Task I - Read and Respond to Mankiw, Romer & Weil

Read Mankiw, Romer & Weil’s (1992) A Contribution to the Empirics of Economic Growth answer the following questions, accordingly.

(i) What is their data source? How do their samples differ? Which countries do they exclude? Do they multiple observations of each country, or just a single observation?

Mankiw, Romer and Weil (1992, p. 412) idenitfy the ‘Real National Accounts’ from Summers and Heston (1988) as their data source. This data set, as Mankiw, Romer and Weil (1992, pp. 412-413) suggests, includes: real income, government and private consumption, investment, and population for almost all of the world other than the centrally planned economies.

They consider three sample 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. We exclude the oil producers because the bulk of recorded GDP for these countries represents the extraction of existing resources, not value added; one should not expect standard growth models to account for measured GDP in these countries.

The second sample excludes countries whose data receive a grade of “D” from Summers and Heston (1988) or whose populations in 1960 were less than one million. Summers and Heston (1988) use the “D” grade to identify countries whose real income figures are based on extremely little primary data; measurement error is likely to be a greater problem for these countries. We omit the small countries because the determination of their real income may be dominated by idiosyncratic factors. This sample consists of 75 countries.

The third sample consists of the 22 OECD countries with populations greater than one million. This sample has the advantages that the data appear to be uniformly of high quality and that the variation in omitted country-specific factors is likely to be small. But it has the disadvantages that it is small in size and that it discards much of the variation in the variables of interest.

(ii) The authours make an idenitifying assumption when estimating the parameters of an un-augmented Solow model. What are their assumptions?

Solow’s model gives simple testable predictions about how savings and population growth rates variables influence the steady-state level of income. The higher the rate of saving, the richer the country. The higher the rate of population growth, the poorer the country.

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

Population growth would be correlated with the technology available to a country because the higher the number of people the more demand for technology per person.

(iv) How do the authors augment the model to include human capital? Does it help?

They first expand the Solow model of Section I to include human capital. We show how leaving out human capital affects the coefficients on physical capital investment and population growth. We then run regressions analogous to those in Table I to see whether proxies for human capital can resolve the anomalies found in the first section.7

They concluded that adding human capital to the Solow model improves its performance. Allowing for human capital eliminates the worrisome anomalies-the high coefficients on investment and on population growth in our Table I regressions-that arise when the textbook Solow model is confronted with the data. The parameter estimates seem reasonable. And even using an imprecise proxy for human capital, we are able to dispose of a fairly large part of the model’s residual variance.

We find that accumulation of human capital is in fact correlated with saving and population growth. Including human-capital accumulation lowers the estimated effects of saving and population growth to roughly the values predicted by the augmented Solow model.

(iv) Does conditional convergence hold?

Overall, the interpretation of the evidence on convergence contrasts sharply with that of endogenous-growth advocates. In particular, they believed that the study of convergence does not show a failure of the Solow model. After controlling for those variables that the Solow model says determine the steady state, there is substantial convergence in income per capita. Moreover, convergence occurs at approximately the rate that the Solow model predicts.

Task II - Part A - Estimating the Depreciation Rate in Australia

(i) Source data on real (Chain volume measures) investment in Australia.

We sourced Australia’s capital investment data from ABS (2014). Refer to Table 2 ‘Expenditure on Gross Domestic Product (GDP)’, column AK ‘All sectors ; Gross fixed capital formation: Chain volume measures’, rows 11 (i.e., Jul-1960) to 65 (i.e., Jul-2014). See below for a graph illustrating the historical movements in Australia’s annual capital investment since 1960 - units in $ Billions.

(ii) Source the current value of non-financial capital stock in Australia.

As of 1 July 2014, the current value of non-financial capital stock in Australia, i.e., current capital (\(\kappa\)), is 5,096.3 - units in $ Billions. Note, this figure is sourced from ABS (2014). Refer to Table 10 ‘National Balance Sheet, Volume/Real and current prices - as at 30 June’, column D ‘Non-financial - Produced assests: Volume measures’, row 65.
\[\kappa = 5096.3\]

(iii) Estimating the depreciation rate in Australia.

Given the values for real investment and the current value of non-financial capital stock in Australia, we are able to estimate the depreciation rate. We know that if there were no depreciation, the current value of non-financial capital would simply be the sum of real historical investment. However, given the existence of depreciation, to estimate, we must caluclate and optimise the absolute difference between the observed non-financial capital stock and the estimated capital stock using the following formula: \[remaining capital_{t}= \sum_{s=0}^t \frac{Investment}{(1+\delta)^{s}}\]

library(dplyr); library(readr)
## 
## 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
setwd("~/Documents/Uni/Subjects/Economics/ECO3EGS/Week 3/ABS Data")


hist_inv <- read.csv("Investment.csv")
hist_inv2 <- hist_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 = hist_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

(iv) What is the depreciation rate?

