Using statistical methods, we analyze the empirics of Economic Growth.

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University of Nevada, Las Vegas
Project 3:
Solow Growth Model
Jared Bilberry
Pat Mitchell
Carol Pineda
Summer Tran
ECON 495
Djeto Assané
19 November 2022
What Causes Economic Growth? A Breakdown of The Solow Growth Model

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Abstract
The purpose of this project is to introduce the empirics of economic growth based on the
Solow [3] model. In “A contribution to the Empirics of Economic Growth” (Quarterly
Journal of Economics Growth, May 1992), Mankiw, Romer and Weil (MRW), [2]
argue that “international differences in per capita income are best understood using an
augmented Solow growth model.” Furthermore, we are testing the hypothesis that poor countries
grow faster than rich countries in terms of per capita growth rate [1]. To replicate some of their
empirical results, we will use their data set covering the period 1960-1985, for non-oil producing
countries. Assume the following models, the Solow Model and the Augmented Solow Model (by
Mankiw, Romer and Weil), where the variables GDP85, IY, POPGR, and SCHOOL are GDP per
working-age person in 1985, investment as a percent of GDP, rate of population growth, and
percentage of the working-age population in secondary school for 1960-1985 respectively.

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(i) Introduction
The Solow Model and the augmented Solow Model by Mankiw, Romer and Weil are both
based on the assumption that the investment rate and the population growth rate are what
determines the long run steady state level of income in a country [2]. Solow’s original model
hypothesized that the investment rate and the rate of population growth have an inverse
relationship, which the augmented model also includes in their model [3]. Mankiw, Romer and
Weil take Solow’s original model one step further by adding in another variable, the
accumulation of human capital. Additionally, it is also seen in the original Solow model that a
country’s per capita growth rate has an inverse relationship with the starting level of income per
person [1].This variable is measured by looking at a proxy variable: the percentage of schooling
for the portion of the population eligible to work. This study aims to study the relationship
between the independent variables (population growth rate, investment as a percentage of GDP,
and the percentage of the eligible working-age population that has received secondary schooling)
and the dependent variable (GDP per working-age person in 1985). It does so by using data from
the time period 1960-1985. The reason we are doing this study is to find evidence for whether
our predictions about the independent variables and dependent variables are consistent with our
findings. Additionally, we are also looking to find out whether the signs of the relationships
between the dependent variable and each independent variable is consistent with our hypothesis
of how each independent variable has a positive relationship with the dependent variable. We
will use various tables and results in order to find out whether our hypothesis about the positive
impact of the independent variables on the dependent variable is correct. By extension, this will
also provide more evidence for the predictions originally posited by the Solow and augmented

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Solow model. We will also be testing whether there is a tendency for poor countries to converge
to rich countries in cases of both unconditional and conditional convergence.
(ii) Review of the Literature
This all starts with Robert M. Solow’s “A Contribution to the Theory of Economic
Growth”. Solow takes the Harrod-Domar model and introduces changes to the long-run growth
model which accepts all of the Harrod-Domar assumptions except that of fixed proportions,
instead supposing that the single composite commodity is produced by labor and capital under
the standard neoclassical conditions. N. Gregory Mankiw, David Romer and David N. Weil take
Solow’s model and argue in their paper, “A Contribution to the Empirics of Economic Growth”,
that, though the predictions of the Solow model are consistent with the evidence to a first
approximation, there are still issues with the model. The Solow model can correctly predict the
direction of the effect of saving and population growth, but it does not correctly predict their
magnitudes. Mankiw, Romer and Weil then created the augmented Solow model in an effort to
better understand the relation between saving, population growth and income by including
accumulation of human and physical capital to the model. In “Economic Growth in a Cross
Section of Countries” by Robert J. Barro, it is observed by Barro that in neoclassical models such
as Solow, Cass and Koopmans, there is an inverse relationship between a country’s per capita
growth rate and its starting level of income per person. There is a force that promotes
convergence across countries regarding their per capita income; when countries have similar
structural parameters for preferences and technology, poorer countries tend to grow faster than
richer countries. The result from this convergence is diminishing returns to reproducible capital
in neoclassical growth models.

