pvarife: Estimate a Panel VAR with Interactive Fixed Effects

In pvarife: Panel VAR Models with Interactive Fixed Effects

Estimate a Panel VAR with Interactive Fixed Effects

Description

Jointly estimates VAR coefficients \beta, latent common factors F, and factor loadings \Lambda for a panel vector autoregression with interactive fixed effects, following the iterative algorithm of Tugan (2021) based on Bai (2009).

Usage

pvarife(y, n_lags, n_factors, n_out = 50L, n_in = 10L, balanced_init = TRUE)

Arguments

y	A numeric array of dimension I \times T \times K (units \times time \times variables). NA values are allowed for unbalanced panels. Following the original implementation, if any variable is missing for unit i at period t, the whole period is treated as missing for that unit. Missing periods are excluded from the coefficient update and their common component is imputed by the EM step. Caution: simulation evidence shows that the point estimator can exhibit noticeable finite-sample bias when the share of missing periods is substantial (roughly above 10–15% at moderate I, T); results under heavy missingness should be interpreted with care and checked for robustness (e.g., on a balanced subsample).
n_lags	Positive integer. Lag order \ell.
n_factors	Positive integer. Number of interactive fixed effects r.
n_out	Positive integer. Number of outer iterations (default 50). Corresponds to out_number in the MATLAB replication code.
n_in	Positive integer. Number of inner PCA/EM iterations per outer step (default 10). Corresponds to in_number in the MATLAB code.
balanced_init	Logical. If TRUE (default), the initial beta estimate is obtained from units that have at least 10 fully observed periods in the last window of the sample — matching the approach of the MATLAB Initial_Step_in_Iteration.m for unbalanced real data. Set to FALSE for balanced panels (e.g., Monte Carlo simulations) to skip this selection step and use all units directly.

Details

The model is

y_{i,t} = \sum_{l=1}^{\ell} \Theta_l y_{i,t-l} + F_t \lambda_i + e_{i,t},

where y_{i,t} is a K \times 1 vector of endogenous variables for unit i at time t, F_t is an r \times 1 vector of unobservable common factors, \lambda_i is a unit-specific loading vector, and e_{i,t} is an idiosyncratic error.

The algorithm alternates between:

1. An inner loop that extracts factors and loadings via PCA (principal components on the residual cross-product matrix) and imputes missing observations (EM step of Bai 2009).

2. An outer loop that updates \beta via least squares after projecting out the estimated factors (using M_F = I - F(F'F)^{-1}F').

Value

An object of class "pvarife_result", which is a list with:

beta

Coefficient vector of length K + K^2 \ell. The first K elements are equation-specific intercepts; the remaining K^2 \ell elements are VAR lag coefficients stacked as [\Theta_1, \Theta_2, \ldots, \Theta_\ell]' (column-major).

ff

Factor matrix of dimension T \times r (one row per time period; analogous to MATLAB f).

factors_mat

Block-diagonal factor matrix of dimension TK \times Kr, built as I_K \otimes f_t'.

loadings

Matrix of dimension Kr \times I (factor loadings per unit, stacked by variable).

sigma

Reduced-form error covariance matrix (K \times K).

u_c

Array of residuals TK \times 1 \times I (NA at unobserved positions).

y_arr

The original input array I \times T \times K (used, e.g., for initial conditions in bootstrap_irf_bands).

y_c, z_c

Stacked outcome/regressor arrays (TK \times 1 \times I and TK \times (K + K^2\ell) \times I).

y_stack, z_stack

Pooled outcome/regressor matrices (complete-case rows only).

i_obs

Integer matrix TK \times I: 1 = observed, 0 = missing.

n_time_i

Integer vector of length I: number of observed time periods per unit (analogous to MATLAB TC).

tnc_i

Integer vector of length I: n\_time\_i \times K (analogous to MATLAB TNC).

n_lags, n_factors, n_vars, n_units, n_time

Dimensions.

References

Tugan, M. (2021). Panel VAR models with interactive fixed effects. Econometrics Journal, 24, 225–246. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/ectj/utaa021")}

Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4), 1229–1279.

Examples

sim <- sim_pvarife(n_units = 30, n_time = 20, n_vars = 2,
                   n_lags = 1, n_factors = 1, seed = 1)
fit <- pvarife(sim$y, n_lags = 1, n_factors = 1, n_out = 5, n_in = 3)
print(fit)

pvarife documentation built on June 13, 2026, 5:06 p.m.