Task One: A contribution to the empirics of economic growth (Mankiw, Romer & Weil 1992)

The data source is The Real National Accounts which was constructed by Summers and Heston in 1988. It is annual observations for the period 1960 - 1985.

The samples differ with countries included. One includes 98 countries, excepting Oil Producing economies due to their GDP resulting primarily from extraction of existing natural resources. The second sample excludes countries with populations of less than 1 million or who have a low rating for data quality and increased likelihood of measurement error resulting in 75 countries in the sample. The third sample consists of OECD countries with populations greater than 1 million. Data from the 22 countries in the sample is uniformally high and discrepancies in country specific factors is likely to be small, a drawback is that the sample is relatively small compared to the other 2 samples used.

The samples include multiple observations of each country including real income, government and private consumption, investment and average growth of the population of working age. The same country can be found in more than 1 sample. The first stratified in samples 2 & 3 to look at the effects of population growth and savings on income per capita.

The authors make the identifying assumption of permanent differences in the levels of technology and that rates of savings and population growth are independent of country specific factors, such as a country specific market shock, inflation or changes in fiscal policy.

The \(A(0)\) term reflects not just technology but resource endowments, climate and institutional structures that may be inherently unique to specific countries. Therefore the authors assume:

\[lnA(0)=\alpha+\epsilon\]

Where \(\alpha\) is a constant and \(\epsilon\) is a country-specific shock.

Population growth is positively correlated with the technology available to the country because with increasing population growth comes increases in the labour force and the numbers of people working in research. The positive externality of the creation of research increases the rate and number of new ideas created and thereby technological innovation. This increases the level of human capital in a country and Total Factor Productivity. This is subject to diminishing returns.

However in countries with high population growth income per capita is lowered because the amounts of human and physical capital have to be distributed amongst more people.

The authors augment the model by assuming human capital depreciates at the same rate as physical capital and they assume decreasing returns to capital.

Solow Steady State Model: \[Y_t=K_t^\alpha(A_tL_t)^{1-\alpha}\]

Where \(0 <\alpha< 1\)

Mankiw, Romer & Weir Augmented Model \[Y_t=K_t^\alpha H_t^\beta(A_tL_t)^{1-\alpha-\beta}\]

Where \(H\) is the stock of human capital and \(\alpha+\beta<1\), implying decreasing returns to capital.

Previous authors have identified that human capital accumulation had a positive impact on growth and development. Azariadis and Drazen (1990) found that no country was able to grow quickly during the post-war period and Rauch (1988) finds that among countries that had achieved 95% adult literacy in 1960, there was strong evidence for income per capita to converge over the period of 1950-1985.

Also by adding growth in human capital to the Solow Equation, this gives an empirically more reasonable prediction about the rate of convergence between countries. Saving and population growth rates influence h*, which we find to be positively correlated with the savings rate and negatively correlated with population growth. Therefore omitting the human-capital term creates bias on the coefficients of saving and population growth. Using the example given on page 423, the Solow model predicts the economy would move to a steady state in about 17 years, with augmentation the model predicts an economy grows to a steady state in around 35 years.

The Solow model only allows for convergence where countries have the same savings and population growth rate. The authors control these factors that Solow prescribes as a steady state and show that conditional convergence does occur amongst countries with similar technologies, population growth and rates of accumulation.

Using the log difference in GDP per working-age person from 1960-1985 as the dependent variable, the authors ran a number of tests with and without controlling for investment, growth of working-age population and school enrollment.

Looking at Table III, we see that testing the initial level of income per capita in 1960 alone has almost no predictive power for the first two sample groups, showing that there is no tendency for poor countries to grow faster on average than rich countries. However it does show significant tendency toward convergence in the OECD sample with an \(R^2 = 0.46\).

Table IV shows the effect of adding their measure of rates of investment and population growth as 2 more independent factors into the model. The new variable further lowers the intercept coefficient and improves the fit of regression significantly across all three sample groups. Table V adds their measure of human capital onto the previous model and once again finds the coefficient of intercept is lowered and further improves fit of regression (now 0.46, 0.43, and 0.65)

Clearly there is evidence that if countries did not vary in their investment and population growth rates, there would be a strong tendency for poor countries to grow faster than rich ones. The authors conclude that differences in fiscal policy, government revenue policies, education policies, political stability and “tastes for children” or population growth rates are the factors exogenous to the model that are unexplained and affect a countries growth rate other that what is explained by the model.

