Panel VAR¶

Panel Vector Autoregression (Panel VAR) models capture the dynamic interdependencies among multiple variables across entities and time. Unlike single-equation models, VAR treats all variables as potentially endogenous, allowing each variable to depend on its own lags and the lags of all other variables. Combined with panel data, this reveals dynamic relationships while controlling for unobserved heterogeneity.

PanelBox provides a complete Panel VAR toolkit: estimation, impulse response functions (IRF), forecast error variance decomposition (FEVD), Granger causality tests, and forecasting.

Available Features¶

Feature	Class / Method	Description
Panel VAR	`PanelVAR`	VAR estimation with entity fixed effects
Panel VECM	`PanelVECM`	Vector Error Correction for cointegrated panels
Impulse Response	`PanelVAR.irf()`	Orthogonalized and structural IRFs
FEVD	`PanelVAR.fevd()`	Forecast error variance decomposition
Granger Causality	`PanelVAR.granger_causality()`	Bivariate and multivariate causality tests
Forecast	`PanelVAR.forecast()`	Out-of-sample forecasting
Lag Selection	`PanelVAR.select_lag_order()`	AIC, BIC, HQIC lag order selection

Quick Example¶

from panelbox.var import PanelVAR
from panelbox.datasets import load_grunfeld

data = load_grunfeld()

model = PanelVAR(
    variables=["invest", "value", "capital"],
    data=data,
    entity_col="firm",
    time_col="year",
    lags=2
)
results = model.fit()
print(results.summary())

# Impulse Response Functions
irf = results.irf(periods=10)
irf.plot()

# Granger Causality
gc = results.granger_causality(caused="invest", causing="value")
print(gc.summary())

Key Concepts¶

Panel VAR Specification¶

The Panel VAR(p) model for \(K\) variables and \(p\) lags:

\[ Y_{it} = \alpha_i + A_1 Y_{i,t-1} + A_2 Y_{i,t-2} + \ldots + A_p Y_{i,t-p} + \epsilon_{it} \]

where \(Y_{it}\) is a \(K \times 1\) vector, \(\alpha_i\) captures entity fixed effects, and \(A_1, \ldots, A_p\) are \(K \times K\) coefficient matrices.

Lag Order Selection¶

lag_result = model.select_lag_order(max_lags=8)
print(lag_result.summary())
# Shows AIC, BIC, HQIC for each lag order

Impulse Response Functions¶

IRFs trace the dynamic effect of a one-standard-deviation shock to variable \(j\) on variable \(k\) over time:

irf = results.irf(periods=20, method="cholesky")
irf.plot(impulse="value", response="invest")

Forecast Error Variance Decomposition¶

FEVD shows what fraction of the forecast error variance of each variable is attributable to shocks in each other variable:

fevd = results.fevd(periods=10)
fevd.plot()

Granger Causality¶

Tests whether past values of variable \(X\) help predict variable \(Y\) beyond the information in past values of \(Y\) alone:

# Bivariate Granger causality
gc = results.granger_causality(caused="invest", causing="value")
print(f"p-value: {gc.pvalue:.4f}")
print(gc.conclusion)

Detailed Guides¶

Panel VAR Estimation -- Model specification and estimation (detailed guide coming soon)
Panel VECM -- Error correction for cointegrated panels (detailed guide coming soon)
IRF Analysis -- Impulse response functions (detailed guide coming soon)
Granger Causality -- Causality testing (detailed guide coming soon)
Forecasting -- Out-of-sample prediction (detailed guide coming soon)

Tutorials¶

See Panel VAR Tutorial for interactive notebooks with Google Colab.

API Reference¶

See VAR API for complete technical reference.

References¶

Holtz-Eakin, D., Newey, W., & Rosen, H. S. (1988). Estimating vector autoregressions with panel data. Econometrica, 56(6), 1371-1395.
Love, I., & Zicchino, L. (2006). Financial development and dynamic investment behavior: Evidence from panel VAR. Quarterly Review of Economics and Finance, 46(2), 190-210.
Abrigo, M. R. M., & Love, I. (2016). Estimation of panel vector autoregression in Stata. Stata Journal, 16(3), 778-804.