Comparing Keynes's five models and Modern Keynesian IS/LM and AD/AS analyses

Even economists who recognize the importance of long-term stagnation theory to Keynes, both in The General Theory and in his theoretical and pol­itical interventions throughout the interwar period, agree that the "model" in the book can only be formally represented as a very-short-term model.

Schumpeter stressed that the secular stagnation model is formalized as a short-run, stable static-equilibrium model. "It is true that he [Keynes] had an aversion to 'periods' and that he concentrated attention upon con­siderations of static equilibrium." Schumpeter said that most economists do not realize "how very strictly short-run his model is and how important this fact is for the whole structure and all the results of The General Theory" (Schumpeter 1946, p. 511). This "limits applicability of this analysis to a few years at most... All the [long-run] phenomena incident to the creations and change in this apparatus, that is to say, the phenomena that dominate the capitalist process, are thus excluded from consideration" (Schumpeter 1946, p. 512).

Thus, in Schumpeter 's opinion, even the secular stagnation argument in The General Theory has to be embodied in a short-run static-equilibrium model because variables that affect the long-term trajectory of the economy, such as technical change and population growth, are assumed to be exogenous constants.

Though it remains true that he tried to implement an essentially long-run vision by a short-run model, he secured, to some extent, the freedom for doing so by reasoning (almost) exclusively about a sta­tionary process or, at all events, a process that stays at, or oscillates about, levels of which a stationary full-employment equilibrium is the ceiling.

(Schumpeter 1946, p. 512, emphasis added)

Note the clear inference here that The General Theory has only one model.

The IS/LM model was created by John Hicks in a 1937 paper (Hicks 1937). In a reconsideration of that paper over four decades later, Hicks wrote: "The IS/LM diagram... is widely, but not universally, accepted as a convenient synopsis of Keynesian theory" (Hicks 1980, p. 139). Note that his IS/LM model is assumed to be a "synopsis" of the entire book, rather than one aspect among many of Keynes's complete theory.

Hicks is correct in the sense that IS/LM models, typically integrated in intermediate-run AS/AD models in which the price level is endogenous, do dominate textbook interpretations of Keynes's theory. I note again that the AS/AD model is perversely un-Keynesian. Wage and price levels are assumed to be exogenous constants in the IS/LM model. When inserted into the AD/AS model, as is typically the case in intermediate macro theory textbooks, the price level becomes endogenous. Under conditions of high unemployment, in which AS is greater than AD, the price level falls, which raises real money supply (money supply/price level; M^S/P). This shifts the LM curve to the right, which lowers the interest rate and thus increases investment and consumption spending, raising AD, income, and employment. In other words, deflation always increases employment, a proposition Keynes consistently and aggressively attacked in the interwar period.

Hicks stressed three related characteristics of the model: (1) it could only apply to "periods" of very short length; (2) expectations had to be strictly exogenous within the period; and (3) both goods and money markets were always in equilibrium.

The first characteristic is required to sustain the second. Unless the "period" is very short indeed, things that influence expectations or confi­dence or any other aspect of the behavioral equations are likely to change. The longer the period, then the less realistic the explicit assumption that expectations are strictly exogenous, the more likely that long-run factors such as technology will change, the more likely balance sheets will be transformed, and thus the less adequate the IS/LM model is to its task. The third characteristic is also required to sustain the second one. If expectations turn out to be wrong, a rational agent would presumably alter expectations in a manner designed to lower expected forecast errors. This would cause shifts in the IS and/or LM curves because expectations of future profits affect the investment function and expectations of future bond prices affect the demand for money function. Hicks's IS/LM model is thus stable by assumption.

Finally, and this is extremely important, note that Keynes's crucial vari­able "confidence" has no role to play - indeed, does not exist - in IS/LM models. I have never seen it referred to in intermediate macro textbooks and cannot remember it being mentioned in any macro literature with the exception of occasional use by Post Keynesians. This silence eliminates a major source of endogenous dynamics in The General Theory.

The time period in Keynes's model, Hicks said, was "a short-period... we shall not go far wrong if we think of it as a year." "Mine [in the IS/LM model] was an "ultra-short-period; I called it a week" (Hicks 1980, p. 141). Hicks wanted to "exclude the things that might happen and might disturb the [model of the] markets" during the period because they would cause the model's behavioral equations to shift (Hicks 1980, p.

Hicks wrote that Keynes's model was a single-period static model in which "expectations were strictly exogenous" and always equal to realizations, which puts the model in direct conflict with much of The General Theory (Hicks 1980, p. 140). This allowed him to stress that the IS/LM model "must be assumed to be, in an appropriate sense, in equi­librium" at all times; "the model in some sense, must be in equilibrium" (Hicks 1980, p. 149).

