James Mill’s Annuity Approach to Capital Theory – Why was it Forgotten?

A hypothesis. Either the Labour theory of value is true or much less wrong than we are led to believe but we have forgotten the key theory which might demonstrate the theory’s veracity under a capitalist economy.

The period between 1820 and 1830 is widely accepted as the apogee of the Ricardian School of English Political Economy. Ricardo had erected a grand theoretical structure which fundamentally modified the classical economics of Adam Smith. In place of Smith’s ‘adding up’ approach to price where costs of production were added to profits to determine price, wages and profits were inversely related to each other. This necessarily led to the rejection of Smith’s ‘labour commanded’ theory of value – as the factors which determined price were unchanged by changes in wages – instead Ricardo argued for a labour embodied approach to value theory.

The theories outlines in ‘Principles of Political Economy’ were incomplete. The theory worked well for labour and variable capital consumed in production (as my recent series demonstrated) but when it came to unequal fixed capitals, unequal in terms of turnover period and/or ratio between fixed and variable capital, the theory had limitations. Some challenged the labour theory from this perspective, notably Torrens and Malthus, other sought to extend Ricardo’s theory to give a fuller description of fixed capital.

James Mill, De Quicncy and McCulloch were the great popularisers of Ricardo’s ideas, especially after his death. James Mill also had a close working relationship with Ricardo during his lifetime, encouraging him to publish, and especially to simplify and clarify his arguments. James Mill was also by far the most important of these three thinkers as he did much more than the simply popularise and systematise Ricardo’s ideas; he filled in many of the missing theoretical gaps. To James Mill we can credit the not altogether benign influence of the ‘wages fund’ theory and the ‘Theory of Markets’ (also known as Says Law though properly originating in Mill). Though both ideas have an element of truth in them it took over 100 years to disentangle both arguments satisfactorily. Ironically Mill’s main work includes a clear statement of how recessions can arise through excessive savings/demand for money – though it lacked the conceptual link between demand and investment that Keynes added.

With regards to arguably James Mills most important contribution in his own ‘Elements of Political Economy’ (second edition 1825) – his ‘perpetuity theory’ of fixed capital, it has taken nearly 200 and to my mind still has not been fully disentangled. His approach was to try to define precisely the contribution to value of fixed capital. Though framed within the context of the labour theory of value, and how to value unequal capitals on an equal basis the valuation issues this raises apply equally to any objective theory of value including cost of production theories.

His definition of capital was as follows:

Whatever is consumed productively becomes capital (OLL P115)

 

For Ricardo fixed capital remained a puzzle and he struggled with it until his death. Though he knew of James Mills’s theories he considered

 

‘What I call exceptions and modifications of the general rule you appear to me to say come under the general rule itself. Works, vol. IX, p. 127

 

Ricardo neither embraced or explicitly rejected Mill’s Perpetuity approach to capital, indeed I can find no direct mention of it. Ricardo only once mentions the application of the theory to the wine in casks example in his final paper Absolute Value and Exchangable Value. Here he expresses the view that if one takes another commodity as the measure of value its value will be constantly changing against the value of the wine even though no new labour has been expended. From a modern perspective we can say that only a standard commodity can be an invariable measure and with the depreciation of fixed capital a new standard system is being created at every moment in time. I speculate that Ricardo did not tackle directly the perpetuity issue as he had direct experience in this aspect of finance and did not understand its underlying mathematics. Ricardo did fully appreciate the complications arising from time to value theory but did not live long enough to hear the ideas of Senior on Cairns on how time, or rather waiting, can be a cost of production in itself.

 

Marx also was well aware of Mill’s theories over fixed capital and though he endorsed one element of them (the joint production method), and criticised Mills very loose definitions of profit and wages he again never directly addressed Mill’s most interesting contributions. His Paris notebooks and Theories of Surplus Value simply skip over them. Marx often spent little time on ideas he agreed with so a possibility is that he treated much of Mill’s approach of fixed capital as given. As far as I can see the only important economists to properly grapple with Mills ideas were Bohm-Bawerk and Sraffa. Much of Sraffa’s project involved mathematising many of Mill’s ideas. Arguably though Sraffa lost his way over some critical areas of Mill’s ideas, replacing Mills dynamic and monetary view with one based on timeless and moneyless infinitely small slices in time, and hence his theories were incomplete.

 

Why was Mill’s quite sophisticated capital theory misunderstood and forgotten? Firstly the English empirical approach to political economy distrusted mathematicisation and applied the Ricardian vice of logically deriving ideas in causal sequence rather than try to develop a schema where certain coefficients were mutually co-determining. Both Torren’s and Mill’s approaches to Capital theory implied use of simultaneous equations. Lack of knowledge of this technique hobbled the development of classical economics and led to its advancement shifting to the mathematically trained in Germany and Russia. Had Marx fully understood Mills he would not have needed to go down the bland ally of transforming values to prices and the problems this created.

The other reason it was forgotten is that the theoretical and mathematical tools necessary to formalise it were not available for another 80 + years. Only towards the end of the 19^th Century did we get satisfactory treatments of depreciation, net present value and the flow of services from investments in the accounting and finance literature, ten introduced to Economics by Fisher. By the time they had arrived many of the theoretical problems relating to capital in value theory had been forgotten.

A reason perhaps is Mill’s sloppy use of terminology and definitions, quite unlike Ricardo. Mill’s confused wages with profits, so his writings require some formalisation to understand. Another is because as McCulloch said of the elements

‘…it is of too abstract a character to be either popular or of much utility’

Indeed the Elements is a precise but rather difficult book to those without a good grounding in the subject it purports to introduce.

What was Mill’s annuity approach to fixed capital? It was one plank in a capital theory which has eight elements all of which are necessary to give a full picture. Underpinning his approach was his simple doctrine that

either … cost of production consists in labour an capital combined; or that one of these may be resolved into the other. If one of them can be resolved into the other, it follows that cost of production does not consist in both combined (page 52)

To say, therefore, that the value of a product is determined by the value of the capital, is of no use, when you have to go beyond the value of the capital, and ask, what it is by which that value is itself determined.(page 54)

Mill’s project involved exploring the capital element, as follows:

 

1. Reviving the Concept that it is the Combination of Labour and Nature that Create Value – This idea was central to the origins of classical economics in Petty and Cantillon, but in Smith and Ricardo had been deemphasised and confined solely to consideration of rent. In Mill it is brought again to the fore. Mill however noted that free goods from nature don’t create value, and rent from differential natural products transfer’s value, only work can create value. For Mill labour transformed nature and wealth and civilisation was the result of that transformation.
2.  The use of Joint Production to Describe Fixed Capital – this approachwas borrowed from Malthus and Torrens (its originator). Marx approvingly quoted Mills application of this approach but sadly there is no evidence of him actually adopting it. There is a mode of viewing the gross return to the capitalist, which has a tendency to simplify our language, and, so far, has a great advantage to recommend it. The case of fixed and of circulating capitalmay be treated as the same, by merely considering the fixed capital as a product, which is regularly consumed and replaced, by every course of productive operations. The capital, not consumed,may be always taken, as anadditional commodity, the result of the productive process.According to this supposition, the share of the capitalist is always equal to the whole of his capital, together with its profits. (page 47 OLLL Edition)

   The early discussions on Ricardo’s theory’s quickly threw up the problem of how to calculate profits when fixed capital depreciates. You cannot then know profits unless you calculate the funding necessary to secure retention of capital (depreciation). The joint production solution was a brilliant solution. It enabled fixed capital to be treated as a stream in time of value equivalent, if the valuation is correct, to variable capital, potentially aiding the solution to other problems in value theory. The problem was not realised, with economic writings as opposed to accountancy theory, until Sraffa’s and Hotelling’s writings. Many of the simple relationships in single production did not hold in joint production, including raising the potential of negative labour values. Perhaps too much has been made of this as Sraffa himself indicated to Schefold late in life. With fixed capital depreciating at steady interest rates negative labour values simply indicates that it has reached its economic life and is a no longer viable technique, a raise in interest rates can accelerate depreciation bringing this forward. There are a variety of vector based optimising methods available which are capable of showing only positive labour values in viable and economically reproducing techniques treating the general joint production case – which is beyond the scope of this article to explore; however given that a viable fixed capital technique will always have positive labour values up to the point of its economic depreciation, and if it becomes viables after that point (for example due to a fall in interest rates) then it can simply be treated as a free good attracting rent. Therefore it is always possible to compare systems of production of different outputs and calculate the positive ‘reduced’ dated labour values.

   Again Mill was unfortunate in that this correct method of depreciating capital by treating each ‘age’ of a machine as a separate commodity was not mathematically formalised until the end of the 19^Th C by Labelle, and then later Hotelling extended the approach

3. The use of an annuity approach to value fixed capital –

   If two commodities are produced, a bale of silk, for example, for immediate consumption, and a machine, which is an article of fixed capital; it is certain, that if the bale of silk and the machine were produced by the same quantity of labour, and in the same time, they would exactly exchange for one another: quantity of labour would clearly be the regulator of their value. But suppose that the owner of the machine, instead of selling it, is disposed to use it, for the sake of the profits which it brings; what is the real character and nature of his action? Instead of receiving the price of his machine all at once, he takes a deferred payment, so much per annum: he receives, in fact, an annuity, in lieu of the capital sum; an annuity, fixed by the competition of the market, and which is therefore an exact equivalent for the capital sum. Whatever the proportion which the capital sum bears to the annuity, whether it be ten years’ purchase, or twenty years’ purchase, such a proportion is each year’s annuity of the original value of the machine.

   Make now a different supposition: that the machine is an article of
   fixed capital, and not worn out, and let us trace the consequences. It was correctly supposed, in the former case, that 100 days’ labour were expended by wearing out the machine; but 100 days’ labour have not been expended in the second, because the machine is not worn out. Some labour, however, has been expended, because 100 days’ labour in a mass has been applied. How much of it shall we say has been expended? We have an exact measure of it in the equivalent which is paid. If the equivalent which was obtained when the machine was worn out, was a measure of 100 days’ labour, whatever proportion of such equivalent is received as a year’s use of the machine when not worn out, must represent a corresponding proportion of the labour expended upon the machine.

   ‘Capital is allowed to be correctly described under the title of hoarded labour. A portion of capital produced by 100 days’ labour, is 100 days’ hoarded labour. But the whole of the 100 days’ hoarded labour is not expended, when the article constituting the capital is not worn out. A part is expended, and what part? Of this we have no direct, we have only an indirect measure. If capital, paid for by an annuity, is paid for at the rate of 10 per cent, one-tenth of the hoarded labour may be correctly considered as expended in one year. (p56-57)’

   A logical step Mill’s failed to make from this was to treated land as an example of fully durable joint production whose value can be calculated through a perpetuity, which could have led to a comprehensive approach to dealing with land and capital together rather than as separate systems.

   Annuities were known as early as Roman times when they were used to pay retired legionnaires salaries. There cost was calculated using early accurist tables of life expectancy. They were widely used in early 19^th C and sometimes even sold to raise government debt.

   A perpetuity is  ‘ a terminating “stream” of fixed payments, i.e., a collection of payments to be periodically received over a specified period of time’ A perpetuity is an annuity with no end date, it has a non infinite present value providing there is a positive rate of interest. What Mill was arguing is that the value of a the output of an item of fixed capital at a fixed point in future time could be precisely and indirectly calculated by calculating the value of an annuity producing precisely that value during the same time period.
   

   The theory, if correct, would redefine price as being equal to labour to one of price being equal to discounted marginal labour. Let’s take each element in turn.

   If one considers a case of constant returns to scale then the marginal contribution of labour does not factor we need only be concerned with average contributions. If we have declining or increasing returns then production will continue so long as the rate of profit remains above the average rate of profit, the additional contribution to value from the additional does of labour being the marginal contribution of labour. At the optimal quantity demanded in terms of maximisation of profits this will also equal the marginal quantity demanded. The marginal quantity demanded being the labour commanded. Indeed Jevons was explicit that providing labour was treated in such marginal terms he had no objection.

   The second issue relates to discounting. If a piece of fixed capital releases accumulated labour over 2 years then one needs to discount the labour released over that period. The cost of doing so is an opportunity cost – as set out by Senior. What rate to apply? If one compares two capital assets you need only compare the two own rates. In a monetary economy however where returns are capitalised and presented as prices of traded stocks and shares we have a monetary single rate of interest for any term.

   This produces an interesting question – did Marx realise that this method requires treatment of marginal discounted labour values rather than average non-discounted values?

4. Treatment of goods which gain in value over time as fixed capital – The most famous example being wine is a cask, a argument misunderstood and later poorly presented by McCulloch. 
   

   ‘It is said that the exchangeable value of commodities is affected by time, without the intervention of labour; because, when profits of stock must be included, so much must be added for every portion of time which the production of one commodity requires beyond that of another. For example, if the same quantity of labour has produced in the same season a cask of wine, and 20 sacks of flour, they will exchange against one another at the end of the season: but if the owner of the wine places the wine in his cellar, and keeps it for a couple of years, it will be worth more than the 20 sacks of flour, because the profits of stock for the two years must be added to the original price. Here is an addition of value, but here it is affirmed, there has been no new application of labour; quantity of labour, therefore, is not the principle by which exchangeable value is regulated. (p 57)

   …The case of the wine in the cellar coincides exactly with that of a machine worn out in a year, which works by itself without additional labour. The new wine, which is one machine, is replaced by its produce, the old wine, with that addition of value which corresponds with the return to capital employed upon the land; and the account which is to be rendered of the one return, is also the true account of the other. (p59)’

Ricardo in the aforementioned quote clearly did not fully understand Mills original argument, as it was not a case of new value being created without new labour but rather that new labour being released slowly over time.

1. Treatment of money capital as ‘accumulated labour’ – These elements comprised a fairly comprehensive approach to value theory. It supplies a framework which is easily capable of explaining rent as well as value of produced commodities, and via rent to explain the influence on value of monopoly. His perspective on money – seeing it as accumulated value – offers a potential approach (though by him unexplored – this was taken up by Senior and Cairne’s) towards treatment of interest as the cost of waiting and the opportunities forgone when purchasing goods with an inelastic supply – the point of criticism by the early marginalist writers over the generality of objective theories of value.

   The power of Mill’s arguments convinced many of the veracity of the objective theory. Arguably he was too convincing as his theories were not developed and formalised. It lead to the easy consensus that problems concerning capital of different compositions posed no threat to value theory and his son’s premature statement that all issues of value theory had been settled.

   we have no practical means of ascertaining before hand the exact quantity of hoarded labour which goes to production, since the only measure we have of its quantity is the price which it brings.(p65)

   The terms though ‘accumulated labour’ (I have not quite got to the bottom of the issue over whether it was Torrens or Mill who first used this term) or ‘hoarded labour’ are imprecise. It is not that thye fixed capital stores labour like some kind of battery, rather by running they are able to leverage value, alongside living labour (to use Marx’s term) which is equivalent to the discounted amount of labour ’embodied’ that would be used without that leverage at the point in time that the fixed capital was created. At that precise singular instant in time there is no difference between the embodies and commanded measures of value as no monetary, price or value shifts can have taken place to take apart these measures.

   Money can also be seen as the crystallisation of this ability to leverage labour, providing it is circulated. If this is not circulated, or if excessively spent on unproductive purposes, the process of reproduction can be harmed. As such the LTV can be extended to also to cover prices of assets and non-produced goods using ‘proxy’ labour values.

Some Implications – I am not nailing my colours to the mast here and saying that Mills approach solves the outstanding issues of value theory or provides a proof of a (modified) labour theory of value. I am currently building a MATHCAD model to test this. However with Mill’s approach many of the traditional lines of attack on the LTV simply fall away they are not applicable. Also there is no transformation problem if one instead uses temporal discounting to bring everything back to NPV of embodies marginal labour. This also implies that transformation back of output prices to input prices, as used in the TSS or ‘New Solution’ approaches is unnecessary as one consistently uses input prices with discounting used for all future anticipated prices. The key difference being in Mill’s approach the reasons and causations for difference between output and input prices are explained. In the ‘without error’ theories simply one set out values is rubbed out and the corrected values written in Also there is no contradiction between any of Marx’s aggregates. I find this interesting as I did not approach the issue from a Marxian perspective of proving Marx without error (note: though I do think Marx made mistakes in his treatment of depreciation). Some may justifiably claim that by use of marginal measures there is no fundamental disagreement with marginal analysis. However if there is a deeper common value theory basis for both the marginal and LTV approaches then understanding this can be useful, especially as the classical approach adds insights on how pricing is dictated by the structure of property ownership, distribution and access to technology. Finally we should not underestimate how central the LTV was to the Political Economist schema, it made some issues such as trade theory, rent theory, tax theory etc. very simple that today seem opaque and difficult. It was used as a tool by the political economists to make many discoveries. Therefore whether or not the LTV theory fully holds we should be prepared to explore theories which narrow or eliminate those errors and see what results they bring.

Shoot That Beaver Part 4: Clearing Up Confusion About the Labour Theory of Value

‘Im glad were moving on to discuss a more realistic model of capitalism’ It was Marx

‘I have a query, our model as proposed by James Mill supposes that fixed capital releases ‘accumulated labour’, what I call dead labour, to create value – but in my models only living labour can create surplus value and only surplus value can create profits. By Surplus value I mean the difference between the price labour is paid and the price of what they produce In those hours.’

‘That’s not a problem’ It was Ricardo

‘For a process producing a surplus that surplus can either go to labour as wages or to capitalists as profits, or landowners as rent’

‘Yes’ replied Adam Smith

‘So’ Said Ricardo, lets set aside rent for a moment and have the surplus split between wages and profits’

‘In our simplified model there was no profits, the wages share was 100%’ ‘So in that case all ‘surplus value’ flows to wages share’

‘The issue I think is what causes that surplus of value to flow to profits – how do profits arise? Then we have a continuum of wages share from 1 to a lower bound’

‘Excellent’ said Adam Smith ‘Because when you have profits you can have stock and it was the introduction of stock, and land, which I set out as the reasons when my simple labour theory of value is replaced by a cost of production theory’.

‘But Smith’ said Ricardo, ‘if we can introduced capital in the way we have suggested we will be two thirds of the way to a full labour theory of value’.

‘Perhaps we are seeing things the wrong way’ suggested Babbage

‘Perhaps it isn’t profits which create stock but rather the converse’

‘Give us an example’ asked Smith

‘Well in our friction-free economy we had people switching between lines of production during the working day to maximise their rate of surplus’

‘Doing so however creates a downtime between lines’ ‘And you may be working on a line which is not your main area of expertise forcing you to extend your working day’

‘However imagine a firm is formed which offers to employ labour but without this switching this attracts a higher rate of surplus – which can then be split between wages to attract the additional labour and profits’

‘A rare example in labour having a choice’ said Marx

‘Even here independent labour not hold out for long if the advantages in terms of division of labour the company possesses are superior’ replied Babbage

‘What is interesting’ added Adam Smith ‘Is that the additional returns to stock, to equity don’t arise from any return to what is conventionally termed a factor return – they return to a particular manner in which those factors are employed together in a firm’

‘Yes’ it was Schumpeter ‘Unless you term entrepreneurship in combining those factors as also a factor’

‘Can we think of other ways in which a firm can attract profits by virtue of its activities as a firm’ asked Adam Smith

‘Easy’ added Schumpeter ‘they can innovate in technique and so long as their competitors cannot keep up they earn what I term ‘super profits’.

