The Quantitative Analytics of the Basic Neomonetarist Model

The paper defines a Neomonetarist model as “a hybrid model… following the Real Business Cycle paradigm as closely as possible except for adding what is logically necessary in order to graft in sticky prices,” choosing this name specifically “to avoid implicating either the New Keynesians or the New Classicals” in the project. The author motivates taking Real Business Cycle modeling seriously because it “has consistently taken dynamics, sensible anticipation of the future, quantitative calibration and the welfare implications of models very seriously,” while motivating sticky prices because they “provide one of the few means of generating large monetary nonneutralities” consistent with the historical evidence assembled by Friedman and Schwartz (1963) on the real effects of monetary policy – evidence the author argues flexible-price models have had little success matching outside of hyperinflationary episodes, since the monetary services sector is simply too small a share of GDP for its distortions to matter much when prices are fully flexible.

The paper assumes an exogenous money-demand velocity V in “the monetarist spirit,” so that the quantity identity MV = PY delivers an aggregate demand curve directly, while “the short-run aggregate supply curve is a horizontal line at the… sticky price P,” with all of the model’s interesting content in what determines the dynamics of that sticky price level. Price-setting itself follows Calvo’s (1982) continuous-time model, in which each firm gets the chance to reconsider its price only at random intervals arriving via a Poisson process with intensity α per unit time; the author picks Calvo pricing for tractability, and justifies focusing on sticky prices rather than sticky wages by appeal to the view that observed wages are installment payments on long-term implicit contracts and so “do not accurately represent a firm’s labor costs,” making sticky wages a poor proxy for sticky marginal labor cost even though observed wages do look sticky in the data.

The paper derives the optimal reset price P_t (the price a firm sets when it does get the chance to adjust) as a discounted, curvature-weighted average of the “instantaneously optimal target price” P^# over the random future interval until the firm’s next price-reset opportunity – formally, “a weighted average of the instantaneously optimal target price over the length of time until the next price decision, appropriately discounted,” where the weight is the curvature of the firm’s profit function with respect to its relative price. This target price P^# is itself pinned down by the condition that marginal revenue equal marginal cost; the gap between the target price and the current price level, linearized, is shown to be proportional to the gap between actual output and a concept the paper calls “full employment output” Y^f – the level of output at which the firm’s instantaneously optimal price would exactly equal the current price level.

Rather than assuming a constant-elasticity-of-substitution (CES) demand system, the paper constructs a general “variety aggregator” Υ(ξ) – where ξ is a firm’s output relative to the aggregate – chosen so that the elasticity of demand ε(ξ), and hence the markup a firm would charge, can vary flexibly with the firm’s own relative output, while still nesting the CES case and being fully consistent with a competitive final-goods-assembly sector. The paper shows this elasticity of demand matters in two ways: it sets the “target markup” μ(ξ) = 1/(1 − 1/ε(ξ)) a firm would charge if free to reprice, and it governs how much a firm’s relative price must fall to accommodate a given increase in its relative output. Letting this elasticity fall sharply as a firm’s market share rises is, the paper argues in its conclusion, “both easy to model and effective at reducing the private cost of price stickiness, making price stickiness more plausible” – because a firm whose markup shrinks sharply when it tries to expand output has less private incentive to adjust its price in the first place.

The paper defines two elasticities, ω (the gap between the slopes of the marginal-cost and marginal-revenue curves facing an individual firm, with respect to the firm’s own relative output) and Ω (the elasticity with which a proportional, economy-wide increase in output raises a firm’s real marginal cost, holding relative output fixed), and shows the reaction function for an individual firm’s instantaneously optimal output has slope Ω/ω with respect to aggregate output – a positive slope that is the paper’s formal measure of strategic complementarity in the Cooper-John sense. The paper emphasizes that “the multiplier… [is] greater for a price game than for an output game,” and that these two elasticities – essentially how fast marginal cost rises and how fast marginal revenue falls as a firm or the whole economy expands – “are the only other information needed to determine these indicators of the degree of strategic complementarity.”