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(iii) Model
The model we will be focusing on is LogGDP85 = + Log(IY) + Log(POPGR) +
β0
β1
β2
Log(SCHOOL) + ε. It examines the effect of the independent variables Log(IY),
β3
Log(POPGR) and Log(SCHOOL) on the dependent variable Log(GDP85). The expected signs
for each independent variable are positive besides Log(POPGR) as shown in table 1, meaning an
increase in any independent variable besides Log(POPGR) will also impact the dependent
variable in a positive manner. For Log(POPGR), we can imagine that as the growth rate of a
population increases the GDP per worker will fall or stay the same, this is because an increase in
the growth rate of population will lower the level of the steady state level of capital per worker,
therefore decreasing output per worker. With advancement in knowledge, this should increase
productivity and /or output per worker, which would be a positive. Finally, the rate of capital
depreciation would cause the capital per worker to decrease. However, overall you cannot tell
whether this would be positive or negative due to the positive and negative effects within Log
(POPGR). Log(IY) has a positive impact because investment is an increase in capital per
worker, so the more capital you have, the more output per worker you have as well. Thus, y = β0
+ + .
β1
𝑥 ϵ
Table 1:
______________________________________________________________________________
Variables: Definition Expected Signs
______________________________________________________________________________
Dependent Variable
LogGDP85 = GDP per working-age person in 1985

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Independent Variable
Log(POPGR) = population growth rate + advancement in knowledge + -
rate of capital depreciation
Log (IY) = investment as a percent of GDP +
Log(SCHOOL) = percentage of the working-age population in secondary +
school, average for 1960-1985
______________________________________________________________________________
(iv) Data and Descriptive Statistics
Table 2: Descriptive Statistics
Above is a table of the descriptive statistics relating to six of the variables involved in the
study. The first section of the table that is an important summary measure of the data is the mean.
The mean of our first variable GDP60 is 2994.898, which means that is the average gross
domestic product per working age person in 1960 from our dataset. The minimum value from
our dataset for GDP60 was 383 and the maximum value was 12,362. The second variable is
GDP85 and the mean was 5309.765, this indicates the average gross domestic product per
working age person in 1985 was much larger compared to 1960. The minimum value from our

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dataset for GDP85 was 412 and the maximum value was 19,723. The third variable from the
table above is the growth of gross domestic product and the mean was 3.99 which indicates that
on average each country’s gross domestic product grew 3.99 percent. For Gdpgr, the maximum
value from the data was 9.2 and the minimum was -.9. The fourth variable is Popgr and the mean
was 2.20, this means on average each country’s population grew 2.20 percent. For Popgr, the
maximum value from the data was 4.3 and the minimum was .3. The fourth variable is IY and
the mean was 17.67 which means each country invested roughly 17.67 percent of their GDP. The
minimum value for IY was 4.1 and the maximum value was 36.9. The last variable from our
table is School and its mean is 5.40, this indicates that on average 5.40 percent of the
working-age population was in secondary school from 1960 to 1985. For school, the maximum
value from the data was 11.9 and the minimum was .4.
There is another important summary measure to consider from the table above and that is
standard deviation. The larger the standard deviation of a variable the more spread out the data is
around the mean and the smaller the standard deviation the tighter the data is around the mean.
When it comes to the standard deviation of GDP60 and GDP85 it appears the standard deviation
is high for both and would infer the data is spread out far from the mean for each variable. The
standard deviation for Gdpgr and Popgr are both relatively small and this would indicate that the
data is tighter around the mean. The standard deviation for IY and SCHOOL is large, concluding
that the data is spread out far from the mean.

