SVAR — Structural VAR

SVAR (Structural VAR) extends VAR by imposing identification restrictions to separate economically meaningful structural shocks (e.g. supply, demand, monetary policy shocks) from the reduced-form errors. As a result, SVAR impulse responses are economically interpretable, not merely statistical correlations.

When to use

Use SVAR when you need to interpret structural shocks (not just forecast). Identification requires economic theory to impose restrictions.

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Identifying structural shocks

The relation between reduced-form errors $\varepsilon_t$ and structural shocks $u_t$: $\varepsilon_t = B u_t$. Restrictions are needed to identify $B$:

Identification	Idea
Recursive (Cholesky)	Variable ordering ⇒ triangular matrix
Short-run	Restrict instantaneous effects to 0
Long-run (Blanchard-Quah)	Restrict long-run effects
Sign restrictions	Impose the sign of responses

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Running in EcoLab

1. Modeling module → Multivariate time series family → SVAR.
2. Choose variables, lag length, and the identification scheme (Cholesky/short-run/long-run).
3. Run; view structural IRF/FEVD; export the replication code.

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Replication code

Stata

* --- SVAR (Cholesky identification) ---
tsset time

* Step 1: Estimate reduced-form VAR
var rate inflation output, lags(1/2)

* Step 2: Impose short-run restrictions (lower-triangular A matrix)
* Define restriction matrix A
matrix A = (1, 0, 0 \ ., 1, 0 \ ., ., 1)
matrix B = (., 0, 0 \ 0, ., 0 \ 0, 0, .)

svar rate inflation output, lags(1/2) aeq(A) beq(B)

* Structural IRFs
irf create sirf, set(svar_irf) step(20)
irf graph sirf, impulse(rate) response(inflation output)

R

# --- SVAR (Cholesky / short-run restrictions) ---
library(vars)

data_var <- cbind(rate, inflation, output)

# Step 1: Estimate reduced-form VAR
var_model <- VAR(data_var, p = 2)

# Step 2: Define restriction matrix A (lower-triangular)
A <- diag(3)
A[lower.tri(A)] <- NA   # free parameters below diagonal

# Estimate SVAR with short-run restrictions
svar_model <- SVAR(var_model, Amat = A)
summary(svar_model)

# Structural IRFs
irf_struct <- irf(svar_model, n.ahead = 20)
plot(irf_struct)

Python

from statsmodels.tsa.api import VAR
import numpy as np
import matplotlib.pyplot as plt

data = df[['rate', 'inflation', 'output']]

# Step 1: Estimate reduced-form VAR
model = VAR(data)
result = model.fit(2)

# Step 2: Cholesky identification (default in statsmodels IRF)
# The ordering of columns determines the recursive structure
irf = result.irf(20)
irf.plot(orth=True)   # orthogonalized (Cholesky) IRFs
plt.suptitle('Structural IRF (Cholesky)')
plt.tight_layout(); plt.show()

# FEVD
fevd = result.fevd(20)
fevd.plot()
plt.show()

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Limitations

• Results depend heavily on the identification restrictions (and variable ordering with Cholesky).
• Requires theoretical justification for every restriction.

Video tutorial

Video Tutorial: Running SVAR in EcoLab

See also

• VAR · VECM · Catalog