(This post will piss some people off. "Nick's blaming the poor; of course they can't help either their poverty or their lack of saving!")

That statement is wrong on many levels. It's wrong theoretically. It's wrong empirically. But most of all, it's wrong because it might make inequality worse. It's the soft bigotry of low expectations. Providence is especially important to the poor. Saying that the poor can't help but be improvident is the last thing they need to hear.

"The poor don't have enough income to save, and can't help going into debt to the rich. Debt is caused by inequality".

If we want a policy that will promote equality of income we should do it because it's a good policy in its own right; not because of some spurious argument about reducing debt. And the sort of policy that would help attain that objective in the long run is one which encourages a higher savings rate by the poor than by the rich. For example: a policy that increased the after-tax rate of return on savings for the poor, relative to the rich. Canada's Tax Free Savings Account (everybody is allowed to save $5,000 per year tax-free) might be such a policy.

Let's start with theory.

A lot of debt is used to finance investment. In physical capital, houses, education, etc. But let's set that aside, because it's not what I am talking about here. I am talking about the distribution across the population of consumption and savings, not investment. Whether those savings are lent to others or used to finance one's own investment is a separate question.

Economic theory of the consumption/saving decision is based on intertemporal utility maximisation. Milton Friedman's Permanent Income Hypothesis is a simplified version of this. If you consume less today you can consume more tomorrow. You compare the marginal utility of present consumption to the marginal utility of future consumption. You compare your personal subjective rate of time preference (your degree of patience or subjective discount rate) to the market rate of interest at which you can borrow or lend.

This theory says that people who have a low rate of time preference (who are more patient) will tend to save, while those who have a high rate of time preference will dissave (have negative saving).

This theory says that people who have temporarily high income will tend to save, while those who have temporarily low income will dissave. Because if they didn't, and just consumed their current income every period, their marginal utility of consumption in good times would be lower than their marginal utility of consumption in bad times. We save and dissave to smooth consumption over time.

This theory does not say that people who have permanently high income will tend to save, while those who have permanently low income will tend to dissave. Consumption depends on permanent income. But the proportion of your permanent income you consume (and hence the proportion you save) need have no relation with the level of your permanent income. Depending on the particular utility function, the relation could go either way. If the intertemporal preferences simply scale up (which is the standard assumption), then consumption and savings scale up with permanent income, and the savings rate (the percentage of income saved) is independent of permanent income.

Start in one equilibrium. Double both income and consumption both today and tomorrow. If the marginal utility of consumption falls by the same percentage both today and tomorrow when consumption doubles (which it must for example if today's and tomorrow's consumption are equal), then you are still in equilibrium. If the ratio of today's to tomorrow's marginal utility of consumption stays the same, then everything scales, and you save the same fraction of your income regardless of whether income is permanently high or permanently low.

Sure, the poor really need to consume today. But they really need to consume tomorrow too. So their need to save is as strong as the rich.

1. Inequality in permanent income will not affect the level of debt.

2. Inequality of transitory income will affect the level of debt. Those having temporarily low income today will borrow from those with temporarily high income today. And will repay the loans in future when the transitory shock reverses. (And it must reverse, because it wouldn't be transitory if it didn't.)

3. Inequality of rates of time preference will affect the level of debt. Those with high rates of time preference will borrow from those with low rates of time preference, until they are credit constrained and cannot borrow more.

That third inequality is what is driving debt in the Gauti Eggertsson and Paul Krugman paper (pdf). Debt is caused by inequality of patience, not inequality of income.

The second and third inequalities are what are driving debt in Matteo Iacoviello's paper (pdf) (HT goldilocksisableachblond). Despite what it says in the abstract of that paper, it is not income inequality driving debt in his model. Debt is not caused by some people being permanently rich and others being permanently poor. Debt is caused by fluctuations of income over time, where one person's fluctuations are imperfectly correlated with others' fluctuations.

A rich or poor person, having a bad year, will borrow from a poor or rich person, having a good year. An impatient person will borrow from a patient person.

Being poor means having low permanent income. Being rich means having high permanent income. Debt is not caused by inequality in permanent income. Debt is not caused by inequality between rich and poor.