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Table 3: Matrix of Correlation Coefficients
Above is a table of the matrix of correlation coefficients. According to the data there is a
moderate inverse relationship between POPGR and GDP85 indicating that the more a population
rises the lower the GDP per worker will be. The correlation between GDP85 and IY is strong and
positive. This would indicate that the higher percentage of a country’s GDP that gets invested the
more it will improve a country's GDP in the long run. School has a strong positive correlation
with GDP85. Therefore, the more people who attend secondary school in a country, then the
higher the GDP per worker of that country will be. The signs of the coefficients are consistent
with our expectations of the coefficients. As previously stated; log((Popgr) has a negative affect,
log(IY) has a positive affect, and log(School) has a positive affect on log(GDP85) which matches
our expectations from Table 1.
Scatterplots: GDP85/Popgr, GDP85/IY, and GDP85/School

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Above are scatterplots for GDP85 in relation to the variables Popgr, IY, and School. On
the left is the scatterplot for GDP85 and Popgr and the results are consistent with the results from
the matrix of correlation coefficients. In the matrix of correlation coefficient for PopGr the
results suggested a moderate inverse correlation. As shown by the scatterplot, the x and y
variables move from top to bottom when going left to right in almost a diagonal line. This
indicates that as Popgr goes up GDP tends to go down, otherwise known as an inverse
relationship. For the scatterplot in the middle we are examining the relationship between GDP85
and IY. According to the matrix of correlation coefficient there was an strong positive
relationship between these two variables. This is consistent with our graph since the plots move
from left to right in the same direction and are not too spread out. Lastly, the matrix of
correlation coefficient for School and GDP85 had a very strong positive relationship. This is
once again consistent with our scatterplot since the plots are on an upwards trajectory moving
from left to right and are tight around one another.
(v) Empirical Results
Table 4: Empirical Results

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This is a reflection of the current GDP in 1985, as a function of investment and the
population growth variable. As expected, investment has a positive effect, and is statistically
significant. We interpret the coefficient that a 1 percent increase in investment will correspond to
a 1 percent increase in output per worker on average. The population growth variable has a
significant and negative growth effect on GDP. The magnitude of the investment variable
coefficient is smaller than in the previous regression, however still statistically significant. The
population growth possesses a similar magnitude as the previous graph. Schooling has a positive
and significant relationship with GDP, as a 1 percent increase in the working age population in
secondary school is associated with a 0.6 percent increase in GDP per worker.
According to Solow: Output per capita is a function of saving rate and population growth.
Saving rate is positively correlated with output per capita, whereas population growth is
inversely related with per capita output. Accordingly, we have the model:
Table 5: Test for unconditional convergence
______________________________________________________________________________
Dependent variable is Log(GDP85) - Log(GDP60)
______________________________________________________________________________
Log(GDP60) .943109
(.0496172)
Constant -.2665776
(.3796046)

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N 98
R-Squared 0.0363
The table above is testing whether there is a tendency for poor countries to converge to
rich countries under unconditional convergence. This was done by using the difference between
LogGDP85 and LogGDP60 as the dependent variable. When looking at the results, there is a
very strong correlation between the two variables. For poor countries, this indicates that there is
a tendency for poor countries to converge to rich countries. Of course, this is only under the state
of unconditional convergence, where we did not use any controls.
According to MRW: Output per capita is a function of saving rate, population growth and
human capital (schooling). Accordingly, we have the model:
Table 6: Test for conditional convergence
______________________________________________________________________________
Dependent variable is Log(GDP85) - Log(GDP60)
______________________________________________________________________________
Solow MRW
Log(GDP60) -.1488957 .1448834
(.0527075) (.0657452)
Log(POPGR) .-0885808 N/A
(.0693268)
Log(IY) .6460532 .337933

