Wednesday, 12 February 2014

The Dynamics of Debt

I mentioned in my recent post on Steve Keen's latest paper that the relationship between debt and spending is a complex one.  This post is intended to give a brief outline of what I think are the main connections there.  The problem with tackling this topic is that whatever you write, there are always caveats and exceptions.  Still, you have to start somewhere.

To look at this, I want to imagine a simple closed economy with no public sector.  I have however, divided the non-financial sector into different types of agents,  This is necessary to construct the debt relationships.  The assets in this economy are loans, deposits and land.  Land is in fixed supply.  The different agents in this economy are:

- Wealthy households, that hold deposits and land and have no borrowing

- Speculators, that borrow to buy land

- Spenders, that borrow to acquire produced goods but hold no assets

- Banks, which make loans and take deposits

The national balance sheet is shown below:




The table below shows the flow of funds for this economy.  I haven't included anything to represent production, so the top two rows sum to total income and total consumption respectively.  These will be equal and opposite.  Otherwise, all rows and columns sum to zero.





p. -ΔAw
p. -ΔAm

Lending activity then matters in different ways.

1. Net new lending to Spenders is equal, by accounting identity, to their additional spending.  As Spenders hold no assets, their spending must be equal to their income plus their change in debt.

The increase in lending may either be seen as a cause of the increased spending, or as a result.  Maybe Spenders want to borrow more, but face credit constraints.  If Banks then relax their lending criteria, that could be seen as the cause of increased lending and spending.  On the other hand, these increases may arise from a change in the inter-temporal preferences of Spenders, in which case we might not want to say that the lending caused the spending.

If the economy was only made up of Spenders, then we would find that aggregate demand was strictly equal to income plus change in debt.  But, obviously it's impossible to have only borrowers without any lenders.

2. Mortgagors are borrowing to acquire land.  As with Spenders, there is a direct link between the amount of their borrowing and their demand for land.  However, there is also a fundamental difference, which is the distinction between stocks and flows.

The demand of Spenders for goods is a flow.  Spending on goods is measured over a period of time.  The demand of Mortgagors for land is a stock[1].  We need to know how much land Mortgagors want to hold at any point in time.  In relation to Spenders, therefore, it is the change in debt that matters.  In relation to Mortgagors, it is the outstanding debt[2].

As with Spenders, we cannot say anything conclusive about cause and effect.  The increased lending and land purchase may arise as a result of changes in bank lending policies or as a result of changes in household preferences.

We are assuming land to be fixed in supply.  The increased demand for land must therefore translate wholly into an increase in price.  The value of the landholdings of the Wealthy and of Mortgagors therefore rises.

So far in this analysis, there is no impact on GDP.  The rise in the value of land may, however, have an impact on spending.  Certain life cycle spending patterns can generate steady state stock-flow ratios between wealth and income.  Rising wealth, in the form of higher land values may then lead to greater spending as agents re-align their wealth income ratios.  In contrast with what happens with Spenders, the extent and rate to which this happens here is an empirical matter.

It is useful to ask what happens to the funds lent to the Mortgagors.  There are two places this can go, as we can see from the flow of funds.  The first is into higher consumption spending, to the extent that the Mortgagors respond to increased wealth as described above.  The other is in net acquisition of land from the Wealthy.  There is nowhere else for the funds to go.

This has an interesting implication.  As the debt of Mortgagors rises, they must either increase their consumption or end up owning more and more of the land stock.  We might therefore expect a continually rising level of Mortgagor debt to eventually translate into higher consumption.

3. The growth of loans requires a growth in deposits.  Note that, although I have chosen here to talk about deposits, there is no requirement that the assets created are monetary, in the sense of being able to be used for making payments.  An expanding loan book matched by expanding non-monetary assets would have the same effect.

So as new loans are made the stock of loans rises and the stock of deposits rises.  We may take the view that there are certain steady state stock-flow ratios in play, in particular that the wealthy have a target ratio of liquid assets to income.  In that case, we might expect the rise in deposits to lead to greater spending by the wealthy.

Mortgagors and Spenders have growing debts, which place a rising debt service burden on them.  The effects of this are complicated.  They may be tempted to borrow more to maintain their previous consumption levels.  However, over the longer term this is likely to be swamped by the limiting effects of high debt income ratios.  In theory, the ratio of a person's assets to income can rise indefinitely.   The same is not true for debt to income ratios.

Overall, the increase in liquid assets is likely to increase spending, but again the extent and pace of this is an empirical matter.

