Can Consumer Debt Burden Adequately Explain Variations in Economic Growth
RickyJesse Daudi
Objective.
Establish the relationship between Consumer Debt Burden and Economic Growth.
The Data.
Source, Frequency & Range
World Bank.
Yearly.
1980 - 2019
1993 - 2019
Variables
Consumption.
Agriculture.
Net Exports.
Growth.
Consumer Debt Burden
Private Debt / Income.
Private Debt / Income (Stocks).
Model Specification.
Debt Burden & Growth
Yt= α10 + α11Yt-1 +…+ α1pYt-p + β11Xt-1 +…+ β1pXt-p
Xt= α20 + α21Yt-1 +…+ α2pYt-p + β21Xt-1 +…+ β2pXt-p
Y - Debt Burden.
X - Growth.
Debt Burden & Factors Influencing Growth
Yt= α10 + α11Yt-1 +..+ α1pYt-p+ β11Xt-1 +..+ β1pXt-p + δ11Zt-1 +..+ δ1pZt-p + Φ11Vt-1 +..+ Φ1pVt-p
.
.
.
Vt= α40+ α41Yt-1 +..+ α4pYt-p + β41Xt-1+..+ β4pXt-p + δ41Zt-1 +..+ δ4pZt-p + Φ41Vt-1 +..+ Φ4pVt-p
Y - Debt Burden.
X - Consumption.
Z - Agriculture.
V - Net Exports.
Packages Used.
This are the statistical and econometric packages used for this analysis
library(readxl)## Warning: package 'readxl' was built under R version 3.6.3library(tidyquant)## Warning: package 'lubridate' was built under R version 3.6.3## Warning: package 'PerformanceAnalytics' was built under R version 3.6.3## Warning: package 'xts' was built under R version 3.6.3## Warning: package 'zoo' was built under R version 3.6.3## Warning: package 'quantmod' was built under R version 3.6.3## Warning: package 'TTR' was built under R version 3.6.3library(tseries)## Warning: package 'tseries' was built under R version 3.6.3library(fBasics)## Warning: package 'fBasics' was built under R version 3.6.3## Warning: package 'timeDate' was built under R version 3.6.3## Warning: package 'timeSeries' was built under R version 3.6.3library(normtest)
library(forecast)## Warning: package 'forecast' was built under R version 3.6.3library(urca)## Warning: package 'urca' was built under R version 3.6.3library(vars)## Warning: package 'vars' was built under R version 3.6.3## Warning: package 'strucchange' was built under R version 3.6.3## Warning: package 'sandwich' was built under R version 3.6.3## Warning: package 'lmtest' was built under R version 3.6.3library(dplyr)## Warning: package 'dplyr' was built under R version 3.6.3library(lmtest)
library(mFilter)## Warning: package 'mFilter' was built under R version 3.6.3library(tidyverse)## Warning: package 'tidyverse' was built under R version 3.6.3## Warning: package 'ggplot2' was built under R version 3.6.3## Warning: package 'tibble' was built under R version 3.6.3## Warning: package 'tidyr' was built under R version 3.6.3## Warning: package 'readr' was built under R version 3.6.3## Warning: package 'purrr' was built under R version 3.6.3## Warning: package 'stringr' was built under R version 3.6.3## Warning: package 'forcats' was built under R version 3.6.3library(svars)## Warning: package 'svars' was built under R version 3.6.3library(rtf)## Warning: package 'rtf' was built under R version 3.6.3library(lmtest)
library(mFilter)
library(tidyverse)
library(svars)
library(rtf)
library(tsDyn)## Warning: package 'tsDyn' was built under R version 3.6.3library(aod)## Warning: package 'aod' was built under R version 3.6.3Setting working directory and importing data.
Note that working directory should be changed for replication purposes.
setwd("C:/Users/HP/OneDrive/Documents/BBS 4.1/Research/Research Codes")
data<-read_excel("~/Book1.xlsx")
daTA=read_excel("~/Book2.xlsx")
colnames(data)<-c("YEAR","PDEBT","CONS","INC","GROWTH","STOCKS","AGRIC","EXP","DBURDEN")
colnames(daTA)<-c("YEAR2","PDEBT2","CONS2","INC2","GROWTH2","STOCKS2","AGRIC2","EXP2","DBURDEN2")
data<-as.data.frame(data)
daTA=as.data.frame(daTA)Descriptive Statistics.
This include the mean and variace and the rtffile function helps us export the table to word.
