IS-LM: an Inquest

Home , Alvin Hansen, Don Patinkin, John Hicks, Treasury View, Value and Capital

IS-LM: An Inquest

William Darity Jr. and Warren Young

Introduction Whether the IS-LM framework is to be vilified for its elusive, chameleon- like character or to be cherished for its flexibility remains an open question. What is not open to question is that its development and widespread adoption as the central mode of analytical expression for macroeconomists in the post-World War I1 era was linked intimately to the endeavor to give mathematical structure to Keynes’s General Theory (1936). In his book, Interpreting MKKeynes: The IS-LM Enigma (1987), one of the coauthors of this article, Warren Young, has examined the social and intellectual interactions among the principal figures involved in the creation of the IS-LM approach. The current essay has a different emphasis. Our focus here is on the tools rather than on the toolmakers. Therefore, we explore the content of the various models purporting to represent Keynes’s message below in comparative fashion, rather than the personalities who developed the models. There is surprising diversity in these early models. What places a macroeconomic model in the IS-LM tradition now seems to be its amenability to inclusion of equations that equate sav-

Correspondence may be addressed to Professor William Darity, Department of Economics, CB ## 3305, Gardner Hall, University of North Carolina, Chapel Hill NC 275 14 and Warren Young, Department of Economics, Bar-Ilan University, Israel. We are grateful to David Colander, Don Patinkin, and Thomas Rymes for valuable suggestions. Patinkin provided us with several valuable documents, including copies of Palander’s work. History of Political Economy 27: I @ 1995 by Duke University Press. CCC 0018-2702/95/$1.50

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ings with investment (yielding the IS schedule) and equations that equate money demand with money supply (yielding the LM schedule).’ Those equations are given diagrammatic representation typically in interest rate-income space as the heart of a model or as one of several diagrams in a multi-quadrant graphical representation of the macroeconomy. It is the fact that the IS-LM apparatus can be imbedded within a larger mathematical structure that makes its essential nature so difficult to pinpoint. For IS- LM has been modified to incorporate wealth effects, portfolio theory, the q-theory of investment, first adaptive and then rational expectations, flow of funds analysis, inside and outside money, the government budget con- straint, so-called menu costs, the foreign sector, and, recently, even gen- eralized increasing returns (on the latter, see Cottrell and Darity 1991).2 The plasticity of IS-LM is so great that its original connection to The General Theory can appear vague to the uninitiated. Indeed, there have been other contenders as mathematical representations of The General Theory. First is the multiplier story, told by Richard Kahn in 1931 as a tale of employment expansion. Kahn’s essay was written as a self-conscious repudiation of the Treasury View. The pin in Kahn’s employment multiplier was the postulate of a stable relationship between the proportion of workers utilized in the investment goods sector (“primary employment”) and the proportion of workers utilized in the consumption goods sector (“secondary employment”). Causation ran from increased primary employment to increased secondary employment: The argument will apply to the effects of any net increase in the rate of home investment. The increased employment that is required in connection actually with the increased investment will be described

1. While declaring the IS-LM model dead on arrival (“The IS-LM model has no greater prospect of being a viable analytical vehicle for macroeconomics in the 1990s than the Ford Pinto has of being a sporty, reliable car for the 1990s” [1993, 68]), Robert King nevertheless admits to its omnipresence. He writes, “every macroeconomic model contains some set of equations that can be labeled as IS and LM components, since these are just conditions of equilibrium in the goods markets and the monetary sector markets” (68). 2. Obviously, we do not agree with King’s (1993) assertion that theIS-LM framework virtually requires suppressing the role of expectations, particularly rational expectations. King’s (1 993, 68, 70-71) assessment is based upon what he describes as “the IS-LM model, as traditionally constructed,” which apparently is represented by Hicks and by Modigliani variants of Keynesian economics, models we discuss in detail below. We have a more expansive view of the IS-LM framework, to the point that IS-LM can be maneuvered to support non-Keynesian or even anti- Keynesian propositions. As our discussion below amply demonstrates, that was true from the outset of the development of IS-LM (see especially our assessment of Hicks’s early construction of the “SI-LL” model).

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as the “primary” employment. It includes the “direct” employment and also, of course, the “indirect” employment that is set up in the production and transport of the raw materials required for making the new investment. To meet the increased expenditure of wages and profits that is associated with the primary employment, the production of consumption-goods is increased. Here again, wages and profits are increased, and the effect will be passed on, though with diminished intensity. And so on ad inJnitum. (Kahn 1972, 1) For Kahn, the expenditure expansion was the intermediate link between the new hiring of workers in the investment goods sector and the stimulus for new hires in the consumption goods sector. In Keynes’s (1936) hands, however, the multiplier became a tale of expenditure expansion and only incidentally a tale of employment expansion. The pin for Keynes’s multiplier was the postulate of a stable propensity to consume. Causation ran from increased investment spending onto increased consumption spending and ,a general increase in national income. Keynes’s version of the multiplier bears a much closer resemblance to that of R. G. Hawtrey than to Kahn’s. Hawtrey (Davis 1980,721; 1981, 216-17) worked out a numerical example in a working paper (Paper No. 66) for the Macmillan Committee in January 1931 that became a part of Hawtrey’s interchange with Keynes over the latter’s Treatise on Money. Hawtrey considered the effects of a rise in investment of $12.5 million after the injection of new funds exercised its full series of expan- sionary repercussions. Eric Davis (198 1,216-17) explicitly attributes to Hawtrey the development of the expenditure version of the multiplier, rather than Kahn’s employment version, that subsequently was utilized by Keynes. However, Peter Clarke (1988,242) contends that there is no recorded indication that Keynes drew directly from Hawtrey’s example, nor is there any recorded indication that Hawtrey recognized his own accomplish- ment: “That Hawtrey’s model embodies the multiplier is, in retrospect, incontrovertible. That it proved suggestive to Keynes is imprescriptible. That Hawtrey himself fully realized what he had done, however, is im- probable” (242). According to Clarke (1988,242), section 6 of Hawtrey’s working paper appears to be a last-minute addition in December 1930, consisting of paragraphs 53-63. When Hawtrey reprinted the paper during the summer of 1932, Hawtrey left out paragraphs 53-70. Writes Clarke with a dint of sarcasm, “The self-effacing Hawtrey may, as Davis

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claims, deserve a more prominent place in the literature on the coming of the multiplier-but notably as the man who, having stumbled upon it, painstakingly suppressed news of its discovery in subsequent publi- cations” (1988, 242). Next, of course, is the familiar 45-degree cross diagram still popular in introductory macroeconomics, promulgated in particular in various editions of Paul Samuelson’s te~tbook.~While the cross diagram is in- ordinately simple, treating national income as the only driving force and outcome to be determined by macroeconomic activity, Samuelson views its univariate character as reasonably valid for the later years of the Great Depression. It may have been simple, but it was not necessarily wrong at the time it was de~eloped.~ A thikd approach has been called the Keynesian cross diagram by Daniel Fusfeld (1985). Among post-Keynesians it is better known as the aggregate demand and supply price approach or the Z-D framework. It is drawn from Keynes’s discussion in chapter 3 of The General Theory, a discussion that has lived a comparatively furtive existence in contrast with IS-LM. Fusfeld ( 1985) provides indirect evidence that Keynes had given some thought to diagrammatic representation of his theoretical apparatus from the chapter 3 perspective from a class that Fusfeld took with Arthur Burns in 1941. But the indirect evidence is highly speculative, and we cannot conclude that the Z-D approach was given Keynes’s imprimatur. We cannot even conclude that Keynes ever saw such an approa~h.~The

3. Paul Samuelson recalls in correspondence dated I6 November I990 that he had “worked out the simple teaching tools [for Alvin Hansen], around 1938.” Modestly he says, “But, like Hicks, I was only putting the already obvious in terms of graphs and math.” What Samuelson calls Hicks-Hansen IS-LM “carried the day at the intermediate level” in his estimation because “it gave a neat 2-dimensional graphing.” But he adds, “The reason the Samuelson-Keynesian saving-investment-cross or C + 1-45 diagram carried the day at the elementary level was its easy I -variable teachability. Hicks-Hansen never broke in at the elementary textbook level: in many revisions I toyed with a draft of it but always settled for a I-variable Y [national income] version along with loose discussion of the influence on I [investment] of the interest rate.” David Colander ( I99 I, 98, 10 I n. 9, 134-35) also has observed that the popularity of IS-LM has been due to its “teachability” at the intermediate and graduate levels. 4. Again in Samuelson’s letter (16 November 1990), he observes that although he influenced Alvin Hansen “a lot” that Hansen only “came to [2-variable] IS-LM after I hung my hat at MIT.” There was no major reason to include the rate of interest as a key actor in th: play, according to Samuelson. He writes, “You must realize that in the pre-war, say 1936-1939, U.S. banks had excess-reserves and the short-run i [interest rate] was often 3/8 of 3/8 of 3/8 of I%! No need then for i to be added to the I-variable Y system.” Provocatively Samuelson goes on to note, “Joan Robinson, Lerner, Kalecki . . . converted the classical infidels to the new Keynes-Kuhnian paradigm by the I -variable model.” 5. Fusfeld also reports that Lorie Tarshis recalls utilizing the Z-D type of apparatus in his

