Task 1

1. What is their data source? How do their sample differ? Which countries do they exclude? Do they include multiple observations of each country, or just single observation?

  1. The data from the first part “The textbook Solow model” is the Real National Accounts recently constructed by Summers and Heston [1988]. In the second part, they begin with data on the fraction of the eligible population (aged 12 to 17) enrolled in secondary school, which they obtained from the UNESCO yearbook. “Endogenous growth and convergence” is the third part which involves data from Table III, Table IV, Table V, Figure I and Table VI.
  2. To understand the relation between saving, population growth, and income, the samples must go beyond the textbook Solow model. Therefore, they augment the Solow model by including accumulation of human as well as physical capital.
  3. They consider three samples of countries, the most comprehensive consists of all countries for which data are available other than those for which oil production is the dominant industry. This sample consists of 98 countries. They exclude the oil producers because the bulk of record GDO for these countries represents the extraction of existing resources, not value added. Their second sample excludes countries whose data receive a grade of “D” from Summers and Heston or whose populations in 1960 were less than one million. Summers and Heston use the “D” grade to identify countries whose real income figure are based on extremely little primary data; measurement error is likely to be a greater problem for these countries. They omit the small countries because the determination of their real income may be dominated by idiosyncratic factors.
  4. Depends on the question is about number of observations or the angle to observation. If it is about numbers, the sample has a large number of countries to observe so that is not much specific details of each countries. And if it asked the angle of the observation, yes, the sample have many types of data involved, such as R square, p-value.

2. The authors make an identifying assumption when estimating the parameters of an un-augmented Solow model. What are their assumptions?

The assumption made by the authors is that technological progress/ growth in technology (g) and depreciation (d) are constant across countries. This is because they believe that technological progress, stemming from the advancement of knowledge , to not be country specific. And the lack of data to estimate the depreciation rates of specific countries, and the unlikelihood of large variations in these rates across country’s is the reason for the second assumption.

3. Can you think of a good reason that population growth would be correlated with the technology available to a country?

If we assume technology creating researchers to be a fixed percentage of a population, the faster the growth in a population, the larger the amount of researchers operating in the country. The more researchers there are in a country, the greater the technological output.

4. How do the authors augment the model to include human capital? Does it help?

As the measurement of human capital is practically difficult, the authors include human capital in the model by restricting their focus to human capital investment (education). The authors measure human-capital accumulation by using a proxy (the variable ‘SCHOOL’) which measures the approximate percentage of the working-age population in secondary school. According to Table II, the inclusion of human capital in the model helps by eliminating anomalies, notably the high coefficients on investment and population growth that are present in the un-augmented Solow model.

5. Does conditional convergence hold?

After testing the model it was found that there was conditional convergence, particularly in income per capita when the variables (population growth and savings rate) that determine steady state in the Solow model are controlled.

Task 2

Part 1

Estimating the depreciation rate in Australia 
library(readr); library(dplyr)
## 
## 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
inv <- read_csv("Investment.csv")
inv2 <- inv %>% arrange(n():1)

dep <- function(depreciation, series, finalvalue){
    objective <- finalvalue - sum(series/((1+depreciation)^(0:(length(series)-1))))
    abs(objective)
}

optim(0.07, dep, lower = 0, upper = 0.2, series = inv2$Investment/1000, finalvalue = 5096, method = "Brent")
## $par
## [1] 0.01501594
## 
## $value
## [1] 0.0002315994
## 
## $counts
## function gradient 
##       NA       NA 
## 
## $convergence
## [1] 0
## 
## $message
## NULL
library(readr); library(dplyr); library(ggplot2); library(reshape2)
## Warning: package 'reshape2' was built under R version 3.2.2
delta <- 0.041
K <- 5096.3
inv <- inv$Investment
kdiff <- function(delta, inv, K){
  
  t <- length(inv)
  
  khat <- sum(inv/((1+delta)^(0:(t-1))))
  
  kdiff <- abs(K - khat)
  
  return(kdiff) 
  
}

Depreciation rate is found to be 4.1%.

Part 2

Balanced growth output in Australia

Part 3

A labour force shock 
library(readr); library(dplyr); library(ggplot2); library(reshape2)

k <- rep(NA, 200)
y <- rep(NA, 200)
y1<- rep(NA,200)
k1<- rep(NA,200)


s <- 0.25
delta <- 0.05
alpha <- 0.4
n <- 0.02
n1 <- 0.02*0.97

k[1] <- 1
k1[1] <- 1

for (t in 2:200) {y[t] <- k[t-1]^alpha
  k[t] <- (1-delta-n)*k[t-1]+s*y[t]}

for (t in 2:200) {y1[t] <- k1[t-1]^alpha
  k1[t] <- (1-delta-n1)*k[t-1]+s*y[t]}



data.frame(t = 1:200, k1, k) %>% melt(id = "t") %>% 
  ggplot(aes(x = t, y = value, colour = variable)) +
  geom_line() +
  ylim(0, 10)

The event effect large number of healthy adults are removed from the labor force. The labor force participation rate decreases by 3 per cent, so the weighted average of labor might decrease, and the output growth will decrease. Since labor force decrease, the output per worker might decrease as well.

Since the total output decrease, the output per person will decrease gradually. Even though those unhealthy adults jump out the labor force, but the population number still maintain the same.

The unhealthy children might affect the education level, in somehow to effect the technical progress and some sorts of endogenous factors. In this model which is B, the Hick-neutral productivity might decline, also effect output slow down.