Stability properties and the legitimacy of comparative static macro-policy analysis in The General Theory and IS/LM models

Keynes argued that Britain needed to shift from classical laissez-faire economic policy to Liberal Socialism not only because the economy was mired in long-term stagnation, but also because of destructive disequi­librium processes based on endogenous expectation- and confidence­formation processes in an environment of fundamental uncertainty and, at times, of fragile endogenous balance sheets.

One implication of Keynes's theory of disequilibrium dynamics is that comparative-static analysis, which must assume stabilizing out- of-equilibrium dynamics, is an illegitimate analytical procedure in a fully Keynesian model. Yet, as mentioned before, Keynes himself used

A digression 277 comparative statics in chapter 10 of The General Theory to provide a con­crete answer to the question of how much increased income and employ­ment would result from a given amount of permanent additional public investment. This appears to make him vulnerable to the charge of incon­sistency on this important question. However, I will show that Keynes warned the reader of The General Theory against relying solely on com­parative statics to address stability questions. He insisted in the strongest terms on the need to incorporate endogenous dynamics into his model.

We turn first to an analysis of the IS curve. The IS curve is the locus of income and interest rate (Y, r) points for which AD_t = C (Y_t) + I (Y_t, r_t) = Y_t = AS_t, where C is consumption spending and I is investment spending. Keynes's criterion for undertaking an investment project is that the mec must exceed the long-term interest rate. The mec is a positive function of the expected annual profit flows over the entire expected life of the project, which may vary from a few years to a few decades.

There are two possible ways to justify this anti-Keynesian assumption, neither of which is satisfactory. The first is to assume that agents believe that the short-term equilibrium value of Y_t is always equal to the expected long-term equilibrium value of Y, denoted here as Y_LR^EX_t. This assumption incorporates long-term expectations into the investment equation as required, but it also implies that firms always believe that the short-term equilibrium value of Y_t and Y_LR^EX_t are equal. However, Y_t will typically change between each adjacent short-period equilibrium, and these changes will be substantial in "interesting times." It would therefore be irrational for firms to believe that future values of Y will always be identical to the present value of Y in the face of persistent evidence that this is not true. The assumption that firms are irrational is not acceptable as a foundation for Keynes's theory. Given fundamental uncertainty, agents do not have the complete and correct information about future states of the economy required to be able make assuredly optimal decisions. However, they should not be modelled as making assuredly incorrect choices either.

In the second case, the value of Y_LR^EX_t is assumed to be an exogenous constant unaffected by changes in Y_t in the short and intermediate run, no matter how many short or intermediate periods there are or what the path over time of Y_t looks like. This leads to two problems in the theory behind the IS curve. The first problem is caused by the fact that long-term capital investment in the short-run IS model is a positive function of Y_t.

differs in value from the correct variable - the long-term expectation of future Y.

The second problem is that this model provides no hint of how agents form their guesses about the value of Y_LR^EX_t, never mind their process for deciding on the degree of confidence they should place in their calculation of Y_LR^EX_t. Keynes insisted that long-term expectations are endogenous - see chapter 12 of The General Theory and his 1937 QJE article. They are formed by extrapolating the trajectory of the economy over the relevant past except if there are specific reasons to expect a change in this trajectory. Keynes specifically assumes that the elasticity of the mec with respect to recent values of the actual profit rate or of stock prices is not small. But if, contrary to Keynes, we assume that long-term expectations are unaffected by the movement of the economy over time, we have to ask: where else can they possibly come from? To paraphrase Mao Tse-tung's comment on the origin of "correct ideas": long-term expectations "do not fall from the sky." It is irrational to build an economic theory on the foundation of this deus ex machina, and it is decidedly un-Keynesian as well.

There are two situations in which the fully exogenous long-term expect­ation assumption is less objectionable, though it is still objectionable. If the economy were to sink into a deep and long depression that squeezed almost all optimism out of the economy, as in the mid-1930s, one might expect long-term expectations to become relatively - though not abso­lutely - unresponsive to short-term movements in the economy. It might take quite a while - perhaps as long as a few years - for an upturn to create significantly more optimistic expectations or to reduce confidence in the pessimism of the era.

If we add to these problems the fact that the IS model does not incorp­orate the confidence variable at all, it seems clear that the specification of the IS curve is incapable of adequately representing Keynes's theory.

Is an IS equilibrium stable? Suppose the economy should find itself at a point in (Y, r) space (with Y on the horizontal axis) that is below and to the left of the IS curve. Will endogenous forces cause Y to return to a point on the IS curve or not? The answer given by textbook Keynesian theory is a definitive yes. The answer given in The General Theory is that some­times it will and sometimes it will not. It all depends on the behavior of expectations and confidence.