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main resuscitators of the Z-D approach in the United States have been the late Sidney Weintraub (1957) and Paul Wells (1977). And Weintraub’s efforts did not come about until twenty years after The General Theory was first published. Keynes’s multiplier approach seemingly was readily absorbed in the IS-LM approach as an underpinning of the IS schedule; all that was required was to distinguish between induced and autonomous expenditures, hold the interest rate fixed, and get the latter exclusively on the right-hand side of the equation. The 45-degree cross-Tarshis’s “monstrosity”-is arguably a special case of the IS-LM model where monetary considera- tions, and the rate of interest, are of negligible importance. IS-LM’s only serious rival, then, for formalization of The General Theory would have to be the Z-D framework: But the Z-D apparatus- with its difficult emphasis on entrepreneurial expectations of profitability as the basic determinant of current employment-has never shared the broad appeal of IS-LM. In the late 1940s in a coquettish mood, Paul Samuelson was advising bypass of chapter 3 of The General Theory: “Like Joyce’s Finnegan ’s Wake, the General Theory is much in need of a companion volume providing a ‘skeleton key’ and guide to its contents: warning the young and innocent away from Book I (especially the difficult Chapter 3) and on to Books 111, IV, and VI. Certainly in its present state, the book does not get itself read from one year to another even by the sympathetic teacher and scholar” (1947, 149).6 Hansen (1953) attempted to provide just such a “skeleton key” shortly

own work at Cambridge prior to 1937! Tarshis is quoted aying, “I know that from very early (before 1937) I was using such a figure; I don’t remember any lecture of Keynes on it, nor do my notes on his lectures (seven a year!) refer to the problem, so I suppbse I got it from JR [Joan Robinson] or RF [Richard F. Kahn] or another student who was in Cambridge, or most likely on my own, but no one ever corrected me until I came up against the 45” monstrosity; and I dismissed that one from the beginning, fervently” (in Fusfeld 1985, 389 n. 3). Both Patinkin and Rymes have expressed skepticism in correspondence with us about Tarshis’s claim that he got Z-D from Joan Robinson or Richard Kahn in the late 1930s. Indeed, Rymes urged us to examine two of Tarshis’s textbooks (1947; 1967). The earlier text has a verbal rendition (Tarshis 1947,360-65,369) consistent with the cross diagram, but no such picture is present in the text. Indeed, the text even features some decidedly Kaleckian themes, such as mention of the role of the degree of monopoly. The later text (Tarshis 1967,372-73) contains an explicit presentation of the 45” “monstrosity” in all its diagrammatic glory. 6. Evidently in the mood of an agenf provoccrreur when writing this essay, Samuelson also observed that “until the appearance of the mathematical models of Meade, Lange, Hicks, and Harrod, there is reason to believe that Keynes himselfdid not truly understand his own analysis” (1947, 146). We will examine all four of these mathematical models below, as well as Keynes’s reactions to them.

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thereafter with his highly popular Guide to Keynes, with its chapter- by-chapter explanation of the contents of The General Theory. While Hansen (1953,25) described chapter 3 of The General Theory as “highly important,” he went on to provide an exposition of its contents that was much closer in spirit to the 45-degree cross than the Keynesian cross. Hansen’s (1953, 39) “skeleton key” then characterized all of book 2 as a “detour”; similarly, Hansen wrote that chapters 16 and 17 “are indeed another detour which could be omitted without sacrificing the main argument” (1953, 155). Chapter 17, in particular, contains important aspects of Keynes’s development of interest rate theory and the foundations for his distinctive arbitrage-based theory of relative prices, that is, Keynes’s “value” theory. When these “detours” are stripped away and chapter 3 is deformed into the cross-diagram model, then the basis for question- ing whether The General Theory is represented adequately by standard variants of IS-LM-in particular the early variants-is lessened signifi- cantly. Our task here is to examine the early mathematical models of Keynes’s General Theory, which frequently also were attempts to formalize the “classical” economics that Keynes chose to confront. We are concerned primarily with their content and their implications for macroeconomic theory. We are also concerned with their success in propagating a mode of thought that has been dominant in macroeconomic analysis for virtually half a century.’

Some Early Mathematical and Graphical Representations of Keynes’s General Theory: A Critical Review The most influential of the early papers purporting to give a mathematical structure to The General Theory clearly is John Hicks’s “Mr. Keynes and the Classics: A Suggested Interpretation” (1937), which appears to be the point of origin of the IS-LM diagram.* Peculiarly, despite the fame of this particular paper, the diagram may well have been the only genuinely unique contribution Hicks made in it. Hicks’s paper was one of three presented at a session of the Economet-

7. In what follows generally a consistent notation will be used at the expense of failure to preserve the notation used by each of the authors in the originals. This is intended to facilitate comparison between the models. 8, Hicks (1937) actually called the diagram the SI-LL apparatus. We speculate that it was Hansen’s efforts that led to the now familiar IS-LM label.

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ric Society meetings at Oxford in September 1936 in a symposium on Keynes’s General Theory. In retrospect it was a remarkable session; the other two contributors were James Meade and Roy Harrod. Hicks had read both of the others’ papers prior to preparing his own (Young 1987, 20-39). There are grounds for believing that he also had read a paper by David Champernowne (1936) that sought to model the differences between “classical” and “Keynesian” economics and that Champernowne had submitted his paper to the Review of Economic Studies before The General Theory was published. Hicks was a joint editor of the Review, and Champernowne was convinced that “Hicks . . . had at least a passing acquaintance with the article” (Young 1987, 82-83). There has long been speculation, partially fueled by Hicks himself, that his teaching of Walrasian general equilibrium theory at the London School of Economics and his development of the lectures that became Value and Capital intersected with his attempt to interpret The General Theory in terms of a mutually interdependent system of simultaneous equations (Young 1987,4446). It seems more likely that the influences ran from Meade and Harrod, no Walrasians themselves, and possibly from Champernowne, whose paper is the most Walrasian in spirit of the four, although it is unlikely that Champernowne had had direct exposure to the Walrasian method. Furthermore, prior to writing “Mr. Keynes and

the ‘Classics’ ” (1936), Hicks had reviewed The General Theory for the Economic Journal with no hint of IS-LM, never mind Walras (Young 1987, 72). Table 1 provides a comparison of the mathematical models in the three Oxford conference papers. Meade (1937) sought to explicate Keynes’s system without trying to establish how Keynes broke with ‘‘classical” economics. Harrod (1937)’ on the other hand, was deeply concerned with identifying the dividing line between Keynes’s theory and what Harrod referred to as the “traditional theory.” Hicks (1937) evidently took Meade’s model verbatim with the exception of equations (8), (9), and (lo), and he took on Harrod’s effort to draw’the partition between Mr. Keynes and the classics. The Meade and Hicks models are identical through the first seven equations. They constitute a two-sector model with a consumption and investment goods sector. The first two equations indicate that output in each sector depends on the volume of employment in each sector. The third equation says total employment is the sum of employment in each of the sectors. The fourth equation establishes the fixity of the

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Table 1 Models from the Oxford Conference Session

Meade ( 1937) Hicks (1 937) 1. C = C(Nc) 1. C = C(Nc) 2. / = /(NI) 2. / = /(N/) 3. N = Nc + NI 3. N = Nc + N, 4.w=w 4.w=w 5. Pc = W/C‘ 5. Pc = W/C‘ 6. PI = w//’ 6. PI = W//l 7.y = PCC + PI/ 7.y = PCC 4- PI/ 8; y = (l/s)PJ 8. M\. = il 9. r = re/PI 9. M” = ky 10. L(r) = PlK/(M - ky) 9b. M.’ = L(r)or M” = L(r,y) 10. /(r)= S(r,y)

Harrod (1937) “Traditional Theory” “Keynes Theory” 1. i = i(/) I. i = i(/) 2.i =r 2.i =r 3. /(r)= S(r) 3. I(r) = Shy) 4. r = r(M,y)

nominal wage in the relevant period. The fifth and sixth equations are the output price equations. Each sector’s output price is determined by marginal product factor pricing. The seventh equation, the last equation shared jointly between the Meade and Hicks models, is the equation for nominal national income, the sum of the money value of output in each sector. Meade closes his version of Keynes’s system with the three remaining equations. The first of these is the multiplier equation. It says that national income is determined by the value of output of the investment goods sector scaled up by the multiplier, one over the propensity to save. The second of these sets the rate of interest, Y, equal to the marginal efficiency of capital. The latter is defined by Keynes ( 1936,135) as that discount rate which sets the present value of the expected stream of profits associated with ownership of a capital asset equal to its supply price. Meade evidently treats profits as having a perpetual constant expected value for simplicity and the supply price of a capital asset as being given by the price of the investment good. In Keynes’s (1936, 136-37) analy-

