Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy

CEE ask what combination of nominal and real frictions lets a dynamic stochastic general-equilibrium (DSGE) model generate both an inertial rise in inflation and a persistent, hump-shaped rise in output after a monetary policy shock (Introduction, p. 1). Rather than calibrating the model to a handful of unconditional moments, they discipline it against the full estimated dynamic response of the economy to a specific, identified shock — the model’s impulse responses are estimated to match, as closely as possible, the impulse responses from an estimated VAR, using minimum-distance estimation (Section IV, Eq. 21, p. 17).

The shock is identified from a nine-variable recursive (Cholesky) VAR with four lags estimated on quarterly U.S. data, 1965Q3–1995Q3, with variables ordered so that the GDP deflator, GDP, consumption, investment, the real wage, and labor productivity are assumed not to respond contemporaneously to the policy shock; the federal funds rate is ordered seventh (so its innovation is interpreted as the policy shock); and real profits and M2 growth are allowed to respond contemporaneously (Section II, pp. 5–8). A subset of the model’s parameters (price markup, Calvo wage and price stickiness, interest semi-elasticity of money demand, investment adjustment costs, habit formation, and capital-utilization curvature) is then estimated by minimizing a weighted distance between the model’s impulse responses and the first 25 periods of the VAR-estimated impulse responses, using a diagonal weighting matrix built from the sampling variances of the empirical responses (Section IV, Eq. 21, p. 17); other parameters, including the money-growth process governing the size and persistence of the shock itself, are taken directly from the VAR via a King-Watson (1996)-style procedure (Section IV, p. 16).

On the nominal side, both goods prices and wages are set in Calvo contracts: with fixed probability each period, an intermediate-goods firm (or a household selling differentiated labor) cannot reoptimize and instead resets its price (or wage) using lagged aggregate inflation as an indexation rule (Eqs. 8, 16, Section III.B and III.D, pp. 9–14). On the real side, the model adds habit formation in consumption (marginal utility depends on consumption relative to last period’s, Eq. 11), convex costs of changing the rate of investment rather than its level (Eq. 13/20), variable capital utilization with a convex utilization cost in terms of output (Eq. 22), and a working-capital channel in which firms must borrow from intermediaries to pay their wage bill in advance, so that the nominal interest rate enters real marginal cost directly (Eq. 18) — meaning a fall in the policy rate mechanically lowers marginal cost and dampens inflation.

The benchmark estimation puts the Calvo price parameter at ξ_p = 0.60 (average contract length ≈ 2.5 quarters) and the Calvo wage parameter at ξ_w = 0.64 (≈ 2.8 quarters), with a habit parameter b = 0.65 and an investment-adjustment-cost parameter κ = 2.48 (Table 2, Section V.A, p. 17). The habit estimate is close to the 0.70 found by Boldrin, Christiano, and Fisher (2001); the price markup estimate (λ_f = 1.20) is close to Rotemberg and Woodford (1995). The investment elasticity 1/κ = 0.40 means a temporary 1 percent rise in the price of installed capital raises investment 0.40 percent (a permanent rise would raise it roughly 55 percent). The capital-utilization curvature parameter σ_a is driven to its imposed lower bound of 0.01, and the authors report that its standard error cannot be computed because the estimation algorithm effectively breaks down there — a limitation they note explicitly (Section V.A, p. 18).

The model’s impulse responses fall within the two-standard-deviation confidence interval of the VAR-estimated responses for most variables (Figure 1, Section V.B, p. 21): inflation shows no noticeable rise until roughly three years after an expansionary shock, matching the data’s inertia; output rises for nine quarters, with a cumulative response of 3.14 percent, more than 78 percent of which occurs after the wage and price contracts in effect at the time of the shock have already been reoptimized — a “contract multiplier” (ratio of quarters output stays elevated to average contract length) of 3.7. The money stock peaks about three quarters after the shock and returns near zero by roughly eight quarters, while output peaks almost twice as large as the money-stock peak and about half a year later; the price level shows essentially no change despite the extended money-supply expansion (Figure 2, Section V.B, pp. 21–22). The model’s capital-utilization series tracks the Basu-Fernald-Shapiro (2001) utilization measure well but performs less well against FRB capacity utilization and electricity consumption; notably, the authors report the model if anything understates the empirical rise in utilization rather than relying on counterfactually strong utilization (Figure 3, Section V.B, pp. 23–25).

Sticky wages are crucial and sticky prices play only a limited role. Setting price stickiness to zero (ξ_p = 0) and re-estimating leaves the wage-stickiness estimate “virtually unaffected,” and the authors state this “substantiates our claim that sticky prices play a limited role in accounting for the good fit of the benchmark model” (Section VI.B.1, p. 29) — inflation falls more and output rises more on impact, but inflation inertia and hump-shaped output persist because wages are still sticky. By contrast, setting wage stickiness to zero (ξ_w = 0) produces a sharp, persistent real-wage rise and an inflation surge, output rises only briefly before reverting, and re-estimating forces price stickiness to unity (implausibly rigid); the authors conclude “sticky wages play a crucial role in allowing the model to account for the effects of a monetary policy shock” (Section VI.B.1, p. 29).

Variable capital utilization is the paper’s key real friction: removing it (fixing σ_a at 100) roughly cuts the output response in half and makes inflation rise substantially more on impact, and re-estimating without it drives price stickiness to ξ_p ≈ 0.92 — an average contract length exceeding three years, which the authors call “clearly inconsistent with existing microeconomic evidence, e.g., Bils and Klenow (2004)” — and pushes the price markup to an implausibly high 1.85 (Section VI.B.3, p. 33). Conversely, adding variable capital utilization alone to a model stripped of other real frictions is enough to bring the inflation path back within the empirical confidence bands and restore most of the output persistence (contract multiplier ≈ 3, with about 65 percent of the output rise occurring after reoptimization) (Section VI.B.3, p. 40).

Without the working-capital channel, inflation no longer declines after an expansionary shock (because the fall in the policy rate no longer lowers marginal cost directly), and re-estimating pushes price stickiness to ξ_p ≈ 0.89 (roughly 2.5-year contracts), which the authors again call implausible relative to microeconomic evidence (Section VI.B.3, pp. 38–39). A model stripped of all three real frictions (small investment adjustment costs, no habit formation, no working capital) shows no inflation inertia and non-persistent output effects; its contract multiplier falls from 3.7 to 2.3, only 46 percent of the output increase occurs after reoptimization (versus 78 percent in the benchmark), and re-estimation drives both Calvo parameters to unity — which the authors describe as “a dramatic illustration of our claim that inference about nominal rigidities is sensitive to getting the real side of the model right” (Section VI.B.3, p. 39). Habit formation and investment adjustment costs matter much less for inflation inertia and output persistence per se; their main role is shaping the timing of consumption, investment, and the interest rate responses (Section VI.B.3, p. 40).

CEE acknowledge an apparent conflict with Chari, Kehoe, and McGrattan’s (2000) finding that small nominal frictions cannot generate persistent real effects, and identify three sources of the difference: contract-length assumptions (CEE’s empirically estimated ≈2.5-quarter price contracts versus Chari et al.’s imposed 1-quarter contracts), different persistence measures, and different real frictions included in the model (Section VI.B.3, pp. 40–42). They note that if their own model is forced to use 1-quarter contracts, it too generates little persistence — so the disagreement is not about the theory of price/wage stickiness generating persistence in the abstract, but about which contract lengths and real frictions are empirically supported.