Model Class
Structural VAR
Identified time-series
Local Projections (Jorda 2005)
Direct impulse-response estimation
DSGE Model
Structural general equilibrium
Factor-Augmented VAR (FAVAR)
High-dimensional identified time-series
Data-Driven Models
Data-Driven Models
Model Class
Structural VAR
Identified time-series
Local Projections (Jorda 2005)
Direct impulse-response estimation
DSGE Model
Structural general equilibrium
Factor-Augmented VAR (FAVAR)
High-dimensional identified time-series
Stationarity Required
Structural VAR
Yes (or use in first-differenced / cointegrated form)
Local Projections (Jorda 2005)
Less sensitive -- LP estimates are consistent under weaker conditions
DSGE Model
Model generates its own stationarity via detrending
Factor-Augmented VAR (FAVAR)
Yes
Handles Multivariate
Structural VAR
Yes, designed for multivariate systems (typically 3-8 variables)
Local Projections (Jorda 2005)
Yes, but estimation is equation-by-equation
DSGE Model
Yes -- all macro aggregates jointly determined
Factor-Augmented VAR (FAVAR)
Yes -- handles hundreds of variables via factor extraction
Captures Nonlinearity
Structural VAR
No -- linear propagation of shocks throughout
Local Projections (Jorda 2005)
Yes -- easily extended to state-dependent LP
DSGE Model
With modification (perturbation beyond first order)
Factor-Augmented VAR (FAVAR)
No
Estimation Complexity
Structural VAR
Medium
Local Projections (Jorda 2005)
Low
DSGE Model
High
Factor-Augmented VAR (FAVAR)
Medium
Forecast Horizon
Structural VAR
Short-Medium
Local Projections (Jorda 2005)
Short-Medium
DSGE Model
Medium-Long
Factor-Augmented VAR (FAVAR)
Short-Medium
Interpretability
Structural VAR
High -- structural shocks have economic labels and causal interpretation
Local Projections (Jorda 2005)
High -- same impulse-response output as SVAR
DSGE Model
Very high -- shocks have deep structural interpretation grounded in preferences and technology
Factor-Augmented VAR (FAVAR)
Medium -- factor shocks lack direct economic labels unless identified post-hoc
Min Data Requirement
Structural VAR
80+ observations per variable (quarterly); more for proxy SVAR due to instrument availability
Local Projections (Jorda 2005)
Similar to SVAR, but long-horizon estimates lose observations
DSGE Model
40+ observations; Bayesian estimation with informative priors
Factor-Augmented VAR (FAVAR)
Large cross-section of variables (50+) for reliable factor estimation
Missing Data
Structural VAR
No
Local Projections (Jorda 2005)
No
DSGE Model
Yes
Factor-Augmented VAR (FAVAR)
Yes
Computational Cost
Structural VAR
Low for recursive; moderate for sign restrictions (Monte Carlo over rotations); moderate for proxy SVAR
Local Projections (Jorda 2005)
Low (OLS at each horizon)
DSGE Model
High (MCMC for full posterior)
Factor-Augmented VAR (FAVAR)
Moderate (PCA + VAR + identification)
Typical Use Case
Structural VAR
Identifying and measuring the dynamic causal effects of macroeconomic shocks (monetary policy, oil prices, fiscal spending)
Local Projections (Jorda 2005)
When VAR lag dynamics may be misspecified, or when state-dependent responses are needed
DSGE Model
When a fully articulated structural model is needed for counterfactual policy analysis
Factor-Augmented VAR (FAVAR)
When the researcher wants to condition on a large information set without running a huge VAR
Key Weakness
Structural VAR
Results are sensitive to identification assumptions, which are fundamentally untestable
Local Projections (Jorda 2005)
Noisier at long horizons due to direct estimation without parametric smoothing
DSGE Model
Relies on the entire model specification being correct -- misspecification of any equation contaminates all shocks
Factor-Augmented VAR (FAVAR)
Factor rotation indeterminacy adds an identification layer on top of the SVAR identification problem
| Attribute | Structural VAR | Local Projections (Jorda 2005) | DSGE Model | Factor-Augmented VAR (FAVAR) |
|---|---|---|---|---|
| Model Class | Identified time-series | Direct impulse-response estimation | Structural general equilibrium | High-dimensional identified time-series |
| Stationarity Required | Yes (or use in first-differenced / cointegrated form) | Less sensitive -- LP estimates are consistent under weaker conditions | Model generates its own stationarity via detrending | Yes |
| Handles Multivariate | Yes, designed for multivariate systems (typically 3-8 variables) | Yes, but estimation is equation-by-equation | Yes -- all macro aggregates jointly determined | Yes -- handles hundreds of variables via factor extraction |
| Captures Nonlinearity | No -- linear propagation of shocks throughout | Yes -- easily extended to state-dependent LP | With modification (perturbation beyond first order) | No |
| Estimation Complexity | Medium | Low | High | Medium |
| Forecast Horizon | Short-Medium | Short-Medium | Medium-Long | Short-Medium |
| Interpretability | High -- structural shocks have economic labels and causal interpretation | High -- same impulse-response output as SVAR | Very high -- shocks have deep structural interpretation grounded in preferences and technology | Medium -- factor shocks lack direct economic labels unless identified post-hoc |
| Min Data Requirement | 80+ observations per variable (quarterly); more for proxy SVAR due to instrument availability | Similar to SVAR, but long-horizon estimates lose observations | 40+ observations; Bayesian estimation with informative priors | Large cross-section of variables (50+) for reliable factor estimation |