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sis, investment proceeds until the marginal efficiency of capital is equal to the rate of interest on money. Meade simply utilizes the equilibrium condition in equation (9) without investigating the process leading up to equalization. The interest rate that sets the limit on the marginal efficiency of capital is determined by the equilibrium condition for liquidity preference, given by equation (lo), where the right-hand side is the ratio of the money value of the existing stock of capital goods to cash balances held for speculative purposes.’ Meade’s system can be solved as follows: Substitute the multiplier equation (8) into equation (lo), eliminating nominal income, y, and substitute equation (6) for the price of investment goods in equations (9) and (10). Treat the nominal wage, 20, expected profits, re,the capital stock, K,the money supply, M, and the proportion of income held for transactions purposes alone, k, as given. Equations (9) and (10) then can be solved jointly to determine the equilibrium rate of interest and investment goods sector employment. Once NT is known so is the money value of investment goods, (PII)*, which means that via the multiplier equation (8) a solution can be obtained for the equilibrium level of national income, y*. The equilibrium value of consumption goods, (P,C)*, can be found by calculating the difference y* - (PII)*. Once ( PcC)* is known, the equilibrium level of employment in C-goods production, Nc*, also can be derived. Because Meade does not explicitly specify an investment function, the path from his model to IS-LM is not obvious. The last two equations do suggest an alternative graphical apparatus, which can be called the AA/MEK apparatus. The diagram would have to be drawn in interest rate, investment sector-employment space (see Darity and Cottrell 1987). This keeps at the fore the two-sector character of the model and the primacy of the investment goods sector. An additional interesting feature of the Meade version of Keynes’s system is that his use of the marginal efficiency of capital brings expected profits explicitly into the analysis. If the state of long-term expectation is treated as a given, then expected profits can be treated as a parameter of the system. If expected profits are endogenized, then the issue of the stability of the system comes

9. The interest rate, r, must be the yield on some asset, but cash balances pay no interest and the only nonmoney asset is physical capital whose yield is necessarily given by the right- hand side of equation (9). The model can be made logically tight by introducing equities as claims to physical capital to insure that equations (9) and (lo) can be properly interpreted as an equilibrium condition (see Darity and Cottrell 1987).

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to the surface, an issue that drew substantial interest from the Oxford conference participants when Meade explored the implications of the elasticity of expected future yields with respect to present profitability. Hicks, in contrast, suppresses expected profitability with his investment schedule, which, presumably, is premised on a given state of long- term expectation. That schedule appears in equation (lo), where it is set equal to the savings function that is treated as dependent upon variations . in both the interest rate and the level of nominal income. The key for Hicks, however, is the distinction that he draws between the classical and Keynesian systems based upon equations (9a) and (9b). The alleged classical equation is (9a) in which the demand for money depends in proportionate fashion only upon the level of nominal income via the famous “Cambridge k.” The alleged Keynes equation is (9b) in which money demand depends not only upon nominal income but also the rate of interest. Hicks then proceeds to argue that in the classical system monetary equilibrium determines national income, and savings and investment equality determines the interest rate. In the Keynes system the determination of both income and interest is consequent upon the mutual interaction of the monetary and aggregate demand sides of the economy. At this stage Hicks introduces his SI-LL diagram, with the proviso that Keynes’s willingness to include both interest and income in the money demand function is actually a step back toward the classicals, epitomized by Marshall in Hicks’s eyes. For Keynes to have a truly distinctive theory, Hicks argues, he must assume that the interest elasticity of money demand is exceptionally high, pushing income determination to be dic- tated by the equality between savings and investment. This would reverse causation altogether from the classical system h la Hicks. Diagrammatically Hicks’s classical case can be interpreted as the vertical LM curve in (r,y)space. His “moderate” Keynes case is one where the IS curve is negatively sloped, the LM curve is positively sloped, and their intersection jointly determines both the rate of interest and national income. His extreme Keynes case is the instance where the LM curve is vertical, the case known in the literature as the so-called liquidity trap.

10. Ironically, Hicks (1939) was to develop the concept of elasticity of expectations more fully in Value and Capital. Unfortunately, as Peter Rappoport (1992) writes, “Meade’s paper has largely been ignored, and expectations and the stability issues they raise have had a shadowy existence in the Keynesian arena” (356). Rappoport provides a comprehensive examination of the stability properties of a one-sector version of Meade’s General Theory model.

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A word of caution is in order. In Hicks’s classical case fiscal policy is not absolutely sterile. Shifts in the IS curve up and down the vertical LM schedule do not alter the level of nominal income, but they can alter the level of employment. This is because changes in the rate of interest can induce variations in the composition of output between investment and consumption goods. If the sectoral supply elasticities are not identical, each compositional change will bring about a change in total employment. Hicks (1937, 149) made this point himself. What of Harrod, the earlier source of the distinction between classical economics and Keynesian economics? Harrod has the volume of investment determining the level of the marginal efficiency of capital (see table 1). ’ I As investment expands, the marginal efficiency of capital declines; investment will expand, thereby lowering the MEK, until it reaches the rate of interest; hence the second equation in Harrod’s version. Where does the interest rate come from? For the classical economist, it comes from the savings-investment equality. And that’s the end of the “traditional” story as far as Harrod is concerned. For Keynes, according to Harrod, the key step is the introduction of income in the savings function, rendering it impossible to determine the interest rate exclusively by the savings-investment equality. The monetary equilibrium provides the second equation that completes the system, equation (4), which is not shared in common by both models. Since Har- rod’s “traditional” theory model lacks a monetary sector altogether, it cannot be given an IS-LM treatment, but certainly his version of Keynes’s theory can be given precisely that type of diagrammatic treatment.’* One wonders whether the impact of the Meade and Harrod papers would have been as great as Hicks’s paper had either one of them attempted to present a geometric apparatus. But the appeal of Hicks’s .approach was not merely the fact that he drew a picture, but also that he

1 1. Harrod always tended to soften the dimensions of the break with “traditional theory,” presumably for strategic reasons. Again, this is evident in his calling i the marginal product of capital rather than the marginal efficiency of capital in his text. Substantively there is no difference, however, because although the marginal product of capital has connotations of a physical productivity, there is nothing in Harrod’s specification of the model that compels such an interpretation. Harrod’s conservatism is further reinforced by his well-known assessment in the same article: “In my judgement Mr. Keynes has not affected a revolution in fundamental economic theory but a re-adjustment and a shift of emphasis” (1937,85). 12. The sectoral structure of Harrod’s model is ambiguous. His y is also nominal income. It could be a one-sector model with y = PY, where Y is the only type of output or it could be an n-sector model where y is a nominal GNP aggregate.

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could use that single apparatus to draw a series of pictures that represented the classicals and Keynes-whether accurately or not-as special cases of a more general model. Meade had not set as his task a demon- stration that Keynes’s system could be derived from a “more general” framework, and Harrod’s juxtaposition of the traditional theory with the Keynes theory did not afford the same parallelism of structure provided by Hicks’s structure. While Hicks’s approach plainly had its marketing advantages, it is not apparent that it had substantive advantages over either of the other two papers. Keynes rarely became heavily engaged in discussions of the mathematical models purporting to represent his Generul Theory, seeming to take on an air of bemused ambivalence and implying that all of them failed to (or could not) incorporate what he viewed as the key feature of his theory, his emphasis on subjective uncertainty (see Keynes 1937; Young 1987, 9-11). Of course, Keynes must have been pleased to stimulate so much intellectual activity so quickly in response to The General Theory, precisely the reaction he had been disappointed not to obtain from his Treatise on Money. His brief letter to Hicks dated 3 1 March 1937, written after Hicks sent him the Oxford conference paper about a month after the conference, has been widely misinterpreted as an endorsement of Hicks’s effort (see, for example, Patinkin 1990b). Although the letter is by no means a repudiation of Hicksian SI-LL, Keynes’s criticisms run deep. Keynes opens the letter with a misleading greeting, “At long last I have caught up with my reading and have been through the enclosed. I found it very interesting and really have next to nothing to say by way of criticism” (CW 14:79). He then proceeds to level his criticisms. Aside from some adverse comments about Hicks’s choice of notation being inconsistent with Harrod’s, the remainder of Keynes’s letter goes to matters of crucial importance. First, Keynes (CW 14:79) denies that the vertical LM curve is particularly “classical” because it is not consistent with the classical presumption that money is neutral: From one point of view you are perhaps scarcely fair to the classical view. For what you are giving is a representative belief of a period when economists had slipped away from the pure classical doctrine without knowing it and were in a much more confused state of mind than their predecessors had been. The story that you give is a very good account of the beliefs which, let us say, you and I used to hold.

