dcce (version 0.4.2)

granger_test: Dumitrescu-Hurlin Panel Granger Causality Test

Description

Tests whether \(x\) Granger-causes \(y\) in a heterogeneous panel, following Dumitrescu & Hurlin (2012). For each unit \(i\) a bivariate VAR-type regression is fitted: $$y_{it} = \alpha_i + \sum_{k=1}^{K} \gamma_{ik} y_{i,t-k} + \sum_{k=1}^{K} \beta_{ik} x_{i,t-k} + u_{it},$$ and the individual Wald statistic for \(H_0^{(i)}: \beta_{i1} = \cdots = \beta_{iK} = 0\) is computed.

Usage

granger_test(data, unit_index, time_index, y, x, lags = 1L)

Value

An object of class dcce_granger with elements:

W_bar

Mean Wald statistic across units.

Z_bar

Standardised statistic (large-T).

Z_bar_tilde

Small-sample adjusted statistic.

p_value_Z

p-value for Z-bar.

p_value_Zt

p-value for Z-bar tilde.

unit_wald

Named vector of per-unit Wald statistics.

N

Number of units used.

T_bar

Average time-series length.

lags

Lag order.

Arguments

data

A panel data.frame.

unit_index

Character: unit identifier column.

time_index

Character: time identifier column.

y

Character: name of the dependent variable.

x

Character: name of the potential Granger-causing variable.

lags

Integer: lag order \(K\) for both variables. Default 1.

Details

The panel statistics are:

W-bar

The cross-sectional average of the N unit-level Wald statistics.

Z-bar

Standardised version: \(\tilde{Z} = \sqrt{N/(2K)} (W\text{-bar} - K) \xrightarrow{d} \mathcal{N}(0,1)\).

Z-bar tilde

Small-sample adjusted version using \(E[W_i]\) and \(Var(W_i)\) from the \(F(K, T-3K-1)\) distribution.

References

Dumitrescu, E.-I., & Hurlin, C. (2012). Testing for Granger non-causality in heterogeneous panels. Economic Modelling, 29(4), 1450--1460.

Examples

data(pwt8)
gc <- granger_test(
  data = pwt8, unit_index = "country", time_index = "year",
  y = "d_log_rgdpo", x = "log_ck", lags = 1
)
print(gc)