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Assignment #1 : Due Sunday, Sept. 3rd (11:59PM)
Download the data in the file titled “Assignment1PWTDataSet.xlsx”. Consider
the Solow model with both population growth and technological progress. In this
assignment you will use the data set from the Excel spreadsheet and, taking the
equations of the Solow model (overly) seriously, (i) back out the difference between
imputed savings rates for the Australian economy and the optimal savings rate as
implied by the Solow model, (ii) construct the difference between the observed level
of consumption per worker and the golden rule level of consumption per worker and
(iii) construct and plot a time-series for output per effective worker.
In conducting the exercise, you will be ignoring data about the amount of govern ment consumption and investment as well as net exports. This is because the model
that has been covered in class also neglects these features. Thus, you don’t want to
take the results too seriously. The point of this exercise is to see how economists
can use data with their models but also to appreciate the limitations that modelling
assumptions can impose on the resulting implications.
For this assignment, assume that the aggregate production function is represented
by a Cobb-Douglas form,
Yt = Kt
α
(AtNt)
1 α
where Yt
is output, Kt
is the period t capital stock, At
is a measure of the level
of technology or productivity in period t, and Nt
is employment during period t.
Capital’s share of output (if we think about the economy as characterized by perfectly
competitive, classical economics assumptions) is given by α and labour’s share of
output is 1 α.
For simplicity, use the continuous-time model’s equations even though you are
using annual data. As you carry out the instructions below, ensure that you are
storing the data in the correctly identified columns and rows. Failure to do so will
likely result in mark deductions. When constructing capital’s share, growth rates
and savings rate data, do not multiply by 100. This ensures that 1 s is not a large
negative number and that n and g are in similar scale as the savings rate.
1. Copy the data (including headings) to sheet one of a new Excel workbook. You
should have columns A through G and rows 1 through 68 filled with data. Row 1
is occupied by headings and Rows 2 through 68 are comprised of data spanning
the years 1953 through 2019.
2. Using data on the capital stock (see legend) construct a measure of investment
for the years 1954 through 2019. To do so, you will need to calculate the
change in the capital stock between each consecutive year and add the amount
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of depreciation that occurs. Total depreciation over a year can be constructed
by multiplying the size of the capital stock from the preceding year by the rate
of depreciation for the current year. This amounts to taking the model’s capital
accumulation equation literally to back out a time-series for investment given a
time series for the capital stock and the depreciation rate of capital. Save this
imputed investment data in a column H and label it “I(t) : Imputed I” in your
spreadsheet.
3. Construct an output measure for each year by adding your constructed measure
of investment to the time-series for consumption that is included in the data
set (Yt = Ct + It). Save this output data in a column I of your spreadsheet and
label it Y = C + I.
4. Construct the annual growth rate of the labour force, nt
, by calculating the
growth rate of the labour force of each year between 1954 through 2019. Save
this data in column J of your spreadsheet labelled “n(t) : emp growth rate”.
5. For simplicity, construct the constant population growth rate, n, as the average
of the population growth rates between 1954 and 2019. Populate rows 3 through
68 of column K in your spreadsheet with this value of n replicated for each year
and in cell K1 label this column as “Ave n”.
6. Using the Solow model’s equation relating output to investment along with your
constructed output and investment data, back out a time-series featuring each
year’s savings rate from 1954 through 2019. Store this data in a column L of
your spreadsheet labelled “s(t) : Imputed Savings Rate”.
7. Calculate the average of the imputed savings rates. Fill rows 3 through 68 of
row M with this number. Label this column “s: Ave savings rate”.
8. Assume that the labour share data included in the data set represents 1 αt
for each period. Construct a time-series for capital share, αt
, for each year from
1954 through 2019. Store this data in column N of your spreadsheet and label it
“Imputed Capital Share”. The constructed data should occupy rows 3 through
68.