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But if you were to go further back, how far back I am not quite sure, you would have found a school of thought which would have considered this an inconsistent hotch-potch. The inconsistency creeps in, I suggest, as soon as it comes to be generally agreed that the increase in the quantity of money is capable of increasing employment. A strictly brought up classical economist would not, I should say, admit that. . . . (79) A bit later in the same letter, Keynes reiterates his point that “a strict classical economist would say that an increase in the supply of money would only raise money incomes and not real incomes” (79).13 This problem does not arise in Meade’s paper since he makes no attempt to explicate the classical system. Nor does it arise in Harrod’s paper because Harrod does.not even present the monetary sector as a facet of his “traditional theory” model. Only Hicks falls into the trap of as- cribing the theoretical proposition to the classicals/Marshallians of the non-neutrality of money. Keynes could have added that Hicks’s horizontal LM curve was an odd representation of The’GeneruZTheory for two reasons. First, Keynes (1936, 207) dismissed the empirical relevance of a condition where liquidity preference has become “absolute,” and second, the horizontal LM curve implies that money is neutral at less than full employment. Cer- tainly the latter is not a Keynesian proposition! In his letter to Hicks, Keynes goes on to write: At one time, I tried the equations as you have done with I [income] in all of them. The objection to this is that it overemphasizes current income. In the case of the inducement to invest, expected income for the period of the investment is the relevant variable. This I have attempted to take account of in the definition of the marginal efficiency of capital. As soon as the prospective yields have been determined, account has been taken of income, actual and expected. But whilst it may be true that entrepreneurs are over-influenced by present income, far too much stress is laid on this psychological influence, if present

13. When Milton Friedman (1974,3I) developed his version of the “simple quantity theory” model, he did not assume a vertical LM curve. His money demand function was sensitive to variations in both income and the interest rate, and his money supply function had the interest rate as an argument! But the level of real income or output was predetermined, presumably at the full employment level, so that changes in the quantity of money only could change money incomes, not real incomes.

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income is brought into such prominence. It is, of course, all a matter of degree. My own feeling is that present income has a predominant effect in determining liquidity preference and saving which it does not possess in its influence over the inducement to invest. (CW 14:79-80) This might suggest that Keynes preferred Meade’s version of The Gen- eral Theory to Hicks’s, since the former introduced expected profitability explicitly into the formalization. But it is hard to reach any clear con- clusions on the basis of Keynes’s correspondence with Meade over the latter’s model. Keynes’s only comment in writing was a postcard dated 14 September 1936 in which Keynes said, “Thanks for the copy of your paper. It’s excellent. I have no criticisms to suggest” (Young 1987, 34). In this instance, though, no criticisms did follow. Keynes’s reaction to Harrod’s paper seems to fall between the au- thentic “no criticism” position he took with Meade and the pseudo-“no criticism” position he took with Hicks. A letter dated 30 August 1936 from Keynes opens with the following enthusiastic greeting: “I like your paper (may I keep the copy you have sent me?) more than I can say. I have found it instructive and illuminating and I really have no criticisms. I think that you have re-orientated the argument beautifully. I also agree with your hints at the end about future dynamic theory” (CW 14:84). Keynes even says he probably should give Harrod’s paper at a conference he is about to attend in Stockholm rather than the one he had written. But then Keynes (84) goes on to complain that Harrod has minimized the scope of the mental struggle Keynes had waged to escape from the classical mode of thought. Keynes also complains that, “You don’t mention eflective demand or, more precisely, the demand schedule for output as a whole, except in so far as it is implicit in the multiplier. To me, the most extraordinary thing regarded historically, is the complete disappear- ance of the theory of the demand and supply for output as a whole, i.e. the theory of employment, after it had been the most discussed thing in economics” (84). Is Keynes actually expressing mild displeasure about the failure of the early formalizers to take up his chapter 3 seriously? Fi- nally, he writes, “You do not show how in conditions of full employment which I should now like to define as the limiting case in which the supply of output schedule ceases to be elastic, my theory merges in the orthodox theory” (85-86). Keynes appears to be reasserting the generality of The General Theory,of which he views the traditional theory as a special case.

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Aside from these three papers, only a subsequent paper by Nicholas Kaldor attacking a position taken by A. C. Pigou drew significant ex- tant correspondence from Keynes. Two other papers coincide tempo- rally with the Oxford conference papers, the papers of Champernowne and W. B. Reddaway. Champernowne’s paper actually predates them, and Reddaway’s paper was written without access to any of them since he was in Australia. Champernowne’s paper is remarkable in a number of dimensions. It was actually written while Champernowne was an undergraduate, and according to him the article “was based on Keynes’s lectures and su- pervisions: this means that I was still only in my second year as an undergraduate reading Economics during most of the time I was writing it . . . reading Part I1 Economics from October 1933 to June 1935” (Young 1987, 83). Champernowne remembers submitting the paper before The General Theory was published, and he mentions “vague recollections” c that he circulated the paper to the Oxford-Cambridge or just the Cam- bridge seminar between 1933-35 (Young 1987,82). Champernowne set for himself the task that informed Hicks’s exercise at the Oxford conference, the construction of an overarching model in which the classical and Keynesian systems could be embedded. The paper fully anticipates Friedman’s imputation of the natural rate hypothesis to the Phillips curve controversy. Champernowne ( 1936) distinguishes between “basic” and “monetary” unemployment, where the former corresponds to that rate of unemployment consistent with the labor market clearing when the demand and supply of labor depend exclusively upon the real wage. Champernowne’s classical case is represented in the bottom left section of table 2. The Keynes model, according to Champernowne, attributes to labor a certain attachment to money wages, which introduces the possibility of what he calls “monetary” unemployment because it “is due to the fact that [the monetary unemployed] or their unions have overlooked a recent fall in the cost of living, whereas the employment of the monetary-employed is due to the fact that they have overlooked a rise in the cost of living” (1936, 204). Hence, Champernowne includes the nominal wage in the labor supply function he attributes to Keynes in addition to the real wage. Champernowne’s paper sits apart from those of Meade, Harrod, Hicks, and Kaldor in one major way-Champernowne’s emphasis on the cen- trality of the aggregate labor market. Eric Davis (1980, 716 n. 2) lists

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Table 2 Champernowne on the “Classicals” vs. Keynes (1936)

The General Model 1. NS(W/P,S,r, w, M) = N“(W/P,S,r,w, M) 2. SS(N,W/P, r, w, M) = S“(N, W/P,r, w, M) 3. MS(M,W/P,r, w, S) = M“(N, W/P,S,r, w)

The “Classical Model’’ The “Keynes Model” I. NS(w/P)= N‘/(w/P) 1. N”(W/P,W) = N“(W/P) 2. S”(N,r) = S“(N,r) 2. Ss(N,r) = S“(N, r, Q) 3. hs= M“(N,r, w) 3. M”(r)= M“(r, Q’) 4.w=w

Champernowne ( 1936) and Leontief ( 1937) as identifying the labor market as decisive in Keynes’s analysis. In contrast, he says Hawtrey, Harrod, and Harry Johnson all viewed liquidity preference as the major innova- tion of The General Theory, while Joan Robinson and G. L. S. Shackle said it was expectations. This failure to gauge variations in the real wage accurately only can be temporary, according to Champernowne, so monetary unemployment cannot persist, “in so far as these oversights are likely to be repaired eventually, the monetary-unemployed are likely to lower the money- wage which they demand, and the monetary-unemployed are likely to raise the money-wage-rate which they demand” (1936,204). Keynesian or monetary unemployment could only be temporary, unless the monetary authorities actively sought to mislead labor (2 16). Champernowne apparently did not perceive Keynes’s (1936, 13) argument that money- wage reductions could have adverse repercussions on aggregate demand leading, in turn, to output price deflation that might leave the real wage relatively unchanged. Although the most general version of Champer- nowne’s model included that potential effect in theory, it is not present in his version of Keynes’s system. Another feature of Champernowne’s Keynes system that deserves mention is his use of the parameters Q and Q I, portmanteau variables that capture “certain influences such as general nervousness, the state of the news and effects due to the expectation of changes in the price-level, etc” (Champernowne 1936, 21 1). Both his classical and Keynesian systems are fully determinate, have the same number of equations as unknowns,

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given the fixity of the nominal wage and given a prevailing state of “general nervousness” in the Keynes case. But his general model in table 2 is underdetermined, since Champernowne has too few equations relative to the number of unknowns. He mistakenly says he has six unknowns and six variables in his text, but that configuration is reached only by count- ing each of the supply and demand functions separately (1936,210). But his model is premised on equality between labor supply and demand, savings supply and demand, and money supply and demand, so he actually has three equations and six unknowns. Still, what is striking is that Champernowne was truly the first to represent The General Theory as a series of interdependent aggregate markets-apparently conceiving of such a construction before The General Theory actually appeared in print. I4 Champernowne’s formulation of the classical and Keynesian systems can be given a three-quadrant diagrammatic presentation-one quadrant for each aggregate market-which is the approach utilized by Champer- nowne. It also can be given the IS-LM presentation augmented with a labor market, as Champernowne acknowledged himself (Young 1987, 83). In the classical case, the IS and LM schedules would appear in interest rate-nominal wage space, since employment and the real wage are determined in the labor market. The price level is determined by implication; it has to be whatever level is required for consistency with the money wage and the real wage. In the Keynes case, the IS and LM curves would appear in interest rate-employment space. The LM curve would be horizontal, but this does not imply neutrality of money. Changes in the quantity of money would displace the entire LM schedule upward or downward. The labor supply and demand schedules, oddly enough, would appear in real wage-money wage space and would determine the real wage rate given the level of employment generated by the intersection of the IS and LM schedules. But this would be a most unorthodox IS-LM framework. Champernowne’s classical and Keynesian cases appear in IS-LM form in figure 1. Diagram (a) represents his classical case and diagrams (b) and (c) represent two versions of his Keynes case. Case (c) is a modest extension of Champernowne’s system, not actually investigated by him, that we find to be of interest. In diagram (a) the level of employment and

14. In his first footnote Champernowne (1936, 201 n. I) references The General Theory without publisher or publication date. He may have had access to the typescript.