Using its high-α (fast individual price adjustment) approximation, the paper derives that the convergence rate κ at which the aggregate economy returns to full employment after a permanent monetary shock is approximately κ ≈ (α + r/2)·√(Ω/(εω)) − r/2 – “the most interesting aspect of this equation is that the convergence rate… depends roughly on the square root of Ω/(ε*ω),” the same combination of elasticities (dubbed the output elasticity of the target price) that measures real rigidity.* The paper draws out the implication directly: “a high degree of ‘real rigidity’ in Ball and Romer’s (1990) sense makes price adjustment slow in comparison to the frequency α at which individual firms adjust their prices,” so that “if [this elasticity] is less than 1, aggregate price adjustment will be slower than the microeconomic rate at which firms get a chance to adjust their prices” – i.e., the same mechanism that makes sticky prices privately plausible for an individual firm also makes the aggregate economy’s adjustment to shocks slower than the individual firm’s repricing frequency would suggest on its own.

The paper argues that “in the absence of some mechanism in a model to allow the relative price of capital and consumption goods to vary, the real interest rate and the net marginal product of capital must always be equal,” which would mean “virtually any stimulus to the economy, including a monetary stimulus, must be associated with an increase in the real interest rate, since virtually every business cycle model implies a procyclical marginal product of capital” – so investment adjustment costs, modeled in the Hayashi (1982) Tobin’s-Q fashion (capital accumulation a concave function of the investment-capital ratio), are introduced specifically to “give the real interest rate a fighting chance to fall in response to a monetary expansion” by letting the price of capital (Q) move independently of the real rate.

No – despite investment adjustment costs being calibrated using empirical estimates of the elasticity of investment with respect to Tobin’s Q (the paper adopts an adjustment-cost parameter implying investment elasticities toward the high end of the empirical range, drawing on Cummins, Hassett and Hubbard 1994, and an implied capital-stock adjustment half-life of about 3.24 years), the paper’s calibrated general-equilibrium solution for the real-rate response to a permanent money-supply increase is r̃ ≈ [.329 − .0322(α+.01)/√ω]M̃, or equivalently r̃ ≈ [.3289 − .0642κ]M̃. Since this expression is positive unless κ exceeds .3289/.0642 ≈ 5.123 – a convergence rate of more than 500% per year – the paper concludes that “unless the half-life for macroeconomic price-adjustment is less than 50 days, a monetary expansion should lead to an increase in the real interest rate,” so that “in terms of intermediate macroeconomics, the IS curve is stubbornly upward-sloping” in this model even with investment adjustment costs doing their best to counteract it.

The paper does not treat the upward-sloping-IS-curve result as evidence against monetary stimulus working through lower real rates in practice; instead, it suggests “it may be necessary to model any real-world tendency for the real interest rate to fall in response to a monetary stimulus as a result of output being temporarily off the IS curve” – i.e., as a disequilibrium or adjustment-path phenomenon rather than a property of the model’s steady-state-consistent IS relationship itself. This framing is consistent with the paper’s broader point (Q6) that realistic degrees of real rigidity make the general-equilibrium adjustment of the whole economy to a shock considerably slower than the rate at which any individual firm resets its own price, leaving room for transitional dynamics the simple calibrated expression does not capture.

The paper closes by stating three conclusions directly: first, “an elasticity of demand falling sharply with a firm’s market share is both easy to model and effective at reducing the private cost of price stickiness, making price stickiness more plausible”; second, “mechanisms that increase real rigidity and thereby make sticky prices more plausible also tend to slow down the general equilibrium adjustment of prices,” so that the aggregate adjustment rate “is likely to be significantly slower than α” whenever there is enough real rigidity to make sticky prices plausible in the first place; and third, “even when investment adjustment costs are introduced to give the real interest rate a fighting chance to fall in response to a monetary expansion, plausible parameter values imply that the real interest rate will increase in response to a monetary expansion.”