‘Why not just profits’ added James Mill ‘After all in perfect competition there is no profits’.

‘Ok’ said Adam Smith ‘ Lets say I invent a new type of arrow machine and other don’t know about it and cant copy it – am I not then able to earn this additional sum?’

‘Yes’ replied Schumpeter ‘You can then either produce arrows with the machine yourself, produce the machines and sell or lease them to manufacturers or franchise the plans for production of the machine’ ‘Both capital owner and manufacturer are indifferent to the ownership of a capital good, it is the income stream from the services it provides that matters’

‘This franchise value is interesting’ said James Mill as you suggest that all three cases are the same as the ‘franchise value’ of a firm whose sole purpose would be to produced the enhanced machine’

‘Franchise value being the book value of a firm operating as a firm aside from its income streams from property, stock, asset sales etc. It is the value resulting from Entrepreneurship and/or Monopoly – without making any value judgement about the ethics of how the source of innovation or monopoly was obtained.’

‘I can see where you are coming from’ said Adam Smith ‘The source of Profits is the franchise value of a firm, added to which are revenues from renting or selling assets it owns’

‘But is not this franchise value also an asset, an intangible one’ Added Hotelling ‘And all income streams from assets are forms of monopoly rents’

‘I like the rent analogy’ added Ricardo ‘It seems to me there are two ways in which the actions of a firm can rise the margins of a process, firstly through innovation it can rise the productivity of labour creating surplus, an intensive margin, secondly through cornering a market by procuring an advantage it can extract surplus from others, an extensive margin’

‘And rent at the extensive margin does not add to price’ added Sraffa

‘So by reconceptualising profits as a form of rent we are able to maintain our modified form of the labour theory of value’ added James Mill ‘Rent does not create value’

In Part 5 ill look at the relationship between demand and price.

Shoot that Beaver Part 3: Clearing Up Confusion About the Labour Theory of Value

‘Im glad you talking about discounts’ It was Fisher.

‘You can calculate the economic depreciation using Sraffa’s formula if you have a rate of return on the machine, which you can do using Hotelling’s maximising method, that way you are calculating the ‘own rate of interest’ on the process to use Sraffa term. Once you know the ‘own rate’ you can then apply that in my Net Present Value formula to discount the value of the goods at the point of sale to the point of capital advanced’

‘Hmm’ Marx was thinking ‘This is a transformation – but a transformation in time – rather it’s a recalculation, of output prices to real input prices.

‘Indeed’ said Fisher ‘And you can also use another of my formulas to calculate the real cost of inflation, this way you have an approach which enables you to calculate viable investments’

‘Yes’ replied Marx ‘some of my followers have applied an approach which recalculate input prices at output price values, The TSS School. The problems is they simply calculate the difference and rub out one set of numbers and write the other in’

‘You’ve been reading Samuelson’ quipped Adam Smith

‘Quite there is no better device to use then you opponents, that’s dialectics for you’

‘What opponents of the recalculation approach say is that business don’t do that – but they do it every day, accountants do it recalculating input prices at anticipated output prices to see if investments are viable, and unlike the TSS school we have had no need of an eraser’

Torrens was intrigued, ‘Of course the big problem with the pure Ricardian approach was time, we had to make all kinds of exceptions for when different processes involved different lengths of time, different turnover, the lifetime of a capital good, because its turnover would be different from the good produced, and the proportion of variable capital and fixed capital because they would have different turnovers’.

‘Yes’ said Marx ‘ I sum these features up in my organic composition of capital’ idea, the ratio between fixed and variable capital in any process, it is the variation of this between processes which account for variance between cost of production and embodied labour values’

‘I can see the direction of your reasoning’ said Ricardo, ‘if we have a means of recalculating all prices so it was if they took place in the same time frame, an instant, as Fisher suggests then those valuation issues go away, we may have an approach which not only applies in a primitive profit free, fixed capital free economy but any economy’

Before we explore that ‘said James Mill ‘id like to explore exactly how you calculate the rate of surplus on a machine, based on the cost of the machine alone or the fixed and variable costs together?

‘Together’ said Sraffa

‘Then you also need to discount variable capital costs including labour inputs’ said James Mill ‘But in a different way, the turnover time is different, and if you don’t employ ‘just in time’ then you need to discount for the time inventory os kept in stock.

‘So’ said Adam Smith ‘ The approach suggested seems to imply a formula, he scratched in the sand

Labour Value=NPV variable capital labour +NPV fixed capital labour

‘Yes’ said Fisher

‘Lets add one small enhancement’ it was Jevons

‘Imagine we don’t have constant returns to scale – that rather we had Adam Smith’s increasing returns or even decreasing returns whatever’

‘Then if a capitalist is considering hiring or firing one units of labour he or she must then consider the marginal contribution of labour, so I would rewrite it.

Marginal Labour Value= NPV variable capital marginal labour +NPV fixed capital marginal labour

‘I shall leave aside marginal consumption issues for a moment as in this simple model we have no ability to gain a premium from scarcity’

‘I always argued that if one considered marginal labour then the marginal theory of value was the same as the labour theory, here we are approaching a proof’

‘Aha so if any marginalists challenge this theory that are also challenging their own theory’ Ricardo was unusually pleased.

‘So in the final analysis’ said James Mill, price is equal to

Sum
NPV variable capital marginal labour +NPV fixed capital marginal labour

‘And again’ said Hotelling, you can use my maximising method to determine the maximum rate of surplus

‘So in the final analysis’ asked Fisher, why use a labour theory

‘Because it connects you to objective reality’ replied Ricardo

‘A purely subjective economy does not exist, the economy is about connections between real things, some of which are more scarce than other and take longer to make than others, by using the LTV we can easily calculate labour and this as later economists have stressed enables you to calculate unemployment and effectual demand its joined up, the distinctions between ‘micro and macro’ are irrelevant as ‘political economy’ always claimed’

Babbage sighed he was going to have to do a lot or programming in Victorian Mathcad

‘Ok’ said Adam Smith ‘We have made good progress in our friction free, scarcity free, rent free, profit free world, lets mix things up and see if this approach applies to modern capitalism’

Continued in part 4

 

 

Shoot that Beaver Part 2: Clearing Up Confusion About the Labour Theory of Value

Ricardo was sceptical

‘Well we will see’ said Mr Ricardo, the quantity will change, but the prices will remain the same – just you see

‘if my theory labour embodied in the proper measure’ is correct then shifts in demand caused by equalisation of factor returns will see a shift in demand but not a shift in price’

Maybe so’ said Torrens ‘But we have a situation where the capital good trades at the price of the labour it commands not embodies, whilst the consumption goods trade at labour embodied’

‘Aha’ said Adam Smith ‘So in our state of pure competition if the labour commanded is greater than the labour embodied then the it will be rational to stay in that line of production, unless more productive lines come along, whilst others will be attracted to labour in that line, with the same provisio, whilst if the converse is the case it is rational to withdraw ones labour from that line of production into lines with a higher rate of surplus.’ ‘So it does not matter if for a time labour embodies and labour commanded are different, over time they will come together to the same rate – in the long run – at least in the frictionless profit free economy we have theorised’.

Babbage was puzzled by his next print out.

‘There is no stable solution, with different value rates of surplus labour shifts to the higher surplus lines of production, but this changes the prices which causes labour to reallocate’ ‘As labour shifts the labour commanded value of arrows shifts back to 2.5, interesting the original labour embodied value, but now both deer and beavers have rates of surplus less than 1 so none hunts deer or beavers and so noone buys arrows’.

‘Hmm’ chipped in James Mill ‘I think you have another hidden assumption, there is a gap in between the labour embodied and labour commanded prices of the variable capital good – so if Mr Ricardo is right and labour embodied alone determines value then we must be missing some aspect of labour embodied. And I think I know what it is – the labour accumulated in the fixed capital of the machines Adam Smith uses to make the arrows. If this is corrected then their will be equal rates of surplus.’

‘Very interesting’ said Adam Smith ‘But first I would like to hear from Mr Ricardo his justification for thinking that only labour embodied determines value’

‘Thank you’ said Ricard ‘For many less rigorous neo-classical economist have found my passages on the subject ‘notoriously difficult’ so let me give you a simple explanation’

‘Labour commanded is the value of labour that an amount of produced goods can purchase’

‘But this is not an invariant measure of value, in some years the labour commanded value may rise but the real wage, the amount of consumer goods such as corn that can be bought with the labour commanded, can fall, So it is not an invariant value. Labour may sometimes purchase greater, and sometimes a smaller quantity of goods, so it is the value of the goods which varies, not that of the labour the wages from which purchase the goods, which has not varied’

‘Yes’ said James Mill ‘Your argument is often stated as one of needing to have an invariant measure of value before you can tackle the issue, but people often miss the importance of TIME in your argument.’

‘Precisely’

‘The external factors such as bard harvest, war, restrictions on imports, these are what change the price of corn’.

‘Ok’ said Torrens, but in our model we have a completely frictionless economy, without war or storms or anything, so what it is that causes the discrepancy between labour embodied and labour commanded?’

‘There is no discrepancy’ said James Mill ‘We have miscalculated labour embodied’ ‘We have missed the value, the accumulated labour, that the fixed capital of the arrow making machine passes on to the arrows and then on to the value of the deer and beavers’ ‘The labour embodied value of the arrows was 2.5 dubloons, the labour commanded value 10 dubloons, I submit that the machinery Smith owns adds 7.5 hours of ‘accumulated labour’ per day.’

‘Aha’ interjected Marx ‘But because of depreciation dead labour – what you term ‘accumulated labour’ cannot add to value, only living labour. That labour applied at the point of production alongside variable capital can do so’

‘But you are wrong’ Said Adam Smith ‘Having now got an eternity to study depreciation we can apply the correct mathematics for depreciation and see if Mill was right, if you were right Marx no-one would ever accumulate capital for form fixed capital goods they would have no advantage in doing so’

‘You see depreciation is an expense – a cost – a price – which must be determined at the same time as all other prices – simultaneously – isn’t that right Hotelling’

‘Quite so’

‘Accountants Mr Smith use the matching principle to match that cost over the economic life of the capital good, note the economic life not the physical life which might be less’

‘This is because the cost of expenses for the fixed capital may be less than its output, however if the capital still has a physical life left may still have a positive scrappage value. Whilst if you have completed your depreciation fund to buy a new machine you don’t need to depreciate it again – it is sunk capital, so it may become economic to keep it in use or sell it.

Such sunk cost capital however is a different commodity to a newly produced capital good, in our simple economy we are only considering produced goods, not found or seized commodities that were not paid for and provide their services for free. Those goods attract rent, not profit or wages’

‘So we should only consider the depreciation and use of the arrow machine during its economic life?’ Asked Smith

‘Correct’ replied Hotelling ‘

‘But we can only calculate that if we know the rate of return on the machine or else we won’t know how long a period to depreciate over, and if we don’t know the cost of depreciation how can we calculate that?’ Asked Ricardo puzzled for once.

‘Not a problem’ replied Hotelling, using my formula you can calculate the returns for each age of the machine, the term which produces the maximum surplus of outputs over inputs is the economic period of depreciation, you then use the matching principle over that period to calculate the value of the per-period depreciation fund’

‘not as simple as that’ Sraffa had arrived.

‘You are rightly treated fixed capital of different ages as separate products – quite rightly – this is an example of joint production – each period production create two products not one, the fixed capital and the consumer good’

‘why does that make a difference’ Asked Torrens, pleased that his method was being applied.

‘Because, and this is a tough one, the assumption behind labour embodied calculations for a product is that the product is the same over the period in which you calculate labour – its called the ‘reduction to dated labour’

‘With joint products you have you have one product, the fixed capital product, which is brand new, so you have to calculate the imputed labour which would have been necessary to produce a machine of that age’

‘Like say purchasing an old machine and repairing it to the same standard as a new one>’ Asked Ricardo

‘Correct’ said Sraffa ‘now with joint products you get two or more prices, so to isolate the component of fixed capital to get its embodied labour you can get negative labour inputs – I know of no reasonable interpretation of this.

‘Hang on’ said James Mill

‘I posited that if we calculated the accumulated labour inputs to the fixed capital good we would bridge the gap between labour commanded and labour embodied, Sraffa seems to be implying that of we did that our calculation would be too high because of negative labour inputs – so instead of understating the embodied labour we would be overstating it.

However, and here’s a thought, what of we then knocked off this negative value from the total embodied labour – what if we ‘discounted’ it, if we come up with a correct method to calculate this discount rate for each product would we not have proven the labour embodied theory of value?’

‘In this approach the value of embodied labour would always be positive if the rate of surplus of the process using labour is sufficient to cover economic depreciation, by using the matching principle negative labour values have an economic interpretation, they are gross input values not net output values. New output values must be positive in a viable process’.

‘Indeed labour embodied and labour commanded values would be the same’ replied Adam Smith ‘All the fuss over the difference’

‘But how do we calculate the discount rates for each product?’ asked Marx

‘And would such rates be consistent with equilibrium prices? Added Hotelling

Continued in part 3

Shoot that Beaver – Clearing Up Confusions About the Labour Theory of Value

Few concepts have caused more confusion in economics than the Labour Theory of Value. Many of the arguments both for and against it have hidden assumptions. This post is an attempt to get to the bottom of the principal issues.

Robinson Crusoe had long departed the Island but instead a party of Economists and Philosophers had been shipwrecked on the way to an ill judged conference in the New World . They quickly saw it as an opportunity to test their ideas.

‘Ok’ said Locke, ‘why don’t I hunt beaver and you Hume hunt deer and we will see how we do’. Neither could imagine Adam Smith hunting beaver.

They decided to use as means of exchange some old dubloons dividing them up equally. Adam Smith advised that so long as the value of the coins was less than the costs of mining and minting new ones it would hold its value.

‘Right’ said Hume, today with 10 hours labour I’ve managed 3 deer, how many beavers Locke’ – ‘two for 10 hours also’.

‘So in terms of equal effort the exchange of deer to beavers is 3:2, 3 1/3 hours labour for beavers and 5 for deer. So if we set 1 dubloon equal to 1 hour then deer cost 3 1/3 dubloons and beavers 5. We are not seeking to hypothesise about the origins of money here simply to use it as a means of exchange in our calculation’.

‘Right’ replied Locke, why do we know that this is a correct price, what if for example I had only worked two hours or been really inefficient and others could be more efficient?’

‘Competition’ chipped in Adam Smith. If someone charges too high a price for the effort involved then you might as well do it yourself, if they charge too low they will be working more hours than others for the same return. That’s why I say the price of goods is equal to the labour commanded by them, which is equal to the amount of labour undertaken in their production.’

‘Ok’ said Hume, it’s what old Weiser calls ‘opportunity cost’ the ‘disutility’ of labour, but who is making a profit here?

‘No one’ ‘each party is covering the cost of their labour and reproducing themselves as a worker. They are realising a small physical surplus which they and their families consume. If the return was less than the ability of each to reproduce their labour they would withdraw it and enter another occupation. I think many of my readers have got confused on this issue confusing a physical surplus per-se with profit, and returns to one factor or another, such as capital, with profit.’

‘Right’ said Locke ‘ We are getting to the bottom of things’ ‘Your later commentators, such as Engels I think, said this simple labour theory of value only operated under barter, I think we have shown with our monetary system that this is not correct’

‘Yes’ said Smith ‘let’s be clear what I did say’

‘In that early and rude state of society which precedes both the accumulation of stock and the appropriation of land …’ (p 65; Oxford/Liberty Fund edition)

‘So I was saying that it didn’t apply when there is rent’ ‘The phrase ‘accumulation of stock’ is often misinterpreted, stock cannot accumulate unless there is a separate entity a firm, which is profitable, the capitalisation of which is the value of the stock. In our simple system there is no profits rather each is self-employed, so each simply earns a factor income, wages for sale of consumer goods for Hume and Locke and wages for sale of capital goods for myselfurn on the capital goods is not profit, I could rent them out for example and under the free completion assumption we have adopted the returns are driven down to just that necessary to retain it in production’.

‘I note Ricardo is arguing with some other Economist at the other end of the beach, I think they may join in with our discussions later.’

‘But isn’t there a set of hidden assumptions’ replied Hume ‘firstly in this simple exchange there is no capital goods and no land only one factor labour’

‘correct’

‘Also you assume as you stated that there is what our successors called ‘perfect competition’ that anyone can enter cost free another goods market and produce goods in it’

‘That is right’ said Smith ‘I made quite clear in the Wealth of Nations that under such ‘perfect competition’ there is no ‘profit’ above the return of factors – and m friends Ricardo and Marx would like to discuss that later, about whether the theory holds in cases when there is profit,

‘but first lets see if the theory holds if we introduce capital goods’.

‘Great’ said Hume ‘what do you have in mind?

‘Well said Smith I’ve been saving some food and that has enabled me to spend a day whipping up some bows and flint arrows. Smith had managed to make 20 arrows. ‘The bows are a gift just pay me for the arrows’. ‘Oh and lets ignore that Voletrra chap for a moment and imagine an infinite number of deer. Note this means that initially we will only be dealing with ‘variable’ capital, capital consumed alongside labour, rather than ‘durable’ or ‘fixed’ capital which I would hope we look at later.’

So off Hume and Locke went and spent a day hunting. Hume this time managed 7 Deer, Locke only 3 beavers as the arrows were less effective given Beavers Tendency to duck underwater.

They met at the end of the day.

‘Ok’ said Smith ‘ How many Deers and Beavers are you going to give me for my arrows’

Locke noted that they had each used up 10 arrows in the day ‘I think our successors called this depreciation’

‘Yes terrible of me to omit this in my writings’ said Smith

‘So you will each need to set aside a fund, a depreciation fund, each day to buy new arrows. The fact that they only last a day makes that easy to calculate’

‘My productivity has been increased by 50%’ said Hume, ‘so rather than 2 hours labour for a deer its 1’

‘So has mine’ said Locke, but less so ‘rather than 5 hours to catch one beaver its now 3 1/3’.

‘So now do deer and beavers exchange at the ratio of 5:3 1/3?’

‘Hang on’ said Smith, so how much are you going to pay me for 10 arrows?

‘ Well’ said Hume ‘if the labour theory is correct then you spend 1/2 hour on each arrow so that’s what I should pay you ½ hours worth of Deer in dubloons’

‘But you will be paying me ½ your daily output for a capital goods which doubles your output’ replied Smith ‘you would be no better off’.

‘Its even worse for Locke, he would be paying me half his daily output for a decrease in the production he takes home, from 2 Beavers to 1 1/2 , he would be worse off and so rationally would not use arrows.’

‘But I’d already worked that out so I’ve developed a more efficient method, I’ve cast the arrows in metal, now I can make 40 in a day. What difference does that now make?’