DATA=subset(data,select = -c(YEAR))
Descriptive_Stats<- basicStats(DATA)
Descriptive_Stats<- t(Descriptive_Stats)
Summary_Stats=subset(Descriptive_Stats,select = c(Minimum,Maximum,Mean,Median,Stdev,Skewness,Kurtosis))
subset(Descriptive_Stats,select = c(Minimum,Maximum,Mean,Median,Stdev,Skewness,Kurtosis))## Minimum Maximum Mean Median Stdev Skewness Kurtosis
## PDEBT -4.132492 5.979962 0.164361 -0.179352 2.050080 0.127684 0.541197
## CONS -5.909583 7.145463 0.296197 0.021849 2.861785 0.221903 0.750519
## INC -4.982609 5.783640 -0.019257 0.375599 2.467468 -0.018533 -0.622787
## GROWTH -0.799494 8.405699 3.970454 4.353389 2.284124 -0.333041 -0.957920
## STOCKS -1.798716 2.481331 0.018137 0.000000 0.718151 0.644174 3.246805
## AGRIC -3.716587 3.758899 0.099085 0.074834 1.421605 -0.102167 0.470213
## EXP -2.687517 3.872383 0.151450 0.241005 1.555311 0.206267 -0.237120
## DBURDEN -6.918950 8.819477 -0.059483 -0.099107 2.421063 0.700942 4.004651rtffile <- RTF("Descriptive_Stats.doc")
addText(rtffile, "\t\tTable 1: Descriptive statistics \n\n", bold=TRUE, italic=FALSE)
Variable<-rownames(Summary_Stats)
addHeader(rtffile, title="\\i Descriptive stats ")
addTable(rtffile, cbind(Variable, Summary_Stats), font.size=8)
done(rtffile)Plotting individual variables.
We convert the individual variables into time series data and plot them for visualization.
PDEBT<-ts((data$PDEBT))
CONS<-ts((data$CONS))
INC<-ts((data$INC))
GROWTH<-ts(data$GROWTH)
STOCKS<-ts((data$STOCKS))
AGRIC<-ts((data$AGRIC))
EXP<-ts((data$EXP))
DBURDEN<-ts((data$DBURDEN))
plot(PDEBT)
plot(CONS)
plot(INC)
plot(GROWTH)
plot(STOCKS)
plot(AGRIC)
plot(EXP)
plot(DBURDEN)
Stationarity tests.
I use the augmented Dickey-Fuller test to investigate whether our varaibles are stationary.
adf.test(PDEBT)##
## Augmented Dickey-Fuller Test
##
## data: PDEBT
## Dickey-Fuller = -2.1292, Lag order = 3, p-value = 0.5228
## alternative hypothesis: stationaryadf.test(CONS)##
## Augmented Dickey-Fuller Test
##
## data: CONS
## Dickey-Fuller = -3.7387, Lag order = 3, p-value = 0.03488
## alternative hypothesis: stationaryadf.test(INC)##
## Augmented Dickey-Fuller Test
##
## data: INC
## Dickey-Fuller = -2.8251, Lag order = 3, p-value = 0.2496
## alternative hypothesis: stationaryadf.test(GROWTH)##
## Augmented Dickey-Fuller Test
##
## data: GROWTH
## Dickey-Fuller = -3.1206, Lag order = 3, p-value = 0.1337
## alternative hypothesis: stationaryadf.test(AGRIC)##
## Augmented Dickey-Fuller Test
##
## data: AGRIC
## Dickey-Fuller = -2.6813, Lag order = 3, p-value = 0.3061
## alternative hypothesis: stationaryadf.test(EXP)##
## Augmented Dickey-Fuller Test
##
## data: EXP
## Dickey-Fuller = -2.2976, Lag order = 3, p-value = 0.4567
## alternative hypothesis: stationaryadf.test(DBURDEN)##
## Augmented Dickey-Fuller Test
##
## data: DBURDEN
## Dickey-Fuller = -3.5067, Lag order = 3, p-value = 0.05552
## alternative hypothesis: stationarySTATIONARITY TEST RESULT
All variables are non-stationary hence we need to first difference them.
PDEBT_diff<-diff(PDEBT,differences=1)
INC_diff<-diff(INC,differences=1)
GROWTH_diff<-diff(GROWTH,differences=1)
AGRICS_diff<-diff(AGRIC,differences=1)
EXP_diff<-diff(EXP,differences=1)
DBURDEN_diff<-diff(DBURDEN,differences=1)Stationarity tests on differenced data.
