Q2hw5
Mai AlSwayan
4/22/2017
Data Obtained: -Real Output Per Hour of All Persons (roph) -total hours worked measured as Nonfarm Business Sector: Hours of All Persons. (thw)
obtain data on Real Output Per Hour of All Persons and for total hours worked measured as Nonfarm Business Sector
library(Quandl)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericroph <- Quandl("FRED/OPHNFB", type="zoo")
thw <- Quandl("FRED/HOANBS", type="zoo")log and log diff. change
logroph <- log(roph)
logthw <- log(thw)dlroph <- diff(logroph)
dlthw <- diff(logthw)par(mfrow=c(1,2), cex=0.8)
plot(roph, xlab="", ylab="", main="Real Output Per Hour of All Persons", col="blue")
lines(thw, col="red", lty="dashed")
legend("topleft",c("output/hour", "hours worked"), bty = "n", col = c(4,2), lty = c(1,2))
plot(dlroph, xlab="", ylab="", main="Real Output Per Hour of All Persons % change", col="blue", ylim=c(-0.14,0.14))
lines(dlthw, col="red", lty="dashed")
form dataset for VAR model
logcombdata <- cbind(logroph, logthw)dlcombdata <- cbind(dlroph, dlthw)ERS tes
Log test
library(urca)test <- ur.ers(logcombdata, type="P-test", lag.max=12, model="trend")
summary(test)##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept and trend
##
## Value of test-statistic is: 25.9987
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 3.96 5.62 6.891st Diff. test
test1 <- ur.ers(dlcombdata, type="P-test", lag.max=12, model="trend")
summary(test1)##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept and trend
##
## Value of test-statistic is: 0.7814
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 3.96 5.62 6.89Estimate a bivariate reduced form VAR using AIC
library(vars)## Loading required package: MASS## Loading required package: strucchange## Loading required package: sandwich## Loading required package: lmtestvarp <- VAR(dlcombdata, ic="AIC", lag.max=8, type="const")
varp##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation dlroph:
## ===========================================
## Call:
## dlroph = dlroph.l1 + dlthw.l1 + dlroph.l2 + dlthw.l2 + dlroph.l3 + dlthw.l3 + const
##
## dlroph.l1 dlthw.l1 dlroph.l2 dlthw.l2 dlroph.l3
## -0.061099629 0.063118172 0.051485308 -0.196577779 0.005240038
## dlthw.l3 const
## -0.192381110 0.006233742
##
##
## Estimated coefficients for equation dlthw:
## ==========================================
## Call:
## dlthw = dlroph.l1 + dlthw.l1 + dlroph.l2 + dlthw.l2 + dlroph.l3 + dlthw.l3 + const
##
## dlroph.l1 dlthw.l1 dlroph.l2 dlthw.l2 dlroph.l3
## 0.1065853542 0.6259177078 0.1047852502 -0.0181069034 0.0884737276
## dlthw.l3 const
## -0.0441193518 -0.0002739886summary(varp)##
## VAR Estimation Results:
## =========================
## Endogenous variables: dlroph, dlthw
## Deterministic variables: const
## Sample size: 276
## Log Likelihood: 1939.243
## Roots of the characteristic polynomial:
## 0.7387 0.7387 0.4311 0.4311 0.4069 0.4069
## Call:
## VAR(y = dlcombdata, type = "const", lag.max = 8, ic = "AIC")
##
##
## Estimation results for equation dlroph:
## =======================================
## dlroph = dlroph.l1 + dlthw.l1 + dlroph.l2 + dlthw.l2 + dlroph.l3 + dlthw.l3 + const
##
## Estimate Std. Error t value Pr(>|t|)
## dlroph.l1 -0.0610996 0.0592136 -1.032 0.30307
## dlthw.l1 0.0631182 0.0712786 0.886 0.37667
## dlroph.l2 0.0514853 0.0559621 0.920 0.35840
## dlthw.l2 -0.1965778 0.0840083 -2.340 0.02002 *
## dlroph.l3 0.0052400 0.0550610 0.095 0.92425
## dlthw.l3 -0.1923811 0.0731269 -2.631 0.00901 **
## const 0.0062337 0.0007462 8.353 3.56e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.00793 on 269 degrees of freedom
