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George H. Blackford, Ph.D.

 Economist at Large

 Email: george(at)rwEconomics.com

 

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The Theory of Interest

Robertson versus Keynes
and

The Long-Period Problem of
Saving and Debt

This book is available in Kindle and paperback format at Amazon.com for a nominal contribution to this website.

 

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 Copyright, 1983-2018

(Last Revised 7/4/18)

 

Preface

Prologue

 

Summary of Chapters:

Chapter I: Robertson versus Keynes

Chapter II: Walras, Marshall, and the Theory of Interest

Chapter III: The Long-Period Problem of Saving

Chapter IV: The Long-Period Problem of Debt

Chapter V: Concluding Observations

Appendix A: Keynes’ Theory of Interest

Appendix B: The Structure of Keynes’ Implicit Model

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Preface

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In the Preface to The General Theory of Employment, Interest, and Money, John Maynard Keynes wrote:

The composition of this book has been for the author a long struggle of escape, and so must the reading of it be for most readers if the author’s assault upon them is to be successful, — a struggle of escape from habitual modes of thought and expression.  The ideas which are here expressed so laboriously are extremely simple and should be obvious.  The difficulty lies, not in the new ideas, but in escaping from the old ones, which ramify, for those brought up as most of us have been, into every corner of our minds.  (1936, p. viii)

It is argued below that the failure of policy makers to escape the old and accept the new led to the adoption of economic policies over the past forty-five years that culminated in the Crash of 2008 and the economic stagnation that followed.  It is further argued that this failure arose from an inability to appreciate the role of Marshall in the development of Keynes’ thought. I find Keynes’ simple ideas to be easily understood from the perspective of Marshall and beyond the ken of the Walrasian paradigm of neoclassical economics that underlies the worldview of policy makers.

While the primary purpose of this monograph is to provide a definitive explanation of the way in which the rate of interest is determined and to explain the connection between the central thesis of The General Theory and the economic problems we face today, the manuscript is written in such a way as to explain Keynes’ general theory from the perspective of Marshall. As such, it is a primer on The General Theory of Employment, Interest, and Money, directed toward economics students in the hope that it will facilitate their ability to go beyond the Walrasian perspective of Neoclassical economics to gain a deeper understanding of Keynes and of the way in which the economic system actually works in the real world.

George H. Blackford
July 4, 2018

 

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Prologue

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In November of 1936, Dennis H. Robertson proclaimed: “it is not as a refutation of a common-sense account of events in terms of supply and demand for loanable funds, but as an alternative version of it, that Mr. Keynes' account as finally developed must be regarded.” (p.183) The following February, Keynes asked Robertson to provide “at least one reference as to where this common-sense account is to be found.” (p. 210) Thus began the controversy that evolved into what became known as the liquidity-preference / loanable-funds (LP/LF) debate.  This debate continued long after Keynes’ death in 1946 when the torch was passed from Keynes to the Keynesians.

With the Keynesians in charge, the debate took a decidedly Walrasian turn.  While some Keynesians continued to defend Keynes’ argument from A Treatise on Money to the effect that the rate of interest cannot change in response to a change in saving or investment in the absence of a change in income, the vast majority fully embraced John R. Hicks’ 1936 argument to the effect that it makes no difference which theory one accepts since the static equilibrium properties of the two theories are the same.  The Keynesians embraced Hicks’ argument in spite of the fact that Keynes had rejected it in June of 1937. 

In response to the Keynesians, Robertson and his fellow anti-Keynesians continued to insist that Keynes was wrong in his rejection of the idea that the rate of interest is determined by saving and investment through the supply and demand for loanable funds irrespective of whether the equilibrium properties of the two theories are the same.  The position of the anti-Keynesians was best summarized by Harry Johnson in 1961:

The liquidity preference-loanable funds debate turns on the question of whether the rate of interest is better regarded as equilibrating the flow of funds onto and off the market for securities or as equilibrating the demand for and supply of the stock of cash.  The answer, which is now so deeply embedded in mathematical argument that no one can be sure he has got it right, seems to be that…it makes no difference…provided… one is concerned only with the determination of the equilibrium level of the rate of interest….  The two theories become different, however, when applied to dynamic analysis of disequilibrium situations.… In a dynamic context, the loanable funds theory definitely makes more economic sense; and the sustained resistance of Keynesians to admitting it, evident most notably in the prolonged defense…of the proposition that an increase in the propensity to save lowers the interest rate only by reducing the level of income, is a credit to their ingenuity rather than their scientific spirit.  (Johnson, 1961, pp. 6-7)

And so it went until Robertson died in 1963, a point in time at which the Keynesians had come to so dominate the discipline of economics that there seemed to be no need for them to continue to respond to the anti-Keynesians on this issue, and the controversy seems to have just petered out.

Since it made no difference to Keynesians which theory was assumed, the Keynesians walked away from the debate confident they were victorious as they concentrated on the equilibrium properties of their models.   And since the anti-Keynesians were no longer rebuffed by the Keynesians, the anti-Keynesians walked away equally confident of the victorious nature of their performance.  Thus, the debate ended with both sides declaring victory.  As a result, the issues of the Robertson / Keynes controversy have never been resolved, for while it is generally agreed that the two theories have identical static equilibrium properties, there exists no consensus as to the nature of their dynamic properties.[1]

The failure to achieve a consensus in this regard has had the gravest of consequences for it left the discipline of economics with two theories of interest, each of which seems plausible and neither of which is fully understood.  The result has been a persistent ambiguity with regard to numerous theoretical and practical problems relating to  the way in which saving affects the economic system.  The reason is, Keynes argued throughout The General Theory that saving is a nemesis that plagues the economic system by inhibiting economic growth and employment.  It was this argument that Robertson challenged in his controversy with Keynes.  Thus, even though the primary focus of the LP/LF debate was on the determination of the rate of interest, the substance of the debate — as framed by Robertson and the anti-Keynesians — was concerned with the way in which saving affects the economic system.  As a result, the anti-Keynesians walked away from the debate believing their view of the beneficial role of saving had been vindicated. 

