Nicholas Russell, Matthew Kourlinins, Nicola Simpson, Jack Nguyen
#select libraries to use within test
library(dplyr); library(ggplot2)
##
## Attaching package: 'dplyr'
##
## The following objects are masked from 'package:stats':
##
## filter, lag
##
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
#open data set pwt71.csv in R studio, and name data set pwt
pwt <- read.csv("pwt71.csv")
#filter the data of pwt to only include years more recent or equal to 1985,
#group all data together for each nation, summarise this grouped data to give population growth,
#investment share of ppp, and the ppp converted gdp per capita in 2010
pwt.ss <- pwt %>% filter(year>=1985) %>%
group_by(isocode) %>%
summarise(n = log(last(POP)/first(POP))/n(),
Inv = mean(ki)/100,
y = last(y)) %>% filter(!is.na(Inv))
#test plot the data set pwt.ss
qplot(Inv, n, data = pwt.ss)
pwt.ss %>% ggplot(aes(x = Inv)) +
geom_density()
#create a new data set by working out the log of required numbers, as well as including g and delta
g <- 0.03
delta <- 0.02
pwt.ss2 <- pwt.ss %>%
mutate(lnS = log(Inv),
lnY = log(y),
lnNGD = log(n + g + delta))
#create a linear model using the natural log of investment plus the natural log of n + g + delta
linear_model <- lm(lnY ~ lnS + lnNGD, data = pwt.ss2)
#view data created with model through summary
summary(linear_model)
##
## Call:
## lm(formula = lnY ~ lnS + lnNGD, data = pwt.ss2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.58394 -0.74338 -0.00635 0.64977 3.06547
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.9330 1.5663 -5.703 5.73e-08 ***
## lnS 1.0019 0.1928 5.198 6.24e-07 ***
## lnNGD -4.8203 0.5439 -8.863 1.67e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.002 on 156 degrees of freedom
## Multiple R-squared: 0.4467, Adjusted R-squared: 0.4396
## F-statistic: 62.98 on 2 and 156 DF, p-value: < 2.2e-16
#create a non-linear model from data set pwt.ss2, then set value of alpha for equation to 0.4
nonlinear_model <- nls(lnY ~ (alpha/(1-alpha)) * lnS - (alpha/(1-alpha)) * lnNGD,
data = pwt.ss2, start = list(alpha = 0.4))
#view data created with model through summary
summary(nonlinear_model)
##
## Formula: lnY ~ (alpha/(1 - alpha)) * lnS - (alpha/(1 - alpha)) * lnNGD
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## alpha 0.683072 0.007119 95.96 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.152 on 158 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 6.132e-10
#create second non-linear model from data set pwt.ss2, then set value of alpha for equation to 0.4 and A to 1
linear_model2 <- nls(lnY ~ log(A) + (alpha/(1-alpha)) * lnS - (alpha/(1-alpha)) * lnNGD,
data = pwt.ss2, start = list(A = 1, alpha = 0.4), control = nls.control(warnOnly = T))
#view data created with model through summary
summary(linear_model2)
##
## Formula: lnY ~ log(A) + (alpha/(1 - alpha)) * lnS - (alpha/(1 - alpha)) *
## lnNGD
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## A 2.22427 0.54212 4.103 6.54e-05 ***
## alpha 0.61202 0.02847 21.499 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.118 on 157 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.125e-08