The New IS-LM Model: Language, Logic, and Limits

The model consists of a forward-looking IS equation, a Fisher equation, and an expectational Phillips curve – “yt = Et yt+1 - s[rt - r] + xdt,” “Rt = rt + Et pi_t+1,” and “pi_t = beta Et pi_t+1 + phi(yt - y-bar_t) + x_pi_t” – each of which “can be built up from microfoundations,” in contrast to the traditional IS-LM model’s postulated behavioral equations (Section 2, pp. 49-51). King identifies two respects in which it is genuinely new: first, relative to Hicks’s (1937) original model, the price level is fully endogenous and cannot be solved for without specifying a monetary policy rule; second, relative to even the 1970s rational-expectations IS-LM model of Sargent and Wallace (1975), the new IS equation makes current output depend on expected future output (not present in Sargent-Wallace), and the new Phillips curve makes current inflation depend on expected future inflation rather than a backward-looking expectation of current inflation (Section 2, p. 53). He cautions explicitly that these forward-looking relationships cannot be analyzed by simple curve-shifting on an IS-LM diagram when expectations are rational, since “it is necessary to solve simultaneously for current and expected future variables” (p. 54).

A neutral monetary policy is one that keeps output always equal to its capacity level, yt = y-bar_t; solving the Phillips curve forward under this constraint yields “pi_t = beta Et pi_t+1 + x_pi_t = sum_(j=0)^infinity beta^j Et[x_pi,t+j],” meaning the neutral inflation rate is entirely a function of current and expected future “inflation shocks” (Section 3, pp. 55-56). If there are no inflation shocks, “the solution is that the inflation rate should always be zero” – and, reversing the causal direction, “a central bank which keeps the price level constant also makes output always equal to the capacity level.” Crucially, King stresses that shocks to aggregate demand, to the determinants of capacity output, and to money demand “do not affect the price level under a neutral monetary policy regime” at all – a policy conclusion he notes Rotemberg (1996) called “mom and apple pie” because it recurs across many related, more fully articulated models (Section 3, p. 55).

King builds the Phillips curve from Calvo-style staggered price-setting – each firm faces a constant per-period probability of being unable to adjust its price – combined with forward-looking optimal pricing in which firms setting a new price today rationally weight expected future nominal marginal cost, and then closes the model with the assumption that real marginal cost is proportional to the output gap, psi_t = h(yt - y-bar_t) (Section 4, pp. 58-64). He is explicit that this last step is “a final – heroic – assumption,” calling it “a shortcut that avoids modeling of the labor market, which is complicated, difficult, and controversial” (p. 62). Combining the backward-looking price-level-averaging equation, the forward-looking optimal-price equation, and this marginal-cost assumption yields the Phillips curve’s structural parameter phi = h(1-eta)(1-beta*eta)/eta, tying the reduced-form slope directly to the microeconomic probability of price adjustment (eta) and the marginal-cost elasticity (h) (Section 4, p. 62).

No – with beta close to one, the model’s “long-run slope” of the Phillips curve, (1-beta)/phi, is negligible, so a permanent, credible shift in trend inflation has essentially no lasting effect on output (Section 5, pp. 68-71). But King shows, following Lucas (1972b) and Sargent (1971), that a naive Solow-Gordon-style regression of inflation on lagged (adaptive-expectations) inflation and the output gap will spuriously estimate a large, exploitable long-run trade-off if inflation is actually persistent under rational expectations: with inflation following an AR(1) process pi_t = rho*pi_(t-1) + e_t, such a regression would estimate a coefficient of zero on lagged inflation and infer a long-run trade-off of (1-rho)/phi percentage points of output per point of inflation, “even though no tradeoff was actually present” (p. 69) – the Lucas-Sargent critique restated within this specific model.