| Missing Data | No | No | Yes | Yes |
| Computational Cost | Low for recursive; moderate for sign restrictions (Monte Carlo over rotations); moderate for proxy SVAR | Low (OLS at each horizon) | High (MCMC for full posterior) | Moderate (PCA + VAR + identification) |
| Typical Use Case | Identifying and measuring the dynamic causal effects of macroeconomic shocks (monetary policy, oil prices, fiscal spending) | When VAR lag dynamics may be misspecified, or when state-dependent responses are needed | When a fully articulated structural model is needed for counterfactual policy analysis | When the researcher wants to condition on a large information set without running a huge VAR |
| Key Weakness | Results are sensitive to identification assumptions, which are fundamentally untestable | Noisier at long horizons due to direct estimation without parametric smoothing | Relies on the entire model specification being correct -- misspecification of any equation contaminates all shocks | Factor rotation indeterminacy adds an identification layer on top of the SVAR identification problem |
Local Projections (Jorda 2005) does better
LP handles misspecified lag dynamics better because it doesn't rely on the VAR's parametric propagation mechanism. If the true data-generating process has nonlinearities, time-varying parameters, or long-memory features that the VAR misses, LP impulse responses remain consistent (though less efficient). LP also extends naturally to state-dependent responses by interacting the shock with a regime indicator.
Structural VAR (SVAR) does better
SVAR produces smoother impulse responses with tighter confidence bands at long horizons because the parametric VAR structure imposes cross-horizon restrictions that LP discards. When the VAR is correctly specified, SVAR is more efficient. SVAR also delivers joint impulse responses, variance decompositions, and historical decompositions as automatic byproducts -- LP gives only the impulse response.
Switch when: Switch to LP when you suspect the VAR's linear lag structure is misspecified, when you want state-dependent responses, or when the VAR residuals show signs of nonlinearity. Stay with SVAR when the linear VAR fits well and you need the full structural decomposition toolkit.
DSGE Model does better
A DSGE model provides structural shocks with deep microfounded interpretation -- the monetary policy shock is explicitly the deviation from the Taylor rule, the technology shock is explicitly TFP. DSGE counterfactuals can answer questions SVAR cannot: what would have happened under a different policy rule? The model also imposes cross-equation restrictions from optimizing behavior, which disciplines the estimation when the model is correct.
Structural VAR (SVAR) does better
SVAR imposes far fewer structural assumptions. A DSGE requires specifying the entire economy -- preferences, technology, market structure, fiscal rule, monetary rule -- and misspecification of any piece contaminates everything. SVAR lets the data determine the lag dynamics and only imposes the minimal restrictions needed for identification. When the researcher distrusts the full DSGE specification, SVAR is more robust.
Switch when: Switch to DSGE when you need policy counterfactuals that require a complete model of the economy, or when you want shocks with deep structural labels. Stay with SVAR when you want to avoid the risk of full-model misspecification and only need reduced-form impulse responses to identified shocks.
Factor-Augmented VAR (FAVAR) does better
FAVAR handles large information sets -- hundreds of time series -- by extracting common factors and running the VAR on those factors plus a few key observables. This avoids the curse of dimensionality that makes standard SVAR infeasible beyond 8-10 variables. Bernanke, Boivin, and Eliasz (2005) showed that conditioning on a large information set resolves the price puzzle that plagues small-scale monetary SVARs.
Structural VAR (SVAR) does better
SVAR is more transparent about what's identified. The variables in the SVAR are directly observable -- GDP, CPI, the federal funds rate -- and the identification restrictions apply directly to those observables. In a FAVAR, the factors are latent and their economic interpretation is ambiguous. The identification problem has an extra layer: first you must argue what the factors represent, then you must identify structural shocks within that factor space.
Switch when: Switch to FAVAR when you have a large panel of time series and suspect that a small VAR omits important information (symptom: price puzzles, counterintuitive sign of responses). Stay with SVAR when the system of interest is small enough that all key variables can be included directly.
The most active debate concerns the prior over the rotation matrix Q in sign-restricted SVARs. Baumeister and Hamilton (2015) argued that the standard uniform prior on Q is inadvertently informative about structural parameters. Arias, Rubio-Ramirez, and Waggoner (2018) proposed algorithms that allow researchers to specify priors directly on structural parameters while maintaining correct coverage of the identified set. A separate debate concerns the reliability of proxy SVAR when instruments are weak: Montiel Olea, Stock, and Watson (2021) developed weak-instrument-robust inference methods, but these are not yet standard in applied work.
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