The following code produces posterior draws using the algortihm
described in Koop et al. (2010).
# Reset random number generator for reproducibility
set.seed(7654321)
# Obtain data matrices
y <- t(data$data$Y)
w <- t(data$data$W)
x <- t(data$data$X)
r <- data$model$rank # Set rank
tt <- ncol(y) # Number of observations
k <- nrow(y) # Number of endogenous variables
k_w <- nrow(w) # Number of regressors in error correction term
k_x <- nrow(x) # Number of differenced regressors and unrestrictec deterministic terms
k_gamma <- k * k_x # Total number of non-cointegration coefficients
k_alpha <- k * r # Number of elements in alpha
k_beta <- k_w * r # Number of elements in beta
# Priors
a_mu_prior <- data$priors$noncointegration$mu # Prior means
a_v_i_prior <- data$priors$noncointegration$v_i # Inverse of the prior covariance matrix
v_i <- data$priors$cointegration$v_i
p_tau_i <- data$priors$cointegration$p_tau_i
sigma_df_prior <- data$priors$sigma$df # Prior degrees of freedom
sigma_scale_prior <- data$priors$sigma$scale # Prior covariance matrix
sigma_df_post <- tt + sigma_df_prior # Posterior degrees of freedom
# Initial values
beta <- matrix(0, k_w, r)
beta[1:r, 1:r] <- diag(1, r)
sigma_i <- diag(1 / .0001, k)
g_i <- sigma_i
iterations <- data$model$iterations # Number of iterations of the Gibbs sampler
burnin <- data$model$burnin # Number of burn-in draws
draws <- iterations + burnin # Total number of draws
# Data containers
draws_alpha <- matrix(NA, k_alpha, iterations)
draws_beta <- matrix(NA, k_beta, iterations)
draws_pi <- matrix(NA, k * k_w, iterations)
draws_gamma <- matrix(NA, k_gamma, iterations)
draws_sigma <- matrix(NA, k^2, iterations)
# Start Gibbs sampler
for (draw in 1:draws) {
# Draw conditional mean parameters
temp <- post_coint_kls(y = y, beta = beta, w = w, x = x, sigma_i = sigma_i,
v_i = v_i, p_tau_i = p_tau_i, g_i = g_i,
gamma_mu_prior = a_mu_prior,
gamma_v_i_prior = a_v_i_prior)
alpha <- temp$alpha
beta <- temp$beta
Pi <- temp$Pi
gamma <- temp$Gamma
# Draw variance-covariance matrix
u <- y - Pi %*% w - matrix(gamma, k) %*% x
sigma_scale_post <- solve(tcrossprod(u) + v_i * alpha %*% tcrossprod(crossprod(beta, p_tau_i) %*% beta, alpha))
sigma_i <- matrix(rWishart(1, sigma_df_post, sigma_scale_post)[,, 1], k)
sigma <- solve(sigma_i)
# Update g_i
g_i <- sigma_i
# Store draws
if (draw > burnin) {
draws_alpha[, draw - burnin] <- alpha
draws_beta[, draw - burnin] <- beta
draws_pi[, draw - burnin] <- Pi
draws_gamma[, draw - burnin] <- gamma
draws_sigma[, draw - burnin] <- sigma
}
}
beta <- apply(t(draws_beta) / t(draws_beta)[, 1], 2, mean) # Obtain means for every row
beta <- matrix(beta, k_w) # Transform mean vector into a matrix
beta <- round(beta, 3) # Round values
dimnames(beta) <- list(dimnames(w)[[1]], NULL) # Rename matrix dimensions
beta # Print
#> [,1]
#> l.R 1.000
#> l.Dp -3.946