‘Ok’ said Hume now I can shoot 20 Deer a day, each ½ an hours labour, ½ a dubloon, the arrows are now ¼ of an hours labour so if I give you 2 ½ hours labours worth, 2 ½ dubloons worth or 5 Deer, then I will make 7 ½ dubloons a day when before I made 7.’

‘And for me’ said Locke, ‘its now 1 1/6 hours per beaver, 6 beavers a day so if I pay you Smith 2 ½ dubloons worth of Beaver which is 1 1/6 x 2 ½ = 2.0167 beavers I will have 6-2.0167 beavers left at the end of the day 3.983333 beaver which is worth 4.64 dubloons.

‘And I’, said Smith, ‘will make 3,983333+7.5 dubloons a day = 11.4833 dubloons a day I’m quids in! – though to be fair we haven’t calculated my outlay costs’.

Hang on, said Torrens overhearing, there’s a problem. If Smith makes over 11 dubloons a day (perhaps less when we consider cost of metal) and Locke only makes just under 4 why should not Locke make only arrows, indeed why should even Hume not make only arrows?’

‘Because if we only made arrows we would have no-one to sell arrows to, nothing to eat and no hats to wear’ Said Hume, rather pleased with himself.

Precisely, said Torrens ‘Imagine I was investing in one or another of your three processes’ ‘I would invest in the one which makes the most profit’, ‘But equal capitals must produce equal value, as I have said many times, which means competition again, as Smith and Ricardo have emphasised is the levelling factor, a price will exist that equals out that rate of return.’

‘But the rate of surplus (in price terms) here must be equal across all three goods’ says Adam Smith ‘otherwise someone would transfer their labour to another good’s production, although in this simplified case the rate of surplus is measured in wage units, so we don’t need to calculate them separately’.

‘But would then will we still have a zero rate of profit?’ said Locke.

‘Let’s work it out’, sad Torrens, ‘and lets be careful not to mistake a surplus from a profit if is simple a higher wage return on labour, lets instead look at the ratio between monetary value of the inputs to production and outputs from production’.

‘Remember our constraints, we need a set of prices which ensure the rate of return on all three goods in monetary terms is equal, otherwise capital in advance will switch to other lines of production, and the monetary return per unit of labour is the same otherwise labour will switch ‘.

‘Please also note how simplified our system is, no profit, no stocks, no lending, no interest, a constant period of turnover of 1 day and only variable capital not fixed capital’ Said Torrens

‘There is savings however to advance towards the variable capital produced, what Mc Culloch in a phrase I adopted called ‘accumulated labour’.

‘These are precisely the qualifiers which I and Malthus stated meant that when they didn’t apply the ‘simple’ labour theory of value would not hold.’ ‘Also returns are constant, so the average value of labour is the same as the marginal contribution’.

‘Babbage over here has programmed Mathcad Victorian Edition into his difference Engine’ ‘Babbage what’s the results?’

After much wirring and cranking the results were punched out

‘The first run is without any reallocation of labour’

‘Assuming a numeraire of a hours labour equal 1 dubloon the price of beavers is 5 dubloons, the price of deer is 16.667 dubloons and the price of arrows is 10 dubloons’

‘So lets work out the rate of surplus again for each line of production’, said Hume ‘because it seems these are radically different and so labour would be reallocated’

Babbage scribbled some notes

‘As the input hours are the same we can ignore them as they make no difference to the calculation Hume advances funding for 10 arrows worth 100 dubloons, the output is 20 beavers worth 333.3 dubloons, so the rate of surplus is 3 1/3’

‘For Locke he also advances 100 dubloons, his output is 6 beavers worth 30 dubloons so his rate of surplus is -0.66

‘For Adam Smith we haven’t calculated his input, but for simplicity assume his input is metal which costs 100 dubloons a day, his output is 40 arrows worth 400 a day so Smiths rate of surplus is 4’

‘So we have the same problem again’ said Torrens ‘Shooting beavers is not a viable technique, so labour and capital will be reallocated to the other two lines and unless the rate of surplus is even for both ‘in equilibrium’ then capital ‘accumulated labour, and ‘live labour’ as Marx calls it will continue to be reallocated.

‘So lets do the calculations again with these assumptions’ said Babbage, and perhaps we should ask Ricardo’s opinions as he stresses this process of reallocating capital and labour.

‘This is interesting, without production of beavers then the prices of everything else remains the same’

‘Indeed they must’ its was Ricardo ‘as the labour embodies in each product is the same’ ‘If we divide the budget, 100 dubloons, by the labour ratios of your first calculation you come up with the same price, 16.66 dubloons for Deer and so on – so a simultaneous equation was unnecessary, the system was ‘overdetermined’

‘I was wondering when you were going to ask for our opinions’ Said Ricardo arriving with his friends. ‘I would very much like to explore the impact of the variables Torrens set out on the Theory, as well as any impact of differences between ‘labour embodied’ in production and ‘labour commanded’ by the value of what is produced.’

‘Things are going to get a lot less empirical’ signed Adam Smith

‘Not necessarily’ said Ricardo, with Babbage’s Engine we can quickly test and simulate our theories so lets do it.

‘Lets try this again’ said Babbage ‘Hume will reallocate some of his labour to making arrows until the rate of surplus in both arrows and deers is the same. ‘ ‘The total ‘given demand’ to use malthus’s phrase, or ‘effective demand’ to use Keynes’s is set at 200 dubloons for the turnover period, we assume no hoarding, no savings’

The story picks up in part 2.

Creating money without an accompanying asset – the Rowe – Keen discussion on bank assets

Nick Rowe has an interesting thread with a number of good contributions about Steve Keen’s Theory of Effective demand.

Here’s what I think Steve Keen is maybe trying to say:

Aggregate planned nominal expenditure equals aggregate expected nominal income plus amount of new money created by the banking system minus increase in the stock of money demanded. (All four terms in that equation have the units dollars per month, and all are referring to the same month, or whatever.)

And let’s assume that people actually realise their planned expenditures, which is a reasonable assumption for an economy where goods and productive resources are in excess supply, so that aggregate planned nominal expenditure equals aggregate actual nominal expenditure. And let’s recognise that aggregate actual nominal expenditure is the same as actual nominal income, by accounting identity. So the original equation now becomes:

Aggregate actual nominal income equals aggregate expected nominal income plus amount of new money created by the banking system minus increase in the stock of money demanded.

Nothing in the above violates any national income accounting identity.

Only last year he said he didn’t get it, but clearly has had second thoughts.

Much of this lack of understanding comes from confusion about the tools used. Those used to thinking in terms of ex-post accounting identities have struggled with whether there is an exposte- ex ante discrepancy. Those used to fixed periods and thinking of money as a stock struggle with how to conceptualise income and spending as instantaneous time flows. Those used to the GDP definition of income as deriving from value added struggle with how net purchases and sales of assets affect income. Those used to the loanable funds approach struggle with how demand can be affected by debt which they simply see as a transfer of existing income. Thankfully most but not all) of these issues have been tackled through Keens adoption of a double entry approach and its mathematisation with the aid of the Fields Institute. Most of the comments dealt with such issues of clarification and misunderstanding and I wont repeat them here, you can read the original thread and comments. Its us small usual bunch of monetary theory suspects im afraid, we could all fit in a telephone box.

Keen responded on Nick’s Blog

you’ve done a very good job of providing a Rosetta Stone between standard Neoclassical macroeconomics, and the perspective on endogenous money macroeconomics that I put forward

and then more fully on his own that

This is the first concerted (and very accurate) attempt to put my endogenous money approach in a form that Neoclassically trained economists can understand. This could be the start of a real dialogue in economics.

A quick note on Nick’s approach then ill look at an unresolved issue or two from the blog debate.

Keen has traditionally tackled the issue from actual realised income then placed back in the monetary circuit i.e. not saved (hoarded). Nick reformulates this in terms of the language of intertemporal optimisation beloved of neoclassical economics.

To give a very simple example lets say someone earned a disposable income of 10,000 dollars a month and they save 5,000 a month totalling 100,000 over time towards deposit on a house requiring a 500,000 loan. In previous months there actual nominal income 5,000 dollars equals expected nominal income (10,000 dollars) minus ‘increase in the stock of money demanded’ – savings in plain English – (5,000 dollars). In the month they get a loan there realized expenditure is 10,000 dollars minus, plus the 100,000 loan plus 10,000 disavings.

Keen has never explicitly covered the treatment of savings in this manner but I have long felt, and said a number of times on this blog, that his logic implies such a treatment. Indeed a number of historical predecessors of Keens approach to the circuit such as Norton and Johannssen.

Outstanding issues though concern what happens when a bank credits money without an accompanying financial asset and the difference between banks and nonfinancial institutions.

Rowe on this

Steve…If I sell my computer to my bank, the money supply expands. If I then buy that computer back from my bank, the money supply contracts.

Similarly: If I sell my IOU to the bank (if i take out a loan), the money supply expands. If I then buy that IOU back from the bank (if I repay the loan), the money supply contracts…

What’s special about banks is not what they buy with the money they create, but that they create money. And thinking about banks as buying and selling computers or land can help us make that distinction more clearly.

Steve replies

No, in the first case the bank is making a purchase of a commodity from you that it has to source from the liabilities and equity side of its ledger–not the asset side. To do otherwise is to commit seignorage–to use its capability to produce the IOUs we all use for transactions for its own use. So when a bank buys goods from non-banks, it uses the funds it has legitimately earned from its business of lending, not by using its capacity to create money. So there is no change in the money supply in either case.

He expands on this in his own blog

ending by an S&L … transfers money from its bank account to the borrower’s account, and therefore does not alter the total amount of money in existence. Lending by a bank … increases both the bank’s assets and its liabilities and thus increases the amount of money in existence. If workers try to get out of money and into gold .., they reduce their bank accounts but increase those of the dealers from whom they buy the gold….The only action that can take money out of the banking system is a withdrawal of money as cash

Nick Edmonds on the other hand, expanding his point on his own blog, disagrees. He argues from T accounts and accounting identities that non-bank financial institutions lending does increase the amount of money in circulation but not the overall stock of money and so this can have similar affects, though ultimately the ability to do so will be limited by the amount of savings they can attract.

Rowe in summing up his approach

Steve: I think (maybe) the biggest difference between us (in this context!) is that you focus more on the asset side and I focus more on the liabilities side of banks’ balance sheets. Let me state my view, to see if this clarifies things.

What’s on the asset side matters for a bank’s solvency and liquidity if people want to redeem their money. This matters a lot for commercial banks, which promise to redeem their money at a fixed exchange rate for central bank money. It matters also for central banks that promise to redeem their monetary liabilities at a fixed exchange rate for gold or USD or some other good. … If there’s a risk of insolvency or a bank run, the size and composition of the asset side matters. But provided the assets are good enough so we can ignore those risks, it is only the liabilities side that matters in the money-creation process.

So in my view:

A bank buying an IOU

A bank buying a computer

A bank buying a meal at a restaurant for its staff to celebrate Christmas

A bank giving money to charity

are all the same, in terms of creating money, and their effects on the liabilities side, though they will have very different effects on the asset side.

Ok the way I think about it is to distinguish between clearing banks and bank like institutions, shadows banks (including mutual funds utilising fractional reserve lending), and none bank financial intuitions (S&Ls, full reserve savings banks and the like) as each has very different mechanisms to back the credits they issue.

Whats special about banks?

Lets say a bank buys a computer, to use Nick’s example, if the computer company has an account at the same bank they can simply credit money in their account. If they don’t they can simply issue a cheque and create the money to redeem it, the end result is the same. The bank has increased its liabilities without creating an accompanying asset, the same as giving the money to charity. The key restraint on them doing so however is their balance sheet. A bank cannot issue money to buy the whole world’s supply of computers, they are restrained in doing so by the right hand side of their balance sheet, their capital, their equity, retained earnings and assets. Keen has tried to develop a theoretical approach whereby bank’s ability to lend is constrained by their charter value, the intangible asset that banks trade on from being a bank able to credit money and engage in fractional reserve lending/maturity transformation. I have tried to expand this into a mathematical model that takes account of banks capital and reserve ratios. I term this the lending power approach reviving a term from early endogenous banking theory.

Banks cannot expand their lending books without cost, and neither can they expend their asset of lending power on none loans (as in Nicks example) without opportunity cost. A bank forgoes potential profit on a loan in favour of a diversified portfolio which includes assets with a rate of return which may be higher than loans. This is the approach to bank portfolios which the later Toblin explored in several papers.

If a bank credits an account or redeems a cheque the Central Bank will accommodate that monetary demand. If they do so in terms of a loan then the creation of money will be cancelled out over the term of the loan by debt repayments and the bank as interest as profit. This interest payment is simply a transfer payment from the non-bank sector to the bank sector. If it credits a liability without creating an asset then it must run down an existing asset to stay solvent, which must come from pre-existing savings and profits. So the effect on the liabilities side is the same (Nick is right about this) but Nick neglects the constraints on banks ability to do so and that they can only do so through dissaving, which is already included in this framework.

Similarly Nick Edmonds argument is another case of a credit without an asset creation – as only banks and shadow banks can do so (the only difference between banks and shadow banks is that the central bank acts as lender of last resort for the former only, and clearance of final payments occurs through banks only), which also involves dissaving. Lets give an example. Lets say savings and loans typically create x billion of loans over a period and this is cancelled out by x billion of savings. Lets say interest rates change and there is a net increase of lending and net dissaving. Then from the formula above we have a net change in debt and a net dissaving, which cancel each other out.

Therefore only bank and shadow bank lending has a net macroeconomic effect.

How Quickly Does A Hot Potato Get Cold? Moving the Endogenous Money Debate On After Krugman’s Mea Culpa

It seems like the debate on endogenous money has moved on to new ground with not just Krugman but Scott Sumner now saying pah – so what! Lets now hope that the debate moves on to a higher level.

Krugman in supporting Tobins paper ‘Commercial Banks as Creators of Money’ says this refutes

refutes, in one fell swoop, the nonsense one hears about how said mechanics of bank lending change everything about the role banks play in the economy.

Whilst for Sumner

I get lots of commenters coming over here breathlessly telling me the wonderful news—it’s been discovered that banks don’t actually loan out reserves! How does one even respond to that sort of ferver?  Now I have a simple answer; “it’s a simultaneous system.”

Indeed the debate over the causality of the monetary transmission mechanism has obscured a much older and deeper theoretical debate which I hope we can now return because it is has never been comprehensively resolved. Wray’s recent post saying the debate goes back to the banking/currency school debate telling as I had started a post saying similar.

the 1980s debate over “exogenous” versus “endogenous” money was in a sense a reprise of the Banking School-Currency School controversy of the early 19th century. The Banking School took the endogenous money side, while the Currency School was a precursor to Milton Friedman’s Monetarist exogenous money.

Before we start digging into the relevance of this economic history this lets consider where I think Krugman is coming from. To my mind both he and Sumner both are exhibiting the Woodfordian brand of monetarism which is now dominant, the only distinction in their assumed models is Krugman believes fiscal policy is needed at the ZLB and Sumner does not. What I think Krugman is implying is that given the MV=PT identity the ‘hot potatoness’ of money gets cold pretty quickly – using the bank portfolio justification of the Tobin paper – so unlike the Friedmanite fixed V assumption it rises but quickly falls. Money is neutral ‘in the long run’ but this happens swiftly. In Sumner’s view this period outside equilibrium is only short term, at equilibrium ‘its a simultaneous system’ again – so what. So you can still hold to the position that money is but a veil and banks are just intermediaries between lenders and borrowers. In this story Central Banks can still influence the level of prices by changing interest rates. Krugman has shifted in his explanation of this, no longer the textbook ‘money multiplier’ from Central Bank money to excess reserves, but instead the portfolio behaviour of banks changed (after Tobin) by changes to the fed funds rate, which then influences the extent to which account holders wish to hold cash or other assets.

(note: I don’t think Scott Fulwilers response that banks can rapidly cool the hot potato by putting excess reserves in Central Banks reserve accounts is helpful – isn’t Krugman’s point that the Potato gets quickly cold? In any event if there are profitable lending opportunities and they don’t have reserve of tier I capital constraints they wont and whatever the banks preferences the transmission mechanism will continue providing account holders have excess reserves and the receiving bank for the deposits finds itself with new liquidity enabling new profitable lending.)

Of course the blogosphere, such as Cullen Roche, has been coruscating that he hasn’t moved beyond money 101, referring to loans being created from reserves etc.. I think its too easy to dismiss this strand because of its sloppy terminology. That doesn’t logically mean his is theoretically wrong necessarily. Of course loans are not created from reserves – but Krugman is using an old definition of reserves, consider Bagehot. Bagehot in Lombard street made the distinction between ‘currency reserves’ and ‘banking reserves’ (The latter being the modern definition vault cash + central bank reserves, the latter being the liabilities of the bank towards depositers), whilst Krugman and most textbooks seem to be referring to the former, as do much of the writings of the great economists. This confusion leads to chaos when it becomes extended to thinking of ‘excess reserves’ without clarity in terms of excess of what. I have been guilty of this charge myself, picking up terminology from old textbooks when the endogenous theory was predominant. I apologise. I have not as some (such as the Positive Money website have accused me of) stated that loans can be created from reserves (banking reserves), that is impossible as money held as either vault cash or in central bank reserves must be accounting identity be money that is capital of the bank (assets or equity) and not liabilities – otherwise banks would be guilty of a Ponzi scheme. Loans can only be created from a transfer from the assets side of a balance sheet in cash, the registering of a liability and the creation of a new asset to reflect future repayments. ‘Currency Reserves’ (deposit liabilities) cannot be used to create loans whilst they remain on the left side of a balance sheets, however I like many endogenous money thinkers like Torrens, Davidson and Phillips (see this historical note by HumpreyHumpryHumpr) hold that the fractional reserve process is one where banks temporarily leverage the stock of their deposits as assets for lending providing they can satisfy the ex post accounting requirement for honouring liabilities. They ensure this by ensuring that the cash flow into the bank from loan repayments and new deposits is greater than the cash flow from the bank from honouring deposits (vault cash requirements). Indeed it was jewellers noticing that deposits held in their vaults could be leveraged in this way that led to the invention of modern (fractional reserve as opposed to full reserve) banking. So I don’t think Krugman’s terminology is the key issue, rather it relates to the issue of whether it matters that the large majority of money is today bank created (endogenous).

In the paper by Tobin Krugman refers to Tobin made a mistake, he realised in later writings. Steve Keen adds to the debate

Tobin the Younger imagined that newly created bank money could be taken out of the system in a form other than bank deposits or cash, Tobin the Elder realizes that those are the only two options at the systemic level. Individuals might get out of bank deposits into (say) gold, but to do so they transfer money from their deposits in one bank into the deposits of the gold dealer in another bank. The only way for money not to be held in a bank is for it to be converted into some other kind of asset that is not a bank liability first. The only candidate here is cash [my emphasis]

Tobin was repeating the ‘hot potato’ view of money. The term ‘hot potato’ was a colourful metaphor invented by Patinkin, referring to the cumulative process ideas of Wicksell. In fact the idea is much older and goes back to Henry Thornton in 1802. (Wicksell likely picked up the concept from the way Ricardo and JS Mill presented Thornton’s ideas in simplified form).