The combined effect of these things is to produce a complex dynamic response to an increase in debt.  Introducing a public sector and an overseas sector complicate this further.  But although the patterns that emerge do depend on agent behaviour, thinking about the relationships this way can bring out some important insights into longer term dynamics.

[1] We could derive a flow demand for land as the difference in the stock demand from period to period.
[2] With assets that are heterogenous and less liquid, like land, the flow of debt may also matter because the market may only react slowly to sudden changes in demand.  I am ignoring this here, in order to be able to focus on the contrast with loans to Spenders.


  1. I have to remind myself to think of stocks vs flows when thinking about stuff like Keen's work. It's easy to get sloppy and fail to maintain the distinction , and even when I try , the distinction often gets fuzzy.

    Let me give a quick-and-dirty example of why I still think Keen is on the right track. Here's a pic from Calculated Risk showing housing starts vs unemployment :

    Here , housing starts can be seen to be a good proxy for economic activity , as it's a leading indicator for unemployment and recession/recovery , with the notable exception of the late '90s and the dot-com boom , when housing construction was not as significant a player. Now look at this FRED chart of housing starts over the same period , along with mortgage debt from the Z1 , on the right scale showing % yoy change in the mortgage debt stock :

    The yoy change in the mortgage debt stock correlates well with the level of spending represented by housing starts , but at best it's coincident , and often it looks like starts lead mortgage debt. We wouldn't expect otherwise though , going by Keen's formula. We want to look at the change in the change in the mortgage debt stock to see that :

    Here , the 2nd derivative of the debt stock does a better job of leading changes in housing start activity , especially so on the downside. The 2010 upward move of the mortgage line predicts a turn up in starts that occurs about a year later , and my guess is that the next tick of the starts line will be upward , based on the mortgage trend line. Using construction loans rather than mortgages would probably be even better given the lag of mortgages relative to the associated housing starts.

    I don't know why there seems to be so much resistance among economists to this idea. Most economists - aside from the rabid anti-fiscalists - readily accept that gov't deficit spending supports some level of incremental economic activity , and that a deficit twice as big would support roughly twice as much , all else equal and assuming no binding constraints. The deficit is nothing more than the change in the gov't debt stock , analogous to the first FRED chart above. Similarly , most economists would expect no effect on economic growth when the deficit remains unchanged yoy , but would expect a change if the deficit goes up or down significantly. This is the so-called fiscal impulse , which is effectively the 2nd derivative of the gov't debt stock , analogous to the second FRED chart.

    Why is the fiscal impulse accepted wisdom , while the credit impulse is ignored , if not ridiculed ?


    1. Keen's first attempt linked activity to the change in debt. His more recent version effectively links activity to the level of debt. My point here is that both matter. Furthermore, because of the role of asset prices, the effect of changes in debt levels can take some time to play out. I think this means it is quite hard to pick out the relationship from the data. We can see that there is something going on, but I don't think we can be sure of the exact dynamic relationship.

      I suspect the conceptual distinction people are making between fiscal effects and credit effects is to do with loanable funds concepts. People often think that if private sector agent A lends to private sector agent B, then A will cut his spending as much as B increases his. They then conclude that private sector debt has no effect (Keen clearly believes this, except in the special case of bank lending). Some people don't think this applies if A buys government bonds. Others do believe it applies to government bonds and they believe in full crowding out, unless the government expenditure is matched by money creation. My own view is that it is not either/or but rather a question of degree (and actually I think the degree of difference is relatively small).

    2. I think you're probably right about the loanable funds concept being the obstacle to the recognition/acceptance of the credit impulse and its effects. One group who has not resisted are the big finance and investment types. The "credit impulse" is now measured for virtually every investable country globally , for which the appropriate credit data is available. Although its not the only indicator that can signal short-to medium-term changes in economic activity , it's thought by many to be among the best for those countries with a sizable credit market.


    3. Nick,

      I think what you say here is critical, " They then conclude that private sector debt has no effect (Keen clearly believes this, except in the special case of bank lending)."

      I think any form of credit (this goes back to the Tobin critique which you and Ramanan discussed a few months ago) adds to demand. Bank lending is special but not in the way that Keen thinks. What it does is create an asset (demand deposit) that has no "beta" to the economy. Rather it has a negative beta (As long deposits are guaranteed. otherwise bank deposits are like arb strategies, their beta is well-hidden!). Having a significant quantity of such an asset will actually facilitate normal NBFC credit. And so does government deficit. That is why the MMT types fixate on that without fully realizing why.

      More generally, thinking about money as a medium of exchange is a dead end and will lead you to ideas like inflation expectations, which our intuitions rightly tell us will have no real influence. Money as an uncorrelated asset and as an asset that has an option value of waiting (to buy other assets on the cheap) is far more critical for understanding the modern financialized economy.