adf.test(PDEBT_diff)## Warning in adf.test(PDEBT_diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: PDEBT_diff
## Dickey-Fuller = -5.018, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationaryadf.test(INC_diff)##
## Augmented Dickey-Fuller Test
##
## data: INC_diff
## Dickey-Fuller = -4.0007, Lag order = 3, p-value = 0.02003
## alternative hypothesis: stationaryadf.test(GROWTH_diff)## Warning in adf.test(GROWTH_diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: GROWTH_diff
## Dickey-Fuller = -4.8665, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationaryadf.test(AGRICS_diff)##
## Augmented Dickey-Fuller Test
##
## data: AGRICS_diff
## Dickey-Fuller = -3.8795, Lag order = 3, p-value = 0.02471
## alternative hypothesis: stationaryadf.test(EXP_diff)## Warning in adf.test(EXP_diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: EXP_diff
## Dickey-Fuller = -4.5271, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationaryadf.test(DBURDEN_diff)## Warning in adf.test(DBURDEN_diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: DBURDEN_diff
## Dickey-Fuller = -5.5287, Lag order = 3, p-value = 0.01
## alternative hypothesis: stationaryNormality tests.
Convert variables into vector format for the skewness and kurtosis test functions to operate on
PDEBT_diff_v<- as.vector(PDEBT_diff)
CONS_diff_v<- as.vector(CONS)
INC_diff_v<- as.vector(INC_diff)
GROWTH_diff_v<- as.vector(GROWTH_diff)
AGRICS_diff_v<- as.vector(AGRICS_diff)
EXP_diff_v<- as.vector(EXP_diff)
DBURDEN_diff_v<- as.vector(DBURDEN_diff)NORMALITY TEST
t.test(PDEBT_diff_v)##
## One Sample t-test
##
## data: PDEBT_diff_v
## t = -0.064831, df = 38, p-value = 0.9486
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -1.0658881 0.9997364
## sample estimates:
## mean of x
## -0.03307584t.test(CONS_diff_v)##
## One Sample t-test
##
## data: CONS_diff_v
## t = 0.6546, df = 39, p-value = 0.5166
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.6190462 1.2114402
## sample estimates:
## mean of x
## 0.296197t.test(INC_diff_v)##
## One Sample t-test
##
## data: INC_diff_v
## t = -0.01401, df = 38, p-value = 0.9889
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -1.115116 1.099788
## sample estimates:
## mean of x
## -0.007664003t.test(GROWTH_diff_v)##
## One Sample t-test
##
## data: GROWTH_diff_v
## t = -0.015762, df = 38, p-value = 0.9875
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.7507999 0.7391985
## sample estimates:
## mean of x
## -0.005800699t.test(AGRICS_diff_v)##
## One Sample t-test
##
## data: AGRICS_diff_v
## t = 0.22418, df = 38, p-value = 0.8238
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.5037638 0.6292279
## sample estimates:
## mean of x
## 0.06273204t.test(EXP_diff_v)##
## One Sample t-test
##
## data: EXP_diff_v
## t = -0.32399, df = 38, p-value = 0.7477
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.7695859 0.5572389
## sample estimates:
## mean of x
## -0.1061735t.test(DBURDEN_diff_v)##
## One Sample t-test
##
## data: DBURDEN_diff_v
## t = 0.015532, df = 38, p-value = 0.9877
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -1.067867 1.084380
## sample estimates:
## mean of x
## 0.00825669NORMALITY TEST RESULTS All variables are normally distributed.
Cointegration Test.
