Evidence and data

Use stationarity checks, lag selection, residual diagnostics, and forecast evaluation before interpreting impulse responses.

Calibration or measurement

Lag length, variable ordering, transformations, and sample window shape the result.

Boundaries

• Reduced-form VARs do not identify causal shocks.
• Small samples can overfit.
• Regime changes can break stability.

Use guidance

When sufficient

Forecasting and conditional projections of a small set of jointly determined macro variables when the data-generating process is reasonably stable and the question does not require causal identification. Out-of-sample evaluation of GDP, inflation, and interest-rate paths is the canonical use case (Sims 1980 Econometrica). The reduced form is also a valid first-pass check of whether the joint dynamics among a variable set are internally consistent with a maintained theory.

When sketch only

Do not use the reduced-form VAR as evidence about structural causal effects. The model is atheoretic by design; the ordering of variables in a Cholesky factorization imposes an identification assumption that must be defended separately. Impulse-response functions from an unidentified VAR describe correlations, not the response to a well-defined shock.

When to switch

Switch to an SVAR (empirical:svar) when causal identification is required. Switch to a BVAR (empirical:bvar) when the variable count is large enough that OLS estimation overfits and shrinkage priors are needed to stabilize the forecast. Switch to a state-space model when the panel has missing data or unobserved components that require the Kalman filter.

Falsification signal

Out-of-sample forecast errors that systematically exceed a naive random-walk or AR(1) benchmark across multiple episodes and variable choices indicate the VAR's lag structure is overfit or the parameters have shifted. A rolling-window evaluation showing stable in-sample fit but deteriorating out-of-sample accuracy is a concrete warning that the model is not capturing the underlying dynamics.