Impact of Gross Domestic Spending on R&D ON GDP Percapita annual growth
Aden Omar
2023-05-14
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oecd_data <- read_csv("~/Downloads/mydatta.csv")## Rows: 198 Columns: 5
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): country, Indicator, measure
## dbl (2): year, GDS_Res_devel
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## between, lag, leadlibrary(WDI)
wdi_data<-WDI(country =c("CAN", "USA", "ITA", "CZE", "JPN", "FRA", "TUR", "IRL", "POL"),
indicator = c( "NY.GDP.PCAP.KD.ZG", "BX.KLT.DINV.WD.GD.ZS","SL.UEM.1524.ZS", "SL.TLF.ACTI.1524.NE.ZS", "NE.EXP.GNFS.ZS" ),
start=2000,
end=2021,
extra=FALSE,
cache=NULL)#Change variable names
library(WDI)
library(dplyr)
my_data<-wdi_data%>%
rename(country=iso3c,
count=country,
FDI_netinflows=BX.KLT.DINV.WD.GD.ZS,
youth_unemp= SL.UEM.1524.ZS,
GDP_percapita=NY.GDP.PCAP.KD.ZG,
lbr_force=SL.TLF.ACTI.1524.NE.ZS,
net_export = NE.EXP.GNFS.ZS)#Combine data
combi_data<-cbind(oecd_data,my_data)nrow(combi_data)## [1] 198combi_data %>%
is.na()%>%
sum()## [1] 0#Declare as a panel data
mydata<-pdata.frame(combi_data, index = c("country", "year"))
head(mydata)## country Indicator measure year GDS_Res_devel count iso2c country.1
## CAN-2000 CAN GDEXPRD PC_GDP 2000 1.858470 Canada CA CAN
## CAN-2001 CAN GDEXPRD PC_GDP 2001 2.021156 Canada CA CAN
## CAN-2002 CAN GDEXPRD PC_GDP 2002 1.971695 Canada CA CAN
## CAN-2003 CAN GDEXPRD PC_GDP 2003 1.967807 Canada CA CAN
## CAN-2004 CAN GDEXPRD PC_GDP 2004 1.997333 Canada CA CAN
## CAN-2005 CAN GDEXPRD PC_GDP 2005 1.971243 Canada CA CAN
## year.1 GDP_percapita FDI_netinflows youth_unemp lbr_force net_export
## CAN-2000 2000 4.2026826 9.1710243 12.685 64.39 44.20924
## CAN-2001 2001 0.6901612 3.8419213 12.879 64.66 42.03996
## CAN-2002 2002 1.9038520 3.2191477 13.625 66.53 40.05866
## CAN-2003 2003 0.8880302 0.7829676 13.631 67.33 36.86599
## CAN-2004 2004 2.1296309 0.1414659 13.471 66.84 37.32777
## CAN-2005 2005 2.2340594 2.1781638 12.416 65.87 36.85671nrow(mydata)## [1] 198mydata%>%
is.na()%>%
sum()## [1] 0summary(mydata)## country Indicator measure year
## CAN :22 Length:198 Length:198 2000 : 9
## CZE :22 Class :character Class :character 2001 : 9
## FRA :22 Mode :character Mode :character 2002 : 9
## IRL :22 2003 : 9
## ITA :22 2004 : 9
## JPN :22 2005 : 9
## (Other):66 (Other):144
## GDS_Res_devel count iso2c country.1
## Min. :0.4653 Length:198 Length:198 Length:198
## 1st Qu.:1.0910 Class :character Class :character Class :character
## Median :1.6042 Mode :character Mode :character Mode :character
## Mean :1.7320
## 3rd Qu.:2.2198
## Max. :3.4678
##
## year.1 GDP_percapita FDI_netinflows youth_unemp
## Min. :2000 Min. :-8.5958 Min. :-11.678 Min. : 3.671
## 1st Qu.:2005 1st Qu.: 0.6118 1st Qu.: 1.097 1st Qu.:11.008
## Median :2010 Median : 1.7623 Median : 2.000 Median :16.608
## Mean :2010 Mean : 1.9610 Mean : 4.230 Mean :17.499
## 3rd Qu.:2016 3rd Qu.: 3.7156 3rd Qu.: 3.637 3rd Qu.:21.864
## Max. :2021 Max. :23.2009 