Dist_Plots {BHSBVAR}

Plot Posterior Distributions Against Priors

Description

Plot Posterior Distributions Against Priors.

Usage

Dist_Plots(results, A_titles, H_titles = NULL, xlab = NULL, ylab = NULL)

Arguments

results

List containing the results from running BH_SBVAR().

A_titles

(n x n) matrix containing the titles for the plots of the estimated parameters in the coefficient matrix A. n is the number of endogenous variables.

H_titles

(n x n) matrix containing the titles for the plots of the estimated parameters in the coefficient matrix H (default = NULL). n is the number of endogenous variables.

xlab

Character label for the horizontal axis of historical decomposition plots (default = NULL). Default produces plots without a label for the horizontal axis.

ylab

Character label for the vertical axis of historical decomposition plots (default = NULL). Default produces plots without a label for the vertical axis.

Details

Plots posterior distributions against prior distributions.

Author(s)

Paul Richardson

Examples

# Import data
library(BHSBVAR)
set.seed(123)
data(USLMData)
y0 <- matrix(data = c(USLMData$Wage, USLMData$Employment), ncol = 2)
y <- y0 - (matrix(data = 1, nrow = nrow(y0), ncol = ncol(y0)) %*% 
             diag(x = colMeans(x = y0, na.rm = FALSE, dims = 1)))
colnames(y) <- c("Wage", "Employment")

# Set function arguments
nlags <- 8
itr <- 5000
burn <- 0
thin <- 1
acc <- TRUE
h <- 20
cri <- 0.95

# Priors for A
pA <- array(data = NA, dim = c(2, 2, 8))
pA[, , 1] <- c(0, NA, 0, NA)
pA[, , 2] <- c(1, NA, -1, NA)
pA[, , 3] <- c(0.6, 1, -0.6, 1)
pA[, , 4] <- c(0.6, NA, 0.6, NA)
pA[, , 5] <- c(3, NA, 3, NA)
pA[, , 6] <- c(NA, NA, NA, NA)
pA[, , 7] <- c(NA, NA, 1, NA)
pA[, , 8] <- c(2, NA, 2, NA)

# Position priors for Phi
pP <- matrix(data = 0, nrow = ((nlags * ncol(pA)) + 1), ncol = ncol(pA))
pP[1:nrow(pA), 1:ncol(pA)] <-
  diag(x = 1, nrow = nrow(pA), ncol = ncol(pA))

# Confidence in the priors for Phi
x1 <- 
  matrix(data = NA, nrow = (nrow(y) - nlags), 
         ncol = (ncol(y) * nlags))
for (k in 1:nlags) {
  x1[, (ncol(y) * (k - 1) + 1):(ncol(y) * k)] <-
    y[(nlags - k + 1):(nrow(y) - k),]
}
x1 <- cbind(x1, 1)
colnames(x1) <- 
  c(paste(rep(colnames(y), nlags),
          "_L",
          sort(rep(seq(from = 1, to = nlags, by = 1), times = ncol(y)),
               decreasing = FALSE),
          sep = ""),
    "cons")
y1 <- y[(nlags + 1):nrow(y),]
ee <- matrix(data = NA, nrow = nrow(y1), ncol = ncol(y1))
for (i in 1:ncol(y1)) {
  xx <- cbind(x1[, seq(from = i, to = (ncol(x1) - 1), by = ncol(y1))], 1)
  yy <- matrix(data = y1[, i], ncol = 1)
  phi <- solve(t(xx) %*% xx, t(xx) %*% yy)
  ee[, i] <- yy - (xx %*% phi)
}
somega <- (t(ee) %*% ee) / nrow(ee)
lambda0 <- 0.2
lambda1 <- 1
lambda3 <- 100
v1 <- matrix(data = (1:nlags), nrow = nlags, ncol = 1)
v1 <- v1^((-2) * lambda1)
v2 <- matrix(data = diag(solve(diag(diag(somega)))), ncol = 1)
v3 <- kronecker(v1, v2)
v3 <- (lambda0^2) * rbind(v3, (lambda3^2))
v3 <- 1 / v3
pP_sig <- diag(x = 1, nrow = nrow(v3), ncol = nrow(v3))
diag(pP_sig) <- v3

# Confidence in long-run restriction priors
pR_sig <-
  array(data = 0,
        dim = c(((nlags * ncol(y)) + 1),
                ((nlags * ncol(y)) + 1),
                ncol(y)))
Ri <-
  cbind(kronecker(matrix(data = 1, nrow = 1, ncol = nlags),
                  matrix(data = c(1, 0), nrow = 1)),
        0)
pR_sig[, , 2] <- (t(Ri) %*% Ri) / 0.1

# Confidence in priors for D
kappa1 <- matrix(data = 2, nrow = 1, ncol = ncol(y))

# Set graphical parameters
par(cex.axis = 0.8, cex.main = 1, font.main = 1, family = "serif",
    mfrow = c(2, 2), mar = c(2, 2.2, 2, 1), las = 1)

# Estimate the parameters of the model
results1 <- 
  BH_SBVAR(y = y, nlags = nlags, pA = pA, pP = pP, pP_sig = pP_sig,
           pR_sig = pR_sig, kappa1 = kappa1, itr = itr, burn = burn,
           thin = thin, cri = cri)

# Plot Posterior and Prior Densities
A_titles <- 
  matrix(data = NA_character_, nrow = dim(pA)[1], ncol = dim(pA)[2])
A_titles[1, 1] <- "Wage Elasticity of Labor Demand"
A_titles[1, 2] <- "Wage Elasticity of Labor Supply"
par(mfcol = c(1, 2))
dist_results <- 
  Dist_Plots(results = results1, A_titles = A_titles)