This has created a situation in which the role of saving in the economic system is not well understood by policy makers since economists take positions on both sides of the issue—some arguing that saving inhibits economic growth and employment (demand-side economics) and others arguing that economic growth and employment are stimulated by saving (supply-side economics).  The result has been a rudderless guide to ad hoc policies over the past fifty years that has led us to where we find ourselves today, faced with a bitter divide over the appropriate response to the economic, political, and social crisis that has been developing throughout the world since the Crash of 2008—a divide in which neither side seems to be able to understand why the other is so confused.  

I believe that given the history of the LP/LF debate, this divide cannot be bridged in the absence of a clear understanding of the way in which the rate of interest is determined within the context in which the issue was originally raised by Keynes, namely, within the context of the Marshallian paradigm of supply and demand.  There are many grounds on which one can criticize this paradigm, but I suspect that almost all economists recognize its essential validity, and I can’t even imagine what it would be like to try to make sense out of a market economy in a principles course without the concepts of supply and demand as put forth by Marshall .  If we are unable to start with an explanation of the way in which prices and quantities are determined by the actions of decision-making units in individual markets within the context of a Marshallian, partial-equilibrium analysis, how is it possible to provide a causal explanation of the way in which prices and quantities are determined within any economic model?

It is the purpose of this monograph to sort through the issues of the LP/LF debate in order to provide a definitive explanation of the way in which the rate of interest is determined within the Marshallian paradigm of supply and demand, and, beyond this, to explain the fundamental connection between the central thesis of Keynes’ General Theorythat consumption is the driving force for economic growth and employment, not saving—and the economic, political, and social problems we face today. 

Chapter I: Robertson versus Keynes reviews the arguments of the controversy between Robertson and Keynes that are essential to understanding the issues that separated the two sides in the LP/LF debate. 

It is argued that whether or not the loanable-funds theory is consistent with the Marshallian paradigm of supply and demand is the seminal issue raised by Keynes in The General Theory, but this issue became lost in Robertson’s conflation of three separate issues raised by Keynes: 1) whether or not the rate of interest is determined by saving and investment, 2) whether or not an increase in the propensity to save can stimulate the formation of capital, and 3) whether or not full employment can be maintained in the long run by monetary policy alone.  Even though all three of these issues were raised by Robertson in his controversy with Keynes, and even though Keynes disagreed with Robertson on all three of these issues, the first became the focus of the LP/LF debate while Keynes’ arguments with regard to the other two became peripheral.  These three issues are examined in detail below, the first in Chapter II and the second and third in Chapter III.

The importance of the relationship between expectations and income in Keynes’ general theory is also examined in Chapter I.  Keynes argued that whenever production takes time, at each and every point in time at which a decision must be made concerning employment and output that decision must be made on the basis of currently held expectations with regard to the costs to be paid and receipts to be received in the future as the output is being produced and when it is sold.  This argument has a clear implication with regard to income which Keynes defined as the value of output produced.  It implies that whenever production takes time, income is earned (accrues) before the output being produced in generating income is actually sold.   This makes income a psychological phenomenon, determined in the minds of decision-making units, and this value cannot be separated from the current expectations of these unit.

The psychological dependence of decisions concerning employment, output, and income on expectations is of the utmost importance in Keynes’ general theory for it is this dependence that provides the distinction between the way in which expected and realized results affect decision-making behavior: Expectations with regard to the future affect current decisions directly whether these expectations are realized in the future or not; realized results affect decisions only after the results are (or are not) actually realized, and, even then, only to the extent they affect existing stocks of capital assets and subsequent expectations.  This distinction lies at the very core of Keynes’ view of casualty for it establishes the temporal order in which events must occur which makes it possible to separate cause and effect.  It is the ability to separate cause and effect by way of this distinction that makes it possible to provide a causal analysis of dynamic behavior within the analytic framework developed by Keynes throughout The General Theory.

It is argued that this distinction marks a fundamental difference between Keynes’ and Robertson’s methods of analysis in that Robertson defined income as the value of output sold.  The only way the value of output sold can be equal to the value of output produced as sales change randomly over time is if expectations are unit-elastic and adjust instantaneously to changes in sales.  This means that, by virtue of his definition of income, Robertson’s method of analysis is that of comparative statics in that Robertson implicitly assumed expectations adjust instantaneously in such a way as to achieve a state of static equilibrium each period.  Robertson then examined how these states of static equilibrium change from period to period.   Thus, it is argued that given the implicit assumption of unit-elastic expectations and instantaneous adjustment that provides the foundation on which Robertson’s arguments rest, Robertson’s analysis of the way in which income and the rate of interest are determined within each period is purely ad hoc and is irrelevant to Keynes’ causal / dynamic analysis of this problem.

Chapter II: Walras, Marshall, and the Theory of Interest examines the fundamental difference between the methodologies of the Walrasian and Marshallian paradigms.  It is argued that while the methodology of Walras is descriptive and static, that of Marshall is causal and dynamic, and the reason for this difference is to be found in the nature of the Walrasian budget constraint. 

The Walrasian budget constraint assumes the choices of decision-making units are made simultaneously at a point in time.  This constraint also assumes choices are  constrained by realized income as defined by sales which is, of course, the essence of Robertson's definition of income.  It is argued that while this may be the way in which budgets are created in the real world, it is not the way in which choices are made.  Real world choices are made sequentially through time, not simultaneously at a point in time, and neither households nor firms are, in fact, constrained in their choices by income, realized or otherwise, at the point in time at which a choice must be made.

The real-world choices of decision-making units are constrained by a) the value and liquidity of their assets, b) the availability of sellers of goods at various prices, c) the availability of buyers of goods at various prices, and d) by their access to credit.  The rate at which decision-making units receive or earn income, realized or otherwise, at the point in time at which a choice must be made has no way of affecting that choice other than through its effects on expectations as anyone who has purchased a home, a car, or has simply walked the aisles of a supermarket knows implicitly, and as any business owner who has had to meet a payroll knows implicitly as well.  Decision-making units have no alternative but to be guided by their expectations with regard to the income they expect to receive in the future and are constrained by the way in which the income they have received in the past has affected the stock of assets they hold in the present, as Keynes  insisted, but they are not constrained by the rate at which they actually receive or earn income in the present or in the future at the point in time at which a choice must be made. 

