augmented solow growth model with a theory on corruption
TRANSCRIPT
Eddie Terrenzi
Augmented Solow Growth Model with a Theory
on Corruption
Abstract:
Studies done by other scholars have augmented the Solow Growth Model to include more
variables in order to better explain differences in growth and income across countries.
Much of the research that has been done has broken down countries into groups with
similar GDP and income per capita. The groups are compared with one another to
examine differences between them. Dividing countries into these groups for comparison
does not capture the differences within each group. What if the countries were divided
based on their level of corruption. Then we ask the question how much the variables of
population growth, investment in human capital, and national investment effect output
per worker? In addition to this we ask how important are these variable to each group of
countries when controlling for corruption? Then lastly, can differences in growth and
wealth be explained by levels of corruption?
Introduction:
One of the criticisms of the Solow Growth Model has been that it does not explain
differences within rich countries, nor does it explain differences within poor countries. It
does, however, explain differences between the rich and poor countries. It is because of
this that a new method of grouping countries should be used to examine the importance
of investment, capital, efficiency, and population growth. This paper proposes a new
method of comparing countries using the augmented Solow Growth model by comparing
countries according to their level of corruption. I believe that corruption affects many
variables in the model. It is well known that corruption does affect efficiency, which is
accounted for in productivity growth. However, corruption also impacts capital formation
and can set barriers to technological growth. Another consequence of corruption is that it
affects investment. It may not be that people of a country don‟t have enough income to
save, or that their marginal propensity is low because they have to spend all they make. In
countries where corruption is high, people are less likely to save and invest for the fear
that their investment may be taken away or that their returns on their investment may be
for the profit of the government. By controlling for corruption we are able to include oil
rich countries, which have been treated as their own group in other studies (Nonneman
and Vanhoudt, 1996). This was because most of their capital accumulation and high
savings rates have been to due to oil production increases. This study aims to show that
differences in growth and GDP can be explained by levels of corruption. In addition to
this proposal, I believe that each of the determining variables of the augmented Solow
Growth Model have different values of importance for each groups level of corruption.
The thesis for Part A is as follows:
In comparing output per worker across countries, higher levels of corruption
reduce output per worker while reducing the positive effects of investment in human
capital and investment in physical capital on output.
The second part to this study will categorize countries into three groups by their
level of corruption. The results from the analysis will allow us to compare the factors of
production for output per worker among the three groups. Each groups‟ factors of
production should be weighted differently due to the effects of different levels of
corruption. The thesis for Part B is as follows:
In comparing countries, those with higher levels of corruption will have different
weighted factors of production values than those with lower levels of corruption. The
differences in output can be attributed to the negative effects that result from corruption.
This approach to explaining growth differences does not rule out the variables of the
augmented Solow Growth Model but rather believes that the contribution of each variable
towards growth will vary from group to group.
Data and Methods:
There are two Sections to this study. The first section will examine the
contributions of the factors of production on GDP at an aggregate level. The definition of
aggregate level refers to all the countries of the world that are in the data set. There are a
total of 182 countries in this data set. The second section of this study divides the
countries into three groups of 52 observational units. The three groups are titled High
Corruption, Medium Corruption, and Low Corruption. The corruption values are taken
from Kaufmann, Kray, and Zoido-Lobaton study on governance (2002). This measure is
defined as “control of corruption”. This measures the perceptions of corruption or, more
plainly, the exercise of public power for political gain (Kauffman, Kray, and Zoido-
Lobaton; 2002). The scaling for corruption can be interpreted simply by labeling a
country with a low corruption value as having low corruption and visa-versa for high
values. The data that will be used is from the World Bank 2000 Data set. Output per
worker (YL) is calculated by taking total GDP for the year 2000 and dividing it by the
total labor force in 2000. Human capital [s(h)] is measured by taking the average percent
of GDP spent on education from the period 1985-2000. This value is then divided by 100
for decimal form. Physical capital [s(k)] is measure in a similar way. For this measure we
take the average national investment as a percent of GDP over the period 1985-2000.
This value is then divided by 100 for decimal form. These values were obtained from the
Penn World Table. The last variables in the study are depreciation and technological
growth. Mankiw, Romer and Weil (1992) assume that technological growth and
depreciation are approximately the same across all counties. Thus, technological growth
(g) and depreciation )( equal .05 or 5%. Population growth (n) is defined as the rate of
growth of the labor force over the period 1960-2000. This value varies from country to
country. In the regression labor force growth is added to the constant g (.05). This
gives us gn or 05.n .