King shows that the degree of gradual, backward-looking price-level adjustment (the coefficient theta, which rises with the microeconomic stickiness parameter eta) governs how a change in nominal income splits between output and prices on impact and how persistently that output effect decays, and that this persistence is a genuine model prediction as long as the underlying nominal-income process itself has some persistence (Section 4, pp. 65-68). Simulating a permanent one percent rise in nominal income with theta = 0.20, output rises by 20% of the shock on impact and then decays geometrically at rate theta as the price level gradually catches up (Fig. 2, p. 65) – but King notes this comes with a strict limit: “if the changes in nominal income growth are permanent (rho=1) and market discounting is small (beta=1) then… there is neutrality independent of the degree of underlying price stickiness,” so the mechanism generates persistence for temporary or partially-persistent nominal shocks but collapses to full and immediate neutrality for permanent ones (Section 4, p. 70).

The New IS curve is forward-looking because it is derived from the modern (Hall-style) theory of optimal consumption, in which efficient consumption growth is positively related to the real interest rate – yielding a near-unit coefficient on expected future output, ct = Et ct+1 - s[rt - r] (Section 6, pp. 71-74). King shows that if the expectations theory of the term structure holds, iterating the IS curve forward over n periods (assuming output returns to capacity by then) replaces the short real rate and the omitted Et yt+1 term with a single long-term real rate, yt = -sigma*r^n_t + Et y_(t+n) + xdt with sigma = sn – so “the implied coefficient on the long rate is much larger than s” and fits better empirically, “because the long-term real interest rate ‘stands in’ for the influence of expected future output” (p. 73). He also derives that the natural (capacity-consistent) real rate rises whenever capacity output is expected to grow faster, so a recovering economy with high expected growth should show a high real rate, and vice versa (Section 6, p. 74).

In a simple flexible-price benchmark responding only to current inflation deviations, King shows the rational-expectations equilibrium is unique only for an “aggressive” response, tau greater than 1 (or a symmetric aggressive negative response, tau less than -1); values of tau in between -1 and 1 admit a continuum of “sunspot” equilibria in which inflation can be arbitrarily volatile with no change in fundamentals (Section 7, pp. 75-77). Extending the analysis to the sticky-price New IS-LM model, King derives the exact boundaries analytically and finds, “in contrast to conventional wisdom,” that the zone of indeterminate outcomes is larger under sticky prices than under flexible prices, not smaller – for a rule responding only to current inflation the lower admissible boundary is tau_0 = -2(1+beta)/(phi*s) - 1, which only approaches the flexible-price boundary of -1 as prices become fully flexible (Section 7, pp. 78-79). For a purely forward-looking rule responding only to expected future inflation, King (citing Bernanke and Woodford, 1997) shows both very weak and very strong responses can produce indeterminacy, so “it is also important that it not respond too aggressively” (p. 80).

Yes – King shows that adding a term responding to deviations of the price level itself from a target path, Rt = r-bar_t + Et pi_t+1 + f(Pt - P-hat_t) + xRt, guarantees a unique stable equilibrium for any f > 0, regardless of how the rule responds to the inflation rate per se (Section 7, “An Alternative Nominal Anchor,” pp. 80-81). This formalizes an idea King attributes to Goodfriend and King (1997): that a central bank “can have a greater degree of freedom in the short-run dimensions of its policy rule if it adopts a specification which recognizes the importance of the price level,” since a price-level anchor removes the aggressiveness requirements on inflation-response coefficients that a pure inflation-targeting rule needs to rule out sunspots.

King flags three: the model cannot, from within itself, explain why stabilizing output at capacity is actually welfare-improving (that requires stepping outside to models where capacity output and welfare are explicitly derived); it offers no structural account of what an “inflation shock” actually is, since standard candidates like productivity or energy-price shifts operate through marginal cost, a channel already in the pricing equation, not as free-standing price shocks; and it omits investment and capital altogether, which King calls “an important, if not fatal, flaw” (Section 9, pp. 88-89). He is candid that his own use of a simplified, non-fully-derived exposition here departs from his usual practice of building “small-scale fully articulated models,” explaining that the goal of this article is only “to provide a simple exposition of the New IS-LM model and to exemplify how it is currently being used,” not to establish or test its predictions against actual U.S. or international data – a task he explicitly leaves to “much recent progress” elsewhere in the literature and “a great deal of work” still to be done (Section 9, p. 89).