Even though the Walrasian budget constraint is called a “constraint,” it does not actually constrain the choices of decision-making units.  As a result, the only situation in which it is relevant is when decision-making units and the system as a whole are in a state of static equilibrium.  It has no relevance when the system is not in a state of static equilibrium, and even when the system is in a state of static equilibrium the Walrasian budget constraint is little more than an accounting identity that makes it possible, through aggregation, to eliminate a redundant equation in models that assume the system is over-determined.

There is no mystery about this.  It is well known that by virtue of the simultaneity assumption implicit in the Walrasian budget constraint a causal analysis of dynamic behavior is impossible in Walrasian models. It is the mythical Walrasian tâtonnement/ recontract auctioneer that causes prices to change within the Walrasian paradigm, not decision-making units that actually exist in the real world. 

This does not mean models that rely on this methodology are not useful or meaningful. They are, in fact, exceedingly useful and have proven to be invaluable in the analysis of economic problems when employed in conjunction with Keynes’ Marshallian methodology. But it does mean that such models cannot be used to establish the temporal order in which events must occur—that is, the order in which their endogenous variables must change in response to a change in an exogenous variable—and, thus, they cannot provide the basis for a causal analysis of dynamic behavior

There are two reasons the situation is fundamentally different within the Marshallian paradigm:

  1. The ceteris paribus assumption of the Marshallian paradigm makes it possible to explain the determination of prices and quantities and what will cause prices and quantities to change in terms of the behavior of those decision-making units (e.g., buyers and sellers) that actually have the power to determine and change prices and quantities bought and sold in markets. 
     

  2. There must be a change in the behavior of those decision-making units that actually have the power to determine and change prices and quantities bought and sold in markets before a change in price or quantity can occur (e.g., supply or demand must change before the price or quantity can change) within the Marshallian paradigm.  This makes it possible to establish the temporal order in which events must occur which makes it possible to separate cause and effect.

It is the ability to separate cause and effect and to explain why prices and quantities change in terms of the behavior of those decision-making units that actually have the power to determine and change prices and quantities bought and sold in markets that make it possible to provide a logically consistent, causal explanation of dynamic behavior by way of Marshall’s ceteris paribus methodology.  This is why the seminal issue with regard to the theory of interest raised by Keynes in The General Theory is whether or not the loanable-funds theory is consistent with the Marshallian paradigm of supply and demand. 

Keynes demonstrated through his old argument in A Treatise on Money that the need for money to finance transactions in a monetary economy means that the prices of assets cannot change (other than by way of distribution effects which can go either way) in response to a ceteris paribus increase in saving if output and the supply and demand for money are given.  In this ceteris paribus situation, the concomitant decrease in the demand for consumption goods that corresponds to an increase in saving means producers of consumption goods will no longer be able to obtain the money needed to finance their current scale of operations through sales.  If employment, output, and income are to be maintained in this situation, producers in the consumption goods industries must be willing to borrow money or sell assets in order to obtain the money needed to finance accumulating inventories and other expenditure obligations that are required to maintain their current scale of operations.  As a result, the total value of money willingly borrowed at the initial rates of interest plus the value of assets willingly sold at the initial prices of assets must be exactly equal to the total value of the increase in saving. 

This means that there are no economic reasons for rates of interest or prices of assets to change (other than by way of distribution effects) in this ceteris paribus situation.  This also means that Marshall’s ceteris paribus methodology cannot be used to explain the behavior of rates of interest or prices of assets in terms of the flows of saving and investment since a ceteris paribus change in the behavior of savers (or investors) cannot cause a change in rates of interest or prices of assets.

What is significant about this ceteris paribus situation, however, is that while there are no economic reasons for rates of interest or prices of assets to change, there are economic reasons for employment, output, and income to change.  The accumulation of debt and depletion of marketable assets on the part of producers of consumption goods must eventually lead to a change in expectations with regard to the profitability of producers continuing to maintain their current scale of operations.   This change in expectations must eventually motivate producers in the consumption-goods industries to reduce employment and output.   The resulting fall in income can, ceteris paribus, be expected to reduce the level of saving until the willingness to save is equated with the willingness to invest since it is at this point, and only at this point, that producers in the consumption-goods industries will be able to eliminate the necessity to increase debt and sell assets in order to maintain their scale of operations, and savers will be able to accumulate all of the assets they wish to accumulate.

This means that in order to provide a logically consistent, causal explanation of the way in which a change in saving or investment affects the economic system through time that is consistent with Marshall’s ceteris paribus methodology it must be assumed that income, not the rate of interest, is determined by saving and investment. 

This leaves the determination of “the rate of interest in the air.  If the rate of interest is not determined by saving and investment in the same way in which price is determined by supply and demand, how is it determined?" (Keynes, June 1937, p. 250) To answer this question, Keynes developed his liquidity-preference theory which “makes the rate of interest depend on the present supply of money and the demand schedule for a present claim on money in terms of a deferred claim on money.” (p. 241) All that is needed to understand how this works in Keynes’ general theory is to follow the causal chain of events implied by Marshall’s ceteris paribus methodology as the system adjusts to an increase in saving through time.

The fall in employment, output, and income that results from a ceteris paribus increase in saving must also cause a fall in the demand for money.  And just as there are economic reasons for income to change in response to a  ceteris paribus change in saving, there are economic reasons for rates of interest to change in response to a ceteris paribus fall in the demand for money. 

A fall in income must cause a fall in the demands for transactions and precautionary balances that, given the supply of money, must increase the supply of what will be referred to in this monograph as speculative balances, that is— money balances decision-making units have no use for other than to lend or  to hold as an asset.  What happens to the prices of existing non-debt assets in this situation will depend on the supplies and demands for non-debt assets, but what happens to the prices of debt assets and rates of interest will depend crucially on the supply and demand for money.  