I used a Johansen cointegration test for this. Since all my variables were non stationary, I will test them as a whole set.
dset=cbind(GROWTH,DBURDEN)
VARselect(dset,lag.max = 10,type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 10 1 1 1
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 3.647539 3.836779 3.993302 4.183261 4.303555 3.994634 3.800391
## HQ(n) 3.737190 3.986198 4.202487 4.452214 4.632275 4.383122 4.248646
## SC(n) 3.927778 4.303845 4.647194 5.023979 5.331100 5.209005 5.201589
## FPE(n) 38.431597 46.667919 55.191867 68.124650 79.452103 61.391692 54.468130
## 8 9 10
## AIC(n) 3.765603 3.857608 3.280853
## HQ(n) 4.273626 4.425397 3.908410
## SC(n) 5.353627 5.632458 5.242529
## FPE(n) 58.517917 74.598801 51.938211cointest<-ca.jo(dset,K=2,type = "trace", ecdet = "const", spec = "transitory")
cointest##
## #####################################################
## # Johansen-Procedure Unit Root / Cointegration Test #
## #####################################################
##
## The value of the test statistic is: 9.3655 21.8973print('H0 r=0')## [1] "H0 r=0"cointest@teststat[2]## [1] 21.89727print('H0 r=1')## [1] "H0 r=1"cointest@teststat[1]## [1] 9.365487cointest@cval## 10pct 5pct 1pct
## r <= 1 | 7.52 9.24 12.97
## r = 0 | 17.85 19.96 24.60datset=cbind(CONS,AGRIC,EXP,DBURDEN)
VARselect(datset,lag.max = 10,type = "const")## Warning in log(sigma.det): NaNs produced
## Warning in log(sigma.det): NaNs produced
## Warning in log(sigma.det): NaNs produced## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 7
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 6.132211 6.318066 5.721176 5.942213 5.700565 0.8761625
## HQ(n) 6.431048 6.855973 6.498151 6.958257 6.955679 2.3703461
## SC(n) 7.066343 7.999503 8.149918 9.118260 9.623918 5.5468205
## FPE(n) 466.270853 598.378347 390.120655 699.015006 1140.211813 44.7493508
## 7 8 9 10
## AIC(n) NaN -Inf -Inf -Inf
## HQ(n) NaN -Inf -Inf -Inf
## SC(n) NaN -Inf -Inf -Inf
## FPE(n) -5.296205e-47 0 0 0cotest<-ca.jo(datset,K=7,type = "trace", ecdet = "const", spec = "transitory")
cotest##
## #####################################################
## # Johansen-Procedure Unit Root / Cointegration Test #
## #####################################################
##
## The value of the test statistic is: 2.7385 6.7538 50.7411 260.3002print('H0 r=0')## [1] "H0 r=0"cotest@teststat[2]## [1] 6.753805print('H0 r=1')## [1] "H0 r=1"cotest@teststat[1]## [1] 2.73853cotest@cval## 10pct 5pct 1pct
## r <= 3 | 7.52 9.24 12.97
## r <= 2 | 17.85 19.96 24.60
## r <= 1 | 32.00 34.91 41.07
## r = 0 | 49.65 53.12 60.16Scatter plot of consumer debt burden and gdp growth.
This is for visual representation of the relationship between the two variables.
ggplot(data=data)+geom_point(mapping=aes(x=GROWTH,y=DBURDEN))
ggplot(data=data)+geom_point(mapping=aes(x=CONS,y=DBURDEN))
ggplot(data=data)+geom_point(mapping=aes(x=AGRIC,y=DBURDEN))
Determining how well the variable lags explain themselves.
acf(GROWTH,main="ACF for Growth")
pacf(GROWTH,main="PACF for Growth")
acf(CONS,main="ACF for Consumption")
pacf(CONS,main="PACF for Consumption")
acf(AGRIC,main="ACF for Agriculture")
pacf(AGRIC,main="PACF for Agriculture")
The VECM model.
MODEL1=VECM(dset,2,r=1,estim=("2OLS"))
