DSGE Models for Monetary Policy Analysis

The chapter has a dual purpose: a selective pedagogical review of how New Keynesian DSGE models are built and used for monetary policy questions, and an original empirical exercise estimating a medium-sized DSGE model on US data via Bayesian impulse response matching (Abstract, p. 286; Section 1, pp. 286-289). It proceeds from a simple three-equation NK model (Sections 2-3), through applications of that simple model to specific policy questions — the Taylor principle, monetary policy and inefficient booms, output-gap measurement — and finally to the estimation of a medium-sized model matched to VAR-based impulse responses (Sections 5-6), closing with open questions (Section 7).

The working capital channel assumes firms must borrow to finance some or all of their wage and materials bill before receiving sales revenue, so a parameter ψ (0 to 1) controls how much of variable input costs must be financed at the beginning of the period (Section 2.1.2, p. 291). With ψ=1, the full input cost is financed; with ψ=0, none is. This modifies effective input prices (Eq. 9, p. 292) and, once combined with Calvo pricing, adds a direct interest-rate term to the NK Phillips curve (Eq. 35, p. 298): π̂_t = κ_p[γ(1+φ)x_t + α_ψR̂_t] + βE_tπ̂_{t+1}, where α_ψ = ψ/[(1-ψ)β+ψ]. When γ=1 and ψ=0 the equation collapses to the standard NK Phillips curve; when ψ>0, a rise in the nominal rate R_t directly raises marginal cost and current inflation, independent of any change in the output gap.

Following Basu (1995), the chapter lets intermediate-good production combine labor and materials, Y_{i,t} = z_t H_{i,t}^γ I_{i,t}^{1-γ}, where materials I_{i,t} are units of aggregate output itself (Eq. 8, p. 291). When γ=1 there are no materials inputs; when γ<1, the aggregate price index becomes partly a cost input for individual firms, which interacts with the working capital channel and, as shown in Section 3.1, with the stability properties of the Taylor rule.

Not necessarily: in the standard case (γ=1, ψ=0) the Taylor principle (r_π>1) does guarantee a unique non-explosive equilibrium, but when the working capital channel is strong and the materials share is realistically low, the same Taylor principle can instead become “a source of instability” (Section 3.1, pp. 303-308; abstract, p. 286). The mechanism: if the central bank raises the policy rate in response to a rise in expected inflation, the working capital channel makes that rate increase itself raise marginal cost and realized inflation, so the policy response can validate rather than counteract self-fulfilling inflation expectations — the same “articulate the risk” logic the classic model uses to defend the Taylor principle (p. 303) is reversed once financing costs feed directly into pricing.

Christiano-Trabandt-Walentin’s (2010a) unemployment extension models a large household whose members differ in disutility of work, defines the unemployed as those who searched but did not find work at the efficient wage, and shows unemployment carries information about the (otherwise unobserved) output gap that can be recovered via limited-information Bayesian estimation (Sections 3.3.1-3.3.4, pp. 311-326). Separately, the chapter asks whether the popular HP filter is a good proxy for this model-implied output gap; fitting the NK model to US data suggests the conditions for the HP filter to perform well “may be satisfied,” but the authors stress “there are several caveats that must be taken into account before concluding that the HP filter is a good estimator of the output gap” (pp. 287-288, 326-330) — a hedged, model-dependent conclusion, not a general endorsement.

The estimation is a two-step Bayesian impulse-response-matching procedure, following Rotemberg-Woodford (1997) and Christiano-Eichenbaum-Evans (2005), on quarterly US data from 1951:Q1 to 2008:Q4 (Section 5, pp. 345-350). Step 1 estimates a 14-variable, 2-lag VAR (lag chosen by Schwarz/Hannan-Quinn criteria, though AIC would select 12) and identifies three shocks: a monetary policy shock (contemporaneous-only restriction on the federal funds rate), a neutral technology shock (identified by two long-run restrictions — only technology shocks affect long-run labor productivity, and only the investment-specific shock affects the long-run relative price of investment), and an investment-specific technology shock (the second long-run restriction alone). This yields 397 stacked impulse responses (3 shocks x 9 variables x 15 horizons, minus 8 contemporaneous restrictions on the monetary shock). Step 2 chooses the DSGE structural parameter vector θ to minimize the (Bayesian) distance between these VAR-estimated responses ψ̂ and the model-implied responses ψ(θ), using an approximate likelihood (Eq. 86, p. 347) with a weighting matrix estimated by bootstrap (10,000 realizations) with Newey-West correction. The posterior is computed by random-walk Metropolis (600,000 draws, 100,000 burn-in, 27% acceptance rate), cross-checked against a Laplace approximation.

