Tuesday, 18 June 2013

Productive Debt vs Speculative Debt

There is an interesting issue that crops up again and again in discussions about the relationship between debt and GDP.  This is the distinction between debt incurred for real expenditure and debt incurred for purchase of existing assets (whether physical or financial).

On the face of it, the immediate use of new borrowing should make a big difference since it's obvious that the former implies actual GDP spending and the latter does not.  However, if we consider the full stock-flow dynamics, the distinction is less clear.

To look at this we can consider a consumption function, where household spending (C) is a function of disposable income (YD), new borrowing (ΔL) and lagged net wealth (V-1).

                         C = α1 . YD + α2 . ΔL + α3 . V-1                                  0 ≤ α2 ≤ 1

The proportion (α2) of new borrowing used for current spending clearly has an immediate impact. However, a proper accounting framework will require that if any new debt is not spent currently, then net wealth will be correspondingly higher.  In the next period, spending will be greater as a result and will continue to be greater until any difference in net wealth has been eroded.  In its simplest form, the cumulative effect on income will be the same.

The chart below illustrates the impact for a simple model. (A specification of this model is given at the end of this post.).  The chart shows the cumulative effect on income for a one-off permanent increase in the absolute level of loans.

Cumulative GDP (deviation from base-line)
The results in the graph above are based on the assumption that the asset allocation of borrowed funds matches that for net wealth.  More precisely, it assumes that if households invest 30% of their net wealth in deposits, then they will also invest 30% of any money borrowed for investment purposes into deposits.  (This is the assumption used in Godley and Lavoie*).  However, in general, people do not borrow money to invest in bank deposits.  The people who hold bank deposits are not borrowers, but people with net wealth.  Where money is borrowed for financial investment, this is much more likely to be for the acquisition of housing or marketable securities.  If we reflect this in our asset allocation assumptions, the results of our simple model show that, in the long-run, debt for asset purchase actually has a greater impact than debt for spending. This is shown below:

Cumulative GDP (deviation from base-line)

This result arises because the debt creates a permanent change in the structure of investors' portfolios. The greater concentration of demand into variable price assets inflates values giving a more sustained wealth effect.

One way to think about this counter-intuitive result is as follows.  In the simple model, with government spending and tax rates fixed, any change in the level of government debt held by the private sector can only come about via differences in national income, since that is the only free variable to affect the new issuance of bonds.  The long-run impact therefore ultimately depends, not on anything that happens currently, but rather on the willingness of the private sector to hold government debt.  In the latter scenario, the decision of households to invest more into marketable securities (including government bonds) has the perverse effect of reducing overall private sector bondholdings, because of the impact of the accounting constraints on banks' balance sheets.

In the real world, there are plenty of factors which could lead to a reverse effect.  For a start, once growth is factored in, the front-loaded impact of borrowing for spending means that it may permanently push income ahead of the curve of the static steady state.  It is also worth noting that the incorporation of yields into the portfolio preference functions will affect the results.

The point I wish to make is simply that the impact of the purpose of debt is a much more complex issue than is at first apparent, and that careful consideration of the full stock-flow dynamics is necessary to really bring this out.

Model Specification

The model is based on three sectors: households, banks and government.  There are four asset classes: Bank deposits, government bonds, household loans and real assets (say, housing).  The last is represented by a quantity multiplied by a price index.  This is shown in the balance sheet matrix below:



Real Assets

B + k.p

Banks are assumed to have nil net worth.  This implies that household net worth must equate to total private sector bondholdings plus the value of real capital.

Government bonds
Bonds held by banks
Bonds held by households
Consumer spending
Government spending
Household loans
Household net wealth
Household disposable income
Physical assets
Price index of physical assets

Greek letters are parameters.

GDP is consumer spending plus government spending

Y = C + G

Household income is the after-tax share of GDP

YD = ( 1 - τ ) . Y

The household budget constraint determines the change in money.

ΔD = YD - C + ΔL - ΔBh

Household net wealth is assets less liabilities

V = D + Bh + p . k - L

Consumer spending is based on disposable income, new borrowing and lagged net wealth.

C = α1 . YD + α2 . ΔL + α3 . V-1         

Households allocate their gross asset holdings between bonds, real capital and deposits in constant ratios.

Bh = θb . ( V + L )

p . k = θk . ( V + L )

As k is constant, this latter equation is used to determine p.
The assumption about portfolio allocation is modified in the alternative scenario.  New spending loans are added back into net assets and allocated as before, but the non-spending loans are assumed to be fully invested in either bonds or real assets, but not deposits.  The portfolio equations are replaced with the following:

Bh = θb . [ V + L0 + α2 . ( L - L0 ) ] + θb / ( θk + θb ) . ( 1 - α2 ) . ( L - L0 )

p . k = θk . [ V + L0 + α2 . ( L - L0 ) ] + θk / ( θk + θb ) . ( 1 - α2 ) . ( L - L0 )

where L0 is the outstanding loan balance at the start of the simulation.  This is treated as before (and assumed to be invested across all assets) to keep the simulations comparable and avoid having to change any parameters or opening stocks values.