Max. : 81.248 Max. :42.707
##
## lbr_force net_export
## Min. :23.83 Min. : 9.036
## 1st Qu.:34.22 1st Qu.: 22.548
## Median :40.83 Median : 29.364
## Mean :43.56 Mean : 39.180
## 3rd Qu.:52.82 3rd Qu.: 46.668
## Max. :69.37 Max. :134.415
## glimpse(mydata)## Rows: 198
## Columns: 14
## $ country <fct> CAN, CAN, CAN, CAN, CAN, CAN, CAN, CAN, CAN, CAN, CAN, …
## $ Indicator <pseries> "GDEXPRD", "GDEXPRD", "GDEXPRD", "GDEXPRD", "GDEXPR…
## $ measure <pseries> "PC_GDP", "PC_GDP", "PC_GDP", "PC_GDP", "PC_GDP", "…
## $ year <fct> 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2…
## $ GDS_Res_devel <pseries> 1.858470, 2.021156, 1.971695, 1.967807, 1.997333, 1…
## $ count <pseries> "Canada", "Canada", "Canada", "Canada", "Canada", "…
## $ iso2c <pseries> "CA", "CA", "CA", "CA", "CA", "CA", "CA", "CA", "CA…
## $ country.1 <pseries> "CAN", "CAN", "CAN", "CAN", "CAN", "CAN", "CAN", "C…
## $ year.1 <pseries> 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 200…
## $ GDP_percapita <pseries> 4.20268257, 0.69016125, 1.90385200, 0.88803015, 2.1…
## $ FDI_netinflows <pseries> 9.1710243, 3.8419213, 3.2191477, 0.7829676, 0.14146…
## $ youth_unemp <pseries> 12.685, 12.879, 13.625, 13.631, 13.471, 12.416, 11.…
## $ lbr_force <pseries> 64.39, 64.66, 66.53, 67.33, 66.84, 65.87, 66.24, 66…
## $ net_export <pseries> 44.20924, 42.03996, 40.05866, 36.86599, 37.32777, 3…#Run a simple linear regression
library(knitr)
library(car)
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## • Search for functions across packages at https://www.tidymodels.org/find/OLS_simple<-lm(GDP_percapita~GDS_Res_devel, data=mydata)
kable(tidy(OLS_simple))| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 2.7782796 | 0.6026574 | 4.610048 | 0.0000072 |
| GDS_Res_devel | -0.4718742 | 0.3148141 | -1.498898 | 0.1355090 |
OLS<-lm(GDP_percapita~ GDS_Res_devel+FDI_netinflows+net_export, data=mydata)
kable(tidy(OLS))| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 2.2687966 | 0.5507179 | 4.119707 | 0.0000561 |
| GDS_Res_devel | -1.1575621 | 0.3214476 | -3.601091 | 0.0004025 |
| FDI_netinflows | 0.1326912 | 0.0363034 | 3.655063 | 0.0003310 |
| net_export | 0.0289881 | 0.0116581 | 2.486517 | 0.0137445 |
library(ggfortify)## Registered S3 method overwritten by 'ggfortify':
## method from
## autoplot.glmnet parsnipautoplot(OLS)
Fixed effects using Least squares dummy variable model
Section 1: Building 4 panel data models for our data
#1: Pooled(OLS)
library(plm)
pooled<-plm(GDP_percapita~ GDS_Res_devel+FDI_netinflows+net_export, data=mydata,
index=c("country", "year"), model="pooling")
summary(pooled)## Pooling Model
##
## Call:
## plm(formula = GDP_percapita ~ GDS_Res_devel + FDI_netinflows +
## net_export, data = mydata, model = "pooling", index = c("country",
## "year"))
##
## Balanced Panel: n = 9, T = 22, N = 198
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.50405 -1.17746 0.14958 1.69368 9.18980
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) 2.268797 0.550718 4.1197 5.614e-05 ***