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(.0864117) (.1048134)
Log (School) N/A -.0381035
(.06712)
Constant -.1408021 .3886471
N 98 98
R - Squared 0.0363 0.3954
Similar to table 5, the above table is demonstrating the results of our study testing
whether there is a tendency for poor countries to converge to rich countries. The difference with
this table is that it does so under conditional convergence, meaning there are controls in place.
The controls that we used for this table are the variables Log(GDP60), Log(POPGR). Log(IY),
and Log (School). The results from this table clearly indicate that there are differences between
the Solow and MRW models when studying poor countries. When comparing the results between
the Solow and MRW models for poor countries, they differ greatly.
When testing for the tendency of poor countries converging to rich countries, we are to
look at the Constant row for results. Under the Solow model, this sign is found to be negative.
This means that there is no evidence for this tendency of poor countries experiencing conditional
convergence to rich countries. As for the MRW model, the result is found to be positive. This
means that there is evidence that there is a tendency for poor countries to experience conditional
convergence to rich countries. The sign on the coefficient of Log (GDP60) for Solow and MRW
is consistent with expectations since we knew that the MRW model accounted for more
variables, which helped to explain GDP in the real world better.

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(vi) Conclusion
The purpose of our study has multiple aspects, starting with finding out the exact
relationship - either positive, negative or zero - between each independent variable and the
dependent variable. Each independent variable was expected to have a positive effect on the
dependent variable LogGDP85, and their individual mean impacts are as follows: POPGR 2.201,
IY 12.672 and SCHOOL 5.396. The data also seems to be tighter around the mean for GDPGR
and POPGR, but spread out far from the mean for the variables GDP60, GDP85, IY and
SCHOOL. From the matrix of correlation coefficients, we see that there is a moderate inverse
relationship between POPGR and GDP85, showing us that the more the population growth rate
rises, the lower the GDP per worker will be. GDP85 and IY have a strong positive correlation,
indicating that when more of a country’s GDP gets invested, the more it will improve that
country’s GDP in the long run. Last is the correlation between GDP85 and SCHOOL, which is
strongly positive and indicates that when more people attend secondary school, the GDP per
worker in that country will rise.
From our empirical results we can see the true effects of each independent variable and
their statistical significance. The variable IY has a positive effect and its coefficient
interpretation is that each percentage increase in investment corresponds with a percentage
increase in output per worker on average. POPGR affects the dependent variable negatively, and
finally, SCHOOL has a positive relationship with GDP85, where a percent increase in the
working age population in secondary school is associated with a 0.6 percent increase in the GDP
per worker. From our expected signs, we anticipated the effects of the independent variable on
the dependent variable correctly.

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Using the difference between LogGDP85 and LogGDP60 as the dependent variable, we
see that there is a tendency for poor countries to converge to rich countries, but this analysis is
under the state of unconditional convergence, in which we did not use any controls. When we
use conditional convergence, the results differ greatly between the Solow and MRW models.
Under Solow, the Constant variable is negative, but for MRW that variable is positive. Solow
predicts that poor countries will not have a tendency to converge to rich countries, while MRW
predicts the opposite.
Some limitations between using the Solow and MRW models is the need for
unconditional convergence to achieve consistent results between the two models. With no
controls, both the Solow and MRW models come to the same positive result, but when we
remove that unconditional convergence and add controls Solow goes negative and MRW remains
positive. Individually, the Solow model does not really explain long run growth, while the MRW
model does not recognize the differences in growth patterns of countries used in the sample.
Overall, analysis of the data typically proves that poor countries have the possibility of
converging into richer countries with an increase in the population growth rate, investment and
further secondary schooling for the working-age populace.

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References
[1] Robert J. Barro, “Economic Growth in a Cross Section of Countries” The Quarterly Journal
of Economics. Vol. 106 May 1991: 407- 444.
[2] Mankiw, G., Romer, D., and Weil, D. “A contribution to the Empirics of Economic Growth.”
The Quarterly Journal of Economics. Vol. 107, May 1992: 407-437.
[3] Solow, R. “A Contribution to the Theory of Economic Growth.” The Quarterly of Economic
Growth.” Vol. 29, 1956: 65-94.

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APPENDIX

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18. 18

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