Tobin was presenting a ‘new view’ of money whereby instead of the old ‘loanable funds’ view of money where those with money lend to those without – and bank intermediate, rather banks intermediate between those with different portfolio preferences for leverage. The ‘hot potato’ view of money is that cash loses value, relative to other assets, because of inflation and (in times of growth) growth of capital, so those who hold cash quickly convert it to other assets or spend it if it is excess of their preferred ‘cash balance’. Ultimately people only hold cash because of the value of goods its can be used to purchase. Different kinds of asset have different ‘own rates’ if interest and so the velocity of circulation of those assets depends on these own rates. A shift in (real) interest rates will change the value of a portfolio between cash and other assets and may induce someone to hold more cash and demand loans by extending their leverage. This view I believe to be essentially correct and an advance on the earlier Cambridge Cash Balance/Liquidity Preference view of Keynes and his followers because it saw liquidity preference as a result of portfolio decisions caused by variance in rates of return within the portfolio and not a cause.

[note you will find some on the blogosphere notably Mike Sproul claiming that money is not a hot potato because for everyone getting rid of money there must be someone who desires it and who therefore must regard the potato as cold, this is unconvincing, the issue is one of velocity not single exchange and how hold long money is held as a cash balance before being spent on other assets].

For the younger Tobin then the hot potato of money gets cold very quickly, so the ‘long run’ of money neutrality arises quickly. For the Elder Tobin only liquidity preference can lead to changes in cash balances in the system as a whole. Therefore the hot potato gets cool much more slowly and therefore bank creation can have a much more lasting effect. For both Tobin’s however portfolio preferences were key.

But the hotness issue, which is really about the speed of return to a money equilibrium, is not the only issue at hand. The second and related issue is whether money creation itself affects the absolute price structure of the economy. This is why the old banking school/currency school debate is important. There were two issues at hand:

1. What is it that gives money its value? – the value of assets which back it (the ‘backing theory’ also called the real bills doctrine first set out by John Law) held by the banking school, or the quantity of the assets which back it – the quantity theory held by the currency school
2. What happens if there is excess money creation by banks? –the banking school held that excess money creation was impossible as if any individual held an excess cash balance that money would ‘reflux’ back to the bank – including from repayment of debts, the currency school held that the absolute level of prices would rise because the real bills doctrine imposed no limits in how much banks could issue and because the assets used to back up the currency would inflate.
   

The debate was not about whether money was endogenous – that was accepted on all sides – rather it was then about whether the banking system required an anchor to prevent inflation. This is why Wray’s view that exogenous money proponents are heirs to the currency school is simplistic. Rather the currency school were arguing, like modern endogenous money thinkers, that money was not simply a veil. For the currency school this was because it has real effects because the value of assets which backed money issue were nominated in money units.

If now it is accepted in all sides that money is endogenous it is time to return to this historic debate. Does money creation have real effects? I believe it does and I believe that both the banking and currency school were wrong. Put simply my approach is to consider what money when created is spend on. I intend to expand on this idea in a full paper with lots of math and diagrams but heres a flavour

Lets go back to the origins of the debate. Henry Thornton held that if the bank rate of interest was well below the prevailing rate of profit in an economy then money would be created to excess and this would be inflationary. Note this is not the Wicksellian explanation of the ‘cumulative process’ which relies on lending below a ‘natural rate’ of interest. Wicksells ideas were contaminated by Bohm-Berwick and his idea of natural rates of interest in a pure barter economy, this is untenable for as Sraffa pointed out there is no single ‘own’ rate or natural rate in a barter economy. Thornton’s original conception does not suffer from this flaw. Now in modern terms creating loans is not the only option available to banks, they can create other assets, banks hold portfolios like any other economic agent. So if the rate of interest is lower than the prevailing rate of profit then they will invest in other assets or if the prevailing rate of profit is negative may simply park reserves at a central bank. From our early lending power- required leverage model this will shrink the supply of lending power and so raise the interest rate back to the prevailing rate of profit. However if the banks are obtain money at a rate below the rate of profit they are presented with an arbitrage opportunity. Central Banks set interest rates for their own lending to banks (discount rates) and for interbank borrowing to maintain reserve requirements (federal funds rate in the states) and ensure that actual interbank market rates are the same as their set rates through open market operations such as purchasing bonds from banks. If a bank finds itself more liquid through having cash from selling a bond its level of reserves will be above its central bank reserve requirements – it has ‘excess reserves’. This is an asset to the bank, and a hot potato, it can keep it as a central bank deposit, invest it in securities or treat it as capital to expand its lending power. Note it does not require exogenous money creation per-se to purchase bank assets, merely the leveraging of a bank balance sheets. However it is much easier for a central bank to push down interest rates if it does so through money credited to its own balance sheets (such as through qe). If this is then used to buy securities and it is the same category of securities the central bank bought then this is price neutral. Therefore it is only possible for central bank operations to push prices up overall (as opposed to affecting price differential between different types of security) if the money is transmitted into extra lending, at times when profits in the economy are low this transmission mechanism is broken.

A lot of things have to happen on the way before an additional unit of credit affects prices.

a) It must not be saved

b) It must not be used to buy inventory in excess supply

c) It must be used for purchase of assets where scarcity rents can be charged, or;

d) If used for investment it must not be used to expand production where inputs are free goods

e) If used for investment it must be in an industry where there is a degree of monopoly rather than perfect competition

e) If not free goods and there is a degree if monopoly the holders of inputs must be able to charge scarcity rents on those factor inputs

Notice the points at which the process tree results in an increase in prices, at c and e, both involve spending on assets or non-produced means of production. In both cases the price is affected by the rent that the holder of the assets or the non-reproduced means of production can charge. For all other components the price reflects labour inputs only up till the marginal point at which labour is no longer scarce (full employment). So if interest rates plus risk and liquidity premiums is equal to the prevailing rate of profits then the labour theory of value holds because all components of price can be broken down into labour and rent, and rent can be broken down into labour, and the marginal opportunity cost of a unit of labour is equal to the value added. Once there is variation however been bank lending rates and the rate of profit this elegant relationship breaks down and the value created by capital goods is no longer equal to the value of labour embodied in it.

Imagine if all bank credit was spent solely on new production and not purchase of existing assets. Imagine too that no one was able to charge scarcity rents in non-reproduced means of production (only practical I think through taxing such rents, including scarcity rents on money). In this case an expansion of bank credit would not lead to inflation because credit creation would be exactly matched (assuming no malinvestment) by increased productive capacity. This approach is very Minskian because it makes a distinction between credit used for asset purchases and used for real investment.

Seen in this way inflation is always and everywhere a rental phenomenon, the ability to extract rent being a function of the inequality in the distribution of the resource, Any money created which does not attract rentals will stay in or reflux back to the banking system without affecting prices, any that does attract rentals will also reflux back until the non-rental components decline asymptotically to zero so they no longer affect prices. I think the key unresolved issue from this is whether this gravitates around an equilibrium or constantly under and overshoots creating a limit cycle – or likely the latter. Hence excessive credit creation for purposes of asset purchases drives the business cycle.

Notice how we have tackled Henry Thornton’s critique of John Laws Real Bills doctrine – the backing theory of money. Here money would be fully backed because it would be backed by real investment, not by speculative asset price increases, so the ‘numeraire’ effect of expansion of money would be fully compensated for by real growth. Of course if there were malinvestment that Thortons critique applies and the real bills dpoctine falls too because the value of assets backing money are inflated

I’m more and more wondering whether a formal process model of the monetary transmission process is needed (taking inspiration from Kahn/Kaldors model of the keynsian multiplier) which can account for all flows in the circuit. I hope to more fully set this out, including the necessary maths showing the relationship between V and P, in future posts. I also in future posts want to examine the classical arguments used against the real bills doctrine and to what extent they still hold in the light of this analysis.

Note:  I don’t mean to imply here that central banks are the sole cause of business cycles and cost push has no role in inflation.  Even with perfect central bank oversight from growth some real products will be in short supply, classically housing which is slow to respond to demand increases.  This will create scarcity rents and increased demand for credit, which the central bank will be forced to accommodate.  This is not money creation, is is not creating the addition units of account, banks do that, rather it is accommodating demand for additional units of exchange to accommodate demand to clear the units of account.  Central banks are forced to operate in this manner to avoid a cash or credit crunch.  The false idea that control of this ‘monetary base’ was possible was the idea behind monetarism’s assertion that inflation is always and everywhere a monetary phenomenon but monetary base control proved impossible in practice.  In all cases inflation only bites because an ultimate scarcity of real resources causing a cost push.

Should Post-Keynsians Stop Hounding Krugman Now?

Post Keynsians have often critcised Krugman for although he holds in his sites many of the same enemies as Pk’ers do his academics writings and textbooks seem every bit as beholden to neo-classical orthodoxy as Mankiw.

Many of us have noticed a shift in Krugman’s positions over the last couple of years.  Quiggan blogs on this at Crooked Timber

Paul Krugman’s recent columns, responding in various ways to JM Keynes, Michal Kalecki and Mike Konczal have made interesting reading, signalling a marked shift to the left both on economic theory and on issues of political economy

Although Krugman clearly is a progressive I dont see this so much in left-right terms.  After all many of those economists who hold many of the key theoretical views of post Keynesian practice in quant/financial circles in London and are hardly progressives, though they are much closer to the action than those stuck in ivy league ivory towers, and similarity the influence of many Austrian strands are apparent amongst many key PK thinkers.   Rather I like to see it as a paradigmatic theory issue, just as Ricardo and Marx were very similar on the issue of theory but were capable of holding very different political positions.

Krugman notes approvingly of the post and thread.

If Jrugman is moving towards the position that the ‘centreground’ of neoclassicism is untenable, to use quiggans terminology, though all the better.  However Krugman needs to engage particularly on monetary theory.  Even a few months ago Krugman was writing extraordinary posts on how he ‘doesnt get’ what banks had to do with the issue of debt!

’Im all for including the banking sector in stories where it’s relevant; but why is it so crucial to a story about debt and leverage?

And his beloved IS-LM model untenably rests on loanable funds assumption (see my post here).

Certainly we need someone of Krugmans weight to help resolve many of the unresolved theoretical issues, of course we also need to rewrite the textbooks, but until Krugman starts to seriously engage in these issues, rather than to causally dismiss any idea that doesnt emit from the strsterile elie neoclassical realm of academe, he isn’t helping much.

 

 

A Simple Post-Keynesian Alternative to IS-LM

Edit:  There is a steady stream of visitors to this page (thank you) however since writing this paper I have realised that I was wrong about the ‘liquidity premium’ it exiosts and is an addition to interest, hence that part of the paper needs rewring.  Keynes (and Kaldor) (as ever) were ahead of us.

 

I have a pdf of this post here, I will be posting in on SSRN once I have had some feedback.

Introduction

“The IS-LM model can be criticised on two very different grounds: one can question its relevance to a money economy because it is static and it ignores the changes in expectations that are the driving force of the economy in, for example, Keynes’s model, or one can accept its formal structure but question its usefulness in analysing the problems at hand. Since it is so widely used in the monetary policy debate it can better be evaluated in its own terms.” (Chick 1977 ) P133

“For in a world that is always in equilibrium there is no difference between the future and the past and there is no need for Keynes.” (Robinson 1974 ) P174

Although the Hicksian IS-LM  (investment saving–liquidity preference money supply) approach to understanding Keynes (Keynes 1936) (from Hick’s famous 1937 article Mr Keynes and the Classics (Hicks 1937)) has come under severe criticism, not least from Chick above and Hicks (the model’s inventor) himself in 1981 (Hicks 1980-1981). (Pasinetti 1974) lays the blame on the IS-LM for the divergence of orthodox “Keynesian” macroeconomics from the economics of the General Theory. For Joan Robinson IS-LM is was “bastard Keynesianism” for Chick it shows ‘Pseudo dynamics’. For Leijonhufvud:

In the General Theory, Keynes proposed a theory in which flexible money wages would not restore the economy to full employment and very flexible wages would produce financial catastrophe. The IS-LM model, which originated as an attempt to formalise the verbal economics of Keynes, led after years of debate to the seemingly inescapable conclusion that unemployment had to be due to the downward inflexibility of money wages. (Leijonhufvud 2011)

However IS-LM it remains important for two reasons. Firstly as a ‘classroom gadget’ (to use Hick’s term) to explain the broad parameters of macro from which the equally criticised AD-AS curve can be derived, secondly, despite its crudeness it has had some clear empirical success in explaining a narrative of monetary policy at the zero lower bound. One thinks for example of Krugman’s use of it regarding Japan and, contra, the forecasting failures of those who have predicted hyperinflation. IS-LM seems to represent the front line of misconception and misunderstanding between Old Keynsians and Post Keynesians, which is a pity given the similarities of analysis and policy prescriptions of the two camps despite their differing methods.

So a simple tool that bears the same features of IS-LM is needed, one axis income, the other the interest rate, one curve a demand function showing supply of money, and another showing demand for money, is a useful heuristic device. The problem is that the classic IS-LM model mispecifies both what is being supplied and demanded and is set within an overall general equilibrium assumption. If we correctly specify the terms of what is being supplied and demanded and create a dynamic disequilibrium framework for adjustments to the market interest rate we will I believe have a more robust and equally simple replacement, and at least set out a solid common ground between the two camps.

The IS Curve and the Loanable Funds Assumption

The initials IS stand for “Investment and Saving equilibrium” and imply that the ‘supply’ of money is the equilibrium point of savings and investment. [Fig 1]

Fig 1 The Basic IS-LM model

To quote Wikipedia

the IS curve can be said to represent the equilibria where total private investment equals total saving, where the latter equals consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus). In equilibrium, all spending is desired or planned; there is no unplanned inventory accumulation.

In the comparative static Edgeworth box which constrains the IS curve the assumption is that for planned investment there is an accompanying ‘pot’ of money, in terms of planned savings both to make that investment and to fund the purchase of produced goods. In other words we have a classical loanable funds assumption. Indeed a frequent interpretation of IS-LM is that IS represents loanable funds and LM represents liquidity preferences and that the intersection of both curves at the interest rate reconciles both theories. This is certainly the interpretation of Krugman (Krugman 2009 )

My favorite of [the] approaches [explaining IS-LM is to think of IS-LM as a way to reconcile two seemingly incompatible views about what determines interest rates. One view says that the interest rate is determined by the supply of and demand for savings – the “loanable funds” approach. The other says that the interest rate is determined by the trade-off between bonds, which pay interest, and money, which doesn’t, but which you can use for transactions and therefore has special value due to its liquidity – the “liquidity preference” approach. (Yes, some money-like things pay interest, but normally not as much as less liquid assets.) (Krugman 2011)

And frequently in textbooks

For if we take the equation of the IS curve – for simplicity excluding the government sector and international trade:

1. Y national income=Consumption + Investment

Then

1. Investment =Y-Consumption

So as consumption rises as a proportion of income the fund of unspent monies (savings) falls. This is used to derive a downward sloping IS ‘supply’ curve. However the assumption must be that these idle balances are ‘savings’ which finance consumption.

However this is very much against the revolutionary thrust of Keynes General Theory which is based on the idea that investment is not created from savings rather the causality runs the other way, investment creates savings.

As an identity this must be true at all times, whether or not the economy is at equilibrium. The IS curve however assumes that both money and all goods markets are at equilibrium. But for Keynes aggregate saving is determined by aggregate investment, and the macroeconomic relation is an identity, not an equilibrium.

S = I at all rates of investment. Y either definable as C+S or as C+I. S and I were opposite facets of the same phenomenon they did not need a rate of interest to bring them into equilibrium for they were at all times and in all conditions in equilibrium. (CW XXVII, pp 388–9) (Keynes)

[A] relationship is set up between aggregate savings and aggregate investment which can be very easily shown, beyond any possibility of reasonable dispute, to be one of exact and necessary equality. (Preface to the French Edition, CW VII, p xxxiii) (Keynes)

It was this realisation which led Keynes to develop as of necessity his alternative liquidity preference approach as an alternative means of determining interest rates, a preference determined after the decision to save.

This creates a problem, by themselves both liquidity preference and investment/savings are indeterminate for a theory of interest. Krugman is clear on the indeterminacy of the ‘supply side’ of lending within the loanable funds approach, in a firmly wicksellian description of a cumulative process. Indeed De Long has described Krugman and his old-Keynesian approach as ‘neo-wicksellian’.

Suppose that desired savings and desired investment spending are currently equal, and that something causes the interest rate to fall. Must it rise back to its original level? Not necessarily. An excess of desired investment over desired savings can lead to economic expansion, which drives up income. And since some of the rise in income will be saved – and assuming that investment demand doesn’t rise by as much – a sufficiently large rise in GDP can restore equality between desired savings and desired investment at the new interest rate. That means that loanable funds doesn’t determine the interest rate per se; it determines a set of possible combinations of the interest rate and GDP, with lower rates corresponding to higher GDP. (Long 2012)

(Hansen 1953) also showed the indeterminacy of the demand side- the liquidity preference – LM side. Interest rate is determined by the total demand for and supply of money, and some of the key motives for holding money are determined by income; but, income is determined by investment, and the investment is determined by interest rate and in Keyne’s schemes the marginal efficiency of investments, so interest rate and income are all indeterminate. The solution for Hansen was the simultaneous determination of liquidity preference and investment through adapting the IS-LM model. Through Hansen’s influence on his students this became, with the addition of the Phillips curve, the foundation of the neo-classical synthesis.

Supporters of IS-LM accept both indeterminacies and uses Hansen’s method through the intersection of the IS and LM curves determine the point where the goods and money markets are in equilibrium and so the interest rate and level of output are simultaneously determined.

The Equilibrium and Partial Interpretations of IS-LM

A common assumption is that the IS curve represents equilibrium in the goods market and the LM curve represents equilibrium in the money market [fig 2]. This is certainly the view expressed by Hicks in his later recantation of the model.