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(4 w r

r* --XNlI I

(b) I. W

I I

N* N W* W

N* N T,, w‘ WI w

Figure 1 Champernowne’s classical and Keynes variations.

the real wage rate, W, is determined by the intersection of labor demand and supply schedules in a classical aggregate labor market. Given the level of employment, the IS-LM apparatus determines the interest rate and the money wage rate, w. Indeed, strictly speaking, only the savings- investment equality, represented by the horizontal IS curve, determines the interest rate. All the action dictating the output and employment performance of the economy occurs in the labor market. In the Keynes case (b) the money wage is flexible, and in the Keynes case (c) the money wage rate is sticky. In case b, employment and interest are determined by the interaction of IS and LM. Here, the monetary

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equilibrium sets the interest rate, and the intersection of IS and LM sets the level of employment. Here, Champernowne’s unusual “labor market” takes the level of employment as given, thereby determining the real wage consistent with the corresponding level of demand for labor. The role of the supply curve for labor is to determine the nominal wage rate at the point where it intersects with the horizontal labor demand schedule. Certainly this is not a standard labor supply schedule; it really is an equilibrium locus of all combinations of real and nominal wage rates consistent with employment level N*. Although all markets clear, it is not evident that the economy is at “full employment.” An increase in aggregate demand-consider a rightward shift of IS-rould lead to an employment expansion that would be supported by a change in both the real wage rate and the money wage rate. However, in case (c), where a sticky money wage prevails, an inconsistency arises. Although the intersection of IS and LM mandates employment level N*, if the money wage rate is fixed at any value other than w*, the conditions of labor supply will not support such a level of employment given real wage rate, W*. If the money wage is at 150, there will be an excess demand for labor and if the money wage is at Wl, there will be an excess supply. Thus, the sticky-wage version of Cham- pernowne’s Keynes case can lead directly to the non-market clearing economics that Patinkin (1956) later would argue is the valid interpretation of Keynes’s economics. Although Champernowne himself did not investigate this aspect of the model, it is an implication of this system. Reddaway’s contribution, on the other hand, leads directly to the IS- LM approach, although he did not draw the diagram in his review of The General Theory for the Economic Record (Reddaway [ 19371 1964,99- 108). Reddaway ’s construction was developed fairly independently of all other influences. He had attended some of Keynes’s lectures and had received some supervision from Keynes prior to the publication of The General Theory. He also bad been given a copy of the book by Keynes to take to Australia with him, and, at 23 years of age, he was asked to do the review by the editor of the Economic Record on the grounds that he knew more about The General Theory than any other economist in Australia (Young 1987,74-76). His 1937-vintage model appears in the first column of table 3. Like Champernowne’s it is a one-sector model, but, unlike the four previous models, real income appears for the first time instead of employment or nominal income. Reddaway’s 1937 equation (4) also partitions the

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Table 3

Reddaway in 1937 I. s = S(Y) 2. I = I(r) or I(r, Y) 3.S=I 4. M = L,(Y)+ L*(Y)

Kaldor’s Truncheon for Pigou ( 1937) The “Pigou Model’’ The “Keynes Model” I. M” = M”(Y) I. M” = /;I 2. M“ = MqY, w,N) 2. M“ = M“(r,w, N) 3.w=lil 3.w=lil 4. M”= M“ 4. M” = M“ 5. I = I(r) 5. I = I(r) 6. S = S(r) 6. S = S(r, W, N) 7./=s 7./=s

components of money demand between the transactions demand, which depends only on real income, and the speculative demand, which depends only on the rate of interest. Equations (1) to (3) plainly constitute the basis for the IS schedule in interest rate-real income space, and equation (4) provides the LM schedule in the same space. In a reprise on the 1937 model in 1963, Reddaway (1964, 108-23) chose to modify his old model to place the emphasis on consumption instead of saving. This is a stylistic twist. Reddaway 1937 and his first 1963 model are really identical. A second 1963 model is a bit different, since he introduces government spending, all devoted to consumption goods purchases, in contrast with private consumption expenditures. The latter are out of disposable or after-tax income, augmented by transfer payments, D. Nicholas Kaldor (1937,745-53) apparently was the first economist to apply Hicks’s SI-LL diagram in a paper. This was within a few months

of the publication of,Hicks’s “Mr. Keynes and the ‘Classics,’ ” and it was in the context of a critique of a paper by Pigou. Kaldor’s paper drew substantial attention from Keynes; in fact, this paper may have generated more Cambridge correspondence than any other attempt to provide a mathematical structure for The General Theory in the 1930s and 1940s from a wide range of parties (Young 1987,107-15). Keynes himself was

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mobilized primarily not because of Kaldor’s paper per se but because of his enthusiasm for a good fight with Pigou. The debate really was over the effects of money wage reductions. Kaldor seeks to explain why money wage reductions lead to employment increases in Pigou’s system-now the representative classical system- while they may not in Keynes’s system. The nub of the matter is the omis- sion of income and income distribution effects from the Pigovianklassical savings function and their inclusion in the Keynes savings function (see table 3). In interest rate-employment space, the Pigou SI curve is horizontal, since the savings-investment equality determines the rate of interest. If money wages are cut, the positively sloped LL schedule will shift to the right, raising employment at the same interest rate. The Keynes cases are open to alternative outcomes. If savings are inversely related to the rate of interest and the absolute value of the derivative of the savings function with respect to the interest rate exceeds the absolute value of the derivative of the investment function with respect to the interest rate, the SI curve will be positively sloped. A money wage cut actually could reduce both the interest rate and employment as the SI curve shifts downward, if the SI decline more than offsets the rightward shift of the LL curve. Regardless, the two curves shift in potentially offsetting directions. Another possibility is the case where the money supply or the money demand elasticity with respect to the interest rate approaches infinity, giving us the horizontal LL curve. But now it will be important that changes in money wages have negligible effects on either savings or investment. I or S, or both, should have as arguments the rate of interest and real output-but not the income distribution. Otherwise SI will shift in response to each variation in the money wage. The other case that supports Keynes’s claim about the potential neutrality of money wage variations is one where the savings and investment functions are interest inelastic and the income distribution effect is ab- sent from the savings function. This leads to a vertical SI curve in (r,N) space. Money wage cuts that shift the LL curve to the right will have no effect on the level of employment. The key point according to Kaldor is that Keynes’s system is open to the possibility that money wage reductions will not alter the employment level, while Pigou’s system is not. And Kaldor’s facile manipulation of the IS-LM framework reveals early how nicely special cases can be associated with special shapes of the schedules.

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Abba Lerner, who wrote extensively on The General Theory through- out his entire academic career, did not write down a full equation system to represent his interpretation. But he made extensive use of the IS-LM apparatus. Perhaps most notable is his use of the apparatus to address the same debate over Pigou’s position on the invariability of the reduction in money wages leading to an employment increase-a position Pigou backed away from in the aftermath of Kaldor’s paper. In a methodolog- ical discussion of the Swedish ex ante approach that bridged into a critique of Pigou, Lerner (1939,436-49) put IS-LM diagrammatics through their paces. Perhaps most interesting was Lerner’s ( 1936) brilliant verbal exposition of The General Theory for the International Labour Organiza- tion. In some respects thereafter his interpretation of The General Theory displays slippages. From 1938-39 onward Lemer advocated a diagrammatic approach and essentially illustrated and “verbalized” Hicks’s “mathematical approach.” In a 1938 paper, Lerner distinguishes between M,the amount of money available in an economy, and A, “the value, at each rate of interest, of all the other assets in the economy” (1947,653). In his 1939 paper he also distinguishes between “money” and the “value of assets other than money (A)”; in other words, he identifies at least two spheres of finan- cial activity. Lerner (1939, 272) stresses the importance of the savings function S = F(r,Y) where he actually presents a “diagrammatic presentation of a simplified system of interdependent relationships” (269). This is accomplished by drawing a flow chart with both direct and indirect effects. The key Keynesian model utilized by Lerner was his 1938 essay “Al- ternative Formulations of the Theory of Interest” originally published in the Economic Journal (1947, 634-54). Aside from his push toward a more complex asset structure in his work than had been characteristic of the mathematical Keynes models of the late 1930s, Lerner also began a very difficult exploration of disequilibrium phenomena. It was apparently these steps toward disequilibrium analysis that prompted a rather stern rebuke from Hansen (1953, 148-51) in A Guide to Keynes, who could not conceive of IS-LM in anything but an equilibrium mode.’’ Oscar Lange’s 1938 contribution to Economica is especially interesting as a formalization of The General Theory. Measuring all of his

15. IS-LM has been extended explicitly to cover models of disequilibrium in the “non- Walrasian” sense by Barro and Grossman ( 1976), in the aftermath of Patinkin’s (1 956), Clower’s (1965); and Leijonhufvud’s (1968) contributions.