Task Two

Part One: Estimating the Depreciation Rate in Australia

##Using Data Series 'All Sectors: Gross Fixed Capital Formation: Chain Volume Measures'

# value of Non-Financial - Produced Assets: Volume Measures 5096.3 billion - 2014/06/01

# function for depreciation rate 

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] 0.0411923
## 
## $value
## [1] 0.0001865847
## 
## $counts
## function gradient 
##       NA       NA 
## 
## $convergence
## [1] 0
## 
## $message
## NULL
delta <- 0.0411923
# This gives an Answer of 0.0411923 or a Depreciation Rate of 4.12%

Part Two: Balanced Growth Output in Australia

# Finding alpha - The Capital Share

#Taking information from National Balance Sheet.


GMI2014 <- 130748 #Gross Mixed income
GOS2014 <- 540302 #Gross Operating Surplus
GNI2014 <- 1546910 #Gross National Income

# Capital Share being the ratio of Gross Operating Surplus (The Production of Incorporated enterprises that is earned by Capital) and GRoss National Income less Gross Mixed Income.

alpha <- GOS2014/(GNI2014-GMI2014)

# The Capital Share is 0.3815256 or 38.152%

# finding S - Savings Rate
#finding the Mean of the last 5 values of the Gross Fixed Capital Formation:

GFCF2010 <- 365284
GFCF2011 <- 379094
GFCF2012 <- 422600
GFCF2013 <- 430844
GFCF2014 <- 424279

GFCFmean <- sum(GFCF2010, GFCF2011, GFCF2012, GFCF2013, GFCF2014)/5

# Mean of GFCF = 404420.2

#Finding mean of GDP - Last Five Values of the Gross Domestic Product
GDP2010 <- 1295727
GDP2011 <- 1407865
GDP2012 <- 1488028
GDP2013 <- 1520944
GDP2014 <- 1583557

GDPmean <- sum(GDP2010, GDP2011, GDP2012, GDP2013, GDP2014)/5

# The mean of GDP is 1459224

# S is the Ratio of Investment (Gross Fixed Capital Formation) to Output

s <- GFCFmean/GDPmean

# The saving Rate is 0.2771474 or 27.77%

# The Growth of the Labour Force by taking the mean of the Percentage change of the last four years.

n1 <- ((11790.9-11595.1)/11595.1) # Change between June 2010-2011
n2 <- ((11956.9-11790.9)/11790.9) # Change Between June 2011-2012
n3 <- ((12167.8-11956.9)/11956.9) # Change Between June 2012-2013
n4 <- ((12532.8-12167.8)/12167.8) # Change between June 2013-2014

n <- (n1+n2+n3+n4)/4

# N is 0.01965016


# The Growth Rate

g <- 0.016

# The Model


k <- rep(NA, 200)
y <- rep(NA, 200)
k[1] <- (s/(n + delta))^(1/(1-alpha))
for(t in 2:200){
  y[t] <- k[t-1]^alpha
  k[t] <- (1-delta-n)*k[t-1]+s*y[t]
}
plot.ts (k)

plot.ts (y)

# steady state y 2.548115

yworker <- 2.548115
ypop <- yworker*12569.6/23865.229  #Labour Force/Population

# Steady State per person is 1.342069

Part Three: A Labour Force Shock

nfall <- n*0.97
# the fall of 3% is 0.01906066

k1 <- rep(NA, 200)
y1 <- rep(NA, 200)
n5 <- rep(0.01906066, 200)
n5[1] <- n
k1[1] <- (s/(n5[t] + delta))^(1/(1-alpha))
for(t in 2:200){
  y1[t] <- k1[t-1]^alpha
  k1[t] <- (1-delta-n5[t])*k1[t-1]+s*y1[t]
}

plot.ts (k1)

plot.ts (y1)

# The new output per worker is 2.563466
yworkerfall <- 2.563466

ypopfall <- yworkerfall*12569.6/23865.229  #Labour Force/Population

# Steady State per person is 1.350154

# The Children will either be:
# a) crippled 
# b) dead
# c) able recover with no problems
# d) miraculously immune
# and Iron Lungs will dominate the landscape.
## Warning: Removed 2 rows containing missing values (geom_path).