Sunday, 25 September 2011

Jubilee Fatigue

The Jubilee is a wonderful idea.  A time when debts are forgiven.  This practice dates back to ancient times and it is wonderful as an idea insofar as it, perhaps temporarily, alleviated some of the suffering indebted humans have experienced, a suffering humanely documented in David Graeber's recent book on debt.  The idea is that, by order of the king, all debts owed are to be written down to zero.  The lender is no longer entitled to get his principal back.  Graeber claims to show how this made some economic sense in times when the burden was so great that there was a growing risk of peasants abandoning the fields and becoming masterless men, and hence not as useful to the rich elites; he ends his book with a single concrete proposal - for the world to enact another debt Jubilee.  This fits with earlier anarchist anti-globalisation demands (of course the  Jubilee 2000 movement takes its name from these cultural phenomena).  I accept that debt forgiveness can sometimes be the best economic outcome for society, if the situation for the indebted is great enough.  This is a lot more certain in my head if the debt is private debt and not government-routed debt, since that raises a whole number of issues around institutional corruption.  Graeber must also likewise believe that debt forgiveness can sometimes be the right thing to do morally, sometimes not.  Since if you always forgive debt, then you weren't making a loan in the first place, but performing a more or less random act of charitable giving, which has its own cultural trajectories.

I'd like to look at a couple of simple mathematical models for the Jubilee event.  As always with mathematical models, the first steps involve a degree of simplification (just like with cultural histories, which perform radical simplifications of human behaviour, but in their own way).

My first assumption, see if you like it, is to state that the enactment or not of a Jubilee year has no effect on the psychologies or degrees of selfishness of lenders.  They are free, of course, to adjust their behaviour, but they still feel the same way about things - about making a profit, about being in the business of lending, etc, regardless of whether the legal domain they're in decided to enact a Jubilee or  not.  In particular, I assume they aren't overcome with any degree of remorse, and they don't start acting in a more forgiving way in their financial dealings.  Nor do I assume they become nastier.  They will just treat this a change in the business climate and adjust their workings, then carry on as before.

Second, of the many kinds of Jubilee humans have experienced, from ancient Egypt to the middle east, I'll focus on the 50 year jubilee of old testament lore, in particular the post 1300 version of christian jubilee which happens every 25 years.  What's important about the specification of the jubilee in the model is how frequently it occurs, and how reliably.  In ancient times, the arrival time was perhaps more random, with a greater or lesser periodic element.  However, I don't want to introduce a stochastic element at this poit nor do I want my periods to be variable.  So I'll just assume that when a culture is in jubilee mode, this means that debts get written down to zero on a 25 year period.  When it is not in jubilee mode, the debtor still needs to pay back the principal.

Next, and solely for the purposes of exposition, I'll assume that everybody's debt matures on the 25 year proposed jubilee year.  In other words, that no-one has a choice on the maturity of the debt - it will always mature on the next 'potential jubilee date.'  So if we are 3 years away from the next potential jubilee year, then you can only strike a 3 year loan.  If you are 24 years away, you can only strike a 24 year loan.  This artificial constraint just makes the analysis simpler, and nothing significant to the argument hangs on it.

Likewise to keep this posting short, assume that the borrowers you see in your lending house are all homogeneously of the same credit quality.   It would be interesting from a historical perspective to know how lenders distinguished the peasants' credit worthiness in practice, but it is probably fair to say that even amongst peasants in a particular geographic region there was probably an income power law distribution.  So your only job as a lender in this simple world I've created is to decide what interest rate (or coupon) you'd like to charge the peasant.  In detail, this can be expressed as three elements a so-called risk free element, and then an element based on your estimate of peasants' creditworthiness, and finally an element which represents your own profit.  To spell this out a bit, when a peasant approaches you to ask for a loan, you might decide to offer him a loan at 10% per annum, where the 10% is made up of a 6% rate to match local government securities whose investment you forgo in order to offer this peasant your money instead, plus a so-called 'credit spread' of 3% based on your own experiences of how often peasant borrowers pay back.

Where's your profit, you might ask, since this could be considered a 'break even' price.  I,e, you could set your credit spread to minimally reflect the aggregate risk of default to you from peasants you make loans to. In other words, if peasants were currently always paying back all their debts, then your fair price would incorporate a very low credit spread, and if there were a lot of peasants who didn't manage to pay back, the credit spread would be higher.  You'll always add on a final slice of interest for your own personal profit, otherwise you are running a charity organisation, not a provider of loans.  This slice can be a big as you are greedy, or as small as you can bear, in order to feed your family.  So what you're doing on each transaction is working out the 'fair' price for the loan for N years to this peasant, given he doesn't have any collateral to hand over to you (if he did you'd reduce the credit spread correspondingly), then adding more on for your own profit.  At this point I'd like to point out that many small scale lenders in local communities across cultures and times were only moderately well off - perhaps they live in the same village, or rented a town shop, or had a family of mouths to feed.

