Dynamic Stochastic General Equilibrium

The four blocks

A New Keynesian DSGE model has four interlocking blocks of equations, all derived from optimization. They feed each other through prices, quantities, and expectations.

• Households. A representative household chooses consumption C, labor supply N, and assets to maximize discounted lifetime utility. First-order conditions deliver the consumption Euler equation and the labor-supply equation. These are the Ramsey block.
• Firms. Monopolistically competitive firms produce differentiated goods. Under Calvo pricing, only a random fraction (1-θ) can reset prices each period. Aggregating firm decisions yields the New Keynesian Phillips curve, π = β·E[π'] + κ·x, where x is the output gap and κ is the slope.
• Central bank. Sets the nominal interest rate following a Taylor rule, r = ρ·r' + (1-ρ)·(r* + φ_π·π + φ_x·x) + ε^r. The coefficients φ_π and φ_x govern how aggressively the bank fights inflation and output gaps.
• Government. Often a simple block: collects taxes, issues debt, and provides spending shocks. Plays a minor role in baseline New Keynesian; expanded in fiscal DSGE.

Market clearing closes the system: aggregate output equals aggregate demand C + I + G; the labor market clears; the asset market clears. Add shocks (productivity, monetary, markup, government, risk premium) and you have the system.

The three-equation New Keynesian skeleton

Strip the model down to its essentials and it becomes three log-linearized equations around the steady state, where x is the output gap, π is inflation, and r is the nominal interest rate:

x  =  E[x']  −  (1/σ) · (r  −  E[π']  −  r*)         (IS, Euler-equation linearized)
π  =  β · E[π']  +  κ · x  +  ε^cost                 (NK Phillips curve)
r  =  ρ · r'  +  (1−ρ)(r* + φ_π · π + φ_x · x)  +  ε^r  (Taylor rule)

This is the workhorse you'll find in introductory monetary economics. The Smets-Wouters model extends it with habit persistence in consumption, sticky wages alongside sticky prices, investment adjustment costs, variable capital utilization, and seven shocks. The result is roughly 30 equations in 30 endogenous variables but the spirit is the same: a Ramsey-style household choosing optimally, firms setting prices under Calvo frictions, a central bank following a Taylor rule.

Worked example — a monetary policy shock

Smets-Wouters (2007) calibration of the U.S. version. Parameters include σ = 1.4 (intertemporal elasticity), β = 0.99 (discount), θ = 0.66 (Calvo probability), ρ = 0.81 (interest smoothing), φ_π = 1.98, φ_x = 0.13, h = 0.71 (habit), shock std σ_r = 0.24.

Simulate a 1 standard-deviation contractionary monetary shock ε^r = +0.24% (annualized about +1%). The impulse responses peak around quarters 2-4 with:

• Output gap x: −0.6% peak (recession).
• Inflation π: −0.4% peak (disinflation).
• Hours worked: −0.5%.
• Consumption: −0.4%, smooth, returns to baseline over 12 quarters.
• Investment: −1.8%, sharper response, lags behind output by 1 quarter.
• Nominal rate: rises 0.24% on impact, decays back over 8 quarters under interest smoothing.

The empirical impulse responses estimated by VAR (Christiano-Eichenbaum-Evans 2005) match these magnitudes closely — about 1% rate hike produces 0.4-0.6% output decline at peak with a 2-4 quarter lag. The match earned the Smets-Wouters framework rapid adoption at the ECB and Fed.

Estimation — Bayesian, not classical

DSGE models have dozens of parameters and limited data (40-60 years of quarterly observations is typical). Classical maximum-likelihood estimation faces identification problems: many parameter vectors yield similar fits. The standard solution is Bayesian estimation. The researcher specifies priors on parameters from theory and micro-evidence, then updates them with macro data using the likelihood. Markov Chain Monte Carlo (MCMC) samplers explore the posterior.

This sidesteps identification issues but introduces priors as research-design choices. Critics argue priors do too much of the work; defenders argue micro-evidence priors are well-justified. Smets-Wouters (2007) is the canonical demonstration: the paper estimates ~30 parameters with informative priors and shows the resulting model fits U.S. data well.