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Table 4 From Lange to Timlin

1. c = C(Y,r) I. c = C(Y,r) 2. 1 = /(r,C) 2. I = I(r,Y) 3.Y=C+/ 3.Y=C+I 4. Q = wMS 4. r = L(M,Y) 5. MD= M”(r,Y) 6. MS= MD

variables in Keynes’s wage-units, a practice only pursued again among the early mathematical expositors of Keynes’s economics by Lawrence Klein, Lange sought to bring forward the underconsumptionist theme by making current investment depend on the current level of consumption expenditure. This meant, in turn, that the investment function becomes sensitive to the magnitude of the propensity to consume. The higher present incomes and the higher the propensity to consume, the more favorable the signal to producers of intermediate goods to expand their operations. An inventory adjustment story would be easy to tell in this context. Also Lange’s approach is not far removed from an investment accelerator effect. In table 4 the ease with which the Lange model could be converted into an IS-LM representation should be transparent. Equations (1) to (3) constitute the IS schedule in interest rate and income measured in wage-units space. Equations (4) through (6) provide the corresponding LM schedule. Mable Timlin’s (1942, 8) still more compact four-equation system for Keynesian analysis, “the skeleton structure,” which she attributes “(with some minor changes)” to Oscar Lange, is even more obviously an IS-LM model in interest rate-income space. Later in the same text when Tim- lin (1942, 142) initiates her intriguing discussion of Keynes’s system of “shifting equilibrium,” she repeats the same model.I6 Keynes did comment favorably on Lange’s paper in his debate with Dennis Robertson in the June 1938 Economic Journal (Young 1987,81). A more isolated one-sector Swedish attempt to formalize The General Theory mathematically was the endeavor of Tord Palander (1942) to distinguish between “traditional theory” and Keynes’s theory (see table 5). The key for Palander, as it was for Kaldor, was the changed specification

16. What is entirely unique to Lange (1938) is his welfare economics-motivated examination of the conditions that determine the “optimum” propensity to consume.

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Table 5 A Swedish Version (Palander 1942)

“Traditional Theory” “Keynes Theory” 1. 1 = /(r) 1.1 = 1(r) 2. s = S(r) 2. s = S( Y) 3.l=S 3.l=S 4. r = L*(M*) 4. r = L*(M - MI) 5. M2 = M - MI 5. M, = Y/VI 6.M=M 6.M=M

of the savings function. Palander’s “traditional” model is not really sus- ceptible to representation through IS-LM, because income is nowhere to be f0unTi.l.The interest rate is determined by the intersection of the investment and savings schedules. The money markets must take the interest as given, and the interest rate simply dictates the division of the quantity of money between its transactions and speculative uses. On the other hand, Palander’s version of the Keynes theory can be represented quite easily with the IS-LM apparatus in interest rate-real income space. Palander, however, drew some outrageously complex and elegant three-dimensional diagrams to illustrate his models! Next we consider Modigliani’s highly influential 1944 paper published in Econornetrica that represents several key transitions: (a) the models are somewhat more expansive, heralding the arrival of the large empirical macromodels, (b) there is evidence of a desire to insure that the aggregative models bear some consistency with underlying microeco- nomic optimizing behavior, and (c) there is stress placed on the potential dichotomy between the monetary and real sides of the economy. Modigliani works with a one-sector model, where the only important distinction between the classical and Keynesian systems is the presence or absence of money wage flexibility (compare the block of equations [9] to [ 121 in table 6, respectively). Indeed, Modigliani threw down the gauntlet in 1944: Keynesian economics amounted to nothing more than rigid wage economics because the levels of employment and output were construed as being determined directly by conditions in an aggregate labor market. The classical labor market had labor supply and demand functions that only had the real wage as an argument, and the classical labor market always cleared. The Keynesian labor market did not always clear. The same inner message still lies at the core of the more complicated

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Table 6 Modigliani's Decisive Labor Market, Two Vintages

1944 "Classical System" "Keynesian System" I.MS=M 1. MS= M 2. MD= (L,rY) 2. MD= L(r, Y) 3. MS = MD 3. MS= MD 4. / = I(r, Y) 4. / = l(r, Y) 5. s = S(r, Y) 5. s = S(r, Y) 6.S= 1 6.S=I 7. Y = PX 7. Y = PX 8. X = X(N) 8. X = X(N) 9. w = X'(N)P 9. w = X'(N)P 10. w = N"-'(N)P 10. w = ~rw,+ BN"-~(N)P 1 I. N" = NS-'(W/P) 1 I. N" = N"(W/P) 12. (W/P)= N"-'(N) 12. (W/P)= N,v-'(N)

1963 "Keynesian System" I.MS=M 2. M" = L(r, Y, P [/uol> 3. MS= M" 4. / = (r,x, KO) 5. c = C(K,N W/P,r[Vo/P]) 6.S=X-C 7. x = X(N, KO) 8.S=l 9. w = X'(N)P 10. N = N"(W/P) at W = Wo if ND > NS N = x'-'(W/f) at W = Wo if N" > ND 11. M = Mh + M* 12. Mh = Bh + M*h 13. BP = B(r, X, N, P, W[Ko], [Go + 41) 14. BP + B,h = G

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model Modigliani advanced in 1963. The extended model brought on board adaptations to address the controversy that had arisen over the distinction between inside and outside money. The asset structure of Modigliani 1963 is far more refined than the simple asset structure of 1944-cash balances and some implicit interest-bearing asset. The block of equations (1 1) through (14) decompose the quantity of money between the supply of bank money and government money held privately outside of banks. The supply of bank money is further decomposed between the bank demand for bonds and government money held by banks. Equa- tion (13) is the private demand for bonds function. Finally, the sum of the private and bank demand for bonds equals G,the supply of government bonds. Nevertheless, despite the more intricate asset structure of the model, fluctuations in employment ultimately are due to rigid nominal wages that result in an excess supply of labor in the classical labor market (see equations 9 and 10 under the 1963 system). Modigliani’s 1944 classical model is a pure case of the dichotomy between the real and monetary sides of the economy. The quantity of money only can affect the general price level or nominal incomes; real output is determined by labor market clearing and the aggregate production function. The dichotomy only breaks down in the Keynesian system because variations in the price level can now feed back onto the real wage, since the labor market does not clear. While Modigliani’s paper was extremely influential, especially among the emerging cohort of applied macroeconometricians, the populariza- tion of IS-LM really must be attributed to Alvin Hansen (1949; 1953) in two volumes published by McGraw-Hill. Hansen actually was the first to distinguish between the “economics of Keynes” and “Keynesian economics” (of the Hicks-Hansen variety) and this was two decades before Leijonhufvud (1967). For example, in his 1947 paper “The Gen- eral Theory” in the Seymour Harris volume, Hansen asserted that “it would be a mistake . . . to make too sharp a dividing line between pre- Keynesian and Keynesian economics. . . . Moreover a correct appraisal of Keynes’s work cannot be made by confining attention to the contents of The General Theory” (1947a, 133-34). In a second paper in the same volume, Hansen said “friend and foe alike have become Keynesians” (1947b, 193). In both papers, somewhat idiosyncratically, Hansen advocated a com- bination of Keynes’s and Dennis Robertson’s-or, as he put it, “Key- nesian” and “Robertsonian”-approaches. Moreover, in Monetary and

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Table 7 Alvin Hansen and IS-LM (1949)

Accelerator with Wealth Effects Diagrammatic Model l.MS=M l.MS=fi 2. MD= L(Y, r, A) 2. MD= (Y,r) 3. MS = MD ‘3.MS = MD 4. I = I(r, Y, A) 4. I = I(r) 5. C = C(Y,A, r) 5. c = C(Y) 6. Y = C + I 6.Y=C+I

Fiscal Policy, Hansen said “considering the Keynesian system as a whole without concentrating too narrowly on certain passages in The General Theory there is much more agreement between Robertson and Keynes than appears on the surface” (1949, 81 n. 1). The 1949 book is based on Hicks 1937 (see Hansen 1949,71 n. l), but he changes the terminology of LL to LM (see Hansen 1949,77-78; Young 1987,117). And Hansen’s chapter 5 changes more than notation. Here, he advocates taking a broad view of the Keynesian theory of income determination of income and the rate of interest rather than a view based “narrowly on certain passages in the General Theory,” that is, the “economics of Keynes” (1949, 80). Hansen’s equations (see table 7) are in real terms and appear in two different forms. The first is replicated in the first column of table 7. Here, Hansen includes the real value of assets, A, in the money demand and aggregate demand relations. His investment function also includes an accelerator. l7 This is certainly an intriguing model. But it is not the model that is used for diagrammatic purposes; instead Hansen purges the system of the real asset and accelerator effects to generate the simpler model in the second column that is amenable to straightforward representation as an IS-LM picture. It is only somewhat Hicksian, though, because Hicks’s interesting two-sector repercussions are eliminated altogether in Hansen’s representation in interest rate-real income space. By 1953, Hansen (14748, 154-55) attacked the “economics of Keynes” outright and quite vehemently. The most curious message in Hansen 1953 (143-44) is his advocacy of IS-LM as an amalgam of Keynesian-Pigovian-Robertsonianand Swedish approaches. Apparently the phase when the classicals had entered a “confused state of mind” had crossed the Atlantic on a lag.