Hicks argued that the IS/LM model itself offers no procedure for analyzing out-of-equilibrium processes. Outside general equilibrium, "we cannot say much about" what would happen, presumably because "saying much" would require a theory of endogenous expectation forma­tion outside equilibrium (Hicks 1980, p. 149). If the economy was off the curves, agents' expectations would be "disturbed."

The core IS/LM model thus does not specify out-of-equilibrium dynamics; it only specifies equilibrium positions. This creates two problems. First, specifications of disequilibrium processes in IS/LM models are theoretically ad hoc in the sense that they are not derived from the basic theoretical propositions in the model about the investment and consumption functions or the liquidity-preference function. The theorist can add on any assumption about what happens out of equilibrium he or she pleases, be it stabilizing or destabilizing, without being in conflict with the core equilibrium model itself. Second, the disequilibrium process added to the IS/LM model is in direct conflict with the theory of disequi­librium processes used by Keynes in the book.

We have, then, facts before us; we know or can find out what. did actually happen in some past year (say, the year 1975). And since the theory is to tell us what would have happened, the variables must be determined. And that would seem to mean that the model, in some sense, must be in equilibrium. Applying these notions to the IS-LM

A digression 275 construction, it is only that point of intersection of the curves which makes any claim to represent what actually happened (in our "1975").

(Hicks 1980, p. 149, emphasis added)

Hicks went on to say that the assumption of equilibrium in the IS/ LM model will not egregiously distort reality as long as the economy is moving in a smooth and stable manner and the length of the period in the model is not too long. "But [this assumption] is dangerous. Though there may well some periods of history, some 'years', for which it is quite acceptable, it is just at the turning points, at the most interesting 'years', where it is hardest to accept it" (Hicks 1980, p. 150). I take him to mean that the IS/LM static-equilibrium model is only useful in helping us make sense of economically stable periods that are relatively short. It is not able to explain business cycle movements (model 3) and it certainly does not apply (without substantial modification) to turbulent, out-of-equilibrium periods such as the mid-1920s to mid-1930s (models 4 and 5), the period The General Theory was written to explain.

Having argued that the IS/LM model must remain in equilibrium with expectations equal to realizations at all times, in his early 1980s article, Hicks acknowledged that this cannot possibly be true for the LM curve. His argument, which is convincing, is as follows: the LM curve is the locus of (Y, r) points at which the real money supply (M/P) is equal to the demand to hold real (or price-adjusted) money as an asset. The demand to hold money, L (for liquidity preference), is assumed to be a positive function of current income (the "transactions" demand) and a negative function of the current interest rate (the "speculative" demand). The money supply, M^s, is traditionally assumed to be set by the Central Bank.³ We can write the traditional LM curve as (M^S/P)_t = L (kY_t, r_t), where P is the price level, k is a constant, and kY_t represents the transactions demand to hold money in period t.

Keynes's speculative demand to hold money, which links money demand to the current rate of interest in the LM model, logically requires not only that investors consider the expected future bond price when deciding between holding money and bonds as a store of financial wealth, but also that they are uncertain about or have less than complete confidence in their expectations. He made this crystal clear, as was demonstrated in chapter 16. If investors knew the future value of interest rates (and bond prices) with certainty, they would hold all of their financial wealth above the minimum amount of money needed to finance transactions in the form of bonds, no matter how low the expected interest rate was. As Hicks

put it: "there is no sense in [a desire for] liquidity, unless expectations are uncertain," and uncertainty must therefore be reflected in the equations of the model (Hicks 1980, p. 152). In the absence of uncertainty about expected future bond prices, there is no risk of capital loss on bond-holding and therefore no reason at all to hold money as an investment asset.

Thus, if investors are not uncertain about the expected future bond price, there is zero speculative demand for money and M^d = kY. In equilib­rium, the demand for bonds must equal the total financial wealth available to invest in either money or bonds (W) minus kY, where W is a constant. Since in equilibrium kY = W - M^s, the LM curve would be a vertical line at Y = (W - M^s)∕k, and the equilibrium values of Y and r would be set at the point of intersection of the IS curve and the vertical LM curve.

A vertical LM curve means that shifts in the IS curve have no effect on the equilibrium value of Y. How un-Keynesian! Thus, the multiplier on new public investment spending will be 1. To explain the process that leads to this result, we have to perform a comparative static analysis that assumes equilibriums are stable. Sustained new public investment will shift the IS curve to the right. With the rightward shift in the IS curve caused by increased investment, Y will be higher than it was at the old equilibrium interest rate. This will increase the transactions demand for money, causing M^d to exceed M^s. Investors will sell bonds to get money, which will drive the interest up until the curves intersect at the vertical LM curve once again, leaving the equilibrium value of Y unchanged. New public investment will have "crowded out" an equal amount of private investment and consumption via rising interest rates.⁴ How classical! This is one of several reasons why any model not based on genuine uncertainty about future economic states cannot legitimately claim to be a model of The General Theory.