DSGE vs other macro frameworks

	New Keynesian DSGE (Smets-Wouters 2007)	RBC (Kydland-Prescott 1982)	Old Keynesian (Klein 1950s)	VAR (Sims 1980)	Heterogeneous-Agent DSGE / HANK (Kaplan-Moll-Violante 2018)	Agent-Based
Microfoundations	Yes	Yes	Limited	None	Yes, heterogeneous	Behavioral rules
Sticky prices	Calvo	No	Implicit	—	Often	Possible
Central bank role	Taylor rule	None	Discretionary	Estimated	Taylor + heterogeneity	Designed
Linearization	Around steady state	Around steady state	—	—	Often partial nonlinear	Nonlinear
Crisis dynamics	Limited (needs frictions)	Poor	Reduced-form	Atheoretical	Better	Can capture cascades
Used by central banks	Workhorse	Methodological foundation	Older models	Forecasting	Frontier	Rarely

Critiques after 2008

The 2008 financial crisis was a stress test the standard DSGE framework largely failed. The Smets-Wouters baseline had no financial intermediation, no leverage cycle, no bank balance sheets, no default. It could not generate a recession driven by financial-sector stress. The post-2008 literature added these features rapidly:

• Financial accelerators (Bernanke-Gertler-Gilchrist 1999) — collateral constraints amplify shocks.
• Banking blocks (Gerali et al. 2010; Curdia-Woodford) — banks intermediate between savers and borrowers with their own constraints.
• Defaults and risk shocks (Christiano-Motto-Rostagno 2014) — agency-cost financing produces credit-driven cycles.
• Heterogeneous agents (HANK; Kaplan-Moll-Violante 2018) — capture wealth distribution and inequality, important for marginal-propensity-to-consume heterogeneity.

Olivier Blanchard's 2018 essay "On the future of macroeconomic models" called for a "DSGE-plus" approach: keep the framework but recognize its limits. Pure rational-expectations representative-agent DSGE remains a useful benchmark but no longer the only tool central banks use.

Counterarguments

Representative-agent shortcomings. Inequality, distribution, and heterogeneous marginal propensities to consume are zeroed out in standard DSGE. HANK models address this but greatly increase computational cost.

Linearization. Most DSGE models are solved by log-linearizing around the steady state, then simulating the linearized system. This misses important non-linearities like the zero lower bound, financial crises, and large-deviation dynamics. Non-linear and global-solution methods exist but are expensive.

Identification problems. Many DSGE parameters are weakly identified — different parameter combinations produce similar fits. Bayesian estimation sidesteps the problem with priors, but critics worry that priors do too much of the work and "identification by prior" is not a real test.

Empirical fit is moment-by-moment. DSGE models often match impulse responses well but miss the joint distribution of shocks. Out-of-sample forecasts during regime changes (2008-09, COVID) have been notably worse than during stable periods.

Heterodox critiques. Post-Keynesians, modern monetary theory advocates, and complexity economists reject the optimization-and-equilibrium foundation outright, arguing that economic dynamics emerge from interaction, money creation, and credit cycles rather than representative-agent maximization. DSGE practitioners and these critics largely talk past each other.

Common pitfalls

• Conflating DSGE with neoclassical economics. New Keynesian DSGE has sticky prices, monopolistic competition, and significant inefficiencies. It's a synthesis, not a purist position.
• Treating impulse responses as predictions. They are conditional responses to specific shocks. The unconditional path depends on which shocks actually hit and how.
• Forgetting the Lucas critique still applies. Even DSGE parameters can be policy-dependent if the underlying preferences or technology depend on the regime. The framework is robust to policy changes only insofar as its "deep parameters" really are deep.
• Confusing Calvo pricing with menu costs. Calvo is a tractable simplification — random reset probability. Menu-cost models (Golosov-Lucas, Midrigan, Nakamura-Steinsson) are more realistic but harder.
• Reading "general equilibrium" as "Walrasian perfection". DSGE general equilibrium allows market imperfections — monopoly power, nominal rigidities, financial frictions. The "general" just means all markets are modeled jointly.