17. Presumably this was due to Samuelson’s influence on Hansen (see note 5 above).

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Table 8 Lawrence Klein and the Decisive Interest Rate

-~ ~~~ ~~ ~~ ~~ “Classical Model” “Keynesian Model” 1. MS = M 1. MS = M 2. M” = kY 2. M” = L(r, Y) 3. MS = M” 3. MS = M” 4. Y = PX 4.Y=PX 5. x = X(N) 5. x = X(N) 6. W = PX’(N) 6. W = P(I - l/n)X’(N) 7. NS= NS(W/P) 7.NS = F(W) 8. S = S(Y) 8. S = S(r, Y) 9. I = /(Y) 9. I = I(r, Y) IO.S=I 10. S = I?

Lawrence Klein’s 1949 book The Keynesian Revolution originated as Klein’s doctoral dissertation and stands somewhat apart from the other efforts to draw a partition between the classical and Keynesian systems. Klein works with wage-units. While Klein amends the Keynesian labor market to open it to the possibility of unemployment of the non-market clearing variety (see equations 6 and 7 in each column of table 8), more interesting is the puzzle he poses about the interest rate. Klein argues that the classicals always assume that there will be an interest rate that will bring about equality between savings and investment. The Keynesian analysis, he contends, has no such presumption. It may be the case that a negative interest rate is required to equate savings and investment, but since interest rates can never be negative such equalization will be impossible. Thus, the market-clearing problem can shift from the labor market to the goods market with an adverse spillover effect onto employment and output. This is suggestive of an alternative construction that does not rely on the failure of investment and savings to mesh. Suppose a schedule of savings and investment never confront each other in a single market. Suppose instead that savings is determined as a residual after investment activity dictates the level of income generated in the macroeconomy. If the investment schedule takes the form of a marginal efficiency of capital schedule, it may be the case that the interest rate never falls low enough under laissez faire to bring forth the volume of investment that corresponds to full employment. This can be because the interest rate of money has a floor set by its liquidity premium, below which it never

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Table 9 Samuelsonian Stability Analysis

Basic Model Model with Lags I. C(r, Y)= Y - I -a! 1. C(r,,Yf-1) = Y, -I, 2. I = F(r, Y)+ B 2. I, = F(r,, Y,) 3. M = L(r, Y) 3. MI = L(r,, Y,)

can go (see Keynes 1936, 222-44). Klein’s attraction to interest-rate problems has a firm textual basis in Keynes’s chapter 17, one of the chapters relegated to detour status by Hansen. ’ Samuelson’s (1947) contribution to the effort to mathematicize The General Theory predates Klein’s and appears, in part, in a section of his remarkable Foundations of Economic Analysis. Samuelson’s basic model (see table 9) is IS-LM of the Hicks-Hansen variety-actually predating Hansen’s published work on this score. But Samuelson’s innovative step was to introduce an income lag in the consumption function, to push the analytics into the realm of solutions of difference equations. Samuelson (1939) already had pursued the formal analysis of the accelerator mechanism in the investment function at the end of the 1930s, which probably led Hansen to incorporate it into the more complex model that he did not use for graphical purposes. I9 Three more models of the argument of The General Theory merit attention, those of Ira Scott, Eric Lindahl, and Warren Smith in the early 1950s. Scott’s 195 1 paper presents a model that is virtually indistinguish- able from Reddaway’s 1937 paper. Its significance is that it appeared in the Review of Economics and Statistics, a highly visible journal. It is straightforward one-sector IS-LM. Lindahl’s (1954) essay is more inventive. Originally published in Swedish and then published in English in the Economic Record, Lin- dahl constructs an intentionally underdetermined version of the Keynes- ian system, that is, fewer equations than variables. But there is only one more variable than equations (see table 10). Lindahl proposes three

18. Cottrell and Lawlor (I 99 1, 63940) show that, with some manipulation and care, even the argument of Keynes’s chapter 17 can be illustrated with the IS-LM framework. But their discussion also reveals the limitations of IS-LM in displaying the chapter 17 analysis. 19. While the mathematics of difference equations and the accelerator mechanism were alien to Keynes’s mode of presentation, Samuelson (1988) contends they were very much present in the conceptual structure of his argument, if not in The General Theory, then in Keynes’s Galton Lecture, published in the Eugenics Review in 1937 (CW 14).

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Table 10 Lindahl’s Three Closures

I. I = I(r) 2. s = S(Y) 3./=s 4. MD= M(Y) 5. PMD = M* 6. N = N(Y) 7. w = W(N)

Closure 1: W = W* Closure 2: N = N* Closure 3: r = r*

potential closures: first, a closure that fixes the nominal wage; second, a closure that fixes the level of employment; and third, a closure that fixes the rate of interest. It foreshadows a strategy, although not the intent, of Milton Friedman in 1974, when Friedman designed a similarly underdetermined model with three different closure options: first, a simple quantity theory closure that fixed the level of real income; second, an income-expenditure closure that fixed the general price level; and third, his preferred closure that fixed the rate of interest along ostensibly Keynes-Fisher lines. The first of the three closures, the fixed real-wage closure, Lindahl (1954) argues, brings his Keynes-type system closest to the traditional theory’s explanation for unemployment:

As the real wage replaces the money wage as a parameter, Keynes’s theory becomes very similar to the “classical” one, according to which the point of intersection between the curves mentioned above represent equilibrium in the labour market. According to both theories, lower real wages would make higher employment possible. And in both these systems the actual volume of money (M*)has no other function than to determine, together with other factors, the absolute level of prices. (161-62)

Under the second closure, the employment level is treated as predetermined. Lindahl says in this in’stance “assume that workers accept the highest real wage which is in accordance with this employment” (165). The final closure fixes the interest rate, which is “determined automati-

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cally by the monetary authorities” ( 165). Lindahl’s mathematical model of Keynes’s theory is pcedicated on either price or quantity stickiness of some type.20 Finally, Warren Smith’s ( 1956) paper, self-described as a pedagogical tool, appears to be the first extensive use of the IS-LM apparatus in the Southern Economic Journal. Keynesian results are attributed exclusively to circumstances under which the labor market fails to clear. One theoretical possibility is the case popularized in development economics of an infinitely elastic supply curve for labor. A second theoretical possibility, which Smith explores in greater detail, is money wage rigidity for which he offers several potential reasons, thoroughly foreshadowing the New Keynesian economists agenda, which was signaled in Modigliani’s identification of Keynesian economics with wage stickiness. Smith also mentions the Klein case of the inability of the interest rate to fall suf- ficiently to generate adequate investment, but then points out that the Pigou (real cash balance) effect could overcome the problem. Finally, he considers cases where departures from equilibrium are not corrected automatically; although an equilibrium exists, it is unstable. The final table we present, table 11, summarizes in chronological fashion all the models discussed above. The evolution from the Oxford conference in late 1936 to Modigliani’s 1963 model is a fascinating slice of the history of economics. In the next and final section, we assess the implications of that history for contemporary developments.

20. There is, in addition, the option that Lindahl does not incorporate into his mathematical formalization of Keynes’s system-the assumption that the money wage rate is the predetermined variable. Lindahl’s ( 1954) verbal discussion of this case resembles Champernowne’s earlier distinction between “basic” and “monetary” unemployment and Friedman’s later elab- oration of the natural rate of unemployment and the long-run, vertical Phillips curve: “[The] assumption [that money wages are a given parameter] is undeniably justified in a short-run system which is used for a study of the immediate reactions in a certain position. Like other economic subjects the workers are to a certain extent captured by ‘the money illusion’: a certain benefit in cash often weighs heavier than the same benefit in the form of lower prices of consumption goods and usually resistance is stronger against a decrease in real wages which is connected with a lowering of money wages than against a decrease which is caused by a higher cost of living. But from this the conclusion must not be drawn that workers are, also in the long run, insensitive to the changes inreal wages at given money wages, which is assumed in Keynes’s system in its usual form. In any case, it has been instanced that during the last years of inflation, when higher costs of living have almost always provoked compensating demands for wages, the workers’ final resort is to aim at the maintenance of a certain level of real wages” (159).

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Authors Dates, Places and Context of Initial Nature and Types of Sectors Variables

on 25 September 2021 by guest Downloaded from http://read.dukeupress.edu/hope/article-pdf/27/1/1/425946/ddhope_27_1_1.pdf Presentatioflinal Publication and Markets Harrod all three papers given at Econ Jan 1937 one-multi-sector nominal income a Meade Sept. 1936 meeting of RES Feb 1937 two-sector nominal income Hicks Economics Society Econ Apr 37 two-sector nominal income Champernowne RES June 1936 one-sector, general first to explicitly include labor F market 0J b Reddaway ER June 1937 book review of GT one-sector,.real income (first) Kaldor EJ Dec. 1937 reply to Pigou (a) one-sector, nominal income Ys a Lerner Economica Nov. 1939 reply to Pigou (b) two-sector, nominal income n b Lange Economica Feb. 1938 one-sector, real income L a Timlin book-Keynesian Economics, 1942 one-sector, real income b Palander Ekon. Tidsk Dec. 1942 one-sector c Modigliani Econ Jan. 1944 one-sector, real income with lab. mkt., prod. func. a Hansen Monetary Theory and Fiscal Policy book 1949 (also one-sector, real income 1948 papers) b Klein book-Keynesian Revolution 1947 (New York) one-sector with lab. mkt. and prod. func. c Samuelson book-Foundations ( 1947) one-sector Scott RES Winter 195 1 one-sector, real income, lab. mkt., prod. a Lindahl Ekon Tidsk Sept. 1953 conditions ER May and Nov. 1954

Note 1 The followingpublication abbreviations appearin this table:Econ (Economerrica),RES (Reviewof Economic Studies),Ekon Tidsk (Ekonomisk Tidskrift),SEJ (Southern Economic Journal),ER (Economic Record),and REco Star (Reviewof Economic Statistics). Table 11 Continued.

