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.

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