BMR: Bayesian Macroeconometrics in R

# Solve the An-Schorfheide (2007) Model using Uhlig's method

rm(list=ls())
library(BMR)

#
# Setting parameter values as per An and Schorfheide (2007, Table 2)

tau      <- 2.00
kappa    <- 0.15

psi1     <- 1.50
psi2     <- 1.00

rhoR     <- 0.60
rhog     <- 0.95
rhoz     <- 0.65

rA       <- 0.40
piA      <- 4.00
gammaQ   <- 0.50

sigma_r  <- sqrt(0.002)
sigma_g  <- sqrt(0.008)
sigma_z  <- sqrt(0.0045)

gamma    <- 1 + (gammaQ/100)
beta     <- 1/( 1 + (rA/400) )
pi       <- 1 + (piA/400)

#

A <- matrix(0,nrow=0,ncol=0)
B <- matrix(0,nrow=0,ncol=0)
C <- matrix(0,nrow=0,ncol=0)
D <- matrix(0,nrow=0,ncol=0)

#

F12 <- 1/tau
F22 <- beta

#                   c,      pi,         y,         R
F <- rbind(c(       1,     F12,         0,         0),
           c(       0,     F22,         0,         0),
           c(       0,       0,         0,         0),
           c(       0,       0,         0,         0))

G14 <- -1/tau
G23 <- kappa
G42 <- (1-rhoR)*psi1; G43 <- (1-rhoR)*psi2

G <- rbind(c(      -1,       0,         0,       G14),
           c(       0,      -1,       G23,         0),
           c(       1,       0,        -1,         0),
           c(       0,     G42,       G43,        -1))

H44 <- rhoR
H <- rbind(c(       0,       0,         0,         0),
           c(       0,       0,         0,         0),
           c(       0,       0,         0,         0),
           c(       0,       0,         0,       H44))

#

J <- matrix(0,nrow=0,ncol=0)
K <- matrix(0,nrow=0,ncol=0)

#                   r,       g,         z
L <- rbind(c(       0,       0,         0),
           c(       0,       0,         0),
           c(       0,       0,         0),
           c(       0,       0,         0))

M13 <- (1/tau)*rhoz
M22 <- -kappa
M42 <- -(1-rhoR)*psi2

M <- rbind(c(       0,       0,       M13),
           c(       0,     M22,         0),
           c(       0,       1,         0),
           c(       1,     M42,         0))

#

N <- rbind(c(       0,       0,         0),
           c(       0,    rhog,         0),
           c(       0,       0,      rhoz))

Sigma <- rbind(c( sigma_r^2,         0,         0),
               c(         0, sigma_g^2,         0),
               c(         0,         0, sigma_z^2))

#

dsge_obj <- new(uhlig)

dsge_obj$build(A,B,C,D,F,G,H,J,K,L,M,N)
dsge_obj$solve()

dsge_obj$P_sol
dsge_obj$Q_sol
dsge_obj$R_sol
dsge_obj$S_sol

#

dsge_obj$shocks_cov = Sigma

dsge_obj$state_space()

dsge_obj$F_state
dsge_obj$G_state

#

var_names <- c("Consumption","Inflation","Output","IntRate","IntRateS","GovSpending","Technology")

dsge_irf <- IRF(dsge_obj,30,var_names=var_names)
dsge_sim <- dsge_obj$simulate(800,200)$sim_vals

#

y  <- gammaQ + 100*(dsge_sim[,3] + dsge_sim[,7])
pi <- piA + 400*dsge_sim[,2]
R  <- piA + rA + 4*gammaQ + 400*dsge_sim[,4]

ASData <- cbind(y,pi,R)
#save(ASData,file="ASData.RData")