The only way in which a change in permanent income can cause a change in savings is if it causes a change in the pattern of transitory income. For example, as people have become richer over time, the wealth effect on labour supply means they spend a smaller fraction of their lifetimes working, and retire well before dying. Retirement is a time of negative transitory income (current income is below permanent income). So people save for their retirement. And the longer their retirement, the greater the percentage of their income they will save while working.

Here's the nightmare scenario of standard theory (thanks commenter Greg). Take a very simple model with infinitely-lived agents and no investment. Assume all agents have an exogenous flow of income that is constant over time. Assume all agents are identical, except some have low and some have high discount rates. The equilibrium rate of interest will be between the high and low discount rates. The impatient borrow from the patient, for consumption loans. The impatient will initially consume more than their income, and the patient will initially consume less than their income. But over time, the consumption of the impatient will fall and asymptote towards zero (or starvation-level). And the consumption of the patient will rise and asymptote towards their consuming all the labour income of both sets of agents. Debt, and inequality of wealth, rise inexorably over time.

Transfers from rich to poor (i.e. from patient savers to impatient dissavers) will not solve this problem. All they do is reduce the after-tax rate of return to both sets of agents, by an equal amount. The implied tax rate on saving increases the rate of interest, and the patient still save more than the impatient, net of taxes and transfers. It only works if people don't see it coming. But of course they will.

A policy that would help solve this problem is one that gives the poor a greater after-tax return on saving than the rich. That works in two ways. First, it gives those with low savings a greater incentive to save than those with high savings. Second, it means that a given level of saving will accumulate faster if the stock of savings is low than if it is high. One way to implement such a policy would be to put a limit on the amount of saving that could accumulate tax-free. I think that Canada's Tax Free Savings Accounts might do this. They let every person save $5,000 per year without paying tax on the interest earned.

That's what standard theory says.

Does that standard theory make sense? Well, OK, if you are in danger of starvation today it doesn't. Because if you don't consume today the marginal utility of your future consumption is irrelevant. But our ancestors, whose saving and investment created the income we have today, and who were much poorer than we are today, would laugh at us if we gave this excuse for not saving. (Mine, I think, would have been more disgusted than amused).

Does it make sense empirically? Does it fit the facts? I don't know for sure. But the opposite theory, which says that the rich save and the poor dissave, is contradicted by some widely known facts. And big facts at that.

Our grandparents, and great grandparents, despite being massively poorer than us, saved. That's how we have the capital and technology that we have today, that makes us so much richer than them. Real interest rates have not been massively declining, and savings rates have not been massively rising, over the last 200 years as our incomes have massively risen.

China is still much poorer than the rich countries, and yet has a much higher saving rate.

And it's no good just looking at a cross-section of people today and seeing if the savings rate rises with income. Current income is the sum of permanent income plus transitory income. And theory says that transitory income will be saved.

Moreover, current income will be correlated with patience. This is not to say that the poor are impatient. But it is to say that the impatient will tend to become poor. Because the impatient will save and invest less.

The casual assertion that the poor can't afford to save is what bugs me. It bugs me because it ignores theory. It bugs me because it ignores the evidence of our grandparents. But mostly it bugs me because it sends the wrong message.

I understand this only through vague ancestral memories. In the rest of this post I'm talking myth, not history. (I am bad at history).

It doesn't matter that much if rich dissolute celebrities blow their wealth by consuming the lot. (Except they set a bad example for those who can't afford to blow what little wealth they have). In the past, similar rich dissolute aristocrats were the celebrities of the day, and many set a bad example too. But opposing that example was a cultural movement (centred around a religious movement) which promoted a very different set of virtues, and especially for the poor.

Father said that Grandfather paid the farm men's wages on Saturday, to be met by some of their wives on Monday, asking for an advance on next week's wages, because their husbands had already spent the lot on drink. And how the village was split between Tory/Church of England/drinkers and Liberal/Non-Conformist/abstainers.

Commenter Determinant tells me it all changed in the 1930's, for the United Church in Canada anyway, when they shifted from promoting the old virtues towards something more like socialism. I think that was a dead end.

Nowadays the alliances seem to have shifted. The old virtues would now be seen as cultural conservatism, and are more associated with the right than the left of the political spectrum. Which is a pity. It's the poor that need them most.

(This post is not as well argued and evidenced as I want it to be. But I'm aware of the limits of my comparative advantage, so I'm going to stop here and post it as is. And give Frances something to respond to.)