The function estimates the depreciation rate in Australia to be 0.0411923, or 4.1%, using the ABS data.

Task II - Part B - Balanced Growth Output in Australia

(i)

We need to parameterise an Australian model.

(ii)

Get \(\alpha\) (i.e., the capital share) from the 5204 income account. WHat is gross mixed income? Is it capital income or labour income?

Gross mixed income is defined as the income earned by unincorporated entities - sole traders and partnerships. This measure is composed of both labour and capital income.

From the paper titled “Labour’s Share of Income in Growth and Prosperity”, written by the Australian Government Productivity Commission, we take the respective shares of labour and capital income to be 55% and 45%.

alpha <- 0.45

# alpha = 45%

(iii)

Get \(s\) from the expenditure accounts. Note that because Australia imports a lot of capital, take this to be the ratio of investment to GDP. Using the average value for the last five years.

Inv5 <- c(365284, 379094, 422600, 430844, 424279)  
MeanInv <- mean(Inv5)

GDP5 <- c(1397902, 1430354, 1483675, 1520944, 1559662)
MeanGDP <- mean(GDP5)

s <- MeanInv/MeanGDP

# s = 27%

(iv)

Take \(n\) to be the growth rate of the labour force (Cat. 6202). Note that we were taking this to be a single parameter - now let it vary over time (just as our savings did last time).

LForce2014 <- 11567.1137321
LForce2015 <- 11810.7060787
GrowthRate <- (LForce2015 - LForce2014)/LForce2015
n <- GrowthRate

# n = 2%

(v)

Let \(g = 0.016\) Let \(\delta = 0.041\) #g <- 0.016 #delta <- 0.041

(vi) What is the steady state output per worker in 2015?

\[k^{*} = \left( \frac {0.27}{0.041+0.02+0.016} \right)^\frac {1}{1-0.45}\] \[y^{*} = ({k^{*}})^.45\]

kappa <- (s/g+n+delta)^(alpha)
y <- kappa^alpha
retur(y)
[1] 1.778183

Steady state output per worker in 2015 is 1.78

(vii) What is the steady state output per person in 2015?

Steady state output per person can be calculated by multiplying output per worker by the labour force patricipation rate, 65% (ABS)

yPP <- y*0.65
return(yPP)
[1] 1.155819

Output per person in 2015 is calculated as 1.155

Task II - Part C - A Labour Force Shock

Because of yupsters [sic] vaccingating their children, Australia has a polio epidemic and a large number of healthy adults are ‘removed’ from the labour force. The labour force participation rate decreases by 3 percent, permanently.

(i) What Happens to outout per worker?

Output per worker increases as the same amount of capital is spread across a smaller labour force.

(ii) What happens to output per person?

If by ‘removed’ we are to assume the affected percentage of the population is removed from the labour force but remains alive, then output per person will decrease, as output decreases but population remains constant.

If we are to assume ‘removed’ implies a cessation of the existence of the affected percentage of the population, then output per worker will still decrease, however by a smaller amount than under the first assumption. This is because both output and population will decrease.

(iii) What happends to the children?

It is highly likely that the children will experience a reduced standard of living, given the fall in output, and face an increased prospect of a painful, painful death.

NB: Extension granted by Jim Savage on 17/08/15

Bibliography

Australian Bureau of Statistics 2014, Australian System of National Accounts, 20013-14, cat no. 5204.0, ABS, Canberra.

Australian Bureau of Statistics 2015, Labour Force, Australia, Jul 2015, cat no. 6202.0, ABS, Canberra.

Jones, CI & Vollrath, D 2013, Introduction to Economic Growth, 3rd edn, W. W. Norton & Company, New York.

Mankiw, NG, Romer, D & Weil, DN 1992, ‘A Contribution to the Empirics of Economic Growth’, The Quarterly Journal of Economics, vol. 107, no. 2, pp. 407-437.

Solow, R 1957, ‘Change and the Aggregate Production Function’, The Review of Economics and Statistics, vol. 39, no. 3, pp. 312-320.

Summers, R & Heston, A 1988, ‘A New Set of International Comparisons of Real Product and Price Level Estimates for 130 Countries, 1950-85’, Review of Income and Wealth, vol. 34, no. 1, pp. 1-26.