Parameter values and opening stock values are given below:

1.0, 0.5 or 0

Opening Value

G is set at 25 throughout.  k is constant at 100. ΔL is zero, except for period 2 when it is 10.

*Monetary Economics - An Integrated Approach to Credit, Money, Income, Production  and Wealth, Godley W and Lavoie M, (Palgrave Macmillan) 2012


  1. "(This is the assumption used in Godley and Lavoie*)"

    Yes I don't know why they assume that!

    Probably the assumption isn't so wrong because it consolidates households and when some household purchases equities someone else liquidates it and the portfolio equations capture this without going into the transactions step by step. Is that right reasoning - does that make sense?

    This paper of Marc Lavoie doesn't so http://www.levyinstitute.org/pubs/wp325.pdf

    (equation 3 and 4).

    Some typos/characters missing there. There's probably a neat version of that in some book but I haven't found it.

  2. Good spot. I'd seen that paper before, but I hadn't noticed that, I think it makes more sense that way, but I guess in G&L they went the other way just because it's simpler.

    In neither, do they really explore the implications. I think that's a missed opportunity, because it's one where there's a really counter-intuitive result lurking, which is hard to see without using the whole SFC framework.

  3. I'm confused by a couple of things here:

    "However, a proper accounting framework will require that if any new debt is not spent currently, then **net wealth** will be correspondingly higher."

    Are we talking about household net wealth?

    If yes: household borrowing shouldn't affect their net wealth (increases both assets and liabilities) -- whether they spend it or not. ??

    Is the Y axis displaying household income?



  4. Steve,

    That's a good point and I probably didn't express myself very well. You are right that the act of borrowing in itself makes no difference to net wealth, so there is no distinction between the two cases in that respect. The difference between the two cases is only through the impact on spending. If spending is higher, the end period net wealth must be correspondingly lower. This is relevant because of the link I'm assuming between new borrowing and spending in the current period (explicitly in my consumption function).

    Assume $100 is borrowed. The act of borrowing makes no difference to net wealth. I'm then comparing two case: one where the household spends the $100 currently and one where they invest it. Where they invest it, net assets will be $100 higher than where they spend it (actually it's more complicated than that, because of the way expenditure goes round and because of the way asset prices respond, but that's the key part). That was all I meant.

    Y axes on the graphs are meant to be the cumulative difference in GDP. (Using my terms, this is the sum of Y less what the sum of Y would have been with no new debt.) On these numbers, with no new debt, Y is constant at 100. The graphs show that with the new debt, Y goes up for a bit, then settles down to 100 again. In the case of all new debt currently spend, after an initial jump, Y actually fall to less than 100, because households have overspent.

    I might look at re-labeling the graphs to make them clearer.


  5. K that makes sense, and this post nicely demonstrates the post's ultimate conclusion: "impact of the purpose of debt is a much more complex issue than is at first apparent."

    But lime so many other models (jumping several conceptual steps here), it leaves me flummoxed and bereft absent a coherent and complete theory of value (and, hence, price). Much appreciated if you'd sort that out for me in your next post. ;-)

  6. What do you mean by a theory of value? Are you talking about what determines prices and inflation?

  7. Oh I'm forever lusting for an accounting done in utils, not dollars. (i.e., which of the scenarios above results in more human value creation?) This desire is:

    1. A foolish will o' the wisp, and

    2. A realistic expression of the #1 lesson I learned on the first day of my MBA accounting class at NYU: that accounting is an exercise in assigning value to things that in many cases are very difficult or impossible to value.

    cf Steve Randy Waldman on accounting profit vs. economic profit:


  8. A worthy sentiment and works for some things.

    But unfortunately monetary economics is a bit tricky if you ignore $, right?

  9. Nick,

    Just a few words to say that I appreciated your post and the effort to formalize thoughts with math. I have spent considerable time trying to completely understand it.

    I might suggest for the next similar post using math, that you more completely define the terms and maybe the goals.

    I found the concept of "lagged net wealth" difficult to understand in the very first equation which defined household spending. I could see it fairly easy for an individual. For many households, lag-in should equal lag-out except add in the change in basic money supply.

    In a similar fashion, the term "delta L"seemed correct for an individual. For a generalized society composed of many households, I would expect "delta L" should approach zero to recognize that one person's loan is another's borrowed money (bank loans can be viewed otherwise by some).

    I appreciated your post and the considerable effort it took to create the detail. Thanks.

  10. Thank you for your comments, Roger.

    I appreciate that these posts are very brief, given what they are trying to do. This really comes down to my laziness, I'm afraid. I put this sort of stuff on a blog, because I don't want to have to write lengthy papers. Also, I'm not very good at reading other people's stuff if it goes on too long, so I tend to write the sort of stuff I would read myself.