The posterior mean price-stickiness parameter is 0.62 (posterior std 0.04; 95% interval [0.56, 0.68]), implying firms reoptimize prices roughly every three quarters — a moderate degree of stickiness, not an extreme one (Table 3, p. 357). Other key posteriors: interest-rate smoothing ρ_R = 0.87 [0.85, 0.90]; Taylor-rule inflation coefficient 1.43 [1.25, 1.59]; Taylor-rule output coefficient 0.07 [0.02, 0.11]; consumption habit b = 0.77 [0.74, 0.80]; inverse labor-supply elasticity φ = 0.12 [0.08, 0.16], implying a consumption-compensated labor supply elasticity of about 8, which the authors flag as “empirically implausible” under a representative-agent (hours-per-worker) reading, resolved instead by interpreting H_t as the number of workers; and investment adjustment-cost curvature S’’=14.30 [9.65, 18.8]. Wage stickiness (0.75) and full wage indexation to lagged inflation are calibrated a priori rather than estimated (Table 2, p. 356).

At the posterior mean, the model reproduces the empirically observed delayed and gradual inflation response to a monetary policy shock, with inflation peaking about two years after the shock, plus an initial “price puzzle” interpreted as a genuine model-implied feature (via the working capital channel’s effect on labor costs) rather than a misspecification (Section 6.2.2, pp. 358-360; Fig. 10). The authors state: “the notable result here is that the slow response of inflation to a monetary policy shock is explained with a modest degree of wage and price-setting frictions” (p. 358). A key departure from Altig-Christiano-Eichenbaum-Linde (2005, ACEL), which assumed firms fully index non-reoptimized prices to lagged inflation, is that this chapter’s model eliminates that indexation assumption entirely. Without indexation, the model can also reproduce the rapid fall in inflation following a positive neutral technology shock (Fig. 11) — a feature ACEL’s fully-indexed model could not match — while the two models still agree on the monetary-shock response.

Varying the VAR’s estimation start date (from 1951:Q1 through starts as late as 1985:Q4) and its lag length (1 to 5 lags), the resulting range of impulse-response variation is roughly the same width as the 95% probability intervals already reported, leading the authors to conclude “the degree of nonrobustness in the VAR is not great” (Section 6.3, pp. 360-362; Figs. 13-15). Separately, a Laplace approximation to the posterior — much cheaper to compute than full Metropolis-Hastings — delivers posteriors “very similar” to the full MCMC estimates, which the authors suggest makes it useful for early-stage model exploration (Fig. 16).

The chapter is explicit about several unresolved tensions rather than presenting the framework as fully validated. First, the model substantially understates the rise in capacity utilization following a monetary policy shock, though the authors note the utilization data used are for manufacturing only (Section 6.2.2, p. 359). Second, the price puzzle in the underlying VAR is “not statistically significant,” and the chapter’s position — following ACEL and CEE — is that this reflects no econometric specification error but rather the working-capital mechanism (Section 6.1.1, pp. 351-352). Third, and most fundamentally, the intertemporal Euler equation at the core of the DSGE model faces the classic Hansen-Singleton (1983) statistical rejection, creating tension with the finding that the impulse-response-matching exercise fits the VAR-based shock dynamics well; the chapter explicitly labels this an “outstanding question” (Section 7, p. 362) rather than resolving it. Finally, the authors note the chapter’s scope is deliberately limited — it does not cover financial frictions, open-economy extensions, or the broader limitations of monetary DSGE models in detail, because “the literature is too large to review in all its detail” (Section 7, pp. 362-364).