To the extent the increase in the supply of speculative balances increases the willingness of wealth holders to purchase new and existing debt, competition for new and existing debt must, ceteris paribus, lead to a decrease in rates of interest. As the resulting decrease in rates of interest increases the capitalized value of existing non-debt assets and, thereby, lowers the prospective rates of return on the purchase of existing non-debt assets it must force members of the nonbank public (i.e., wealth holders) to either a) accumulate money balances for which they have no use other than to hold as an asset or b) accept lower rates of interest on the debt assets they choose to accumulate. At the same time, banks will be forced to either a) accumulate reserves or b) accept lower rates of interest on the debt assets they choose to accumulate. 

Keynes argued that as rates of interest fall below the rates wealth holders expect to be realized in the future, wealth holders will be motivated to hold a larger portion of their wealth in the form of money and a smaller portion in the form of debt in an attempt to minimize the risk of a  capital loss on holdings of debt in the future.  Thus, to the extent the resulting fall in rates of interest enhances the willingness of wealth holders to hold their wealth in the form of money — that is, to willingly accumulate speculative balances to hold as an asset — the quantity of money demanded must increase.  And to the extent the resulting fall in rates of interest enhances the willingness of banks to accumulate reserves, the quantity of money supplied must fall.  The fall in rates of interest can be expected to continue, ceteris paribus, in this situation until the quantity of money supplied is equal to the quantity of money demanded for it is at this point, and only at this point, that rates of interest will equalize the marginal advantages of wealth holders holding speculative balances as an asset or holding debt and of banks holding reserves or holding debt, and there is no economic reason for rates of interest to change. 

Thus, if we think of the rate of interest in terms of “the complex of the various rates of interest current for different periods of time, i.e. for debts of different maturities” (Keynes, 1936, p. 167n) “and risks” (p. 28) this means that in order to provide a logically consistent, causal explanation of the way in which changes in the demand or supply of money affect the economic system through time that is consistent with Marshall’s ceteris paribus methodology it must be assumed that the rate of interest (so defined), not income, is determined by the supply and demand for money. 

This also means that Robertson’s view of causality can find no theoretical justification within the context of the Marshallian paradigm.  Robertson’s claim that an increase in saving “lowers the rate of interest quite directly through swelling the money stream of demand for securities; and that this fall in the rate of interest increases the proportion of resources over which people wish to keep command in monetary form” (1940, pp. 18-19) has it backwards.  Arguing that an increase in saving “lowers the rate of interest quite directly” implies that the rate of interest can fall in this situation before there is a decrease in income that increases the supply of speculative balances.  This runs afoul of what may be called the antea hoc, ergo propter hoc fallacy.  Such arguments only make sense to those who believe an effect (the fall in the rate of interest) can come before its cause (the increase in the supply of speculative balances), which is apparently what Johnson believed when he wrote:

In a dynamic context, the loanable funds theory definitely makes more economic sense; and the sustained resistance of Keynesians to admitting it, evident most notably in the prolonged defense…of the proposition that an increase in the propensity to save lowers the interest rate only by reducing the level of income, is a credit to their ingenuity rather than their scientific spirit.  (Johnson, 1961, pp.  6-7) 

The “ingenuity” Johnson complained about in this passage was on the part of those who accepted the basic principles of supply and demand in defiance of the “scientific spirit”  of those who insisted that within “a dynamic context, the loanable funds theory definitely makes more economic sense” by way of an antea hoc, ergo propter hoc argument that begins with the assumption that an increase in the  propensity to save “lowers the rate of interest quite directly” and then attempted to rationalize this assumption by arguing that the choices of decision-making units are constrained by sales.  As is demonstrated in Chapter I, this rationalization only makes sense in a static analysis which assumes expectations are unit-elastic and adjust instantaneously to changes in salesan assumption that ignores the temporal order in which events must occur, and, in so doing, renders a causal analysis of dynamic behavior meaningless.

What this means is that it is impossible to provide a causal explanation of the way in which a change in saving or investment affects the economic system through time that does not fall prey to Robertson’s antea hoc, ergo propter hoc fallacy if it is assumed that the rate of interest  is determined by saving and investment.  Nor is it possible to provide a logically consistent, causal explanation of the way in which a change in saving or investment affects the economic system through time if the rate of interest is assumed to be determined by the supply and demand for loanable funds if the supply and demand for loanable funds are defined in terms of the flows of saving and investment.

Robertson and the anti-Keynesians dealt with this problem by assuming that income and the rate of interest are determined simultaneously.  What they missed is that by denying the relevance of Keynes’ old argument to their intraperiod dynamic analysis they limited the relevance of their intraperiod dynamic arguments to the imaginary world of the Walrasian auctioneer. 

The same approach was adopted by the Keynesians as they followed Robertson’s lead when they adopted Hicks’ IS/LM model which combines the supply and demand for money with saving and investment to arrive at the equilibrium rate of interest and level of income simultaneously.  This simply begged the question of causality raised by Keynes since the Keynesians’ method of approach was Walrasian and, therefore, descriptive and static.  Even though some Keynesians defended the logic of Keynes’ old argument in their debate with the anti-Keynesians, the vast majority failed to grasp the relevance of this logic to Keynes’ causal / dynamic methodology and what this logic means with regard to the irrelevance of Walras’ Law and the Walrasian auctioneer to the way in which the rate of interest is determined in Keynes’ general theory.  As a result, when the Keynesians adopted Hicks’ IS/LM model they did not adopt Keynes’ causal / dynamic methodology in spite of the fact that there was nothing to prevent them from doing so other than their fidelity to the tâtonnement / recontract methodology of Walras and their inability to grasp or to appreciate the fact that Marshall’s causal / dynamic methodology is the sine qua non of Keynes’ general theory. 

Keynes demonstrated by way of his old argument that in a monetary economy, that is — in an economy in which either money or debt (i.e., borrowed money) are required as a medium of exchange — the entire Marshallian paradigm of supply and demand breaks down if it is assumed that income is determined by anything other than saving and investment or that the rate of interest is determined by anything other than the supply and demand for money.  If  it is assumed otherwise, the Marshallian implications with regard to the temporal order in which events must occur are inconsistent with the reality that economic transactions require money (or the creation of debt) as a medium of exchange.   This means that anyone who assumes otherwise must, to paraphrase Ohlin, refute the Marshallian supply and demand curve analysis in toto and, in the process, reject any possibility of being able to provide a logically consistent, causal analysis of dynamic behavior in economics

Chapter III: The Long-Period Problem of Saving examines Keynes’ long-period problem of saving, that is — the problem of maintaining full employment in the long run in the face of a declining prospective yield at the margin due to the increasing stock of capital that results from the flow of saving.  Keynes’ understanding of this problem can be summarized as follows: 

  1. As saving increases the stock of capital over time, the increasing stock of capital has a tendency to reduce the Marginal Efficiency of Capital (MEC) (i.e., the demand for investment goods) by reducing the prospective yield on additional units of various capital assets as these assets become plentiful or even redundant. 
     

