js.test: Chi-square test for joint hypotheses

Description

Based on an existing bootstrap object, the test statistic allows to test joint hypotheses for selected entries of the structural matrix B. The test statistic reads as $$(Rvec(\widehat{B}) - r)'R(\widehat{\mbox{Cov}}[vec(B^*)])^{-1}R'(Rvec(\widehat{b} - r)) \sim \chi^2_J,$$ where $\widehat{\mbox{Cov}}[vec(B^*)]$ is the estimated covariance of vectorized bootstrap estimates of structural parameters. The composite null hypothesis is $H_0: Rvec(B)= r$.

Usage

js.test(x, R, r = NULL)

Value

A list of class "jstest" with elements

test_statistic: Test statistic
p_value: P-value
R: Selection matrix
r: Vector of restrictions

Arguments

x: Object of class 'sboot'
R: A J*K^2 selection matrix, where J is the number of hypotheses and K the number of time series.
r: A J*1 vector of restrictions

References

Herwartz, H., 2018. Hodges Lehmann detection of structural shocks - An analysis of macroeconomic dynamics in the Euro Area, Oxford Bulletin of Economics and Statistics

Examples

Run this code

# \donttest{
# data contains quarterly observations from 1965Q1 to 2008Q3
# x = output gap
# pi = inflation
# i = interest rates
v1 <- vars::VAR(USA, lag.max = 10, ic = "AIC" )
x1 <- id.dc(v1)

# Bootstrapping of SVAR
bb <- wild.boot(x1, nboot = 1000, n.ahead = 30)

# Testing the hypothesis of a lower triangular matrix as
# relation between structural and reduced form errors
R <- rbind(c(0,0,0,1,0,0,0,0,0), c(0,0,0,0,0,0,1,0,0),
           c(0,0,0,0,0,0,0,1,0))
c.test <- js.test(bb, R)
summary(c.test)
# }