I accordingly conclude that the only way in which IS-LM analysis usefully survives—as anything more than a classroom gadget, to be superseded, later on, by something better—is in application to a particular kind of causal analysis, where the use of equilibrium methods, even a drastic use of equilibrium methods, is not inappropriate…(Hicks 1980-1981)

Fig 2 The General Equilibrium IS-LM model

In the equilibrium interpretation the labour market is kept in the background, the assumption being at General Equilibrium if the goods and money markets are at equilibrium then according to Walras’s law so must be the labour market, hence the labour market is concealed, kept in the background. This immediately produces a problem for Keynes argues that an equilibrium is possible at less than full employment, this means however that one of the two other markets, goods or money, must also be out of equilibrium, and so the IS and LM curves cannot both be in equilibrium. This is the line of attack pursued by Steve Keen who shows that outside equilibrium the LM curve is indeterminate. Krugman responded

savings and investment curves are what the supply and demand for funds would be if the economy were at full employment. They’re not the curves that actually apply when the economy is operating below full employment. In the IS-LM model, the quantity of funds supplied is always equal to the quantity of funds demanded — because the level of output adjusts. This is true both when the zero lower bound applies and when it doesn’t. (Krugman 2011)

Lets follow this logic through. According to Keynes the IS curve is formed by an identity and so the economy is on the IS curve at all times whether at equilibrium or disequilibrium. If the IS curve lies outside full employment
equilibrium then so must the LM curve. So the LM curve does not represent equilibrium in the money markets. One has to ask what does it represent, and after Keen how is it derived? If it is possible to derive such a curve however then Krugman’s treatment of IS-LM would at least make some sense, avoiding the stock-flow inconsistencies of an investment schedule off the IS curve, however it is a different theory from Hick’s equilibrium one, as De Long said more neo-Wicksellian in nature. I am sure De Long had in mind Lijonufvud here, who on the influence of Wicksell on Keynes states

In allocation theory, we learn that household saving decisions and entrepreneurial investment decisions are to be co-ordinated by the interest rate mechanism. In money and banking, we learn that ‘the’ interest rate is determined by the supply and demand of securities (or of ‘credit’). Imagine a situation where the interest rate cannot do both jobs at once. (Leijohnhufvud 1980)

Given that the money market is in disequilibrium one cannot say that the LM curve represents an equilibrium of money supply = money demand (or strictly in the interpretation used by Krugman loanable fund supply = money demand), although Krugman gives no derivation one could reasonably treat it as a money demand curve and then use the short side rule to determine the money supplied. [fig 3] This interpretation must have come as a surprise to De-long who on his blog had defended IS-LM as a general equilibrium model.

F ig3    The Krugman Partial Equilibrium Interpretation of IS-LM

Away from equilibrium the short side rules. Output is determined by the minimum of supply and demand. The short side of the market determines the level of output; the other side of the market is happy to accommodate that level. In money market disequilibrium the demand for money is less than the supply, the point at which this disequilibrium LM curve intersects the IS curve then determines the supply of money and the gap between this level and the full employment level determines the excess supply of money, translated into output equivalent it represents the level of unemployment.

So at the least the LM curve side of the IS-LM curve might be capable of rescue. However this Wicksellian approach is firmly based on loanable funds. Lijonufvud describes the cumulative process in Wicksell which, transposed to his interpretation of Keynes, seems to have been adopted by Krugman.

Banks are perceived in the first instance as loan intermediaries rather than as money suppliers…when nominal income is rising, investment exceeds saving by the net addition to loanable funds injected by banks. When nominal income is falling, banks let loanable funds “leak out” so that savings exceed investment. In income equilibrium, saving should equal investment; this requires that banks do no more or no less than intermediate the desired savings. (Leijohnhufvud 1980)

This approach can be updated in line with Keynes S=I identity, but it reveals problems. At one interest rate ex ante planned savings and planned investments are equal. After a change in interest rates planned investment increases. If you assume loanable funds then the stock of savings hasn’t yet been formed to fund the increased level of investment at the changed interest rate, if the investment (from whatever source) does go ahead then through the Kahn-Kaldor multiplier process this extra unit of money passes through several hands according to the holders liquidity preference, only after the stock of money declines to an asymptote or is fully exhausted by a consumer having complete illiquidity preference does planned savings then match planned investment. It is quite possible to hold a view of the multiplier where S=I as an identity at every moment, if one assumes the Kahn-Kaldor process generates both the additional savings and investment (a point Basil Moore did not grasp). What the loanable funds approach cannot explain is how savings change to maintain this identity at all times before these savings have been made. Here the loanable funds theory ties itself in knots as if you assume there is additional savings and less consumption due to a change in interest rates (a liquidity preference induced change) how can this square with the investment causing increased consumption from which the savings are made? Stock-flow confusion is at the heart of it – of investment comes solely from a fixed stock, and if investment proceeds at a steady pace so that the stock is immediately exhausted then a change in interest rates cannot lead to an increase in investment until that stock has been enlarged. Of course for banks investment does not take place from a fixed stock but from accounting of future income flows. This is to turn on their head the critique of early reviewers of the General Theory such as Myrdal and Robinson who though that the General Theory was incompatible with loanable funds – it is so loanable funds must go.

This relates also to Victoria Chicks critique of ISLM (Chick 1977 ). For savings to equal investment all new savings must go into bonds. At that point there must be full ‘illiquidity preference’, which requires an interest rate where “all new saving flows into the bond markets”. To the extent that any new saving is in money, it cannot be converted into investment, and so the equilibrium of the system will be disturbed, and the model will not hold. It also leads to the problem of realism as clearly there will always be a transactional desire for money meaning that there can never be full illiquidity preference.

A partial solution to this problem is given by the Kanh-Kaldor process mentioned above. There is no immediate full illiquidity preference, however money passing through several hands will lead to a time lag between ex ante planned investment and ex poste savings, only when the flow of money not held liquid declines asymptotically to zero will there be full bond financing. This however begs the same question, given that the existence of the transactions motive creates a shortfall in bond financing how if you hold a loanable funds view of money is investment financed outside a steady state where there is no money for transactions of consumer goods? This is not a great a problem as it appears as investment is capital advanced and capital advanced includes all monies which sustain labour during the period of investment. This is the ‘pool of funding’ – or as Wicksell stated is a ‘wages flow’. So money for investment automatically supplies money for transactions. You can use a Taylor series type expansion to calculate the time taken for this to happen. The problem is the time gap whilst the savings ex-poste are being made. This gap can be bridged by Crusoe like savings in advance. But this means that the ex-ante liquidity preference needs to be higher in advance so the rate of investment is lower. Keynes finance motive (from his 1937 economic journal article) is the requirement to bridge the gap. One can take a loan to bridge this finance gap and so in advance the liquidity preference is not depressed, rather it is depressed after taking the loan as liquidity preference must then increase. The advantage of financing ex-poste is that by then the investment, under normal circumstances, will have financed economic growth, meaning that the depression in liquidity preference ex poste through loan financing will be less than if it is financed ex ante by Crusoe like savings. The difference is precisely the economic growth caused by the Kahn-Kaldor multiplier from financing the investment sooner rather than later. The problem with loan financing is if the economy does not grow, if the loan financed investment was mal-investment. If it was then the drag from increased liquidity needed to pay the loans act as a negative multiplier.

Another key problem with Krugman’s ‘pure intermediaries’ view of banks is that it assumes that banks undertake a social function of intermediation without regard to the business model of banking, banks are out to make a profit. This means that although there may be a demand for lending banks may not be in a position to fulfil that demand – it may not be sufficiently liquid and conditions may be so uncertain that they cannot make a profit. It is the liquidity of banks that matter in this regard more than individual account holders as these may consider themselves holding considerable liquid accounts and yet these may have been leverage for bad loans. Similarly banks may be considerably liquid but there may not be demand for loans. It is distracting to consider a world where the impatient borrow from the patient without considering the active, rather than the passive, market making and profit taking role of banks.

Similarly Krugman’s view of intermediation between holders of money and those who are illiquid is too narrow. It is income tomorrow that determines ability to pay a loan. In reality most intermediation occurs between a present illiquid customer and the future same liquid customer paying off the loan. It is the ability of banks to do this that creates the model of fractional reserve lending, it is the flow of future bank assets, not the stock of current bank assets Loanable funds) that determines bankl behaviour.

Money Demand Stocks and Flows

In the Hicksian formulation both axes are measures of monetary flows rather than stocks. Keynes, in his 1937 article on the determination of the interest rate stressed that only the demand for the stock of liquidity determined the interest rate. In this interpretation presumably the LM curve is vertical liquidity preference determines the interest rate and the intersection with the IS curve determines investment and effective demand [fig 4]. However in a timeless world any flow variable can be treated as a stock, in a dynamic model stock and flow must enter into the variation of the stock. This was the view of early critics of Keynes on this point such as Hicks, Ohlin and Robertson.

Fig 4     Keynes Verticalist ‘Pure Liquidity Preference’ Theory

We can easily demonstrate this issue by considering what happens when the LM curve intersect the IS curve outside a point of full employment equilibrium and then there occurs an additional inducement for investment such as development of a more productive technology. In this case the additional investment could be funded either by additional savings or additional credit. If funded by additional savings then the flow of savings must increase shifting the supply IS curve up. If through additional credit then the LM curve is shifted to the right reflecting the additional demand for bonds, whilst the IS curve would get steeper reflecting increased returns at higher interest rates. Both of these reflect flow variables Wray (Wray 1992).

Let’s consider the case where the finance gap is formed by additional savings, whilst the savings are being made and before the investment is made then the income levels throughout the economy are reduced through reduction of excess demand, this forces the supply IS curve down and the demand LM curve to the left due to increased liquidity preference to make the savings. Following the investment the LM curve is pushed to the left reflecting price deflation from the more efficient technology given the fixed stock of money. This pushes the interest rate down and the output down. In the opposite case where credit is granted the IS curve is pushed up and the LM curve to the right increasing output and the interest rate. In both cases flow matters in adjusting the LM curve. In both cases although they will have different effects on prices this impact will vary depending on the interest rate, the demand for money curve most be sloped. This is due to the differing purchasing power of the stock of liquid money depending on the interest rate, a combination of the Kalecki effect of debt levels on spending (as debt in enumerated in nominal not real terms) and the Patinkin ‘real balances effect’ as the purchasing power of the stock of wealth will vary with different price levels. In cases where there are high levels of debt and low stocks of wealth then the supply of money curve may slope heavily downwards, conversely where there are low amounts of debt and high stocks of wealth then the demand for money curve is likely to slope steeply upwards.

Another key problem with the liquidity preference stock view is that outside equilibrium the supply of money will expand to fulfil demand until equilibrium is met. Only at that point will you be able to talk of a fixed stock, ignoring the flow of additional money to get you there and how that flow of money was sourced.

The Limits of Loanable Funds and Liquidity Preference

Critics of loanable funds rightly claim that endogenous money prevails in a modern economy. Correcting both the supply and demand for additional money into endogenous money forms is our suggested tactic for replacing IS-LM.

The key issue is that the loanable funds approach is a fallacy not simply that it is indeterminate and is insufficient to account for financing, whilst liquidity preference by itself is similiarly indeterminate and insufficient in a dynamic model.

Keynes’s original intention was that:

The complex of rates of interest would simply be an expression of the terms on which the banking system is prepared to acquire or part with debts; and the quantity of money would be the amount which can find a home in the possession of individuals who—after taking account of all relevant circumstances—prefer the control of liquid cash to parting with it in exchange for a debt on the terms indicated by the market rate of interest.” [Keynes, 1964, pp. 205-06]

Put in simple terms the ‘terms on which the banking system is prepared to acquire or part with debts’ against the willingness of those who wish to acquire ‘a debt on the terms indicated by the market rate of interest’. In the latter case it would appear to refer to the propensity to hold cash as opposed to bonds. Keyne’s model was a deliberately simplified one, two financial assets, cash and bonds, each with varying liquidity.

But note how on both sides of the transaction the expression in the General Theory can easily be (mis)interpreted as loanable funds, the assumption is ‘savers’ give up liquidity – presumably through interest bearing term deposits – and this forms the pool of ‘loanable funds’ which banks lend. Note how Keynes did not refer to the necessary other side of the transaction, those who prefer to acquire a debt giving up the liquidity of any deposit on a loan.

From the post-Keynesian viewpoint it is not savings that create loans rather loans create reserves which then through the multiplier process create savings, indeed greater investment and savings that the original investment. This is the endogenous approach to money. If we are to reconstruct Keynes and Hick’s approaches then we must rebuild it on firmer endogenous money foundations.

Curiously, as both Schumpeter (1954: 1114-1115) and Kaldor noted, before the General Theory Keynes considered that Investment was financed by bank loans and not by prior saving, Keynes also developed an endogenous approach in his articles for the Economic Journal on the Finance motive in 1937. The assumption of exogenous money which permeates most of the General Theory might be seen as a temporary and confusing diversion, it certainly diverted Hicks.

An alternative explanation is that there was no curious and temporary conversion by Keynes to exogenous money at the time of writing the General Theory. Rather with savings seen as determined from an identity caused by investment the interest rate was no longer central to monetary theory, rather Keynes phrase that the quantity of money was ‘fixed’ simply expressed his view that money created resulted from the marginal propensity to invest and income. This could then lead to one of two interpretations of the above quote from the general theory. The exogenous money explanation is that given a tendency to hold bonds rather than cash (liquidity preference) this produces the quality of money in balances which is leant, a net increase in money being created by the central bank. The exogenous money explanation is that banks create money, those who have borrowed then place the receipts in their bank accounts, and then either determine to hold onto it as cash or convert it to bonds. I find the second explanation far more convincing as pages 205-206 of the General Theory clearly set out a causative process running from debt creation to money holdings, and also because the endogenous money textbooks of the pre WWII era all stress that it is the decisions of those who take the receipts of purchases from loans which determine the money that remains in circulation. The term ‘find a home’ I find telling and would seem to imply that the money has passed through one or more hands. Unfortunately it would seem that Hicks took the exogenous interpretation. Looking across all of the supposed references to exogenous money in the General Theory, summarised in Wray(), I find it a stronger explanation to see these as describing endogenous money but simply within a short-term horizon where the supply of money is fixed. The reasoning being I think that Keynes found a comparative static approach more tractable given the savings=investment identity and the multiplier process had cut the ground from underneath the theory that the interest rate was determined by the supply and demand for savings. By taking a purely static approach all the complexities of stocks and flows could be disregarded, outside of time only stocks matter.

The problem though is what happens when a bank finances the purchase of bonds through crediting its own account whilst at the same time maintaining its own liquidity in terms of the demand from account holders for reserves (here we are using the definition of reserves as Bank reserves are the currency deposits which are not lent out to the bank’s clients – liabilities to the bank). Here we come again to Keyne’s finance motive. This providing a bridging gap between ex ante savings and ex poste savings. The price of money is then the price of waiting, the price of forgoing investing in alternative assets. We can extend this argument to apply to a spectrum of financial assets of varying liquidities, periods and returns held in a portfolio, and held by a variety of economic agents. In this approach liquidity like investment is not confined to the demand curve only, it enters into both the supply and demand for additional money curves, as banks which supply money must maintain liquidity (a function of the demand of their customers to withdraw reserves). This is one good reason not to see liquidity preference, despite its importance, as a demand for money.

Another reason to not treat liquidity preference as demand for money per se is that it does not enter into the decision to seek a loan – additional money – this is a quite separate decision. Liquidity preference is important in determining the proportion of cash to be held by an economic agent in their asset portfolio. But liquidity preference is a proportional preference – stating the proportion of wealth and incoming income held as cash. However a demand for money to make an actual purchase is always a real amount not a proportion. If that agent had substantial savings their demand for loans will be less, but it is a fundamental mistake to characterise demand for money as fundamentally an attempt to extend consumption beyond income, to ‘go into the red’. The most attractive candidates for loans will be those with significant savings and substantial future income streams to pay for premium and interest. If the affordability assessment of the lender shows the borrower ‘in the red’ the loan is unlikely to be granted, and of course a borrower would be irrational to seek the loan. For a time a speculative motive may increase demand for loans, as Minksy set out, but permanent asset price increases are never sustainable.

The Supply of Potential Lending – Lending Power

So the IS curve is ill specified. Interest is the price of loaned money, so the supply side curve should show not a loanable fund but the amount of money that would be loaned, that is created, by banks at a given interest rate, whilst maintaining required liquidity.

However Keynes argued that the supply and demand of loans did not affect the interest rate (1937). The argument here was that when investment was proceeding at a steady pace then interest rates would not be affected by flow rates of spending since there would be a constant flow of income into what he termed ‘the revolving fund of finance’ in his 1937 (Economic Journal Article) in response to criticisms (from Ohlins, Hicks and Dennis Robertson).

Planned investment—i.e. investment ex-ante—may have to secure its “financial provision” before the investment takes place; that is to say, before the corresponding saving has taken place… There has, therefore, to be a technique to bridge this gap between the time when the decision to invest is taken and the time when the correlative investment and saving actually occur. (Keynes 1937b: 246)

If investment is proceeding at a steady rate [my emphasis], the finance (or the commitments to finance) required can be supplied from a revolving fund of a more or less constant amount, one entrepreneur having his finance replenished for the purpose of a projected investment as another exhausts his on paying for his completed investment. (Keynes 1937b: 247)

It is possible, then, that confusion has arisen between credit in the sense of ‘finance,’ credit in the sense of ‘bank loans’ and credit in the sense of ‘saving.’ … Credit, in the sense of ‘finance,’ looks after a flow of investment. It is a revolving fund which can be used over and over again. It does not absorb or exhaust any resources. (Keynes 1937b: 247)

In our examination we shall model this circuit of credit through creation of endogenous money, and determine if the supply and demand of loans effects the interest rate. But note the two key assumptions
here, firstly that investment in preceding at a steady state, secondly that the inflows into the fund, the receipts from lending, also form a steady state in keeping the revolving fund topped up.

Taking an endogenous perspective is not to state that state created money does not matter – simply that it is relatively less important. State created money (other than helicopter money) can also be modelled as bank created money by a central bank. Neither does it imply that Crusoe like savings cannot be used to finance investment, business savings for example are often used for this purpose, but this only has an indirect (through liquidity and income effects) rather than a direct effect on interest rates. Finally it does not imply that maturity transformation (or as I prefer it liquidity transformation) cannot be used by banks to leverage idle reserves in a fractional reserve process to expand their profits. Despite all of these qualifications bank created money through the crediting of reserves is the dominant means of money creation. Empirically it must form the starting point of our investigations.

Although banks can create money ‘out of thin air’ to uses Schumpter’s phrase, their ability to do so is not unlimited. We have attempted to show on this blog precisely what that ability – this lending power – is. (the term lending power come from old banking textbooks – such as from Davenport).

At the heart of this explanation is the so called charter value of banks. Accounting has long recognised that firms have a value over and above the value of their tangible assets minus their liabilities. The difference being the value of their intangible assets or goodwill. If a firm closed down then this value is lost. Goodwill is effectively the value of the firm as a firm, over and above its tangible assets, assets which can be rented or bought by anyone. As we have explained the existence of this goodwill is the explanation for firm profits, quite separate from the rents which accrue from owning land or assets. It is the value of the market power, the power of the brand, of knowledge of the market and customer’s knowledge of the value of the brand in the market. Without this goodwill there would only be rent from ownership of resources, no profits. Returns on equities then have a rental element from ownership of the tangible assets purchased with equities, and a profits components from ownership of intangible assets. Profits from goodwill can be seen as a form of differential rent, from ownership of intangible assets.

For banks the charter value is the value of the intangible asset of being able to trade as a bank. It has a fundamental relationship with the value of the banks equity. At the start of the bank it has no liquidity, so equity substitutes for it. When a bank closes it loses its charter value. So the charter value is the value of a bank trading as a bank from retail and merchant banking operations, deposits and loans, rather than as an investment bank buying and selling other assets. Charter value has long been acknowledged in finance and bank accounting but has only recently entered into monetary theory, promoted by Neil Wilson and then taken up by Professor Steve Keen (see here). The charter value is the fundamental component of the lending power of a bank, its ability to lend. When a bank makes a loan the loan is an asset on its balance sheet, whilst reserves are liabilities. But double entry bookkeeping requires that this asset cannot appear from nowhere it must be a deduction from an asset or equity account. Even though a bank can create money electronically through crediting a bank reserve account its withdrawl requires bank liquidity. A factor highlighted when a bank starts before acquiring a loan book or depositors. So lending power, an intangible asset, is debited and its loan book credited. When a

Lending power is not the only factor contributing to a banks charter value, it may charge a fee on deposits or financial advice for example, but lending power is the major component. The accounting formula essentially shows that what the firm owns (its assets) is purchased by either what it owes (its liabilities) or by what its owners invest (its shareholders equity or capital).