  2. The failure of the propensity to save to fall over time (i.e., the propensity to consume to increase) in a way that offsets the negative effects of the fall in the MEC as capital accumulates and prospective yields fall leads to a situation in which a fall in the rate of interest is required in order to achieve the level of investment needed to maintain full employment. 
     

  3. Since the rate of interest is determined by the supply and demand for liquidity and cannot be negative, there are limits to the rate and extent to which the rate of interest can fall. 
     

  4. To the extent a fall in the rate of interest or propensity to save is unable to offset the effects of the fall in the MEC as the capital stock grows and prospective yields fall over time, the rate of investment must fall below the level needed to maintain full employment.
     

  5. Given the propensity to save, even if the rate of interest were to adjust rapidly enough to avoid sporadic unemployment in the short run, in the long run the MEC and rate of interest (adjusted for risk and the costs of bringing borrowers and lenders together) must eventually be forced to zero and can fall no more.  At this point the economy will stagnate as the fall in output and increase in unemployment force net saving and investment to zero.

And it is important to understand that—contrary to what seems to be the neoclassical understanding of this problem—the fall in perspective yield that results from an increase the capital stock is not simply the result of diminishing returns. Increasing the stock of any particular kind of capital good reduces the prospective yield on that particular kind of capital good even in the absence of diminishing returns in terms of output by way of the negative slope of the demand curve for the output that particular kind of capital good produces and the positive slopes of the supply curves of those goods and factors that are complementary to the employment of that particular kind of capital good.

Herein lies the crux of Keynes’ understanding of the long-period problem of saving—there is a limit to the number of steel mills, automobile factories, gas stations, and Starbucks the economic system can profitably support given the distribution of income, state of technology, etc.

It is noted that even though Robertson’s 1936 review of The General Theory criticized Keynes’ analysis in the name of “the long-period problem of saving,” Robertson did not actually discuss this problem in his review.  The problem Robertson actually discussed is what may be called the short-period problem of saving, that is — the problem of achieving full employment in the short run in the face of  an increase in the propensity to save

It is argued that, because of the way in which the Keynesians viewed the economic prosperity that followed World War II as a validation of Keynesian, neoclassical economics as seen through the eyes of Hicks, the controversy that arose from Keynes’ publication of The General Theory focused  on Robertson’ criticisms of Keynes in terms of the short-period problem of saving while the long-period problem was seen to be of secondary importance.  As a result, Keynes’ analysis of the long-period problem of saving did not become an integral part of the neoclassical consensus that emerged in the 1960s with regard to the nature of Keynes’ fundamental contributions to economic thought.  This created a situation in which the effects of the accumulation of capital on the prospective yield of additional increases in the stock of capital were not incorporated into the worldview of policy makers leading up to the Crash of 2008 to the effect that their view of reality contained a vision of the economic system in which monetary policy can be used through its effects on the rate of interest and investment to maintain full employment indefinitely into the future.  This is a vision that is fully consistent with Robertson’s belief that all that is needed to solve the short-period problem of saving is “a progressive increase in the supply of money.” (1936, p. 188) It is also a vision that, if carried to its logical conclusion, presupposes monetary policy can be effective in maintaining full employment through stimulating investment by lowering the rate of interest even if the entire country were to become paved over with concrete and every square inch of land were to sport a factory or high-rise apartment building.

Keynes did not share this vision of the economic system in that he did not believe monetary policy alone would be able to solve either the short-period or the long-period problem of saving.  It is argued that Keynes has, in fact, proved to be prophetic in this regard as we have seen monetary policy effectively lower rates of interest in the midst  of speculative bubbles almost continuously since the early 1980s throughout the Great Moderation on our way to the Crash of 2008 and the secular stagnation that followed.  This is exactly the result that would have been expected from the economic policies put in place leading up to the Crash of 2008 and the economic stagnation that followed if Keynes’ analysis of the long-period problem of saving had been clearly understood

Chapter IV: The Long-Period Problem of Debt argues that the single most important reason for the inability to understand the causal / dynamic nature of Keynes’ theory of interest and, beyond this, to understand the causal / dynamic nature of Keynes’ general theory itself is the perpetual attempt to force Keynes into a Walrasian mold.  Keynes was a protégé of Marshall, not Walras, and the only way to understand Keynes is to think in terms of Marshall’s “organized and orderly method of thinking out particular problems rather than the “method of blind manipulation” of Walras.  (Keynes, 1936, p. 297)

In applying Marshall’s methodology to “the complexities and interdependencies of the real world,” (p. 298) Keynes was able to obtain a number of critical insights as to how the economic system works on his way to The General Theory of Employment, Interest, and Money.  These insights are discussed throughout the text below and can be summarized as follows:

  1. The ultimate justification for production in a market economy is to satisfy the demands of consumers.
     

  2. The truly causal variables in an economy in which the process of production takes time are expectations with regard to the future.
     

  3. The willingness to invest in real assets depends on the prospective yield of those assets — that is, the yield investors expect to receive in the future as a result of investing in those assets.
     

  4. Prospective yields are affected not only by the rate of interest (which affects the cost of investing in real assets) but also by the stocks of existing real assets relative to the demand for the outputs those real assets produce (which affects expectations with regard to the proceeds that can be obtained from increases in the stocks of real assets) as well as by the infamous “animal spirits” that take the investor beyond the limits of rational calculation.
     

  5. The rate of interest is a purely monetary phenomenon, determined by the supply and demand for money as rates of interest adjust to equate wealth-holders’ demands for liquidity with the existing stocks of assets.
     