    4. Srini,

      I'd have to think about this beta analysis you're using there. Are you thinking of the arguments that a large stock of safe assets helps hedge unsafe assets therefore encouraging more lending? I've read that somewhere, although I don't recall where.

    5. Srini, when you say that cash acts as a fixed value reserve, that fits in with how I thought it influenced our economy, I had a go at a post about that

    6. Nick
      I am using beta as a shorthand for a more complex nonlinear relationship. Except for cash and t bonds basically most assets are procyclical.

      Yes, cash is a store of value but I prefer to think of it as an option with a decay equal to inflation. When inflation is low and uncertainty is high, then the option value goes up. Raising inflation expectations increases the decay rate. But when uncertainty is high, small changes in the decay rate will be overwhelmed by the volatiliy. That is why working to increase inflation expectations is futile. What you need is to increase the universe of quasi cash by the government standing behind some assets that are normally safe but have turned risky.

  2. I certainly agree that the relationship between debt and spending is complex!

    There is no question in my mind that the relationship between borrower and spending is near 1:1; borrowers borrow-to-spend so the money results in a near 1:1 increase in GDP.

    The borrowed money does not disappear so we can trace it into the hands of secondary holders. The secondary holders are both early spenders and late spenders. If we tried to relate the money to GDP in a velocity relationship, the velocity would be dependent upon which measurement period the money was used within.

    If we looked over a long time period(s), the original money should return to the borrower so that he could repay the loan. Of course, it is much more likely that the loan would be repaid with money from other borrowings, not the single original borrowing of money.

    It seems to me like a huge problem with debt is that the loaned money returns to the ownership of the lender long before the borrower can repay the loan. This leaves the borrower(s) without money being available for repayment! On a bigger, multiple-borrower scale, lenders can, as a group, alternate between easy lending and tight lending. This practice can set up borrowers for high probability of default in the tight money times of the practice.

    1. And that is exactly the sort of complicated relationship, where examination of a national sheet and flow of funds can help keep track of how the debt relationships are developing.

  3. Nick, isn't an important factor WHO gets to do the increased consumption as mortgage debt increases? As far as I can see, what actually happens is that the flow of funds ends up supporting an ever larger number of bankers who are paid ever more. So we go from an economy with cheap houses and few, modestly paid bankers, to an economy with expensive houses where many people work in banking and those bankers are paid a fortune. It basically is a way to have everyone who isn't a banker, working flat out to provide more and more bankers with a more and more luxurious lifestyle. Added on top of that dynamic is the phenomenon of international capital flows. Oligarchs in the developing world "invest" in developed world mortgage debt (directly or indirectly), so the developed world gets to "import financial capital" and in that way all of the world's oil and other goods gets apportioned to the developed world on credit that is perpetually rolled over and expanded.
    Is it fair to say that our recent "economic recovery" in the UK is all about an expansion in mortgage debt and a consequent flow of capital from the developing world into funding the UK economy?

    1. I haven't gone into it here, but a further extension of this would be to look at the ongoing effects of changes in the distribution of income between wealthy, mortgagors and spenders, due to interest flows. Spenders, almost by definition here, have a high propensity to spend out of income, so we might expect to see changes in aggregate savings ratios as a result of changing debt. That would seem to me to be a natural extension of the model. Looking at the different spending behaviour of different workers would be possible, but I'm not sure that's not a separate issue.

      I do think that there is a relationship between the growing debt and capital inflows. I mentioned in the post that incorporating external sectors adds to the analysis - this is one the important ways in which it does so.

    2. Nick, I guess bankers (just as with other trades such as say clerics, soldiers, scientists or athletes) bridge all of those categories of "wealthy, mortgagors and spenders". The crucial difference though is that expansion of mortgage debt does not lead towards the economy becoming skewed towards having a vast increase in the wage bill going to say clerics. Debt expansion has caused a massive shift towards having very many more, much more highly compensated bankers.
      Steve R Waldman has done a post about how a huge "economic profit" is gathered by finance industry employees: Hidden profits, hidden rents

    3. I agree with most of that. I think the question for this analysis is what macro consequences that shift might have. There may be a story there, but to me it seems a bit more marginal to this analysis. If I was extending this model, there are other things I would think about bringing in first. One of those is the distributional effect of rising asset prices - I think the growth in real house prices in the UK has shifted the balance of wealth in way that does have macro impact, but I'm still thinking about how best to represent this.

      Thanks for the interfluidity link - I'll look at that.

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