My own contribution to this idea has been to examine the role of equity in supporting lending power. By the fundamental equation of accounting

1. Assets = Liabilities +Owners Equity

The accounting equation shows that what the firm owns (its assets) is purchased by either what it owes (its liabilities) or by what its owners invest (its shareholders equity or capital).

When a bank starts up it has no funds to lend. Hence the start-up equity is transferred to an asset account, I term here working capital, to be issued as loans. Each loan has a net present value from the capitalisation of future interest payments. If these funds are retained and not distributed as dividends they become an asset adding to future lending power. Fundamental to this process is the business model of banking. The profit from lending is the costs of the loan minus revenues from interest. If the loan is profitable it likely to be made, with the most profitable loans made first. Hence is incorrect to state that banks are reserve constrained, and better but still slightly misleading to state that banks are capital constrained. A better way of putting it is that banks are profit constrained, and the potential to make profits is the ability to attract capital.

Fig 5 Basic Model of Endogenous Money Creation Through Banking –Without Liquidity Transformation

Please note as deposits are liabilities to banks then increasing a deposit is reducing a liability – hence the negative sign.

[note I wish to thank a number of commentators on my blog in helping to refine this view. Firstly Steve Keen for clarifying that money creation needs to be shown as a liabilities operation. Secondly Bhaskara for clarifying that working capital needed to be shown as an asset side operation, Neil Smith for clarifying the role of Equity and Francis Coppola for clarifying the role of collateral. In this version I have split lending power from bank working capital both as assets. This is because no all assets are necessarily put to work as working capital. This approach also meets both the economic viewpoint of working capital and the accounting definition that is working capital = current assets – current liabilities].

Additions to liabilities are shown negative so when added to assets sum to zero.

Loan Interest is treated as an extension to the loan, where the associated deposit is immediately paid over to the Bank.

	Assets			Liabilities		Equities
Bank Operation	Charter Value – Lending Power	Bank Working Capital	Loan Portfolio	Vault Non Circulating Liabilities	Other Deposits	Safe
Grant Lending Power	+Equity					-Equity
Grant wORKINg cAPITAL	– Working Capital	+Working Capital
Create Credit	+Credit			-Credit
TRansfer MONEY		+Money		-Money
Provide Cost of funding	+Cost of Funding				-Cost of Funding
Grant Loan				+Loan	– Loan
Record Loan	-Loan		+Loan
Charge Loan Interest				+Interest Charge		-Interest Charge
Grant Deposit Interest		-Deposit Interest		+Deposit Interest
TRANSFER Deposit interest				-Deposit Interest	+Deposit Interest
Record LOAN Interest	-Interest Charge		+Interest Charge
REPAY INTErest and premium				-Premium -Interest payment	+Premium +Interest Payment
DELETE CREDIT		-Premium -Interest payment		+Premium +Interest Payment
AMORTIZE LOAN	-Premium -Interest payment		+Premium -Interest payment
Pay Dividends	-Dividends					+Dividends
Restore Working Capital	-Retained Profits	+Retained Profits

Note a bank here has two sources of to create money in its ‘vault’ to lend from. Notes say to ‘pay the bearer’ they are liabilities. We use the term (even though these days it is electronic) as such liabilities don’t have to be circulated, they first have to be leant. Firstly they can be created from existing Crusoe like savings, such as through equity, or from the bank simply crediting an account. The latter course depends on a positive cash flow, profits lending and depositing, or as we shall see the ‘maturity transformation’ of deposits. The second route is classic ‘goodwill’ an asset based on the expectation of future positive cash flows. For a start-up bank they have no choice, they have to use equity to ‘back’ the notes, for a mature bank it will try to minimise the drain on its ability to lend that payment of dividends will bring so it will try to minimise its equity as far as regulators allow – as doing so places the banks solvency and liquidity at risk at times when there is no positive cash flow.

Fig 6     The Two Sources of Loans

When a depositor has a loan credited the liability of the bank to the borrower increases, hence the minus sign. A depositor has to run down an account to pay the loan, hence the liability of the bank to the depositor decreases. Note also how repaying a loan destroys money, but at the same time restores the banks ability to create money – via retained profits of the bank. Paying down a loan also reduces the net present value of the loan portfolio (an asset) as these are limited by the term of the loan. Please note also that this is a single bank model. Loans spent will become deposits in this or another bank and so will dividends.

In the business model of banking. That is the profit of a bank is the cost of the loan minus the revenue from the loan at net present value. What if a bank has lent up to its lending power but still finds that there are additional profitable loans to be made? If the cost of funding the additional lending power still maintains an acceptable level of profit the bank will if it can borrow short to extend its lending power for long term loans. Before long any positive profits will restore lending power meaning short term funding will be the principle requirement. This is the underlying dynamics behind the nostrum that banks make money through borrowing short and lending long. This is known as the reserve window. This is covered in the cost of funding row. It is an addition to the cost of a loan.

Note how in this system there is an initial stock addition to lending power, a flow output (working capital which then creates liabilities – money) and a flow input (interest+premiums), retained profits after payment of dividends are restored to working capital either to expand the loan portfolio or for any other purpose.

We can expand the model to include the maintenance of reserves and capital requirements are required by regulations or the banks own macropudential rules, as well as the fractional reserve (liquidity transformation) process.

The fractional reserve process works by a bank making use of the time between bank deposits and withdrawals. It arose in renaissance Italy (the earliest recorded example is from Venice) when banks realised that they had more reserves on hand then their day to day demand for reserves from depositors required, and hence they could lend it out at interest. This is often termed maturity transformation, though I prefer liquidity transformation. This is not lending from ‘impatient’ to ‘patient’ but rather where an accounts between illiquid accounts and liquid accounts, or course banks in these cases simply make use of this liquidity to ‘borrow’ from the liquid accounts, of course at no interest and lend at interest. So it is better termed liquidity transformation, as it works as a transfer between liquid and illiquid accounts notwithstanding the ‘patience’ or ‘impatience’ of the lender.

The process is to temporarily transfer liabilities to assets (lending power – vault) whilst maintaining a prudential reserve ratio, these reserves may be deposited or required to be deposited in a central bank wherein they become liabilities of the Central Bank. This explains the apparent contradiction that deposit reserves are a liability to the bank whilst central bank reservers are an asset – they become an asset (temporarily) through liquidity transformation The bank needs to be able to transfer money from its working capital to the deposits of its account holders at the rate it requires them. The ‘buffer’ of a reserve helps in this regard then it simply becomes a matter of topping up the required reserve account. In many cases banks can simply create a surplus of non-circulating reserves In some regulatory regimes the granting of credit will also have additional capital requirements, this acts as a cushion in cases of when banks suffer large losses.

Fig 7    Expanded Model with Fractional Reserve Lending (liquidity Transformation)

Only the modified top part of the balance sheet is shown.

The withdrawl ratio is the probability that a deposited unit of money will be withdrawn at any unit of time. It is a measure of liquidity preference, again showing that liquidity preference cannot be treated as an axis by itselof. So for example

	Assets				Liabilities		Equities
Bank Operation	Charter Value – Lending Power	Central Bank Reserves	Bank Working Capital	Loan Portfolio	Vault Non Circulating Liabilities	Borrower Deposits	Safe
Borrow from Deposits	-Deposits*(1-withdrawl ratio)					-Deposits*(1-withdrawl ratio)
Maintain Reserve Ratio	-Deposits*(1- reserve ratio)	+Deposits*reserve ratio
Grant wORKINg cAPITAL	-Deposits*(1-withdrawl ratio) *1+(1-reserve ratio)		+Deposits*(1-withdrawl ratio)* 1+(1-reserve ratio)

Note the double ‘top slicing’ the bank must be able to ensure liquidity by maintaining a withdrawal ratio. It may also be required to deposit a proportion of reserves with the central bank.

Let give an example. Lets say on average the depositor keeps money in the bank for a mean of 40 days, but are paid every 20 days. The withdrawl ratio of that depositor will be 0.75. It is likely to vary between depositors depending on their wealth. If the central bank deposit rate was 0.1. Then 0.25-0.1 = 0.15 of deposits are available for liquidity transformation. The reserve ration can never be greater than the withdrawal ration otherwise liquidity transformation is impossible.

Term deposits can be modelled in exactly the same way, the only difference being that rather than the withdrawl ration being uncertain it becomes contractually fixed. Interest on deposits is shown in Fig x and note that the return to lending power is the spread between the deposit rate and the loan rate. Although deposits of net borrowers and net lenders are consolidated in fig x note how this makes limited difference to net lending power, liquidity transformation applies to all deposits and the only difference is the higher rate of deposit interest.

Then lets say a firm depositing with it has a windfall profit. The bank would then enjoy what is generally known as ‘excess reserves’, reserves in excess of the level necessary from the withdrawl and reserve ration. I am using the old fashioned definition from early C20 banking textbooks of excess reserves rather than the highly contextual modern regulatory definition. The bank would then exceed its own liquidity preference and the ‘excess reserves’ would expand the banks lending power through the process outlined above.

Finally in terms of a simple single bank model lets look at collateral. Those who lend without collateral are making a risk that the loan will default. This may add to the cost of the loan by adding an interest premium. If the cost is high then collateral may be required. Collateral acts as insurance. Lets say there is a 5% risk of a loan then this sum, discounted to NPV is the additional insurance required at the granting of the loan. This can simply be included in the model by multiplying the value of the loan by 1-default risk. If collateral is secured then rather than this addition to the cost of the loan collateral of equivalent value is added to the asset side of the balance sheet. This asset when can also be re-used as collateral on other loans (rehypothecated), its value declines on each re-use – by the “haircut”, or amount of extra collateral required to achieve the same risk reduction. Therefore the ability to extend credit depends on the extent and velocity of credit as a number of papers by Manmohan Singh has noted.

So far we have considered a single bank model, we shall now expand it to account for the transmission of lending power between banks (via loans and dividends) and the similar transmission of state created money. Here we have a puzzle

Let the reserve-to-deposit ratio be, say, 20 percent and the system can, by making loans, create $5 of deposit money per dollar of reserves received. By contrast, the individual bank receiving that same dollar on deposit can lend out no more than 80 cents of it. How does one reconcile the banking system’s ability to multiply loans and deposits with the individual bank’s [relative] inability to do so?  (Humphrey 1987)

The solution was sketched out by a series of writers in the banking school tradition, sketching out how each bank lends out its excess reserves this being deposited by the seller of the good which is loaned for and this bank so expands and so on until excess reserves are eliminated achieving the reserve ratio desired by bankers. Although a bank loses lending power to itself by granting dividends its expands the lending power of the banking system by an amount equal to the residual of the deposited dividends not held as reserves (retained profits being historically called the’ bankers surplus’) expanded throughout the banking system. This is an endogenous versions of the money multiplier.

The key steps in formalizing this process came from (Davenport 1913)and then mathematized by (Phillips 1931)

Manifold loans are not extended by an individual bank on the basis of a given amount of reserve. Instead, as a consequence of lending, the reserve of the individual bank overflows, leaving only the equivalent of a fractional part of the additional volume of loans extended, the overflow cash finding its way to other and still other banks until it becomes the “residualized,” yet shifting, foundation of manifold loans and deposits.

I set out a series expansion of this process here. The result is that we can modify the expansion in lending power from excess reserves as follow:

(2) (1-withdrawl ratio)* (1-reserve ratio)*(1+T)

Where T is the rate of turnover of accounts

This process can also be applied to Central Bank state money creation. Empirically this is less important than bank money – estimates vary but generally 90+% of money is estimated to be endogenous. We can model a central bank with a balance sheet very similar to a private bank. This is an important point as Central Banks were in the main private banks which were taken over by the state. A Central Bank can make profits from its balance sheet like any bank, through lending and liquidity transformation. Its minimum reserve requirements are strictly speaking a form of financial repression which allows it to expand its own lending power. The lending power of banks can be modelled two fold. Firstly as the implicit equity of its sole owners the state. Central banks return profits to the state which is an effect a dividend. The ‘fiscal backstop’ that the state provides to cover any losses on central bank operations is also a form of equity. For this reason I don’t think it is wise to consolidate central bank and state account when looking at money creation.

Central Banks can also expand their lending power unilaterally like any bank. Unlike other banks however they (outside currency unions) are monopoly suppliers of the unit of exchange. So they can ‘print money’ (electronically). Wheras a private bank worries about remaining liquid a Central Bank has no such worries because it has supplied the liquidity and can simply raise deposit requirements or issue more money at will to remain liquid.

Bond/gilt issuance does not imply money creation. Bonds are typically bought from savings and this does not involve net money creation. So deficit financing financed by bonds, as Abbe Lerner pointed out, is likely to be deflationary. There might only be a small multiplier from government budget deficits if the fiscal multiplier of the spending is higher than the spending that would otherwise occurred in the private sector from the money taxed. Indeed the one time in the General Theory Keynes talks specifically about deficit spending he refers to spending financed by bank loans not bond issuance. Richard Werner has recently expounded a similar theory, as did Abbe Lerner, and Hawtry (indeed Hawtry stated that his famous ‘Treasury view’ of crowding out definaitly did not apply to government deficits funded by bank credit).

Fig 8     Fiscal Stimulation from Bond Issuance (from Werner)

Fig 8     Fiscal Stimulation from Bank Borrowing (from Werner)

The one occasion when bonds can be expansionary is where the Central Bank creates money to purchase them, either newly issued bonds or through open market operations on bonds already in circulation. The purchase of such bonds is expansionary and the maturing of the bonds contractionary.

When a central buys a bond from a bank or the state with newly created money the party it bought the money from has ‘excess reserves’ that is money in excess of its current liquidity preference. For the state it typically spends it, for a bank it can spend it, lend it or hoard it. A strong transmission mechanism is needed between this so called ‘base money’ and private bank lending for this to effect overall money in circulation. The breaking down of this mechanism in recent years has shown the limits to which the state can control the money supply. Simply creating excess reserves is no guarantee a bank will lend them. The lending must be profitable and there has to be demand for leverage.

So multiplier processes through lending run in two directions, one from endogenous money one from exogenous money. However the former is far more important than the latter.

Let us look at now at the Keynes ‘steady state’ position of a bank that lends from its initial equity – that credit is created, the loans are paid back, the lending power is restored and new loans are made. A full ‘revolving fund’.

If that bank did not engage in liquidity transformation then any change in its lending power, such as the earlier case of the need to fund new capital because of the discovery of a more productive technique, would have to come for an injection of equity, from prior saving. An increase in the supply of loans would come from an increase in the flow of savings. Therefore the static nature of the revolving fund is only relevant in cases where a firm is simply replacing depreciated capital not improving capital.

When we expand the case to including fractional reserve lending through liquidity transformation then far from the revolving fund remaining static it allows for the exponential growth of lending power providing lending is profitable. This due to profits from interest and not returned as dividends, which is historically known as the ‘banker surplus’ expanding lending power.   Ill present a simple model.  In the first we have a ‘frontier’ start-up bank with limited initial equity $10,000 – lending in conditions of a high rate of profit.  Lets say it fractionally levers that to $90,000, assuming a reserve ratio of 0.1, of lending power leaving $1,000 in reserves.  Lets assume an interest rate of 8% of which the bank makes 5% profit with a 3% inflation rate. let us also assume that the bank pays a 5% dividend, in line with the general rate of profit, recycling 95% of the banking surplus to lending power.  I also assume that the k factor – that is the proportion of the new deposits retained in the bank but not spent is 0.05, and the withdrawl ratio for deposits is 0.8

This produces the following over 20 periods:

Fig 9     Model of Expanding Lending Power

Lending Power	Interest	Profits	Dividends	Reserves	Central Bank Reserves	Excess Reserves	Excess Reserves Leveraged
90,000	7,200	4,500	225	20,000	2,000	18,000	3,600
93,600	4,680	4,680	234	36,634	3,663	32,971	6,594
100,194	5,010	5,010	250	49,958	4,996	44,962	8,992
109,187	5,459	5,459	273	60,639	6,064	54,575	10,915
120,102	6,005	6,005	300	69,212	6,921	62,290	12,458
132,560	6,628	6,628	331	76,101	7,610	68,491	13,698
146,258	7,313	7,313	366	81,646	8,165	73,482	14,696
160,954	8,048	8,048	402	86,119	8,612	77,507	15,501
176,456	8,823	8,823	441	89,737	8,974	80,763	16,153
192,608	9,630	9,630	482	92,671	9,267	83,404	16,681
209,289	10,464	10,464	523	95,060	9,506	85,554	17,111
226,400	11,320	11,320	566	97,014	9,701	87,312	17,462
243,862	12,193	12,193	610	98,621	9,862	88,759	17,752
261,614	13,081	13,081	654	99,951	9,995	89,956	17,991
279,605	13,980	13,980	699	101,060	10,106	90,954	18,191
297,796	14,890	14,890	744	101,992	10,199	91,793	18,359
316,154	15,808	15,808	790	102,784	10,278	92,506	18,501
334,655	16,733	16,733	837	103,464	10,346	93,118	18,624
353,279	17,664	17,664	883	104,054	10,405	93,649	18,730
372,009	18,600	18,600	930	104,573	10,457	94,116	18,823

This spreadsheet is available here (.xslx).

Here we have used a deliberately high interest rate to show the effect more visibly. You can see from this can lending power overall increases much more rapidly than savings (in the Keynesian sense of unspent balances) because of the increase to the revolving fund of finance. If the fund relied solely on ‘top ups’ from profits on loans it grows exactly in line with growth in the economy, no more and no less.  This effect is the same even with purely state created money, the column geadings are the same all that changes is the source of the excess reserves.

Two issues which can be used to make the model more realistic.  Firstly because of a wealth effect savings are likely to rise with income.  Secondly there is a second order effect with excess reserves being placed in other banks – this is a single bank model – we could easily add a 1+T multiplier to the last two columns which would considerably expand lending power based on the turnover rate of balances.

In this case with the supply of endogenous money increasing ceritis paribus interest rates must be pushed down, even if ‘savings’ (funding) and investment are in balance, and even if there is no change in liquidity preference.  Therefore we can be certain that the supply of lending power does impact on interest rates and so Keynes was wrong that only liquidity preference set rates. Also the static nature of the revolving fund does not explain finance for economic growth other than ‘expansion of the market’ through replacing capital stock like for like. As we have shown it does not explain how innovation creates a demand for additional finance, which if supplied from savings or credit both serve to push interest rates up (through increased demand and reduced relative supply of money per unit of investment) as well as the growth effect from the innovation with which banks must compete for funds. Keynes device of a ‘revolving fund’ in a steady state is a crucial device in modelling the monetary circuit, but Keynes was wrong, modelling fractional reserve banking under endogenous &/or exogenous money – although Keynes has an important insight that an increase in investment requires an expansion of the ‘revolving fund’. The fact that under conditions of steady growth the fund increases means that monetary flow must effect interest rates as well as monetary stock, so the supply of lending power, not just the stock of liquid assets, effect interest rates.

