things.

A picture is worth…well, whatever a picture is worth.  But the distinction might be easier to understand in pictures, so I’m going to draw some. 

This first picture more or less depicts his example from the comments, but using my vision of the process, meaning looking at the world as a sequence of accounting periods (years or decades or something), rather than as a sequence of overlapping cohorts each of which happens to occupy some subset of those accounting periods.

And to keep the first picture simple, in each accounting period we will only look at two kinds of people: young and old.  The young are assumed to be working age, vigorous, and productive, and rewarded for that with a high income; the old are living by charity or savings or something, but their income is much smaller.  Here’s a picture of that simple model, with two policy changes that impact the distribution of apples (using Prof. Rowe’s example) between young and old.

In my model, what I would notice about this picture is that at every time period the economy produces exactly 4 apples (no economic growth, either positive or negative).  I would also notice that there are two distribution changes over the course of these 6 time periods: between times 2 and 3 for whatever reason the distribution became more equal between young and old, and between times 4 and 5 it changed back.  You can say that times 1, 2, 5 and 6 were more “fair” because everyone was receiving exactly what they earned, no more and no less, or you can say that times 4 and 5 were more “fair” because the old, whose health no longer allowed them to work, were not as poor as they had been.  In the chart above, maybe the young in time 3 instituted Social Security to maintain a reasonable old-age income for those who had created the world in which they, the young, worked.  In period 5 the young became resentful of the need to reduce their consumption to subsidize the idle old, and eliminated Social Security. 

But Prof. Rowe noticed something else about the chart.  Each generation, or cohort, is a group of people born in a particular time, who travel through their time in this world together and experience the same piece of history, and these cohorts are linked by policy decisions and other events that happen during the various periods in their lives.  Each cohort moves diagonally from the bottom to the top of the chart, young in one time period and old in the next.  So if we add up the apples provided over their lifetimes to the various cohorts in this chart, we see this: 

And now we can see that the changes represented by the blue lines, while they may provide each time period with a distribution of goods that seemed fair to them within that time period, are unfair between cohorts.  The second cohort got a windfall, and received 5 apples over their lifetimes instead of the standard 4, while the fourth experienced a clear burden, because they received only 3 apples over their lifetimes.   So if I understand Prof. Rowe’s model correctly, I think that at a simple level the difference in viewpoint between what I was saying in my post and what Prof. Rowe was saying is that I was looking at vertical (time period) slices of this picture, while he was looking at diagonal (cohort) slices.

It is possible that the differences between the time periods are created by debt: in periods 3 and 4, perhaps the young lend an apple to the old, and expect repayment when they themselves are old.  Actually, if the changes were created by debt, then period 5 above is not quite right: the old in period 5 would have a bond they could cash, so they would demand an extra apple---which would have to come from somewhere.  Since we’ve assumed there is no growth, and no stealing apples across time-segments, then that extra apple has to be extracted from the economy through some kind of tax, or through inflation, or something.  So it might be more reasonable to say the young and the old would each pay a ½ apple tax to pay the debt to the old in that case, so the distribution would really be 2.5 apples for the young, and 1.5 apples for the old.  But the result would be similar: one or more cohorts would get a benefit over their lifetimes from the initial application of the redistribution policy, and one or more would accept a loss to pay for that when the policy was reversed.

But notice three things:

First, the cohort that lost apples over their lifetime did not lose because of the first policy change but because of the second policy change.  There’s nothing strange about this: it is not creating debt that hurts, it’s paying debt back, and---if these changes were the result of borrowing and repaying apples---the second change is paying the debt back.   If we never pay the debt back (ie, if we are able to continually roll over the debt forever), then there will never be a cohort that loses, in this model. 

Second, the blue lines in this picture represent distributional change, not specifically debt or confiscation.  Debt is certainly one way to create an effect similar to this.   But this effect doesn’t have to result from an initial debt, or from paying off a debt at the end.  Any policy change that alters the distribution of income (or apples) between young and old will create a cost or a benefit for some cohort---if the change redistributes income toward older people, then those who were young before the change and become old after had the best of both policies: greater income from the initial policy when they were young, and greater income from the new policy when they are older.  And it works the other way too, of course: a policy change that redistributes income from the old to the young is costly for those who were young before the change, and older after the change.  What could cause a change like that?  The answer is: any of a billion things that can occur in history can do it.  Certainly, as Prof. Rowe has pointed out, debt or confiscation for the sake of redistributing income in a way that seems more “fair” to those who are around and voting in each time period can do it.   Other things that might impact the distribution of income between young and old---or between any two groups, for that matter---include changes in regulations, changes in tastes or technology, changes in education (ie, the young may be more or less educated, depending on whether we invest in maintaining and improving schools or not).  If we’re concerned with perfect intergenerational equity, history itself is our enemy: there is nothing fair about being a part of the generation that emerged into the economy just before the tsunami in Japan or the depression in Spain.   Or here, for that matter.   So even if we borrow, and if that does somehow create a kind of intergenerational inequity for some future cohort, that could still be the fairest thing for us to do if we borrow to reduce the intergenerational inequity created by a current depression. 

Third, things become a lot muddier if we include economic growth.   In the chart below, I used a 30% real growth over the roughly 30 years between the time a cohort is young and the time it is old, and for the two time periods between the blue lines I assumed that some change in conditions, perhaps a change in government policy that taxed the young and subsidized the old, transferred 20% from the young to the old.   

The end result, along the top, is that the total lifetime income of the sequence of cohorts shows a continuous rise.  The fourth cohort would have had more if the policy changes had never taken place, but is it reasonable to assert that life, or policy, has been unfair to them when they are able to consume more than any generation that preceded them?  Why, in general, is the result of generations of economic growth fair between cohorts?  If no redistribution had ever taken place cohort 2 (who initiated the change) would have consumed only 5.59  apples instead of 6.6, and cohort 4 would have consumed 9.45 apples over its lifetime, instead of 8.13.  But is it reasonable to say, in this case, that generation 2, consuming 6.6 apples, has placed an unfair burden on cohort 4, which consumes much more?  Why is that unfair? 
It becomes muddier still if young cohort 2 has worked and borrowed to create the economic growth that provided an improved life for young cohort 3 and young cohort 4. 

So inter-cohort equity is a difficult topic.  Intertemporal equity is much easier: for that, at least as far as current debt might impact it, read my post from last week.  But I think the topic Prof. Rowe raised, the topic of redistribution not just between young and old within a time slice, but between cohorts that cross time slices, can help us make choices.  And I think that a more general version of the simple diagram we’ve been using here will help us look at it. 

But I’ll put off a description of that for my next post, because this post is long enough.



  1. Stuart: "So if I understand Prof. Rowe’s model correctly..."

    I think you do.

  2. It's been fun thinking about this for the last few days. Thanks again for your comments on my earlier post...they were a great stimulant.