~ ~ ~ ~ on 25 September 2021 by guest Downloaded from http://read.dukeupress.edu/hope/article-pdf/27/1/1/425946/ddhope_27_1_1.pdf Authors Dates, Places and Context of Initial Nature and Types of Sectors Variables PresentationFinal Publication and Markets b Hansen book-A Guide to Keynes ( 1953) pedogogical purposes Harrod/Hicks equations Smith SEJ Oct. 1956 “pedagogical purposes” real-money dichotomy c Modigliani R Eco Stat 1963 one-sector, real income includes lab. mkt. prod. func. Harrod independent origin, the publication version seen by implicit in General Theory diagram, p. 180 Keynes (Harrod to Keynes 1935, 1936) and Robertson U 97 commented as did Pigou 2. a Meade independent origin, pre-publication versionseen by none Y w Keynes; integrates portfolio and investment theory a1 Hicks equations from Harrod, notation from Meade originally “CCLL” diagram which can readily be 04 transformed into “SILL” c3 Champemowne Keynes lectures; first to represent GT as series of M-r and N-S diagrams which can readily be CrQ independent agg. markets transformed into “SILL” b Reddaway independent; Keynes’s lectures plus GT none Kaldor uses Harrod/Hicks equations used Hicks SILL-distinguishes possible cases of IS “pos.-slope” LL-horizontal; IS-horizontal a Lerner stresses importance of Hurrodian savings functions “LIS” (1938) flow chart (1939) Y s = F(r,Y)

w w Pw Table 11 Continued.

~ ~~~ Authors Dates, Places and Context of Initial Nature and Types of Sectors Variables

on 25 September 2021 by guest Downloaded from http://read.dukeupress.edu/hope/article-pdf/27/1/1/425946/ddhope_27_1_1.pdf Presentatioflinal Publication and Markets b Lange underconsumption implicit; introduces notionof iso-investment and iso-liquidity “optimum propensity to consume” a Timlin originates in Lange but introduces notion of “shifting iso-investment and iso-liquidity equilibria” b Palander independent 3-dimensional diagrams c Modigliani stresses wage inflexibility,real-money dichotomy Hicks “IS-LM” (SILL) a Hansen Harrod-Hicks equations used Hicks SILL but changed it to IS-LM b Klein possibility of negative value for interest rate IS-LM c Samuelson difference equation form emphasis on stability analysis none a Scott Harrod-Hicks equation 4-quadrant Lindahl real-money dichotomy b Hansen Harrod-Hicks equations IS-LM Smith augmented Harrod-Hicks equations 3-quadrant c Modigliani heavily influenced by Gurley, Shaw, and Patinkin, i.e., by “augmented” IS-LM; apex of “neoclassical” inside-outside money and dichotomy-neutrality synthesis distinctions Darity and Young / IS-LM: An Inquest 35

Formal and Substantive Structures of the IS-LM Models: A Comparative Perspective In the introduction to his book A Market Theory of Money, John Hicks (1989) defines what for him was the “essence of the Keynesian revolution” which meant “abandonment” of a notion of “long term equilibrium” -about which the economy would “fluctuate,” but these fluctuations would be “limited” and “their amplitude could be damped” by means of “wise policy”-to replace it with that of “a short term equilibrium” as the “only equilibrium” possible. We wonder how Hicks would reconcile his position with Keynes’s (1936,465 1) chapter 5 discussion of long-period employment, where, of course, the long-period level of employment need not be full employment. Nevertheless, Hicks (1989) wrote: It was not easy for those who were in my position, in 19367 to accept this . . . so the version of Keynes which we received into our thinking was provided with another anchor, a supposedly constant level of money wages in conditions of less thanfull employment. There were particular reasons why at that date such an assumption appeared to be tolerable. . . . If it was accepted, the presentation of Keynes’s theory could be greatly simplified. There was one way of doing this which I myself put forward, and which has been widely accepted. It is what has come to be known as the IS-LM diagram, which has found its way into so many textbooks. (1-2) It is not our intent to debate the merits of Hicks’s diagram nor to take issue with his interpretation of the early history of IS-LM, for that story already has been told (Young 1987). What Hicks has done is enable us to focus on a number of key aspects regarding the long history of IS-LM and thereby put the various approaches it encompasses in comparative perspective. These aspects are the purpose, means, characteristics, and mode of presentation of IS-LM from 1935-37 onward. With regard to purpose of presentation, this was interpretative or pedagogical. In the first case, the interpretation was for “economists.” In the pedagogical case, this was directed toward either graduate students or undergraduates. As for the means of original and final presentation, this was via the media of conference papers, journal articles, reviews, or books. Regarding the characteristics of the IS-LM model used, this relates to the presentation of the sectors, markets, and variables in the respective

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models. Finally, with respect to the mode of presentation, this refers to whether it was use of equations, graphs, or equations and graphical representation. Table 14 provides-to paraphrase Lekachman-a summary of three decades of IS-LM. This starts after Keynes’s own 1932-33 lectures in which he presented what was essentially a “simultaneous equational representation” of a “monetary economy” and of a “monetary theory of production” (Rymes 1989) via the earliest IS-LM papers of Harrod, Meade, Hicks, Champernowne, and Reddaway, through the works of Kaldor, Lerner, Lange, Modigliani ( 1944), Hansen, Klein, Samuelson, and Lindahl, among others such as Timlin and Palander to the apex of the neoclassical synthesis in Modigliani (1963). What is immediately noticeable is the shift from two-sector and n- sector models such as those of Harrod, Meade, and Hicks, or very so- phisticated and general one-sector approaches such as that of Cham- pernowne, to the simplified one-sector versions of Hansen and Smith. This can be viewed as a regressive or degenerative tendency in IS-LM. However, the IS-LM approach survived this tendency and even stronger tendencies to “undercut” it. Another aspect regarding the mode of presentation of IS-LM concerns the use of mathematical formality to express Keynes’s approach and the usefulness of the mathematical approach to The General Theory. Meade advocated precise mathematical and parametric formalization, while Champernowne included such non-parametric variables as “the state of the news” and seemed receptive to a slightly more “literary” approach to The General Theory. Samuelson, for his part, took issue with the “literary” approach to economics manifest in, for example, both Keynes’s book and Hicks’s Value and Capital (1 939), when he said that “the laborious working over of essentially simple mathematical concepts such as is characteristic of much of modern economic theory is not only unrewarding from the standpoint of advancing the science, but involves as well mental gymnastics of a peculiarly depraved type” (1947, 6). Finally, while Lerner advocated a diagrammatic approach to The General Theory as noted above, he still appreciated the masterful literary style of Hicks’s Value and Capital (Young 1991). As Lerner wrote (1940): Not only do some of the important “Keynesian” results, reached independently and earlier by Professor Hicks, appear in their final form in this volume, but the elegance and precision with which fundamental

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notions are presented and the astonishingly simple way in which the intricate argument unfolds itself make it certain that the book will re- main a classic for students to read and reread long after Mr. Keynes’s book has been rendered obsolete by a more careful presentation of its argument at the hands of other writers. (298) The “more careful presentation” is, it would seem, IS-LM. The tenacity of IS-LM is startling to some qbservers. For example, Stanley Fischer replies to Andrew Policano (1985) as follows: Policano (1985) expresses some surprise that the IS-LM model is still the basic model used in modern macroeconomic textbooks. The ver- satility of the model is responsible for its survival: it can be used to analyze both monetary and fiscal policy in both full employment and unemployment modes; it can generate quantity theory or pure Key- nesian results with only minor modifications. The model is capable of accommodating monetarist and Keynesian views, as Friedman’s (1970) theoretical framework shows. In my view it can also accom- modate a basic rational expectations-market clearing view, though I am not sure adherents of that approach would agree. (Fischer 1987, 247 n. 6)*’ Nor are we surprised by the continuing and ongoing existence of IS- LM as an interpretation of Keynesian economics. For, as Patinkin (1990a) argued at the 1987 conference on “IS-LM after 50 Years,” it has acquired a separate identity-albeit we think chameleonic in nature, like The Gen- eral Theory itself-which precludes its being “forsaken,” even by Hicks (1980) himself. But while we do not agree with Patinkin’s (1990b) view that other interpretations of Keynes are simply invalid, IS-LM in its var- iegated forms has “ruled the roost” in macroeconomics teaching, at least, for the past three decades and even in its new coopted form probably will continue to do so.

References Barro, Robert G.,and Herschel Grossman. 1976. Money, Employment and Injution. Cambridge: Cambridge University Press.

2 1. Robert King (I 993) is one of the “adherents of that approach” who plainly does not agree, having buried and eulogized IS-LM for its alleged inadequacies with respect to the treatment of expectations. However, what should be evident from our essay is how flexible the reach has been of IS-LM macroeconomics from its point of origin in 1936.

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