summary(MODEL1)## #############
## ###Model VECM
## #############
## Full sample size: 40 End sample size: 37
## Number of variables: 2 Number of estimated slope parameters 12
## AIC 140.283 BIC 161.2249 SSR 410.0671
## Cointegrating vector (estimated by 2OLS):
## GROWTH DBURDEN
## r1 1 0.3995348
##
##
## ECT Intercept GROWTH -1
## Equation GROWTH -0.5805(0.2244)* 2.3443(0.9303)* 0.1617(0.2069)
## Equation DBURDEN -0.0121(0.3207) -0.0083(1.3292) 0.0891(0.2957)
## DBURDEN -1 GROWTH -2 DBURDEN -2
## Equation GROWTH 0.1824(0.1451) -0.0243(0.1835) 0.1985(0.1382)
## Equation DBURDEN -0.6347(0.2074)** -0.0246(0.2622) -0.1623(0.1975)MODEL2=VECM(datset,6,r=1,estim=("2OLS") )
summary(MODEL2) ## #############
## ###Model VECM
## #############
## Full sample size: 40 End sample size: 33
## Number of variables: 4 Number of estimated slope parameters 104
## AIC 135.9485 BIC 296.0748 SSR 130.1146
## Cointegrating vector (estimated by 2OLS):
## CONS AGRIC EXP DBURDEN
## r1 1 -0.2658077 0.02023288 0.1515156
##
##
## ECT Intercept CONS -1
## Equation CONS -1.2922(1.0624) 0.6365(0.7923) 0.6154(0.8941)
## Equation AGRIC -0.6263(0.4753) 0.4663(0.3545) 0.5077(0.4000)
## Equation EXP -0.7518(0.4358) 0.5164(0.3250) 0.4184(0.3668)
## Equation DBURDEN -0.1915(0.7258) 0.2203(0.5413) 0.1237(0.6108)
## AGRIC -1 EXP -1 DBURDEN -1
## Equation CONS -1.3359(0.7890) 0.3125(0.5081) 0.3558(0.6732)
## Equation AGRIC -0.7471(0.3530). -0.6728(0.2273)* 0.1386(0.3012)
## Equation EXP -0.3362(0.3237) -0.4485(0.2084). -0.0551(0.2762)
## Equation DBURDEN -0.5133(0.5390) -0.8053(0.3471). -0.5879(0.4599)
## CONS -2 AGRIC -2 EXP -2
## Equation CONS 0.3647(0.8291) -0.1020(0.8677) -0.4958(0.8316)
## Equation AGRIC 0.2768(0.3710) -0.5546(0.3882) -0.3689(0.3721)
## Equation EXP 0.5058(0.3401) -0.8832(0.3559)* -0.3761(0.3411)
## Equation DBURDEN 0.0253(0.5664) -0.9010(0.5927) -0.6755(0.5681)
## DBURDEN -2 CONS -3 AGRIC -3
## Equation CONS 0.3428(0.7544) 0.4771(0.7541) 0.5400(0.9161)
## Equation AGRIC 0.3588(0.3375) 0.3358(0.3374) -0.7571(0.4099)
## Equation EXP 0.3557(0.3095) 0.4826(0.3093) -0.0223(0.3758)
## Equation DBURDEN -0.3676(0.5154) 0.4850(0.5152) -1.2506(0.6258).
## EXP -3 DBURDEN -3 CONS -4
## Equation CONS 0.2161(1.0382) 0.1812(0.7462) 0.0518(0.7496)
## Equation AGRIC 0.6097(0.4645) 0.3674(0.3339) 0.3661(0.3354)
## Equation EXP -0.3703(0.4259) 0.5652(0.3061) 0.5853(0.3075).
## Equation DBURDEN -0.8524(0.7093) -0.0276(0.5098) 0.4410(0.5121)
## AGRIC -4 EXP -4 DBURDEN -4
## Equation CONS -0.0390(1.1591) 0.3564(1.0440) 0.2312(0.5811)
## Equation AGRIC 0.4089(0.5186) 0.2996(0.4671) 0.3046(0.2600)
## Equation EXP -0.0783(0.4755) 0.1717(0.4283) 0.3542(0.2384)
## Equation DBURDEN -0.8661(0.7919) -0.4677(0.7132) -0.1409(0.3970)
## CONS -5 AGRIC -5 EXP -5
## Equation CONS 0.1324(0.5543) 0.3454(1.0183) 0.3301(0.8123)
## Equation AGRIC 0.1785(0.2480) 0.3829(0.4556) 0.5891(0.3635)
## Equation EXP 0.2297(0.2274) 0.0573(0.4177) 0.1643(0.3332)
## Equation DBURDEN 0.3915(0.3787) -0.4801(0.6956) -0.5237(0.5549)
## DBURDEN -5 CONS -6 AGRIC -6
## Equation CONS 0.4150(0.5110) 0.0053(0.4248) 0.0783(0.6117)
## Equation AGRIC 0.3349(0.2287) -0.0848(0.1901) 0.0050(0.2737)
## Equation EXP 0.3694(0.2096) 0.1588(0.1743) -0.5453(0.2509).
## Equation DBURDEN 0.2391(0.3491) -0.1198(0.2902) -0.3577(0.4179)
## EXP -6 DBURDEN -6
## Equation CONS 0.3658(0.6930) 0.3957(0.4035)
## Equation AGRIC 0.5812(0.3101) 0.1491(0.1805)
## Equation EXP 0.0129(0.2843) 0.5409(0.1655)*
## Equation DBURDEN -0.3649(0.4734) -0.0916(0.2757)Converting the VECM to a VAR for diagnostic trsts
MODEL1=vec2var(cointest,r=1)
MODEL2=vec2var(cotest,r=3)Diagnosing our VAR model.
Test for serial correlation
Serial1=serial.test(MODEL1,lags.pt = 12,type = "PT.asymptotic")
Serial2=serial.test(MODEL2,lags.pt = 12,type = "PT.asymptotic")
Serial1##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 46.439, df = 42, p-value = 0.2945Serial2##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 328.09, df = 84, p-value < 2.2e-16Heteroskedasticity test
ARCH1=arch.test(MODEL1,lags.multi = 12,multivariate.only = TRUE)
ARCH2=arch.test(MODEL2,lags.multi = 12,multivariate.only = TRUE)
ARCH1##
## ARCH (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 78, df = 108, p-value = 0.9869ARCH2##
## ARCH (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 210, df = 1200, p-value = 1Normal distribution of the residuals
NORM1=normality.test(MODEL1,multivariate.only = TRUE)
NORM2=normality.test(MODEL2,multivariate.only = TRUE)
NORM1## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 3.0861, df = 4, p-value = 0.5435
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 1.1355, df = 2, p-value = 0.5668
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 1.9506, df = 2, p-value = 0.3771NORM2## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 2.7984, df = 8, p-value = 0.9464
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 0.87322, df = 4, p-value = 0.9284
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 1.9252, df = 4, p-value = 0.7495Impulse response functions.