  6. Monetary policy is limited in its ability to affect the rate of interest by the propensities of wealth holders with regard to their demands for liquidity and the ability of the monetary authority to affect the existing stocks of assets available to meet the demands of wealth holders.
     

  7. Given the existing stocks of assets and the rates of interest determined by the propensities of wealth holders, the level of economic activity is determined by the effective demands for consumption and investment goods, that is — by the proceeds producers expect to receive as they maximize their expectation of profits through the employment of resources in the production of consumption and investment goods.
     

  8. Since the ultimate justification for production is to satisfy the demands of consumers, and since the ultimate purpose of investment is to increase the production of consumption goods in the future, the demand for investment goods is ultimately determined by expectations with regard to future consumption. 
     

  9. And since expectations with regard to future consumption are largely determined by current consumption, the effective demands for consumption and investment goods (hence, the level of economic activity) are largely determined by current consumption.

These insights drove Keynes to the inescapable conclusion that — consumption is the driving force for economic growth and employment, not saving.  Given the force of Keynes’ arguments in defense of this conclusion, it would appear to be rather straightforward and irrefutable.  And, yet, this conclusion had little impact on economic policy leading up to the Crash of 2008. 

It is argued that at least a part of the reason for this is to be found in the way in which Keynes’ analysis of the long-period problem of saving did not become an integral part of the neoclassical consensus that emerged in the 1960s with regard to the nature of Keynes’ fundamental contributions to economic thought.  This created a situation in which the effects of the balance of trade and distribution of income on the long-period problem of saving were not well understood by policy makers.  This made it possible to ignore these effects and to adopt Robertson’s vision of an increasing propensity to save leading to a smooth transfer of resources out of the production of consumption goods and into the production of capital goods if facilitated by an increase in the supply of money without questioning the assumptions on which this smooth transfer is supposed to take place — specifically, without questioning the assumptions with regard to the effects of decreasing consumption and increasing capital on a) expectations, b) prospective yields, and c) the demands for capital assets.   The result was the adoption of economic policies that enhance the aggregate propensity to save by increasing the concentration of income and facilitating trade deficits—policies that only make sense in macroeconomic models that ignore the long-run relationship between consumption and effective demand and assume that saving enhances economic growth and employment. 

It is observed that the result of these policies has been a profound change in the institutional structure of our economic system that led to a dramatic increase in international deficits along with an equally dramatic increase  in the concentration of income.  This, in turn, led to a dramatic increase in saving in the foreign sector (by way of an increase in trade deficits) and at the top of the income distribution in the private sector (by way of an increase in the concentration of income and a higher propensity to save at the top of the income distribution). 

Maintaining the full employment of resources in this situation requires either a) dissaving in some other part of the system or b) an increase in investment.  The way in which this was actually accomplished over the twenty-five years leading up to the Crash of 2008 was through a) an increase in dissaving in the public sector and at the bottom of the income distribution in the private sector and b) an increase in investment as a result of speculative bubbles in the junk bond and commercial real estate markets in the 1980s, in the markets for tech stocks in the 1990s, and in the housing markets in the 2000s.  At the same time, there was a massive increase in debt relative to income that proved to be unsustainable in the long run as it led to the near collapse of the domestic and international financial systems following the Crash in 2008. 

It is argued that the economic stagnation in the United States that followed the Crash of 2008 is easily explained in terms of Keynes’ long-period problem of saving:

  1. The institutional changes that occurred over the thirty-five years leading up to the crash increased saving a) in the foreign sector by way of increasing  international deficits (foreign-sector saving), b) at the top of the income distribution by way of the increase in the concentration of income, and c) in general by way of policies that encourage private- and public-sector saving (such as encouraging private health insurance and retirement accounts and funds, and converting Social Security from a pay-as-you-go to a partial-prepayment system).  The result was an increase in the aggregate propensity to save that  was offset by dissaving in other parts of the private  and public sectors as interest rates fell and the capital stock grew in the midst of speculative bubbles.
     

  2. The persistence of international deficits and the concentration of income after the crash, combined with the unwillingness of the government to continually increase deficits (government-sector dissaving) and the reduction in dissaving in a large portion of the private sector, bolstered the aggregate propensity to save. 
     

  3. The lack of speculative bubbles to generate investment and income in the way in which speculative bubbles  had generated investment and income as the capital stock grew during the twenty-five years leading up to the crash, led to a reduction in the rate of growth of current consumption. 
     

  4. The reduction in the rate of growth of current consumption, combined with the increase in the capital stock during the twenty-five years leading up to the crash, in turn, diminished long-term expectations with regard to future consumption which reduced prospective yields and the willingness to invest.
     

  5. The inability of interest rates to continue to fall in this situation led to the economic stagnation that followed  in the wake of the crash.

Explaining the buildup to the crash itself, however, takes us beyond Keynes’ analysis of the long-period problem of saving. 

While Keynes analyzed the long-period problem of saving in what seems to be intricate detail throughout The General Theory, one aspect of this problem he did not examine is the role played by the flow of loanable funds in the economic system.  Even though this flow does not determine the rate of interest (as Keynes clearly understood), the flow of loanable funds changes the stock of debt in the  economic system over time just as the flow of investment changes the stock of capital in the economic system over time.  And even though changes in neither the stock of capital nor the stock of debt affect the system in a significant way in the short-run, both can have dramatic effects on the system in the long run

There is nowhere to be found in Keynes a systematic analysis of the relationship between the flow of loanable funds and the accumulation of debt comparable to his analysis of the relationship between the flow of investment and the accumulation of capital in spite of the fact that:

  1. The creation of debt plays an essential role in achieving an efficient allocation and full employment of economic resources by providing a mechanism by which purchasing power can be transferred from those who have it and are unwilling to spend to those who do not have it and are willing borrow in order to spend.
     

  2. At the same time, the most serious depressions involve financial crises that have at their root the inability to service debt.
     

  3. If the institutions within society are such that, given the state of technology, the resulting distribution of income requires an increase in debt relative to income in order to maintain full employment in the short run, eventually debt service must overwhelm the system and cause a financial crisis that will make it impossible to sustain full employment in the long run. 