Life is simple in this simple world; let's look at two scenarios.  In one, we're not in jubilee mode, and a peasant walks in to ask for an unsecured loan.  You estimate 10% is a decent rate to offer him.  It is 3 years from the '25 year cycle'. so you know this loan is for 3 years.  Lets say that all loans are for £1

So you know that on this day next year, you expect a payment of £0.1 from the peasant, and £0.1 in year two, and £1.1 in year 3, where you get not only your final interest payment but also your principal back.

You can place a fair value on this loan right now, in case you ever needed to sell it on to your neighbour lender.  It is the discounted present value of all the cash flows.  £0.1 in a year, discounting at the risk free rate of 5% is equivalent to about 9.5p.  The payment at the two year horizon is worth only just about 9p, and the final payment in today's money is just over 94p.  Giving a total in today's money of just a touch over £1.13.

If the king now declares a jubilee, what do you do?  What's there to stop a stampede of people knocking on your door asking to borrow a pound, with the prospect of only paying you back 10p next year, 10p in year two and 10p in year 3?  That sounds like a great deal.  Well, of course, if you're forced to keep your same terms and conditions, then you, and all lenders, would go out of business within minutes of the announcement.  Better just shut up shop immediately, save what you have left, and run away to the sea.

In the absence of a mandate to keep rates the same, and to prevent yourself from rapidly going out of business, you need to come up with a new rate which maintains your business conditions.  If you really were going to enter into a contract with a peasant whereby you lent him £1 right now, but would only get 3 interest payments back, and not the principal, what interest rate would you chose?  Half the work's already done, since we earlier calculated the fair value of the with-principal contract.  It is £1.13.  So, all other things being equal, what would you charge a peasant on such a contract to get back the same fair value?: 49%

That sounds horrendous.  And it is a consequence of a regular jubilee.  But it is important to notice that really it just just a kind of accounting trick.  Both contracts are worth the same - both to the lender and to the peasant.  One is not inherently more unfair than the other - the big interest rate seems usurious but all that's changed is the payment schedule.  In technical terms, the duration has been reduced.  In layman's terms, you're paying is back in more even chunks (just like we do with our mortgage payments).  Of the 49p per year you pay back, actually, only 10% is interest, the rest is early capital repayment.  So if we know with certainty we're in a jubilee mode or we're not in a jubilee mode, the fairness of the loan terms need not change -  but the usefulness might deteriorate, as I'll explain.

In the limit, if you go to a lender and the contract duration is too short, you might not bother asking for the loan, since supposedly you want it to do your own investment or project and perhaps can't afford to pay 49% or more of the loan next year.  So there's a natural floor to the period of certain jubilees.  Above that, everybody adjusts to the state of their world.

Now what happens if there's more uncertainty surrounding the declaration of a jubilee.  Well, you can imagine something similar - only the mathematical calculations would have to involve a probabilistic element. The result is quite different, since the lender can never be certain they'll get the principal back.  Even without running a Monte Carlo simulation you should intuitively appreciate that this uncertainty results in peasant loan interest schedule somewhere between 10% and 49%, based on the probability of jubilee declaration.  (In fact, you could probably work out the implied probability of a jubilee by observing real rates in the marketplace).

The painful conclusion is that you've now asked peasants to pay higher annual interest repayments, even when it turns out no jubilee is declared.  On the other hand, they'll feel like they got a great deal if the jubilee is called.  You've introduced an additional lottery element to lending, and we're all intuitively aware that uncertainty has costs.

So now let's look at the probabilistic process around declaring a jubilee.  Remember, if it is predictable, people adjust and it doesn't have any material effect save from the inconvenience of making loan durations shorten, which is generally not very helpful.  If they were driven not by political dictate but by a genuinely random source, this too would be adjusted for, and rates would adjust likewise.  This lottery dimension has a cost for borrowers and lenders alike in terms of planning their payments.    If it is driven by political and economic circumstances, namely, that the king declares when average welfare is just so dismal, then this too will in time become an observable and measurable phenomenon, with the result that rates rise as we enter dire economic times.  At best this is adjusted for as before, and at worst this triggers a debt deflation spiral. pointlessly increasing human misery.

Insofar as there is even the political possibility of debt forgiveness surely this must, all other things being equal, have a tendency to increase the cost to peasants.  And the moral hazard argument suggests that re-payers subsidise those who fail to pay though having higher rates.  This is less satisfactory than the more certain redistributive model where richer people pay progressively more in taxes to subsidise the poor.  What you've done is side-lined a useful rich/poor redistributive conversation for a much less morally certain one concerning good payers (both rich and poor) versus bad payers (again both rich and poor).  That's a retrograde step.

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