## GDS_Res_devel -1.157562 0.321448 -3.6011 0.0004025 ***
## FDI_netinflows 0.132691 0.036303 3.6551 0.0003310 ***
## net_export 0.028988 0.011658 2.4865 0.0137445 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2586.1
## Residual Sum of Squares: 2026.1
## R-Squared: 0.21653
## Adj. R-Squared: 0.20442
## F-statistic: 17.8725 on 3 and 194 DF, p-value: 2.7736e-10#2: Random
library(plm)
Random<-plm(GDP_percapita~ GDS_Res_devel+FDI_netinflows+net_export, data=mydata,
index=c("country", "year"), model="random")
summary(Random)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = GDP_percapita ~ GDS_Res_devel + FDI_netinflows +
## net_export, data = mydata, model = "random", index = c("country",
## "year"))
##
## Balanced Panel: n = 9, T = 22, N = 198
##
## Effects:
## var std.dev share
## idiosyncratic 9.3593 3.0593 0.961
## individual 0.3836 0.6194 0.039
## theta: 0.2749
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.44461 -1.03006 0.22245 1.43129 8.15542
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) 2.246106 0.722650 3.1082 0.001883 **
## GDS_Res_devel -1.250791 0.414441 -3.0180 0.002544 **
## FDI_netinflows 0.150058 0.036224 4.1425 3.435e-05 ***
## net_export 0.031813 0.013653 2.3302 0.019796 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2385.6
## Residual Sum of Squares: 1929.5
## R-Squared: 0.19119
## Adj. R-Squared: 0.17868
## Chisq: 45.8573 on 3 DF, p-value: 6.0819e-10#3: fixed effects model
fixed <-plm(GDP_percapita~ GDS_Res_devel+FDI_netinflows+net_export, data=mydata,
index=c("country", "year"), model="within")
summary(fixed)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = GDP_percapita ~ GDS_Res_devel + FDI_netinflows +
## net_export, data = mydata, model = "within", index = c("country",
## "year"))
##
## Balanced Panel: n = 9, T = 22, N = 198
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -11.6399 -0.8459 0.4017 1.3942 7.6627
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## GDS_Res_devel -2.324032 1.062215 -2.1879 0.0299227 *
## FDI_netinflows 0.185323 0.036455 5.0836 8.987e-07 ***
## net_export 0.101807 0.028193 3.6110 0.0003922 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2163.3
## Residual Sum of Squares: 1740.8
## R-Squared: 0.19529
## Adj. R-Squared: 0.1477
## F-statistic: 15.046 on 3 and 186 DF, p-value: 8.2732e-09#4:Time-fixed effects model
fixed.time <- plm(GDP_percapita ~ GDS_Res_devel + FDI_netinflows+net_export+factor(year), data=mydata, index=c("country","year"), model="within")
summary(fixed.time)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = GDP_percapita ~ GDS_Res_devel + FDI_netinflows +
## net_export + factor(year), data = mydata, model = "within",
## index = c("country", "year"))
##
## Balanced Panel: n = 9, T = 22, N = 198
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -10.14876 -0.98740 -0.10327 0.93880 6.05823
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## GDS_Res_devel -0.173232 0.962814 -0.1799 0.8574344