The nature of this problem is examined within the context of Keynes’ general theory, and it is argued that the fundamental problem we face today is the fallout from Keynes’ long-period problem of saving combined with what may be referred to as the long-period problem of debt, that is, a situation in which — the institutions within society are such that, given the state of mass-production technology, the full employment of existing resources can only be achieved and maintained through an unsustainable increase in debt relative to income.  It is further argued that the reason we face this problem is the increase in the concentration of income and international imbalances that have occurred over the past thirty-five years that are the result of the institutional changes that have occurred over the past forty-five years.

Finally, it is argued that even within the context of neoclassical economics one is driven to the conclusion that — in the absence of an unsustainable increase in debt relative to income — within a closed economy the viability of mass-production technologies is limited by the extent to which the concentration of income limits domestic mass markets, and within an open economy the utilization of mass-production technologies is limited by the balance of trade as well as the concentration of income.  This means that these two factors set limits on productivity within the economic system: The higher the concentration of income and lower the balance of trade, the fewer the opportunities to take advantage of mass-production technologies; the lower the concentration of income and higher the balance of trade, the greater the opportunities to take advantage of mass-production technologies.

As a result, Keynes’ long-period problem of saving goes a long way toward explaining why developing countries with a high domestic propensity to save and concentration of income and a low balance of trade (low foreign-sector dissaving) have suffered from low productivity growth while those countries in a similar situation with a high balance of trade (high foreign-sector dissaving) that have adopted mass-production technologies while pursuing a policy of export led growth have been able to grow relatively rapidly leading up to the Crash of 2008. 

At the same time, the long-period problem of debt goes a long way toward explaining why export-led growth has proved unsustainable in the long run as the institutions supporting employment in the importing countries led to unsustainable increase in debt relative to income. 

Chapter V: Concluding Observations argues that ignoring Keynes’ analysis of the long-period problem of  saving — combined with a failure to understand its companion, the long-period problem of debt — not only resulted in the adoption of economic policies over the past forty-five years that have taken us down a road that inevitably leads to the kind of financial crisis we experienced in 2008 and the economic stagnation that followed, that same road  leads to the kinds of economic, political, and social problems we faced in the 1930s, the last time we saw the kind of economic stagnation we see developing throughout the world today. 

The fundamental differences between the way in which the government confronted the crisis that began with the Crash of 1929 and the crisis that began with the Crash of 2008 are examined, and it is argued that, contrary to conventional wisdom, the United States economy did not recover from the Great Depression of the 1930s.  What actually happened was the failure of the private sector to cope with the crisis that began in 1929 led to the New Deal and eventually to World War II.  It was the dramatic institutional changes that occurred as a result of the New Deal and World War II — the rise of unions, adoption of a minimum wage, progressive taxation, government regulation of financial institutions, the capital controls of the Bretton Woods Agreement, dramatic reduction of private-sector debt relative to income, and government investment in capital projects as well as in education, social-insurance, and innumerable other government programs — that took us out of the Great Depression and led to the prosperity that followed World War II, not an economic recovery as such.

As a result of these institutional changes, the economic system that emerged from the New Deal and World War II was not the system of laissez-faire that led us into the Great Depression.  The economic system that emerged from the New Deal and World War II was a system that embraced thesomewhat comprehensive socialisation of investment(p. 378) Keynes called for in the final chapter of The General Theory as the government made unprecedented investments in our defense and space programs; paved city streets, country roads, and built the U.S. and interstate highway systems; built and improved water and waste treatment facilities along with ports and dams as it electrified vast regions of our country; expanded social  insurance, regulatory, educational, public health, and public safety systems throughout the land along with other government programs.  As a result of these government investments, the capital stock grew and unemployment remained low in defiance of Keynes’ long-period problem of saving for some twenty-five years following World War II as the government’s contribution to GDP increased from 9% of GDP in 1929 to 17% by 1950, and to 24% by 1970. 

And there were no speculative bubbles that led to financial crises and government bailouts during this twenty-five-year period as the concentration of income fell with a stable international balance, and total debt relative to income decreased from 157% of GDP in 1945 to 141% in 1950, and had bearly increased to 149% of GDP by 1970 in defiance of the long-period problem of debt. 

In other words, it was the economics of Keynes’ long-period problem of saving, not the neoclassical economics of the Keynesians, that was validated by the New Deal, World War II, and the economic pros-perity that followed the war. And the economics of Keynes was further validated by the institutional changes that occurred as a result of the policies adopted during and following the 1970s—suppression of unions, failure of the minimum wage to keep pace with inflation, regressive tax policies, financial deregulation, the abandonment of the capital controls of the Bretton Woods Agreement, failure to enforce antitrust laws, and government neglect of capital projects as well as education, social-insurance, and other government programs.

These policies came into being in an attempt to reestablish laissez-faire, and they are the policies that brought us to where we find ourselves today, faced with the fallout from Keynes’ long-period problem of saving as the contribution of government to GDP fell from 24% in 1970 to 19% in 2007 and by 2017 had fallen to 17% which is where it stood in 1950, far below the 23% average during the prosperous years of the 1950s and 1960s.

At the same time, the concentration of income rose to levels not seen since the 1920s and international deficits to levels not seen since the beginning of the nineteenth century, and we became overwhelmed by the long-period problem of debt as total debt increased from 149% of GDP in 1970 to 349% by 2007 leading up to the Crash of 2008 and was still at 339% of GDP in 2016. 

There are, of course, a number of factors that have the potential to offset the effects of Keynes’ long-period problem of saving — specifically, to offset the tendency for the MEC to fall as the capital stock increases over time — factors such as population growth, technological change that increases the demand for capital and consumption goods, and an increasing balance of trade.  It may even be possible to offset this tendency for a time through economic policies that foster the kinds of speculative bubbles and increases in debt relative to income that made it possible for employment to increase and unemployment to fall in spite of the accompanying increase in trade deficits and concentration of income that we witnessed for twenty-five years leading up to the Crash of 2008.   But there are limits to these offsets, and in light of the economic history of the nineteenth through the beginning of the twenty-first century it would take either an extraordinary degree of ideological blindness or a giant leap of blind faith for someone who knows anything about this history to believe these offsets can be relied upon by way of laissez-faire to avoid the kinds of economic, political, and social catastrophes that were experienced during this period of history.