9. Calculate the average of the imputed capital share data. Fill rows 3 through
68 of column O in your spreadsheet with this average value of the capital share
repeated for every year. Label this column “Ave Capital Share”.
10. You now need to construct a measure for the rate of techonological progress,
g, from the model. To do so, use the equation above for the Cobb-Douglas
production function along with your data from columns I, D, E, G and N to
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create a time series for At
for each year from 1954 through 2019. Put this data
in rows 3 through 68 of column P and label this column “Imputed TFP”.
11. Use the Imputed TFP data of column P to construct the growth rate of TFP
for every year from 1955 through 2019 and store this data in rows 4 through 68
under column Q of your spreadsheet. Label this column “TFP Growth Rate”.
12. Calculate the average growth rate of TFP from column Q. Fill rows 3 through
68 of column R with this number. Label column R “Ave TFP Growth Rate”.
(Note that you are assuming that g is constant over time and hence are using
it for row 3 too.)
13. Take the average value of the depreciation rate data of column F (column F is
labelled “delta”). Fill rows 3 through 68 with this number and label column S
“Ave Delta”.
14. Now we can have some fun. Label column T, “Optimal s – Savings Rate”.
Using what you know about the Solow growth model with population growth
and technological progress, along with the Cobb-Douglas production function,
calculate the savings rate that maximizes steady state consumption per effective
worker. Then using this optimal savings rate, fill out rows 3 through 68 of
column T by taking the difference between this optimal savings rate and your
time-series for the imputed savings rate (column L) for each year spanning 1954
through 2019.
15. Plot the data in column T (vertial axis) against the years of the corresponding
observations (horizontal axis).1 Title the plot “Optimal s – Savings Rate”. (5
Marks)
16. Given the data in your spreadsheet, construct a time-series for consumption
per effective worker for every year between 1954 and 2019. Place this data in
column U under the label “Consumption per Effective Worker”.
17. Assume that the data that you have constructed by taking averages represent
steady state values. For example, the average employment growth rate can be
used to represent the steady state employment growth rate of the Solow model,
the steady state depreciation rate can be viewed as the steady state depreciation
rate of the capital stock, etc. Calculate the golden rule steady state capital stock
per effective worker. Fill rows 3 through 68 of column V with this number and
label the column “Golden Rule Capital Stock per Effective Worker”.
1There are plenty of YouTube videos explaining how to label axes of Excel plots.
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18. Construct the golden rule steady state level of output per effective worker and
populate rows 3 through 68 of column W with this number. Label column W
“Golden Rule Output per Effective Worker”.
19. Construct the golden rule steady state level of consumption per effective worker
and populate rows 3 through 68 of column X with this number. Label column
X “Golden Rule Consumption per Effective Worker”.
20. Calculate the difference between consumption per worker and the optimal level
of consumption “per worker” using the data that you have constructed in your
spreadsheet. Store the results in column Y under the label “Consumption per
Worker – Optimal C per Worker”. Plot this difference in a line graph with the
horizontal axis featuring the year and the vertical axis measuring the data in
column Y.
21. Using the data for Y = C + I that you constructed along with the employment
data and imputed TFP data, construct a time-series for output per effective
worker for each year between 1954 and 2019. Plot this data in a line plot
featuring the year of observation on the horizontal axis and output per effective
worker on the vertical axis. Does it look like Australia shifted from one steady
state to another during this period If so, how would this affect your steady
state calculations above Type your answer at the bottom of the spreadsheet
below your data plots.
Ensure that your plots do not overlap with the data on your spreadsheet. Simply
drag your plots so that they sit below the data on your spreadsheets. Marks will be
distributed across the construction of the numerous columns.
Submit your Excel workbook through course MyUni site. Label the
filename as studentname studentID.xlsx. For example, JoeSmith a1234567.xlsx.
Remember, don’t take these numbers seriously but do take the exercise as a useful
learning experience. Have fun and learn something!
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