The effect of this is that banks, at times of steady growth, will – over time – have less and less need to attract ‘savings’ (funding) to fund loans – so they can afford to lower deposit rates and hence increase profits because of the increased spread between savings and deposit rates.  There cannot be a stable period where savings (funding)=investment under endogenous money as because of the changing size of the revolving fund due to compound interest it is forever shifting.  Also remember investment = funding x turnover – and turnover is affected both by the turnover period of capital and the amount of excess reserves.  The relationship between savings and investment is a profoundly disequilibrium one.

Also with interest rates being pushed down banks will compete for funds with other investments when alternative higher profit investments present themselves, banks may also be tempted to divert liquidity transformation into these sectors. Banks therefore must lend out their lending power for it to continue to expand, so they are forced to take on riskier and riskier investments, either unsecured or with less creditworthy collateral. So long as asset prices appreciate this can continue for some time, but as soon as they show signs of reversing then the ability to grow lending power is curtailed thrown reduced collateral. A collapse in asset prices can lead to bad loans. This dries up the flow of funds into lending power. When its customer’s deleverage this also reduces the inflow of funds. Lending power can then shrink to zero and with deleveraging credit can be net reduced in the economy reducing effective demand.

Lets look at this in distributional and accounting identity terms then the ‘base’ lending power of banks depends on the factor returns of holders of money. It is related to prior ‘savings’ but it is not a one to one identity, as it also depends on the turnover of capital and the ‘depreciation’ of money (inflation). If in one year the rate of interest is equal to the rate of inflation and the loan turns over once then strictly savings=investment. However if the loan is profitable and interest rates are used to expand lending power and those interest payments in turn are recycled to expand leverage then there is no one to one identity, the amount of ‘finance’ as a flow will be greater than the initial savings.

Put formally

(3)    ΔInvestment (stock)= ΔSavings (stock)

(4)    ΔLending Power (flow)= ΔInvested Savings (flow) X turnover x (1/inflation)

Where

(5)     Invested savings= ΔEquity+ Δliquidity transformation+ΔBankers Surplus

And where liquidity transformation = equation (2). So if a financial institution between times T0 and T1 needs to attract ΔInvested Savings (assuming no change in turnover) then from (1) and that ΔSavings=ΔIncome-ΔConsumption it must attract funding from either idle balances or consumption.

I should note that if we treat inflation/depreciation as a cost and bankers profits as a residual then equation () becomes Kalecki’s profits equation expressed as a differential equation rather than a static identity.

So lending power can be expressed as a clear series of flow variables. Interest rates enter twice into the formula, on the return on time deposit and interest on loans topping up lending power when retained as banker’s surplus. The relationship with interest rates in linear however the slope of nthe curve will increase in a non-linear manner at times of economic growth as set out in Fig 9. So the supply of loans, even loans supplied from savings is indeterminate as a theory of interest rates, rather as with the IS curve it describes the equation of a curve – a supply curve.

The horizontal axis for the LP curve is PT – the product of price and transactions – in other words the total amount of income in reserves, and not PY the total amount of value added as measured by GDP. It is the total amount of income of whatever source that determines lending power.

We are examining the outflow from lending power at an instant in time, so in stock flow consistent terms its maximum level will be (in instantaneous time) the rate of inflow to lending power, which can itself be shown as a curve, plus the stock level of lending power – which is a vertical line.

Fig:10     Lending Power Stock and Flow

Together they form the maximum lending power curve as shown on fig 11.

Fig:11     Lending Power Stock and Flow Curves

This effectively is a production possibility frontier curve for money. Here we come to subtle differences with the IS curve. We recall by the savings=investment identity the current state must always be a value on the curve. The lending power inflow curve represent actual cash flows based on actual past levels of investment and current levels of saving, therefore it too represents a fixed set of possible states with no possible states off the curve. Not so the lending power outflow curve. This represents the maximum lending power, it is a set of possibilities that cannot be exceeded. It is perfectly possible for the bank to lend less the residual being the addition to the stock of potential lending power. We can best represent this by treating the vertical axis as the real interest rate. As such a bank will only make a real cash return when rates and the level of returns are both sufficient to cover the costs of the loan. They will also be unlikely to expand lending power flows unless returns are at a competitive rate of profit, otherwise they will seek investment opportunities elsewhere.

Consider a case where the Lending Power stock is positive but (perhaps because of bad debts) the inflow LP curve is below zero as some or all interest rates, but the demands for lending (the RL curve explained below) is positive at real interest rates at some or all levels of interest. At the point of intersection the bank may still make a profit from lending but its lending power stock is rapidly shrinking, as we shall see in a future section if the curves intersect at a negative rate then we see no profitable lending, even if the stock of lending power become positive lending will not recommence until the sum of the lending power stock and the inflow to lending power rises above zero and to a competitive profit rate.

Under circumstances of normal growth lending power will be rapidly exhausted, no stocks will remain as all lending power can profitably lent out and lending power inflow will match lending outflow. Under these circumstances it is easy to lose sight of the stock aspect of lending power which only emerges during a financial crisis.

We can see that lending power increases with the interest rate, therefore we cannot agree fully with the horizontalist argument that the supply of lending curve is horizontal and set by the Central Bank. This is not to suggest that the Central Bank is not accomodationist in responding to requirements for funds from banks. What we have done is effectively formalise the structural constraints on lending from the horizontalist-structuralist debate (summarised in (Fontana 2004))

Demand for Loans –Required Leverage

Demand for loans is not a demand for liquid funds.

The core of endogenous money theory is that the supply of money in modern economies is determined by the demand for credit (bank loans) and that this, in turn, responds to the need for financing production or speculative purchases. (Fontana 2004)

There area two sources for increased invested savings, either purposefully invested savings which lead to a temporary increase in liquidity preference, or idle balances which allow for liquidity transformation. So here we have a problem with a pure liquidity preference approach as an increase in liquidity preference can either, via the first route, lead to an increase in the supply of loans and a decrease in the demand for them (via decreased effective demand), or a decrease in demand for them and an increase in their supply, via the second. Whilst liquidity preference is important it is more useful to examine the purpose for which liquidity is sought.

For planned savings to purchase equity or bonds there must be a decrease in the liquidity preference of the saver, but liquidity preference here is simply a residual after planned consumption and any increased income. It is better to think in terms of asset preference (the inverse of liquidity preference), the preference to hold financial assets that will yield a return in time rather than liquidity preference. The preference for holding an asset with a term and anticipated yield over another asset determining the total portfolio and yield curve. Seen through such Tobinesque spectacles a ‘liquidity preference’ approach to the theory of interest cannot be accused of indeterminacy and circularity. The demand for a loan is a function of expected income and the required leverage of that income to purchase an asset.

That asset may be brought for speculative purposes, as a commodity to produce other commodities, or as a final consumption good. Some goods may indeed may yield multiple of these services, and over time rather than being simply destroyed in the act of consumption. For example a house will yield consumption services as a place as residence whilst at the same time acting as a speculative store of value.

Liquidity preference enters into the determination of the market interest rate through the secondary channel of liquidity transformation of excess reserves, the supply side, not the demand side. It indirectly affects the demand side in that unavoidable overheads cannot be used to either pay loans or save for deposits. For a demand for money (loans) function we must look beyond simple liquidity preference.

This is not to state that there is not a demand for loans where current income is squeezed below current expenditure, and there is a risk that is future expenditure is further squeezed, or future income does not recover there will be a risk of default. In these cases the reasonable borrower and lender must have some rational expectation of improvements in balance sheet positions. Given the uncertainty regarding this they may seek security on the loan and/or larger down payments. In effect these act as insurance on the risk of default. As we explain here insurance is conditional debt creation – a form of credit.

Those who lend without collateral are making a risk that the loan will default. This may add to the cost of the loan by adding an interest premium. If the cost is high then collateral may be required. Collateral also acts as insurance. Lets say there is a 5% risk of a loan then this sum, discounted to NPV is the additional insurance required at the granting of the loan.

So demand for loans is not a demand by the insolvent to be solvent but a demand to bring forward future income into the present. To sacrifice the purchase of future goods for present ones. If a loan is secured without collateral then the cost of insuring against default will need to be added to the interest rate.

The demand for loans then is a demand for leverage of expected income. Demand for leverage we shall term the DL curve. It can be measured in terms of units of unconsumed income x sought leverage, with that sought leverage being the net present value of future income. It is a demand for saving but not savings from current income, but expected income.

Please also note that there is no reliance here on irrationality or so-called Ponzi investors. They may of course exist but they are not necessary to drive a credit cycle. All that is necessary to drive such cycles is an appreciation that at leverage ratios at extremities where a correction is likely. In these circumstances hedging comes into play. An investment decision is a prediction of returns over period. Speculation involves estimations of whether there will excess profits or losses using knowable risks. Speculation has a cost, it has a price the cost is the cost of the hedge. This adds to the cost base of the firm and the price of goods (or the price of money if the commodity demanded is a loan). It shifts the supply curve. Hedging is adopting the opposite position. So investment is a three way vector where any point on a future yield curve is the sum of the speculation vector (return x probability of return) and the hedge vector (loss X (1- probability of return)). So at the top of a market with high volatility and high hedged risks this additional cost can cause asset bubbles to pop. Note this is not intermediation between the risk averse and the risk bearing, as with banking intermediation is not a function but an ex-poste rationalisation of net portfolio decisions. Some by the size and nature of their portfolios can afford to be greater risk takers than others but in this model all will rationally hedge these risks.

Please note that unlike the original IS-LM model there is no stock flow inconsistency. Total income (defined as PT not PY – as GDP being a value added measure exclude asset price speculation) is a flow, as is the services of interest, yet although both axes are flows total a savings ‘fund’ is a fund, as is income left liquid, as is the amount of a loan. Our revised model avoids these dimensional inconsistencies, all variables are flow variables measured in units of money over any period of time. Note how resulting liquidity preference will affect the amount of unconsumed income – and hence the future income stream that can be leveraged. Unconsumed income will also affect the supply of loans curve by creating excess reserves that can be can leveraged as increased lending power. The curves therefore are not independent. There is no ‘real’ curve and ‘money’ curve intersecting, both curves are monetary and shifts in money creation and interest rates have real effects. Money is not a veil.

Also note how we have fully accounted for uncertainty – a common criticism of IS-LM, including of course by Keynes in his letter to Hicks, is that the static view takes insufficient account of expectations. We have included uncertainty over future asset prices (collateral) and income levels in the RL function. By including expectations of future prices and incomes in both curves we have avoided this problem. The end result reincorporates some of Keynes insights into the effect of asset price speculation from the Treatise on Money.

The IS-LM approach, in its classic form, explains short term interest rates only, and then either this is argued to explain long term interest rates, or longer term interest rates are presumed to be entirely independent of monetary considerations. With our approach however we can build an entire yield curve. For any period of loan we can define expected income and expected prices and determine the yield based on the risks of the loan, and we can do without some of the heroic efficient market hypothesis type assumptions regarding portfolio optimisation of modern finance theory. By incorporating a market process where the lender makes the highest efficiency investments first we have also avoided the static assumptions of IS-LM, that it can only explain prices on general equilibrium, and not how that equilibrium is reached or the consequences of departure from equilibrium. The short side here being set by the LP supply curve at high levels of interest (subject to risk) until moving down the schedule of investment until the return on investment (the rental return on capital minus depreciation) is no higher than the risk free rate. (Fig 12] The level of investment being determined by the spread, s, between the real interest rate and the real risk free rate. (Note although interest on excess reserves does marginally increase the risk free rate and hence reduce investment the effect is very small (currently around ¼ of 1%), the current shortage of investment is explained better by falls in the RL and especially the LP curves).

Fig 12 Marginal Propensity to Invest

The rest of the area under the LP curve will either be invested elsewhere (such as in ‘risk free bonds’ or used to increase the stock of lending power of prospects for future lending look improved (such as anticipated rise in interest rates). Even if real interest rates are negative investment may continue providing there is a sufficient spread between the real interest rate and the risk free rate.

Our approach supplements this by the supply of lending power being allocated to borrowers according to the profitability of loans demanded whist maintaining the risk weighted capital requirements of the lending body. If effect this is a marginal efficiency of investment process such as described by Keynes. A great advantage of this approach is that in vesting in loans is treated as any other investment – there is no classical dichotomy between the real and monetary. Conditional on staying within risk weighted capital constraints the lender allocates the most profitable loans first, then the next most profitable until the lending power is exhausted. At that point any excess profit that results from the market power of the lender is exhausted and the LP and DL curves cross and below this interest rate the lender cannot make a profit. As in the diagram below we have moved from left to right down the LP curve. As with all such curves in a cost or production approach the marginal costs of production are the result and not the cause of the market process and the slop of the supply curve represents the degree of monopoly of that sector.

Finally we have all of the pieces to specify the RL – Required leverage – curve in mathematical terms. Our approach here is taken from the school of writers who have taken an asset portfolio approach towards determination of the interest rate, including Walker (), Boulding (), Davidson() and Wray (). Thus far however this approach has modelled the division of a portfolio, rather than the leverage of a portfolio, so it has had a hidden loanable funds assumption.

It is often naively assumed that the demand for leverage is unlimited, because the demand for money is unlimited, however this is not the case as excessive leverage is likely (because of future interest payments) reduce disposable income unless the return on an asset is high. On the issue of optimal leverage we have been influenced by the writings of Ole Peters (Peters 2009)who sets out the ‘leverage problem’ “by how much should an investment be leveraged,” in terms of non-ergodic time and the application of the Kelly formula for optimal leverage. The Kelly formula is as follows, named after a mathematician at Bell Labs. The leverage f is defined as the ratio of the size of your portfolio to your equity. f should equal the expected excess return of the strategy divided by the expected variance of the excess return, or

(6)    

The excess return being the return (N minus the risk-free rate R.), with δ being the standard deviation of the return. f here is the proportion expected income I remaining after transactional living expenses t. So the amount invested is fIt. We can take f as applying both to savings for deposits on loans or from premium and interest payments. The difference between the two being credit and whether payments come from current or future income.

This approach assumes highly aggressive leverage, with initial equity of a scale to pursue it has been shown to produce optimal results, however as Samuelson (79) showed without infinite time and with a limited starting equity less aggressive strategies are to be preferred. These are often dubbed ‘fractional Kelly’, so we may modify the formula to be

(7)     

Where Lamda is a measure (0-1) of the risk aversion of the investor with this inversely proportional to income and inversely proportional to uncertainty and time. By inclusion of lambda we are able to demonstrate the reversal of the yield curve at times of high uncertainty. The amount invested is the leverage ratio f of disposable income –n which is gross income I, minus transactions demand for money t.

So the amount invested, the principal on the loan including interest is

(8)     

Peters rightly sees in the Kelly approach a means of avoiding the ergodic fallacy in probability theory and as an alternative to ‘utility’. Rather than averaging the results of strategies assumed across multiple worlds the optimum strategy is based on the ability to lever, to take risk, based on the success of past strategies. Peters has an important insight about the limits of leverage

if the risk and reward associated with an asset make it optimal to borrow money to invest in it (that is, apply a leverage greater than one) then all market participants should be borrowing to invest. But who will provide the loans and who will sell the assets? Likewise, if market conditions are such that everyone should be borrowing assets to sell them short, then there will be no-one to lend the assets and no-one to buy them back?

The assumption here is of loanable funds, that the money already exists to buy the assets. This fallacy leads Peters to conclude that leverage ratios outside the range 0 to 1 of income must be unstable. Once we allow for endogenous money however this gap between supply of current funds and demand for required leverage can be breached through credit, to be paid for by future income. The insight that the leverage ratio must be between 0 and 1 holds however for future income. If expected income is greater than actual realised future income then the risk is that the loan defaults (collapsing spending power) and current and planned spending on other items is squeezed. Therefore by allowing for expectations of future income we have also a simple model for explaining volatility in credit markets, a model with distinct Minskian properties, driven by asset prices and expectations by market participants in those asset prices.

If we after Werner() split the economy into income from assets and income from production – the latter measured as GDP, then income will have net components, one from changes in income from production, the other from net turnover of assets. The latter is a zero sum in a closed economy, one person’s loss of income from purchasing assets is another’s gain in income. The asset component of income in a closed economy can only continue to grow, rather than hovering around a net zero turnover of assets, where two conditions are fulfilled, firstly a shortage of that asset, secondly the cohorts of net purchasers of the asset remaining larger than the cohort of net disposers. Hence the close association between structural shifts in asset price growth and changes to demographics. Such as the close correlation between the bursting of house price bubbles and the reduction in the baby boomer cohort, as noticed by Nisimura (). If we relax the closed economy assumption then there can be a net change in national income from asset prices as those selling, or buying, enter or leave a country.

In the longer run then leverage is safer if the levels are in line with expected income from growth in the real economy as opposed to growth in income arising from asset prices, as the latter is both more volatile and prone to sharp corrections. Growth cannot be sustained from growth in asset prices, eventually the costs increases from asset price growth will harm the real economy. In the short run the perception of higher income and wealth from holders of assets may increase spending in the real economy through a velocity effect, but in the long run only consumption from real income is sustainable. If therefore the leverage ratio exceeds growth in the real economy asset prices are liable to boom and bust.

There is a major caveat to the application of the Kelly Formula, it assumes that individual investment decisions are all statistically independent, like individual rolls of the nice. In economics this is to repeat the micro-foundations fallacy of composition. The variability of individual leverage decisions are not independent. The greater the total amount of leverage the greater

Empirically lenders will set rules for loan affordability based on current rather than expected future income to avoid this problem, however when lending power is growing quickly experience strongly suggests that lenders will seek out avenues for loans by other means, such as bending rules of ability to pay. This suggests, as Haldene argues, that simple macroprodential rules restricting leverage, such as automatically adjusting reserve ratios, may be more effective than complex measures of value at risk, especially when future uncertainties over investment returns are essentially unknowable.

We can meld our modified Kelly formula with an NPV formula to derive a formula for the DL curve.

(9)    

Where N is the NPV of the asset, and Nn is the expected valuation of the asset at point in time n, The NPV is the same as V the return on the investment, so we can write.

So we can write the amount invested as

(10)    

We can also relate the amount invested to the value of a loan for a term and interest rate.

(11)     

P – the Principal, or amount borrowed

r – the Interest Rate for the specified time period

a – the amount repaid each repayment period

n – the number of payments to be made

And a formula for the net present value of the asset

Combining these (10) and (11) we get.

(12)    

Multiplying both sides by 1/(1+r)

(13)     

Cancelling

(14 )    

So

(15)     

Which is intuitively correct as it is the margin of the return of the asset per period over the cost of the loan per period including the cost of including hedged losses. a here may be interpreted as the budget constraint from disposable income, which is O-T which cancels so

(16)    

So an interesting conclusion is that the demand for leverage is invariant to liquidity preference, this acting solely on the supply side through idle balances. Whatever the level of income, liquidity preference or transactional demand r represents the ratio at which leverage of that income is demanded.