GROWTHirf=irf(MODEL1,impulse = "DBURDEN",response = "GROWTH",n.ahead = 20,boot = TRUE)
DBURDENirf=irf(MODEL1,impulse = "GROWTH",response = "DBURDEN",n.ahead = 20,boot = TRUE)
AGRICSirf=irf(MODEL2,impulse = "DBURDEN",response = "AGRIC",n.ahead = 20,boot = TRUE)
DBURDENirf2=irf(MODEL2,impulse = "AGRIC",response = "DBURDEN",n.ahead = 20,boot = TRUE)
CONSirf=irf(MODEL2,impulse = "DBURDEN",response = "CONS",n.ahead = 20,boot = TRUE)
DBURDENirf3=irf(MODEL2,impulse = "CONS",response = "DBURDEN",n.ahead = 20,boot = TRUE)
plot(CONSirf,ylab="CONS",main="Shock from DBURDEN")
plot(DBURDENirf3,ylab="DBURDEN",main="Shock from CONS")
plot(AGRICSirf,ylab="AGRICS",main="Shock from DBURDEN")
plot(DBURDENirf2,ylab="DBURDEN",main="Shock from AGRICS")
plot(GROWTHirf,ylab="GROWTH",main="Shock from DBURDEN")
plot(DBURDENirf,ylab="DBURDEN",main="Shock from GROWTH")
Variance decomposition.
FEVD1=fevd(MODEL1,n.ahead = 15)
FEVD2=fevd(MODEL2,n.ahead = 5)
plot(FEVD1)
VAR Forecasting.
Forecast1=predict(MODEL1,n.ahead = 10,ci=0.95)
Forecast2=predict(MODEL2,n.ahead = 10,ci=0.95)
fanchart(Forecast1,names = "GROWTH")
fanchart(Forecast2,names = "DBURDEN")
fanchart(Forecast2,names = "AGRIC")
fanchart(Forecast2,names = "CONS")
Using The Stock Consumer Debt Burden.
PDEBT2<-ts((daTA$PDEBT2))
CONS2<-ts((daTA$CONS2))
INC2<-ts((daTA$INC2))
GROWTH2<-ts(daTA$GROWTH2)
STOCKS2<-ts((daTA$STOCKS2))
AGRIC2<-ts((daTA$AGRIC2))
EXP2<-ts((daTA$EXP2))
DBURDEN2<-ts((daTA$DBURDEN2))Cointegration Test.
Dataset=cbind(daTA$GROWTH2,DBURDEN2)
VARselect(dset,lag.max = 10,type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 10 1 1 1
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 3.647539 3.836779 3.993302 4.183261 4.303555 3.994634 3.800391
## HQ(n) 3.737190 3.986198 4.202487 4.452214 4.632275 4.383122 4.248646
## SC(n) 3.927778 4.303845 4.647194 5.023979 5.331100 5.209005 5.201589
## FPE(n) 38.431597 46.667919 55.191867 68.124650 79.452103 61.391692 54.468130
## 8 9 10
## AIC(n) 3.765603 3.857608 3.280853
## HQ(n) 4.273626 4.425397 3.908410
## SC(n) 5.353627 5.632458 5.242529
## FPE(n) 58.517917 74.598801 51.938211cointest<-ca.jo(dset,K=2,type = "trace", ecdet = "const", spec = "transitory")
cointest##
## #####################################################
## # Johansen-Procedure Unit Root / Cointegration Test #
## #####################################################
##
## The value of the test statistic is: 9.3655 21.8973print('H0 r=0')## [1] "H0 r=0"cointest@teststat[2]## [1] 21.89727print('H0 r=1')## [1] "H0 r=1"cointest@teststat[1]## [1] 9.365487cointest@cval## 10pct 5pct 1pct
## r <= 1 | 7.52 9.24 12.97
## r = 0 | 17.85 19.96 24.60datset=cbind(CONS2,AGRIC2,EXP2,DBURDEN2)
VARselect(datset,lag.max = 10,type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 4 4 5
##
## $criteria
## 1 2 3 4 5 6 7 8 9 10
## AIC(n) 7.389921 7.210479 5.146322 -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## HQ(n) 7.487360 7.385869 5.399663 -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## SC(n) 8.370172 8.974931 7.694975 -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## FPE(n) 1739.795443 2185.948467 1197.854586 NaN 0 0 0 0 0 0cotest<-ca.jo(datset,K=4,type = "trace", ecdet = "const", spec = "transitory")
cotest##
## #####################################################
## # Johansen-Procedure Unit Root / Cointegration Test #
## #####################################################
##
## The value of the test statistic is: 2.4124 7.4536 14.5244 53.6833print('H0 r=0')## [1] "H0 r=0"cotest@teststat[2]## [1] 7.453554print('H0 r=1')## [1] "H0 r=1"cotest@teststat[1]## [1] 2.412394cotest@cval## 10pct 5pct 1pct