The history of the nineteenth through the beginning of the twenty-first century clearly shows that the kinds of institutional change that resulted from the New Deal and World War II are essential in combating the effects of the long-period problem of saving and its companion the long-period problem of debt. This is obvious from the way in which the expanded role of government in the economic system led to the economic prosperity that followed, not only in the United States, but in the other countries that adopted similar changes compared to the lack of prosperity in those that did not.

To affect the kinds of institutional changes that came about as a result of the Great Depression and World War II by way of the imperatives of depression and war is hardly an optimal way to achieve economic growth and prosperity. It makes much more sense to address the problem of economic growth and prosperity proactively than to wait for the inevitable economic, political, and social catastrophe that results from economic stagnation and collapse and hope for the best. But avoiding catastrophe requires a clear understanding as to what the problem is.

There can be little hope for the future so long as economists are unable to come to a clear understanding of Keynes’ long-period problem of saving in a way that leads to an overwhelming consensus within the discipline of economics to the effect that — consumption is the driving force for economic growth and employment, not saving — is correct and the failure of economists, both Keynesians and anti-Keynesians alike, to face this reality and address it directly is a serious mistake.

Only by facing this reality and addressing it directly will it be possible to affect the institutional changes needed to solve Keynes’ long-period problem of saving proactively, hopefully, in a way that will make it possible to avoid yet another worldwide conflagration that, in this nuclear age, is likely to be even more devastating than the one that began on September 18, 1931 and reached its climax on August 6, 1945. 

Appendix A: Keynes’ Theory of Interest contains a formal model of Keynes’ liquidity-preference theory of interest that draws a clear distinction between stocks and flows in the determination of the rate of interest.  This  model is used to show how the stock of money is related to the flow of expenditures in Keynes’ general theory, and the fundamental issues which divided Robertson and Keynes in the LP/LF debate are explained within the context of this model.

Appendix B: Structure of Keynes’ Implicit Model outlines the mathematical structure of the model embodied in the implicit adjustment equations of the Marshallian methodology employed by Keynes throughout The General Theory.

It is argued that in a world in which decision-making units do not go into debt simply for the sake being in debt — a world in which debt, in itself, offers no satisfaction or utility — there must be a demand for money for some reason other than the satisfaction of being in debt  before there can be a willingness to borrow money.  Thus, it is assumed that decision-making units borrow only to meet their financial needs for money and lend only to dispose of excess money balances they have no use for otherwise.  This makes the flow of loanable funds an ex post magnitude, determined within the system by the demand and supply of money as dictated by  the need to finance the desired transactions of decision-making units as determined by the implicit behavioral equations of the model.  As a result, there are no redundant equations in Keynes’ implicit model as outlined in this appendix, and Walras’ Law — a law that can only be enforced by a mythical auctioneer — has no relevance in this model, just as it has no relevance in Keynes’ general theory or in the real world.

It is argued that the models of neoclassical economics are, in general, implicit in Keynes’ general equilibrium and aggregate models and are, in effect, special cases of Keynes’ general model, but that this is where the similarity between neoclassical economics and the economics of Keynes ends. Rather than accept the neoclassical view of the economic system as being determined by a set of simultaneous equations, Keynes viewed the system as being determined by a set of Marshallian partial equilibrium models wherein the values of individual variables are determined by the choices of those decision-making units that actually have the power to determine the value of each variable. Accordingly, Keynes argued that, ceteris paribus::

  1. The prices and quantities of non-debt assets and other economic goods and resources are determined by suppliers and demanders in the markets for non-debt assets and other economic goods and resources.

  2. The rate of interest (i.e., the complex of rates of interest on loans and debt assets) is determined by the suppliers and demanders for money (i.e., liquidity) in the money market.

  3. Aggregate investment is determined by investors given the rate of interest and the marginal efficiency of capital as perceived by investors.

  4. Aggregate consumption is determined by consumers given their incomes and propensities to consume.

  5. The levels of employment, output, and income are determined by producers given their effective demands —that is, the proceeds they expect to receive as they attempt to maximize their expectation of profits through the employment of resources given the prices of resources and the state of technology.

  6. And the entire process by which these variables are determined at each point in time is governed by the expectations of decision-making units as their expectations adjust to the realized results that are achieved within the system as the system evolves through time.

This approach made it possible for Keynes to establish the temporal order in which events must occur and, thereby, to undertake a causal analysis of the dynamic behavior of the economic system through time by way of  “an organized and orderly method of thinking out particular problems,…isolating the complicating factors one by one” and after reaching provisional conclusions going back as well as he could, to account “for the probable interactions of the factors amongst themselves” in an attempt to understand how the economic system works in the real world.  (1936, p. 297-8) This was Keynes’ method of analysis throughout The General Theory of Employment, Interest, and Money as he followed the example set by Marshall in his Principles of Economics.

It is further argued that it is the unwillingness or inability of neoclassical economists to examine economic problems in this way that makes the economics of neoclassical economics descriptive and static.  This does not mean that the incredibly powerful descriptive / static tools of neoclassical economics are not useful.  It does mean, however, that these tools cannot provide a fruitful guide to economic policy if they are not used in conjunction with the causal / dynamic methodology of Keynes’ general theory as the economic, political, and social problems we face today bear witness, problems that are the inevitable result of economic policies that — by ignoring Keynes’ long-period problem of saving and its companion the long-period problem of debt — led  directly to the Crash of 2008 and the economic stagnation that followed.

[1]  With regard to this equivalence and lack of consensus on the dynamic properties of the two theories see Ackley (1957), Asimakopulos, Brunner, Davidson, Fellner and Somers, Fleisher and Kopecky, Modigliani, Palley, Horwich, Johnson, Keynes, Klein, Kohn, Lerner, Lloyd, Patinkin, Robertson, Robinson, Rose, Stiglitz (1999), Terzi, Tsiang, and Wray. For surveys of the early literature see Haberler, Shackle, and Johnson (1962). For an analysis of the later literature see Bibow (2009).    

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The Theory of Interest

Robertson versus Keynes
and

The Long-Period Problem of
Saving and Debt

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