    I presume you understand net wealth, as assets less liabilities. Lagged just means I take the previous period value (signified by the -1) rather than the current period value. This is because conventionally the current period value of a stock is its value at the end of the period not the value at the beginning. Using the current value for flows during the period would therefore imply looking into the future. Not necessarily wrong, just not what i wanted to do.

    Delta L is just the change in loans. There is an amount of loans at the start of the period and a different amount at the end of the period. Delta L is just the difference. You're right that one person's debt is another's asset, but you can still have a non-zero stock of loans.

    Most of the ideas I'm using in this type of model are explained in great detail in the Godley and Lavoie book mentioned in the post. I can strongly recommend it.

    1. Thanks Nick. I am now carefully studying your post "Trade Imbalances: Micro to Macro". I appreciate the care and detail you put into your post.

      I need to look at the Godley book. I notice that the Minsky software uses a "Godley Table". Must be a relationship. The Minsky program is in my future.

  11. "In the next period, spending will be greater as a result and will continue to be greater until any difference in net wealth has been eroded. In its simplest form, the cumulative effect on income will be the same."

    Is this actually true? In the UK, £10T is owed between financial firms. That stems from lending used to bid up asset prices doesn't it? I don't see that debt ever leading to increased spending by households. Rather it acts as an overhead that needs to be serviced. A financial burden on the economy.

    1. First of all, much of the gross debt figure you refer to is simply lending back and forth, e.g. inter-bank deposits or intermediated lending. There may be issues with that sort of debt, but it has little impact on either spending or asset prices. Debt representing net new money invested in the stock market must be considerably less, although it still may be significant. I do think this element has an effect on spending.

      Let's take the non-bank private sector (NBPS). The key point here is that for any sector, (if we take income as fixed) that net borrowing must equal expenditure plus net acquisition of financial assets from outside that sector. This is simply an accounting identity.

      Therefore if the NBPS includes non-bank financials, who are borrowing from banks and acquiring existing financial assets, the net borrowed funds have to flow out again from the NBPS, either in the form of expenditure or acquisition of assets from outside the sector. If the initial use of the funds is simply to buy existing assets from other agents included in the NBPS, we know this is not the end of the matter. The accounting dictates it.

      Furthermore, although the NBPS may indeed buy assets from the government or foreign sector, this also has accounting implications. The government can only be a net issuer of financial assets, if it is spending more than it is taxing, and this itself is a function of what is happening with expenditure.

      Ultimately, the answer to what will happen to expenditure depends on portfolio allocation decisions. Very roughly, you have to look at what proportion of the new borrowing will end up recycled back into deposits with the same lenders.

      In terms of the UK economy, I find this general idea a good way of understanding the relationship between mortgage debt house prices and consumer spending. Clearly, such debt is mainly incurred for purchase of existing assets (houses), yet the long-term impact on spending is a powerful one. I believe much of the pattern of household spending over the last couple of decade can be determined from this dynamic alone.

      With regards to borrowing by non-bank financials, there are a couple of points I would make. Firstly, I believe a material part of this borrowing will end up directly recycled back as bank deposits due to the mechanics of cash collateralisation. If the new borrowing can be linked to new lending back to same sector, then the point I was looking at would not apply.

      If there is no such linkage and borrowed funds are simply used to leverage up asset holdings then I would still expect my general idea to hold. There are caveats to it (as I mentioned in the post). I also think that the effect is a slower one for financial assets than housing, because of the way that such assets are held.

  12. Thanks for the detailed reply. I still worry that although mortgage debt expansion gives an immediate boost to overall spending; that is then followed by a long term drain once affordability of debt servicing costs halts the rise in prices. The scenario plays out where all of the surplus production of the economy gets taken as mortgage interest payments and a very very large banking sector is borne by the rest of the economy. The economic drain of having a million extra bankers is much the same as having the Royal family expanded to include the million people next in line to the throne isn't it?

  13. Pretty much agree with that.

    The pattern that this type of model generates is one where new lending creates only a temporary boost. It's not very clear in my charts, I'm afraid, but you'll see in all of them that the lines flatten out. As the graphs show cumulative GDP, what this means is that eventually GDP ends up back where it started.

    This model doesn't include interest payments, but I'd agree that the greater interest burden that comes with higher debt will reduce income. Some of the interest paid to banks is simply recycled back into the economy (as deposit interest and banker's pay), but not all. Part of the UK's growth of household debt has been effectively financed from abroad, as can be seen from the current account deficit.

  14. Hi Nick,

    Interesting article. Two comments/questions:

    - Based on the alternative portfolio equations you present (and which seem correct to me), I find the opposite of what you find: the green and red lines do not cross the blue line, but stay below it (i.e. less cumulative extra GDP in case of more speculative lending).

    - It seems to me that what you show is the difference between direct and indirect consumption, implicitly assuming that extra consumptions does not require investments in productive capacity. It seems to me that the discussions that are going on are more about the difference between investment in new productive capacity versus investment in existing real and financial products.

    Anton van de Haar

  15. Correction on point 1: Nick was correct and I was wrong