The first part is the spread rate s, so put simply the interest rate is equal to the spread multiplied by sensitivity to risk and a volitlity measure of risk of loss.

We can apply the formula to construct a yield curve by applying different values for that term. Note not only lambda will change as the longer the period considered and the closer to a financial crisis the higher δ will be also.

The axis for the LP curve is real interest rates, meaning that real interest rates are assumed for all values of r in the equations above. Clearly there will only be a demand for leverage when investment yield real returns. This avoids a frequent criticism of the IS-LM framework in only working in nominal terms.

So far we only considered positive leverage, but this framework can equally apply to negative leverage, such as where changes to income lead to the non-financial sector deleveraging. Such a change could occur when interest rates have fallen but where there is an expectation that interest rates will rise in the future. In those cases there will be a desire to use a surplus of income now to avoid a shortage of income in the future by paying down debt. The drivers here are both the change in income and the change in interest rates, so if the expected change in interest rates is high enough then households may even reduce an already squeezed consumption in order to delever.

The traditional objection to this derives from the classical dichotomy that money must be neutral as per Scott Sumner

Individuals can get rid of the cash they don’t want, but society as a whole cannot

The answer to this is given by Steve Roth

If households and nonfinancial businesses (the real sector) are holding more money than they want, they can use it to pay off debt to the financial sector. That money disappears.

Kaldor said much the same (the law of reflux) in 1983

Since credit (and hence bank money) varies in response to bank loans the ‘money supply’ cannot be assumed to vary relatively to the money demand: The supply of money can never be in excess of the demand for it… The excess supply would automatically be extinguished through the repayment of bank loans, or what comes to the same thing, through the purchase of income yielding financial assets from the banks. (Kaldor 1983)

Justifying our approach focussing on the supply of and demand for leverage, the supply of leverage can never be greater than the demand for leverage at that interest rate.

The LP-RL model

Placing the LP and RL curves together we have the LP-RL model. The RL curve describes the demand for money creation at a particular interest rate, the LP curve then determines the maximum level of money creation at that interest rate. If the interest rate is set by the market then it will be set by the intersection of the LP and RL curves, representing the partial equilibrium between the demand for and supply of leverage, the point of maximum profit for lenders. This is not necessarily a full employment equilibrium and outside the mythical world of barter there is no ‘natural’ interest rate, only a market one. Where the interest rate is set outside this level then the short side rule applies, and the interest rate will be set by whichever is lower the LP or RL curve. So where the demand for leverage is low then loans will be issued at a much lower rate than lending power allows fig (x), when it is high the lending power of banks will constrain maximum leverage, credit is rationed to the most creditworthy and those paying the highest interest rates.

These curves are not independent the decision to seek leverage has a knock on effect on reserves and hence lending power. Whilst as Lavoie points out the household sector demand for leverage will have a knock on effect on the demand for equities, and hence the demand for leverage by firms. So in a more sophisticated stock-flow consistent approach it may be better to model the RL curve separately for firms and household.

Credit Deadlock, The Liquidity Trap and Investment Stagnation

As the final stage we shall consider the empirical relevance of this new approach to current economic challenges.

On the classic liquidity trap because of the zero lower bound to interest rates the demand for money becomes perfectly inelastic – a flat IS curve, in that case injections into the banking system will be ineffective as lending will not rise – so  increased money supply fails to lower interest rates.

On our formulation the RL curve performs the same function, when it is flat any increase in Lending Power will fail to transmit to additional lending. This, like Keyne’s original formulation, will apply whenever the curve is flat, not simply at the zero lower bound. [fig 13]. Why might demand for leverage be perfectly inelastic at the nominal ZLB? For a bank given the portfolio alternative of either creating or holding cash, and thus earning 0% return, rather than lending it out, profit-seeking lenders will not lend below 0%, as that will guarantee a loss, similarly a bank offering a negative deposit rate will find few customers, as savers will instead hold cash. Interest and premium payments add to t the transactional demand for money, so in these cases where the demand for required leverage is low agents may be actively deleveraging. Indeed where a portfolio contains liabilities at fixed interest rates a shift in interest rates will give an incentive to refinance to maximise future income. The optimum portfolio will therefore be that combination of leveraging of residual income and deleveraging of liabilities which maximises future income from leverage.

The liquidity trap story, though well applied by Krugman and others to Japan, primarily related to the demand for money curve, and by itself does not present a clear narrative of how demand for money (leverage in our case) has become elastic.

Fig 13      Liquidity Trap

A fuller and better explanation comes if we examine the changes to the LP curve during a balance sheet recession. The inflow of funds to lending power may become negative, and as we have shown the stock of lending power will soon become exhausted. This means that the LP curve may intersect the RL curve at a level below the risk free rate lending will dry up, they may even intersect at a level below zero. Even if negative interest rates are permitted if the RL curve is negative due to deleveraging then it will not intersect the LP curve and hence no profitable lending will occur. When the banks cease to lend we have a credit crunch, when the LP curve is below zero and fails to intersect the LP curve we have a Hawtryian Credit Deadlock (Sandilands 2009). In a normal, moderate non balance sheet depression low rates would suffice to revive business, but in severe conditions a ‘credit deadlock’ can emerge in which lenders are too afraid to lend and borrowers too afraid to borrow – a case of an unusually inelastic demand for and supply of loans with respect to the short-term rate of interest. [Fig 14]. Though shown alongside a liquidity trap in Fig 14. this can occur with any LP curve providing it does not intersect the LP curve, which it is unlikely to do given the zero lower bound.

‘[I]f the depression is very severe, enterprise will be killed. It is possible that no rate of interest, however low, will tempt dealers to buy goods. Even lending money without interest would not help if the borrower anticipated a loss on every conceivable use that he could make of the money. .. The deadlock then is complete, and, unless it is to continue unbroken till some fortuitous circumstance restarts activity, recourse must be had to directly inflationary expedients, such as government expenditure far in excess of revenue, or a deliberate depreciation of the foreign exchange value of the money unit.’ (Hawtrey 1931) P330-331

Fig 13 Credit Deadlock

As (Laidler 2006) states

a serious policy error was made in the 1990s [in Japan]… based on a theory of monetary policy that treats the short interest rate as the central bank’s only tool and characterizes the transmission mechanism as working solely through the influence of interest rates on aggregate demand. That theory provided no means for Japanese policy makers to distinguish between a liquidity trap, which is a possible feature of a demand for money function, and a credit deadlock, which is a characteristic of the money supply process, or for them to entertain the possibility that variations in the money supply might affect aggregate demand by channels over and above any effect on market rates of interest.

We may also have a third case [fig 14]where the RL curve is at positive at least at some levels of interest but at low elasticity rates but the LP curve is ineslastic, in these cases deleveraging may have ceased but bank profits and expectations of future income remain low (because for example of austerity), so LP and RL remain low and we have investment stagnation.

Fig 13 Investment Stagnation

Indeed we can see the key feature of a balance sheet recession is not just that demand for leverage falls as does income but with negative balance sheets lending power collapses, and with the need to deleverage and with faling prices the relative importance of the Kalecki effect (deflation not helping repaying loans measured in nominal units) outweighs the Pigou/Patinken real balances effect (purchasing power of balances relatively increasing) leading to long term stagnation.

Therefore the RL and LP curves interact to dictate the pace of investment in different kinds of recession and at different states of that recession. This is something the vanilla IS-LM struggles to cope with in failing to explain, for example, how Japan can be stuck in deflationary stagnation long after deleveraging has occurred.

Further Work

This work is at an early stage however the ability of this model to explain long term stagnation following a balanced sheet recession is hopeful and seems to represent an advance over IS-LM. An approach similar to this appears to be embedded in Krugman’s view of Japan but stuck with an indeterminate loanable funds approach he is not able to articulate it and we are left with handwaving to fill the gap.

We have been able to do so because we have developed a stock-flow consistent model of banking, which shows how changes to supply of money (credit), changes to savings and net asset turnover can all affect investment decisions and hence effectual demand. Further work is to show how distributional effects from interest and all other factor returns influence effectual demand. In a sense we have provided the theoretical scaffordinging to bridge Keynes and Hawtry and revive the npre-war credit cycle view of changes to effectual demand in a manner which is consistent with Keynesian identities.

The next logical stage to extend the approach to an AS-AD curve. The traditional next step with IS-LM, allowing to properly consider the labour market outside GE rather than it remaining in the background. This would be an Effective Demand Effective Supply, ES-ED curve, utilising the analysis we have developed of idle balances to understand change to demand. None of this is a substitute for a full stock-flow consistent model, however by showing the key dynamic in the form of a simple two dimensional graph it does help visualise the state of the macro-economy and therefore may be at least a bearably useful classroom gadget.

Other future steps would include fuller modelling of state money, state bond and central bank operations including QE, as well as within a stock flow consistent framework. The impact of changes to central bank interest rates however are limited because of the dominance of exogenous money, effectively setting the risk free R through the national equivalent of the fed funds rate and bond open market operations to hot that rate. This can reduce the spread s at times of investment exuberance but can never force an interest rate to be lower than markets can profitably lend nor force additional lending at times of stagnation or depression. Creation of state money, or state borrowing from banks (as opposed to bind financing from savings) will however push up the LP curve potentially breaking out of investment stagnation. This is only likely to be effective however if the Rl curve is pushed upwards as well otherwise it will be ‘pushing on a string’ against a low elasticity, this can occur through debt forgiveness or forebearance, higher wages or benefits or higher expected inflation. Higher inflation does depress the spread s and hence investment in normal growth times, however with a flat RL curve this effect will more be more than offset by the RL curve shifting to the left to points of steeper investment elasticity. Public investment can also be helpful but with bind financing deflationary and limited lendind power from low bank profits helicopter money may be more effective.

References:

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Davenport, H. (1913). The Economics of Enterprise. New York, Augustus M. Kelly.

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Hawtrey, R. G. ( 1931). Trade Depression and the Way Out. London, Longmans.

Hicks, J. (1980-1981). “IS-LM: An Explanation.” Journal of Post Keynesian Economics, v. 3: : 139–155.

Hicks, J. R. (1937). ” Mr Keynes and the ‘Classics’: A Suggested Interpretation.” Econometrica Vol.5,(

No.2, ): 146-159.

Humphrey, T. M. (1987). “The theory of multiple expansion of deposits: what it is and whence it came.” Economic Review, Federal Reserve Bank of Richmond: 3-11.

Kaldor, N. (1983). Keynesian Economics After Fifty Years,. Keynes And The Modern World. G. D. N. W. a. J. A. Trevithick, Cambridge University Press.

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. London: Macmillan and New York: , Cambridge University Press for the Royal Economic Society.

Keynes, J. M. (1936). The general theory of employment, interest and money. London,, Macmillan.

Krugman, P. (2009 ). Liquidity preference, loanable funds, and Niall Ferguson (wonkish) The Conscience of a Liberal

Krugman, P. ( 2011). IS-LMentary. The Conscience of a Liberal

Laidler, D. (2006). “Woodford and Wicksell on Interest and Prices: The Place of the Pure Credit Economy in the Theory of Monetary Policy.” Journal of the History of Economic Thought 28(2): 151-159.

Leijohnhufvud, A. (1980). What was the Matter with IS-LM. Recent Developments in Macroeconomic Theories. Florence.

Leijonhufvud, A. (2011). Nature of an Economy. Policy Insight, CEPR. 53.

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Peters, O. (2009) Optimal leverage from non-ergodicity.

Phillips, C. A. (1931). Bank Credit: A Study of the Principles and Factors Underlying Advances Made by Banks To Borrowers, New York.

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Sandilands, R. (2009). Hawtreyan “Credit Deadlock” or Keynesian “Liquidity Trap”? Lessons for Japan from the Great Depression U. o. Strathclyde, SIRE DISCUSSION PAPER. SIRE-DP-2009-14.

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Sraffa’s Hidden Treatment of Money – A Wages Fund

The common assumption is Sraffa had no treatment of money, that any commodity could act as one in his system.  This is an error, it is there but hidden.

I came across this reference in Sraffa’s unpublished notes in an article by Gehrke and Kurz – in the form of a note on von Bortkiewicz, in 1943, when Sraffa had reached a crucial theoretical turn

The transformation of wages [into value – in contrast to von Bortkiewicz]  has been done by introducing (in all but in name) money; and taking the Annual Revenue as unit of money (hence the “proportion” = money wage).(D3/12/35: 9(1-3)

Here we are talking about a specific system of production and what Sraffa terms (in reference to Ricardo) as ‘proportional wages’ that is the w (wage share) in his famous formula r=R(1-w) where r is the rate of profit, and R is the maximum amount of profit (a flow value) over the turnover period (the revenue).

In Ricardo however there is a very simple relationship between proportional wages (the wages share) and the nominal value of an individual workers wage.  This was that capital advanced as wages/population=the wage.  Capital advanced is R(1-w), the wages fund, and in early classical dogma the higher were wages the smaller investment, and increases in wages by one set of workers simply depleted the wages fund for others. Here we can see a close relationship with Kalecki’s profit formula as capital advanced is simply profits minus consumption (including a contribution to a depreciation fund).

You might think that no economic concept has been more discredited than the wages fund.  However none of the theoretical core ideas of classical economics underwent such thoroughgoing evolution as the wages fund doctrine, even surviving in a modified form in Austrian Economics – as first the ‘subsistence fund’ and then the ‘pool of funding’, though picking up a few fallacies on the way, such as the ‘creation of money out of thin air’ depletes this fund.

At the core of the ‘fund’ concept is an important physical relationship that has been completely lost in neoclassical economics. That is the relationship between the physical output (surplus) and the labour force – the land/labour relationship we find in Petty, Cantillon, the Physiocrats , Torrens and Ricardo, where a fund of corn grows, is depleted by consumption, and reinvested for the next turnover period.  Sraffa was of course seeking to restore economics to this objective physical foundation.

The Wages Fund approach was greatly refined over the period of classical economics dominance.  It grew beyond the rigid and false approach of an iron law of wages to embrace that it is is a ‘fund’ which can grow or be depleted through in and out flows over time.  Hence if wages grew this would add to demand which would grow the fund.  It was in this revised form that JS Mill modified the concept in 1869 (it was not a recantation), and FW Taussig  in Wages and Capital: An Examination of the Wages Fund Doctrine  1896,and Frances Amasa Walker in the Wages Question 187, conceptualized it in more stock-flow consistent terms. In particular rather than population as a permanent divisor diluting teh fund labour was treated as the source of wealth and demand.  Though as Marshall commented in such a radically reconceptulised form it lost a lot of its original political economy vigour (or rather from the capitalist side of the argument).

In Böhm-Bawerk’s reconception of the ‘english’ theory it becomes a a stock of consumption goods that sustained a worker until the capital service was on stream.  In his famous Crusoe economy example Crusoe hoarded coconuts for a few days to sustain him through a few days constructing a stick to reach more coconuts.  The fund is fairly easy to model in a world of a single good which is also a consumption good.  When conceived in monetary terms however complications ensued.  Both Wicksell and Blaug have stressed the similarity on the wages fund idea.  Rather than a fixed stock of population and a fixed period of production there now was a fixed stock of population and a fixed stock of capital advanced which sustained a period of production – or as Wicksell more correctly termed it a period of investment.

Some defenders of Sraffa see wages and interest as essentially undetermined in his system – and so should be treated as purely social forces.  Sraffa however, though stressing that both had social components, was more inclined to treat interest as the exogenous variable, and of course the rate of profit has a crucial regulating role for the rate of interest.

Various attempts have been made to graft a monetary basis onto Sraffa, and as a result describe production in monetary term making his theories compatible with Sraffas.  I don’t regard any of these theories as fully satisfactory. One potentially fruitful approach is to regard money as a commodity like any other [ I take the Circuitist approach as implying that money must be a different commodity than those being exchanged not a commodity at all]  which is produced at a profit by holders of money.  Such an approach chimes well with the endogenous theory of money and the business model of banking.  It produces a problem though a it treats interest as a cost of money which capitalists will employ through debt if it produces more revenue at or above the average rate of profit, for the bank then the cost of producing the loan will be less than the revenue hence a profit.  But this requires the rate of interest to be known at the beginning of the period of investment.  In his lectures on value theory Sraffa called this ‘circular reasoning’ requiring value to explain vale.  For this reason I think Sraffa treated interest as exogenous as he was keen for an explanation of value which was invariant through time, but because production takes time there is also the need to fund the goods sustaining labour through time, so Sraffa was also forced to make labour endogenous.  Indeed modern interpretations like that of Sinha see  he approach as  frozen moment in time rather than a process in time gravitating towards any kind of ‘equilibrium’ .

Let us deal briefly with own rates of interest.  Sraffa in his critique of Hayek suggested that each commodity would have its own rate of interest.  So to give an example if over a year maize would produced twice its own seed and wheat three times its own seed then maize would earn a higher own rate of interest than wheat.  This is I think to confuse Agio – productivity – with interest – which I treat as a purely monetary phenomenon – agio on money.  A holder of a company which owns land suitable for growing maize would have higher stock prices than one which holds land suitable for growing wheat.  The equity markets would even out the rates of profit.  So if I borrowed money to buy stock it would be at the average agio.

If money (at interest) is required to sustain labour throughout the period of investment then the cost element of labour is not the sum of labour costs over the period of investment but the discounted cost at the prevailing rate of interest.  Here we assume that this is debt financed rather than through retained profits, but if the rate of profit is low in that industry than these retained profits will rationally be interested in another industry at a higher rate of profit.  If labour is homogeneous for a given production technique across the period of investment then the cost of the last employed unit of labour will be the marginal cost.  But here marginal cost is the residual o0f the avlue process and not the cause of value.  This shows that at the margin the marginal and the cost of production theories are equivalent, however the cost of production approach is more enlighting of the total circular flow of production.

Wicksell Lectures on Political Economy (1901) reconceptualised the concept as a ‘Wages Flow’ It is the flow of capital into investment not a fixed fund of capital, that hires workers and creates incomes. When capital advanced capital turns over faster, through increased demand for example,an originally  fixed fund of capital can generate more investing whenever a surplus of labor seeks jobs.

If one is solely concerned with simple interest then a fall in the rate of interest increases the period of investment, Bohm-Bawerk and Hayeck seem vindicated, however once interest is compounded through retained profits and reinvestment that this simple relationship does not hold – we get Wicksell effects.  So back to Sraffa, it is not simply the case  of reswitching of choice of technique that occurs at higher interest rate, because at a given productivity a technique will take a given period of time which at different interest rates will have have different costs.  Hence at higher interest rates you might get switching back to a technique that takes a longer period of time depending on the period of investment of the goods of which the capital good is composed.

Therefore there is a treatment of money in Sraffa, which can be conceptualised by a ‘wages flow’ like process, but which needs to be modelled in a flow input flow output model of surplus, retained profits and investment.  The challenge is to do so in a manner which avoids the ‘circular logic’ trap.  This will be followed up in a future post.