In the IS model, it is implicitly assumed that the current deterioration in the economy reflected in the point below the IS curve does not alter the expected short-run or long-run value of equilibrium Y or the confi­dence with which expectations are held. I say implicitly because unless

A digression 279 the current value of Y and the long-term expected value of Y, Y_lr^ex, are assumed to be identical, Y_LR^EX_t must be an implicit exogenous shift param­eter hidden in the specification of the investment equation. Because the expected long-term equilibrium value of Y is assumed to be unaffected by movements in Y_t, the IS equation will not shift as the Y_t point moves off the curve. If the decline in investment plus consumption (i.e. in AD) caused by the decline in Y is less than the decline in Y (or AS) itself, inventories will fall at Y values to the left of the IS curve.

Keynes answered the stability question differently. We know from chapters 12, 19, and 22 of The General Theory that, in Keynes's theory, long­term expectations of future variables usually respond fairly quickly to sig­nificant movements in their actual values, and confidence in expectations is sensitive to changes in the accuracy of recent forecasts. If Y is used as a proxy for the mec, then expected future income Y_LR^EX_t will be a function of lagged values of Y (Y_t, Y_t _ ₁, Y_t _ ₂, and so forth). Therefore, if current Y_t drops significantly and unexpectedly below the point on the IS curve associated with the current short-run equilibrium value of Y, investment will decline at all (Y, r) points because Y_LR^EX_t, a shift parameter in the IS equation, will decline. The IS curve will shift left, generating a new - pos­sibly temporary - equilibrium Y at the point of intersection of both curves. What happens next would depend on the specific character of endogenous expectation and confidence formation.

We already showed in our discussion of the Hicks critique that points on the LM curve are assumed to be stable under the assumptions that investors know future bond prices with certainty and that expected values of r and Y are unaffected by changes in the current values of these variables. An analysis of the stability of the LM curve consistent with The General Theory might proceed as follows: suppose the interest rate fell to a point significantly below the LM curve. This means that the price of bonds increased significantly, creating capital gains for bond-holders.

What might a dynamic investment function more consistent with The General Theory look like? It might be written as I_t = I (r_t, Y_t, Y_lr^ex, CF_t),

where Y_LR^EX_t and CF_t (agent confidence in the expectation-formation pro­cess at time t) are endogenous variables determined by extrapolating the recent trajectory of the economy.⁷

Keynes's theory of liquidity preference requires the inclusion of expected future bond prices and the degree of confidence agents have in these expectations to determine what share of their financial wealth investors wish to hold in the form of bonds versus money. Since bond prices and interest rates move in opposite directions, we might write a Keynes-inspired demand for money function as MD_t = M (Y_t r_t, r^EX_t, CF_t), where the expected interest rate r^EX_t (formed through extrapolation from the relevant past) and CF_t are endogenous variables.

We might think of Y_LR^EX_t and r^EX_t as constructed by extrapolation from a distributed lag function of past rates of growth of Y_t and r_t with coefficients that decline as we move back in time from t - 1. The cutoff date for the series might be the point when the current "era" began, per­haps after the most recent crisis, though the value of the coefficients on distant past observations would be relatively small. The function should be consistent with the endogenous boom-bust business cycle discussed in chapter 22. CF_t might also be constructed through a distributed lag function built by extrapolating the percentage error in forecast values relative to actual values in the relevant past. Model 5 requires that these formulations be subject to disruption at crisis points when agents lose all confidence in their ability to foresee the future - as in chapter 12's "abnormal times."

The complete economic model would be composed of the structural equations of the expanded IS/LM model combined with equations that explain how expectations and confidence are formed. The logic of this dynamic process is as follows: the values for expectations and con­fidence are influenced by recent trends of relevant economic variables. Expectations and confidence in turn affect agent decisions that determine current economic outcomes given the structure of the economic model. Current outcomes then influence the next period's values of expectations and confidence - and so on. Steve Fazzari argued that a dynamic process such as this cannot be stationary.

Since agents learn and realized outcomes depend on expectations, the uncertain process being forecast cannot possible be stationary. Learning leads to changing expectations and changes in expectations cause changes in the underlying process... This kind of learning may never reach a self-sustaining state at all.

(Fazzari 1985, p. 73)

A complete formal analysis of this system would require a full specifi­cation of a dynamic mathematical version of this model.⁸ However, for our purposes, in the next section we will look at Keynes's model as a system of augmented IS/LM curves that shift over time in response to exogenous shocks and their own endogenous dynamic forces.