## FDI_netinflows 0.167115 0.027017 6.1856 4.704e-09 ***
## net_export 0.088673 0.023075 3.8429 0.0001732 ***
## factor(year)2001 -3.461052 1.007083 -3.4367 0.0007452 ***
## factor(year)2002 -2.373839 1.004552 -2.3631 0.0192884 *
## factor(year)2003 -1.787673 1.008989 -1.7717 0.0782822 .
## factor(year)2004 0.115139 1.013168 0.1136 0.9096592
## factor(year)2005 -1.065914 1.005158 -1.0604 0.2904923
## factor(year)2006 -1.023189 1.008449 -1.0146 0.3117742
## factor(year)2007 -1.856284 1.010723 -1.8366 0.0680697 .
## factor(year)2008 -4.585767 1.019484 -4.4981 1.288e-05 ***
## factor(year)2009 -8.094483 1.028011 -7.8739 4.347e-13 ***
## factor(year)2010 -1.558586 1.028402 -1.5155 0.1315488
## factor(year)2011 -1.787124 1.042041 -1.7150 0.0882184 .
## factor(year)2012 -4.192751 1.052198 -3.9848 0.0001012 ***
## factor(year)2013 -3.623479 1.059038 -3.4215 0.0007852 ***
## factor(year)2014 -2.825941 1.076867 -2.6242 0.0094997 **
## factor(year)2015 -1.333195 1.072754 -1.2428 0.2157131
## factor(year)2016 -3.873575 1.060959 -3.6510 0.0003503 ***
## factor(year)2017 -1.180737 1.079095 -1.0942 0.2754657
## factor(year)2018 -2.166083 1.102068 -1.9655 0.0510383 .
## factor(year)2019 -2.613205 1.132201 -2.3081 0.0222363 *
## factor(year)2020 -8.104304 1.149955 -7.0475 4.719e-11 ***
## factor(year)2021 1.744280 1.145843 1.5223 0.1298561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2163.3
## Residual Sum of Squares: 747.81
## R-Squared: 0.65432
## Adj. R-Squared: 0.58727
## F-statistic: 13.0131 on 24 and 165 DF, p-value: < 2.22e-16Section 2: Model diagnostics. Which model is the best for our data.
#(i) Pooled vs Random
Breusch-Pagan Lagrange Multiplier for random effects. Null is no panel effect (i.e. OLS better).
plmtest(pooled, type = c("bp"))##
## Lagrange Multiplier Test - (Breusch-Pagan)
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export
## chisq = 5.6663, df = 1, p-value = 0.01729
## alternative hypothesis: significant effectsHere we reject the null and conclude that random effects is appropriate. This is, no evidence of significant differences across countries, therefore we could run a simple OLS regression if were to choose between the two. We need to compare OLS to fixed and see which one is more appropriate.
-OLS wins
#(ii) pooled vs fixed
#After constructing an OLS model, we can also run a pFtest to see which is the better fitted model.
#The null hypothesis of the pFtest is OLS is better than fixed.
pFtest(fixed, pooled)##
## F test for individual effects
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export
## F = 3.8105, df1 = 8, df2 = 186, p-value = 0.0003613
## alternative hypothesis: significant effectsReject the null, we go for fixed. -fixed effect model wins
#(iii) Random vs fixed
phtest(fixed, Random)##
## Hausman Test
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export
## chisq = 16.913, df = 3, p-value = 0.0007366
## alternative hypothesis: one model is inconsistentWe use fixed since p<0.05.
-Fixed model wins
#(iv) Fixed-time effecs model vs fixed
The null is that no time-fixed effects are needed: We conduct two tests for consistency.
#Test 1
pFtest(fixed.time, fixed)##
## F test for individual effects
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export + ...
## F = 10.433, df1 = 21, df2 = 165, p-value < 2.2e-16
## alternative hypothesis: significant effectsp-value<0.05 .We reject null. We need to use time-fixed effects model(fixed.time)
#Test 2
plmtest(fixed, c("time"), type=("bp"))##
## Lagrange Multiplier Test - time effects (Breusch-Pagan)
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export
## chisq = 162.47, df = 1, p-value < 2.2e-16
## alternative hypothesis: significant effectsp-value<0.05 .We reject null. We need to use time-fixed effects model(fixed.time). It is consistent with test 1.
Section 3: Checking model assumptions(fixed time effects model)
#a) Cross-sectional dependence testing:
#H0: The null is that there is no cross-sectional dependence
pcdtest(fixed.time, test = c("cd"))##
## Pesaran CD test for cross-sectional dependence in panels
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export + factor(year)
## z = -1.7352, p-value = 0.08271
## alternative hypothesis: cross-sectional dependenceSince p_value > 0.05,we fail to reject the null. This means that there is no cross-sectional dependence.