## Multiple R-Squared: 0.1176, Adjusted R-squared: 0.09788
## F-statistic: 5.973 on 6 and 269 DF, p-value: 7.068e-06
##
##
## Estimation results for equation dlthw:
## ======================================
## dlthw = dlroph.l1 + dlthw.l1 + dlroph.l2 + dlthw.l2 + dlroph.l3 + dlthw.l3 + const
##
## Estimate Std. Error t value Pr(>|t|)
## dlroph.l1 0.1065854 0.0506809 2.103 0.0364 *
## dlthw.l1 0.6259177 0.0610073 10.260 <2e-16 ***
## dlroph.l2 0.1047853 0.0478979 2.188 0.0296 *
## dlthw.l2 -0.0181069 0.0719026 -0.252 0.8014
## dlroph.l3 0.0884737 0.0471267 1.877 0.0616 .
## dlthw.l3 -0.0441194 0.0625892 -0.705 0.4815
## const -0.0002740 0.0006387 -0.429 0.6683
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.006787 on 269 degrees of freedom
## Multiple R-Squared: 0.4387, Adjusted R-squared: 0.4261
## F-statistic: 35.03 on 6 and 269 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## dlroph dlthw
## dlroph 6.288e-05 7.009e-06
## dlthw 7.009e-06 4.606e-05
##
## Correlation matrix of residuals:
## dlroph dlthw
## dlroph 1.0000 0.1302
## dlthw 0.1302 1.0000Blanchard and Quah approach to obtain an SVAR model
svar1<-VAR(dlcombdata,ic="AIC", lag.max=8)
mysvar1<-BQ(svar1)
summary(mysvar1)##
## SVAR Estimation Results:
## ========================
##
## Call:
## BQ(x = svar1)
##
## Type: Blanchard-Quah
## Sample size: 276
## Log Likelihood: 1932.152
##
## Estimated contemporaneous impact matrix:
## dlroph dlthw
## dlroph 0.006523 0.004509
## dlthw -0.003099 0.006038
##
## Estimated identified long run impact matrix:
## dlroph dlthw
## dlroph 0.007195 0.00000
## dlthw -0.002159 0.01384
##
## Covariance matrix of reduced form residuals (*100):
## dlroph dlthw
## dlroph 0.0062881 0.0007009
## dlthw 0.0007009 0.0046064Result: -From the summary table of svarv, we came to know that one positive deviation technology shcock increases output by 0.006523 and lowers total hours worked by 0.003099. -Similarly, from the summary table of svarv, we came to know that one negative deviation technology shock increases output by 0.004509 while there is increase in total hours worked by 0.006038.
-The long run effect of non-technological shock on output shock is 0.000 and single deviation will increase the total hours worked by 0.007195. -The long run effect of non-technological shock on output will be negative and decrease by 0.002159 and single deviation will increase the index by 0.01384.
Plot the cumulative IRFs based on the SVAR model
mysvar1.irfs <- irf(mysvar1, n.ahead=30)
plot(mysvar1.irfs, plot.type="multiple")
library(vars)irfvc <- irf(mysvar1, n.ahead = 30, cumulative = TRUE)
summary(irfvc)## Length Class Mode
## irf 2 -none- list
## Lower 2 -none- list
## Upper 2 -none- list
## response 2 -none- character
## impulse 2 -none- character
## ortho 1 -none- logical
## cumulative 1 -none- logical
## runs 1 -none- numeric
## ci 1 -none- numeric
## boot 1 -none- logical
## model 1 -none- charactervth <- fevd(mysvar1, n.ahead=60)
summary(vth)## Length Class Mode
## dlroph 120 -none- numeric
## dlthw 120 -none- numericplot(vth)
There are complete differences in the figures. This shift says that by reversing the path of variables, the path of description forecast error variance of each variable by exogenous shocks to other variable is affected. *compare your IRFs with Figure 2 from Gali (1999) AER.: it seems that the results are quite different its more fluctuated in the Gali figure then it is in this case.