Real Rigidities and the Non-Neutrality of Money

The paper opens by noting that a wide range of existing theories (implicit contracts, customer markets, social customs, efficiency wages, insider/outsider models, inventory models, countercyclical markups) explain real wage or price rigidity, but “these explanations have a common weakness… they are theories of real rather than nominal rigidities,” so that “without an independent source of nominal stickiness, prices adjust fully to nominal shocks regardless of the extent of real rigidities.” Conversely, the authors note that while “recent research shows that in principle the nominal rigidities caused by small costs of flexibility can be large” (citing Mankiw 1985, Blanchard and Kiyotaki 1987, and their own Ball and Romer 1987a), “in these models… small frictions have large effects only for very implausible parameter values; for example, labor supply must be highly elastic” – so for plausible parameters, nominal rigidity has large private costs, firms choose only a small degree of rigidity, and nominal shocks have only small real effects.

The paper’s intuition is that price rigidity after a nominal shock is a Nash equilibrium precisely when a firm’s gain from changing its price, given that other prices are fixed, is less than the menu cost – and because a price change when others’ prices are fixed is necessarily a change in the firm’s real price, “if the firm desires only a small change in its real price… then the gain from making the change is small,” so “real rigidity reduces the gain from adjustment” and thereby “increases the range of nominal shocks for which non-adjustment is an equilibrium.” The paper formalizes this in a general model (Section II) where an agent’s utility W(Y, p/P) depends on aggregate real spending Y and relative price p/P, showing that “a broad class of changes in W(·) that increase real rigidity” (measured by a parameter π, the responsiveness of a price-setter’s desired real price to shifts in real money) also raise both the equilibrium degree of nominal rigidity x* and the ratio R of the social to the private welfare cost of that rigidity.

The paper shows that for a range of shocks, both full price adjustment and complete non-adjustment can simultaneously be equilibria, and that “greater real rigidity increases the range of multiple equilibria.” The authors explain this as “strategic complementarity” in price-setting: because an agent’s own desired nominal price depends positively on what other agents charge, “adjustment by others increases his incentive to adjust,” and real rigidity strengthens this complementarity because agents with a strong desire for stable real prices keep their desired nominal prices closely tied to everyone else’s.

Using a continuum-of-farmers model with only imperfect competition and a menu cost (Section III), the paper finds that for an empirically plausible base case – a markup of price over marginal cost and a labor-supply elasticity each corresponding to the parameter value .15 – “the private cost of rigidity is seven tenths of a percent of revenue” for a five percent monetary shock, and the ratio of social to private cost, R, is only 1.2, so that “the welfare cost of the business cycle is still only… slightly greater than the menu cost.” Even under a “generous upper bound” of a markup and labor-supply elasticity both equal to one, R rises only to about 4.5; the authors conclude that “only outlandish parameter values yield large values of R,” and trace the weak result to the empirical fact that labor supply appears inelastic, which gives price-setters a strong private incentive to adjust rather than absorb shocks through quantity changes.

Adding a simple quadratic cost k of changing real prices to the baseline model (Section IV), the paper shows analytically that both the degree of nominal rigidity and R are increasing in k and “approach infinity as k approaches infinity.” Numerically, starting from the baseline real-rigidity parameter π ≈ .127 (R = 1.2), reducing π to .05 (more than halving the responsiveness of desired real prices to demand) raises R only to 3.0; reducing π further to .01 raises R to about 15 (or 150 under the generous markup/elasticity parameters), and π = .001 implies R of roughly 152 (or 1500). The authors are explicit about the limits of this exercise: because the ad hoc cost k “does not tie the degree of real rigidity to parameters of tastes or technology that we can estimate,” the model shows how much real rigidity is needed for large nominal non-neutrality without establishing whether that much real rigidity is realistic.

Building on Stiglitz (1979, 1984) and Woglom (1982), the paper modifies the model (Section V) so that each differentiated good is sold by many farmers, each to his own group of “customers,” with the key assumption that “changes in a firm’s price are observed by the firm’s current customers but not by other consumers.” This produces an asymmetric demand response: “if the firm raises its price, it loses sales both because some of its customers leave… and because its remaining customers buy less,” but “if the firm lowers its price, it sells more to current customers, but it does not attract other firms’ customers, because they do not observe the lower price.” The paper shows this asymmetry (parameterized by ρ, the curvature of the bend in demand around the no-shock price) raises real rigidity, with real prices becoming “completely rigid” as the bend approaches a kink; as in the ad hoc model, the paper finds “a large degree of real rigidity is necessary for a large R” but states it is “again difficult to determine how much real rigidity is realistic, because we do not know realistic values for ρ.”

In the efficiency-wage model (Section VI), real wages respond less than one-for-one to aggregate demand (parameterized so that wages depend on demand with elasticity φ < γ, versus elasticity γ in a Walrasian labor market), which the paper notes works through a different channel than the earlier examples: efficiency wages “increase real price rigidity by lowering W₁₂ while leaving W₂₂ unchanged,” whereas the ad hoc and customer-market models both work by raising −W₂₂. Unlike the previous two sources of real rigidity, the key parameter here – the cyclical responsiveness of real wages to demand – is one “for which we know plausible values,” since “the acyclicality of real wages in actual economies suggests that a high degree of rigidity is realistic”; the authors caveat, however, that the literature has “not yet clearly established” how efficiency wages affect the cyclicality of real wages, so their assumption that efficiency wages substantially dampen that cyclicality is explicitly “tentative.”

For an empirically plausible base case (φ = 1.1, i.e., real wages only slightly procyclical, with a markup and labor-supply elasticity again set to .15), the paper reports that “in a Walrasian labor market, the private cost of rigidity is a huge 38% of revenue, and R is a tiny .02” – so nominal rigidity essentially cannot be an equilibrium – “but with efficiency wages, the private cost is less than one hundredth of a percent and R is 33.” The authors attribute the Walrasian model’s enormous private cost of non-adjustment to self-employed farmers facing a steep, upward-sloping own labor-supply curve, so that when demand falls, failing to cut prices is extremely costly to them individually; efficiency wages break this link by decoupling the wage from the marginal disutility of labor supply, so marginal cost – and hence a firm’s desired price – barely moves with demand. The authors flag that this result is “quite sensitive to moderate changes in parameter values” (raising φ from 1.1 to 1.5 drops R from 33 to 1.4) and, more importantly, that the key parameter φ is “aggregate economic behavior, not a microeconomic parameter of tastes or technology” whose microfoundations the paper has not derived.

The paper’s own conclusion is that “for each model, we find that a large degree of nominal rigidity arises only if the degree of real rigidity is large,” but “we do not fully resolve whether the necessary amount of real rigidity is realistic. This requires development of models of real rigidities in which the degree of rigidity is derived from microeconomic parameters for which we know plausible values.” The efficiency-wage model is presented as the most promising of the three because its key parameter is tied to an empirically observable quantity (real-wage cyclicality), but even there the authors stop short of claiming the mechanism is fully microfounded, since the link between efficiency wages and real-wage cyclicality is itself still an open research question at the time of writing.

The authors note in closing that “Keynes’s argument that workers’ concern for relative wages can lead to nominal wage rigidity is correct if amended slightly: concern for relative wages is likely to reduce but not completely eliminate a firm’s desired adjustment to a nominal shock,” so that “Keynes is correct if there is a small cost to prevent firms from making small adjustments” – i.e., the paper reframes a classic real-rigidity story (relative-wage concern) as exactly the kind of real rigidity that, combined with a small nominal friction, the paper’s general argument says can produce large nominal rigidity.