## r <= 3 | 7.52 9.24 12.97
## r <= 2 | 17.85 19.96 24.60
## r <= 1 | 32.00 34.91 41.07
## r = 0 | 49.65 53.12 60.16Scatter Plot.
ggplot(data=daTA)+geom_point(mapping=aes(x=GROWTH2,y=DBURDEN2))
ggplot(data=daTA)+geom_point(mapping=aes(x=CONS2,y=DBURDEN2))
ggplot(data=daTA)+geom_point(mapping=aes(x=AGRIC2,y=DBURDEN2))
VECM Model
MODEL1=VECM(Dataset,2,r=1,estim=("2OLS") )
summary(MODEL1)## #############
## ###Model VECM
## #############
## Full sample size: 27 End sample size: 24
## Number of variables: 2 Number of estimated slope parameters 12
## AIC 210.2013 BIC 225.516 SSR 13656.29
## Cointegrating vector (estimated by 2OLS):
## daTA$GROWTH2 DBURDEN2
## r1 1 0.02113294
##
##
## ECT Intercept
## Equation daTA$GROWTH2 -0.3228(0.2466) 1.4265(1.0646)
## Equation DBURDEN2 -4.2088(2.9947) 23.1273(12.9267).
## daTA$GROWTH2 -1 DBURDEN2 -1
## Equation daTA$GROWTH2 -0.2513(0.2527) 0.0102(0.0117)
## Equation DBURDEN2 2.7479(3.0685) -0.2601(0.1420).
## daTA$GROWTH2 -2 DBURDEN2 -2
## Equation daTA$GROWTH2 -0.3376(0.2169) 0.0066(0.0105)
## Equation DBURDEN2 3.3361(2.6336) -0.5643(0.1281)***MODEL2=VECM(datset,4,r=3,estim=("ML") )
summary(MODEL2)## Warning in log(det(crossprod(residuals(object))/t)): NaNs produced
