market_data <- read.csv("C:/Users/nesau/Desktop/Model/hoevenaars.csv")The first column represents the quarterly time period, and the other columns represent returns on three asset classets (stocks, bonds, and T-Bills) and three state variables that help predict asset returns (inflation, dividend yield and term spread). Our US quarterly data start in 1952:1 and end in 2008:4
The 90-day T-bill and the 10-year constant maturity yield are from the FRED website
In order to generate the yield spread, we obtain the zero-yield data from Duffee (2002). As these data are only available until 1998:4, we extended the series using the data from Gurkaynak et al (2006)
For inflation, we use the non-seasonally adjusted consumer price index for all urban consumers and all items, also from the FRED website
The real return on 3-month T-bills is constructed as the difference between the logarithmic nominal return on 3-month T-bills and logarithmic inflation
Data on stock returns and the dividend price ratio are based on the S&P Composite. The logarithmic dividend yield is included.
We construct the gross bond return series from 10 year constant maturity yields using the log-linear approximation approach.
Stock and bond return series are included in excess of the real return on the 3-month T-Bill.
The last column in the dataset corresponds to NBER contraction or expansion periods. A contractions starts the peak of a business cycle and ends at the trough, and the expansion starts at the trough and ends at the peak
# rtb = tb - inflation
# excstocks = stocks - rtb
var_data <- data.frame(it=market_data$nomyield, rtb=market_data$realtbillret,
dt=market_data$dy, St=market_data$termspread,
xs=market_data$excstocks, xb=market_data$excbondret)
var_data <- tail(var_data, - 1)
var_data[,2] <- as.numeric(as.character(var_data[,2]))
var_data[,5] <- as.numeric(as.character(var_data[,5]))
var_data[,6] <- as.numeric(as.character(var_data[,6]))
var_data <- var_data * 100
ave <- sapply(var_data, mean)
SD <- sapply(var_data, sd) * 2
var_data[,1] <- var_data[,1] - ave[1]
var_data[,2] <- var_data[,2] - ave[2]
var_data[,3] <- var_data[,3] - ave[3]
var_data[,4] <- var_data[,4] - ave[4]
var_data[,5] <- var_data[,5] - ave[5]
var_data[,6] <- var_data[,6] - ave[6]
library(MTS)## Warning: package 'MTS' was built under R version 3.1.3var_data <- var_data
var_model <- VAR(var_data, p=1, include.mean=F,
output=F)
B <- var_model$Phi
sd.vals <- sqrt(diag(var_model$Sigma))
cor.mat <- var_model$Sigma/outer(sd.vals,sd.vals)
diag(cor.mat) <- sd.vals
Sigma_hat <- cor.mat
rm(cor.mat,sd.vals)
# Table I
print(ave)## it rtb dt St xs xb
## 1.2300382 0.3117574 -3.4886721 0.3033301 1.1797858 0.1639687print(SD)## it rtb dt St xs xb
## 1.3579504 1.3378204 0.8122017 0.5932509 14.9419443 7.8473512# Table II
print(B)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.961414600 -0.002785316 0.03578645 0.079005573 0.0044469711
## [2,] 0.213506887 0.459472807 -0.03026384 0.271044054 0.0025547277
## [3,] 0.009692528 -0.012579857 0.96850609 -0.004182844 -0.0008379167
## [4,] 0.021092507 -0.008367430 -0.02528134 0.821063996 -0.0019062258
## [5,] -1.582123441 0.948602369 3.64002880 0.102640046 0.1138135488
## [6,] 0.459545656 0.387706513 -0.42292777 3.320714848 -0.0759975726
## [,6]
## [1,] 0.0007637403
## [2,] -0.0089072699
## [3,] -0.0026540256
## [4,] 0.0027834186
## [5,] 0.2513361389
## [6,] -0.0868874990# Table III
print(Sigma_hat)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.22203272 -0.34158045 0.054647223 -0.83234576 -0.03421056
## [2,] -0.34158045 0.57097579 -0.081360725 0.15866835 0.06002620
## [3,] 0.05464722 -0.08136072 0.072860093 -0.03516766 -0.98002893
## [4,] -0.83234576 0.15866835 -0.035167655 0.17399828 0.01632275
## [5,] -0.03421056 0.06002620 -0.980028926 0.01632275 7.13520311
## [6,] -0.65358150 0.39730114 0.007626237 0.14329862 -0.01574945
## [,6]
## [1,] -0.653581500
## [2,] 0.397301138
## [3,] 0.007626237
## [4,] 0.143298620
## [5,] -0.015749451
## [6,] 3.777802424