Empirical forecasting models · Sources
VAR sources, papers, and evidence trail
Primary papers, model variants, source notes, and review signals behind the VAR page.
References
Academic and research sources
Peer-reviewed papers, books, and research used to ground model mechanisms or contested interpretations.
[S1] Econometrica
Sims (1980) -- Macroeconomics and Reality (Econometrica). The founding paper. Argued for unrestricted VARs as an alternative to large structural models.
Academic - Econometrica
[S2] Handbook of Macroeconomics
Christiano, Eichenbaum, and Evans (1999) -- Monetary policy shocks: what have we learned and to what end? (Handbook of Macroeconomics). Canonical Cholesky-identified monetary policy VAR.
Academic - Handbook of Macroeconomics
[S3] Journal of Economic Perspectives
Stock and Watson (2001) -- Vector Autoregressions (Journal of Economic Perspectives). The standard survey article. Clear exposition of the methodology and its limits.
Academic - Journal of Economic Perspectives
[S4] Academic
Kilian and Lutkepohl (2017) -- Structural Vector Autoregressive Analysis (Cambridge University Press). The modern reference on structural identification.
Academic
[S5] Econometrica
Macroeconomics and Reality
Sims' VAR foundation.
Academic - Econometrica - dated 1980
[S6] Springer
New Introduction to Multiple Time Series Analysis
Lutkepohl's VAR reference text.
Academic - Springer - dated 2005
Reference sources
Reference material used for orientation; read primary and academic sources first when claims conflict.
[S7] Reference
Litterman (1986) -- Forecasting with Bayesian Vector Autoregressions (Journal of Business and Economic Statistics). Introduced the Minnesota prior for VAR shrinkage.
Reference
Research footing
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.
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