## Warning in log(det(crossprod(residuals(object))/t)): NaNs produced## #############
## ###Model VECM
## #############
## Full sample size: 27 End sample size: 22
## Number of variables: 4 Number of estimated slope parameters 80
## AIC NaN BIC NaN SSR 66.59273
## Cointegrating vector (estimated by ML):
## CONS2 AGRIC2 EXP2 DBURDEN2
## r1 1.000000e+00 0.000000e+00 0.000000e+00 -0.2500760
## r2 -1.387779e-17 1.000000e+00 2.775558e-17 -0.2598083
## r3 -2.775558e-17 -1.387779e-17 1.000000e+00 0.1911052
##
##
## ECT1 ECT2 ECT3
## Equation CONS2 -2.3684(1.3370) 0.8816(1.6694) -1.8637(1.2677)
## Equation AGRIC2 -1.7633(0.0280)*** -0.3935(0.0350)** -2.4851(0.0266)***
## Equation EXP2 0.4099(1.3135) -2.4106(1.6401) -2.1695(1.2454)
## Equation DBURDEN2 -41.5119(4.7324)* 32.9893(5.9089)* -19.4616(4.4871)*
## Intercept CONS2 -1 AGRIC2 -1
## Equation CONS2 1.3234(1.2823) 0.7401(1.0379) 0.4391(1.4767)
## Equation AGRIC2 2.4799(0.0269)*** 0.6163(0.0217)** 0.9652(0.0309)**
## Equation EXP2 1.8939(1.2598) -1.1783(1.0197) 2.4538(1.4508)
## Equation DBURDEN2 5.0623(4.5388) 16.9624(3.6738)* -4.3850(5.2269)
## EXP2 -1 DBURDEN2 -1 CONS2 -2
## Equation CONS2 2.7704(1.5332) -0.0929(0.0646) 0.4577(0.6514)
## Equation AGRIC2 2.8444(0.0321)*** -0.1413(0.0014)*** 0.5663(0.0136)***
## Equation EXP2 1.5574(1.5063) -0.0634(0.0635) -0.1955(0.6400)
## Equation DBURDEN2 31.1070(5.4269)* -0.0090(0.2288) 15.6711(2.3057)*
## AGRIC2 -2 EXP2 -2 DBURDEN2 -2
## Equation CONS2 0.6411(1.0349) 2.5554(1.4607) -0.0067(0.0583)
## Equation AGRIC2 0.8129(0.0217)*** 2.7857(0.0306)*** -0.0480(0.0012)***
## Equation EXP2 0.9845(1.0167) 1.7589(1.4351) -0.0811(0.0572)
## Equation DBURDEN2 -0.5778(3.6631) 37.1997(5.1704)* 0.3896(0.2062)
## CONS2 -3 AGRIC2 -3 EXP2 -3
## Equation CONS2 1.1617(0.6908) 0.9788(0.9287) 1.9312(1.0372)
## Equation AGRIC2 1.2506(0.0145)*** 0.8326(0.0195)*** 2.2208(0.0217)***
## Equation EXP2 -0.7401(0.6787) 2.3158(0.9123) 0.5047(1.0190)
## Equation DBURDEN2 16.4962(2.4453)* 9.7556(3.2870). 30.5958(3.6712)*
## DBURDEN2 -3 CONS2 -4 AGRIC2 -4
## Equation CONS2 0.0349(0.0408) 1.9628(1.0580) -0.9986(0.8312)
## Equation AGRIC2 0.0305(0.0009)*** 2.4490(0.0222)*** -1.1151(0.0174)***
## Equation EXP2 -0.0575(0.0401) 0.5921(1.0394) 0.8949(0.8166)
## Equation DBURDEN2 1.0267(0.1443)* 27.9795(3.7448)* -9.9176(2.9421).
## EXP2 -4 DBURDEN2 -4
## Equation CONS2 1.1514(0.8504) 0.1033(0.0513)
## Equation AGRIC2 1.3828(0.0178)*** 0.0920(0.0011)***
## Equation EXP2 0.5635(0.8354) -0.0074(0.0504)
## Equation DBURDEN2 22.0978(3.0099)* 1.1819(0.1814)*#Convert to a VAR*
MODEL1=vec2var(cointest,r=1)
MODEL2=vec2var(cotest,r=3)test for serial correlation
Serial1=serial.test(MODEL1,lags.pt = 12,type = "PT.asymptotic")
Serial2=serial.test(MODEL2,lags.pt = 12,type = "PT.asymptotic")
Serial1##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 46.439, df = 42, p-value = 0.2945Serial2##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 136.97, df = 132, p-value = 0.3659Heteroskedasticity
ARCH1=arch.test(MODEL1,lags.multi = 12,multivariate.only = TRUE)
ARCH2=arch.test(MODEL2,lags.multi = 12,multivariate.only = TRUE)
ARCH1##
## ARCH (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 78, df = 108, p-value = 0.9869ARCH2##
## ARCH (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 110, df = 1200, p-value = 1Normality of error term
NORM1=normality.test(MODEL1,multivariate.only = TRUE)
NORM2=normality.test(MODEL2,multivariate.only = TRUE)
NORM1## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 3.0861, df = 4, p-value = 0.5435
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 1.1355, df = 2, p-value = 0.5668
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object MODEL1
## Chi-squared = 1.9506, df = 2, p-value = 0.3771NORM2## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 3.4863, df = 8, p-value = 0.9003
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 1.6768, df = 4, p-value = 0.7949
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object MODEL2
## Chi-squared = 1.8095, df = 4, p-value = 0.7707Impulse response
GROWTHirf=irf(MODEL1,impulse = "DBURDEN",response = "GROWTH",n.ahead = 20,boot = TRUE)
DBURDENirf=irf(MODEL1,impulse = "GROWTH",response = "DBURDEN",n.ahead = 20,boot = TRUE)
AGRICSirf=irf(MODEL2,impulse = "DBURDEN2",response = "AGRIC2",n.ahead = 20,boot = TRUE)
DBURDENirf2=irf(MODEL2,impulse = "AGRIC2",response = "DBURDEN2",n.ahead = 20,boot = TRUE)
CONSirf=irf(MODEL2,impulse = "DBURDEN2",response = "CONS2",n.ahead = 20,boot = TRUE)
DBURDENirf3=irf(MODEL2,impulse = "CONS2",response = "DBURDEN2",n.ahead = 20,boot = TRUE)
plot(CONSirf,ylab="CONS",main="Shock from DBURDEN")
plot(DBURDENirf3,ylab="DBURDEN",main="Shock from CONS")
plot(AGRICSirf,ylab="AGRICS",main="Shock from DBURDEN")
plot(DBURDENirf2,ylab="DBURDEN",main="Shock from AGRICS")
plot(GROWTHirf,ylab="GROWTH",main="Shock from DBURDEN")
plot(DBURDENirf,ylab="DBURDEN",main="Shock from GROWTH")
Variance decomposition
FEVD1=fevd(MODEL1,n.ahead = 15)
FEVD2=fevd(MODEL2,n.ahead = 5)
plot(FEVD1)