-In our diagnostics, we will use the time-fixed effect model as we have chosen it as the most appropriate
b) Serial correlation testing
Serial correlation tests apply to macro panels with long time series. Not a problem in micro panels (with very few years
#H0) The null is that there is not serial correlation.
pbgtest(fixed.time)##
## Breusch-Godfrey/Wooldridge test for serial correlation in panel models
##
## data: GDP_percapita ~ GDS_Res_devel + FDI_netinflows + net_export + ...
## chisq = 37.259, df = 22, p-value = 0.02215
## alternative hypothesis: serial correlation in idiosyncratic errorsSince p-value < 0.05, we reject the null and conclude that there is serial correlation.
c) Unit roots/stationarity testing
#H0) The null hypothesis is that the series has a unit root (i.e. non-stationary)
library(tseries)
adf.test(mydata$GDP_percapita, k=2)## Warning in adf.test(mydata$GDP_percapita, k = 2): p-value smaller than printed
## p-value##
## Augmented Dickey-Fuller Test
##
## data: mydata$GDP_percapita
## Dickey-Fuller = -6.2306, Lag order = 2, p-value = 0.01
## alternative hypothesis: stationarySince p-value < 0.05, we conclude that the series does NOT have unit root. In other words, the series is stationary.
d) Heteroskedasticity testing
#H0:The null hypothesis for the Breusch-Pagan test is homoskedasticity
library(lmtest)
bptest( GDP_percapita ~ GDS_Res_devel+ factor(country), data = mydata, studentize=F)##
## Breusch-Pagan test
##
## data: GDP_percapita ~ GDS_Res_devel + factor(country)
## BP = 90.161, df = 9, p-value = 1.511e-15Because p-value < 0.05, we reject Ho; We detect heteroskedasticity
#Section 4: coefficient estimations and significance
# Original coefficients
coeftest(fixed.time)##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## GDS_Res_devel -0.173232 0.962814 -0.1799 0.8574344
## FDI_netinflows 0.167115 0.027017 6.1856 4.704e-09 ***
## net_export 0.088673 0.023075 3.8429 0.0001732 ***
## factor(year)2001 -3.461052 1.007083 -3.4367 0.0007452 ***
## factor(year)2002 -2.373839 1.004552 -2.3631 0.0192884 *
## factor(year)2003 -1.787673 1.008989 -1.7717 0.0782822 .
## factor(year)2004 0.115139 1.013168 0.1136 0.9096592
## factor(year)2005 -1.065914 1.005158 -1.0604 0.2904923
## factor(year)2006 -1.023189 1.008449 -1.0146 0.3117742
## factor(year)2007 -1.856284 1.010723 -1.8366 0.0680697 .
## factor(year)2008 -4.585767 1.019484 -4.4981 1.288e-05 ***
## factor(year)2009 -8.094483 1.028011 -7.8739 4.347e-13 ***
## factor(year)2010 -1.558586 1.028402 -1.5155 0.1315488
## factor(year)2011 -1.787124 1.042041 -1.7150 0.0882184 .
## factor(year)2012 -4.192751 1.052198 -3.9848 0.0001012 ***
## factor(year)2013 -3.623479 1.059038 -3.4215 0.0007852 ***
## factor(year)2014 -2.825941 1.076867 -2.6242 0.0094997 **
## factor(year)2015 -1.333195 1.072754 -1.2428 0.2157131
## factor(year)2016 -3.873575 1.060959 -3.6510 0.0003503 ***
## factor(year)2017 -1.180737 1.079095 -1.0942 0.2754657
## factor(year)2018 -2.166083 1.102068 -1.9655 0.0510383 .
## factor(year)2019 -2.613205 1.132201 -2.3081 0.0222363 *
## factor(year)2020 -8.104304 1.149955 -7.0475 4.719e-11 ***
## factor(year)2021 1.744280 1.145843 1.5223 0.1298561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#arellano - both heteroskedasticity and serial correlation are present. Recommended for fixed effects.
# Heteroskedasticity consistent coefficients (Arellano)
coeftest(fixed, vcovHC(fixed.time, method = "arellano"))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## GDS_Res_devel -2.3240319 0.8014973 -2.8996 0.004186 **
## FDI_netinflows 0.1853229 0.0095512 19.4031 < 2.2e-16 ***
## net_export 0.1018067 0.0412928 2.4655 0.014589 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Considering the data provided, we conclude that Gross domestic spending on R&D is negatively correlated with GDP per capita growth (annual %). 1 percent increase in Gross domestic spending on R&D decreases annual GDP per capita growth by -2.32 % with p-value of 0.004186 .This result is statistically significant at 5% significant level since p-value < 0.05.