For Section I we will run an aggregate regression with and without human capital.
The equation is as follows: )ln()(ln 21 gnksL
Y. The equation with
human capital is as follows: )ln()(ln)(ln 321 gnhsksL
Y. We
then add corruption to the regression. In this study, the values of corruption have been
adjusted relative to the country with the highest level of corruption. Afghanistan has the
highest level of corruption with a value of 1.46608305. The rest of the country‟s
corruption values in the aggregate regression are indexed to this value. Therefore, the
values of corruption are measured as a relative percent of Afghanistan. The new equation
will be: )ln(ln)(ln)(ln 4321 gncorrupthsksL
Y, where
corrupt is the variable corruption. These three equations are lin-log equations. The
dependent variable is in linear form and the explanatory variables are in log form. 1
measures the absolute change in output per worker for a 1% change in investment as % of
GDP. 2 measures the absolute change in output per worker for a 1% change in
investment in education as % of GDP. 3 measures the absolute change in output per
worker for a 1% change in corruption relative to the highest value of corruption. 4
measures the absolute change in output per worker for a 1% change in labor force growth
with depreciation and technological growth being constant.
Section (B) will break the countries down into three groups by level of
corruption. There are 52 countries in each group. This analysis controls for corruption by
separating the countries into the groups. Each group will be examined by the same
equations. The equations and variables are the same as Section (A) except the variable
„corruption‟ will not be included. The two equations are as follows:
)ln()(ln 21 gnksL
Y and
)ln()(ln)(ln 321 gnhsksL
Y
The purpose to this section is to determine how the factors of production vary in weight
between groups with different levels of corruption. The prediction is that as levels of
corruption increase from group to group the coefficients for )(ks and )(hs will be
reduced. The interpretation will be that as corruption increases the contribution of each
explanatory variable to output per worker will decrease. I believe that corruption may
even cause some variables to be insignificant in explaining output per worker.
I have a final note on the error terms and the constant. For this analysis
international trade and investment is exogenous and is assumed to have no effect on each
individual country. I do acknowledge that external forces such as trade and investment do
account for a portion of output per worker. These factors also have an important role in
growth. However, to keep consistent with previous studies and the Solow Growth Model
these variables will be held constant and captured in the error term of the regression. The
error term and the constant will capture efficiency as well.
Results: Part A
All the regressions were run as OLS regressions and the F test was used to test
overall significance. The F test indicated that all of the models were significant. However,
there were variables that tested insignificant within the models. In Part A the most
common variable to be statistically insignificant in the model was the variable NGD. For
this discussion I will refer to NGD as labor force growth since both G and D are assumed
constant. It is important to note that the sign was as predicted. Table 2 shows the results
of all models for Part A. The first model (3A) measured the effect investment and labor
force growth has on output per worker. The explanatory variables are measured in logs
for every model here out. The coefficient of investment estimates that for a one percent
change in the investment rate output per worker increases by $21,799.89 holding all other
variables constant. This is not an unreasonable estimate. I should note that the range for
output per worker is min. $547.80 to max. $110948.80. The average investment range is
min. 2.8% to max. 41.6%. Labor force growth has the correct sign but was not significant
at the 90% level. The variable corruption is added to the next model. The estimators for
both labor force growth and investment decreased. Investment and corruption are both
statistically significant at the .01 level while labor force growth is not. The estimator for
investment decreased to 4872.316. When corruption is added to the model and held
constant with labor force growth a 1% increase in investment predicts a $4872.31
increase in YL. The sign on the estimator of corruption was negative as was predicted. A
1% increase in the relative value of corruption estimates YL will decrease by -$2233.48.
Model 3C combines the effects of investment in human capital as well as physical capital.
Both AVGINV and AVGEDU are statistically significant at the 0.1 level. A 1% increase
in investment estimates a $65914.58 increase in YL holding all other variables constant.
A 1% increase in investment in human capital estimates an increase in YL of $7517.31
holding all other variables constant. In this model labor force growth is not statistically
significant. This model uses the factors of production for the augmented Solow Growth
model. Here we see that human capital is important to output per worker but not nearly as
important as investment in physical capital. Model 3D includes all of the variables. The
coefficient for investment and corruptions are both significant at the .01 level. Investment
in human capital and labor force growth are not significant. All the signs are correct as
predicted in the model. The coefficient for investment is about the same as in model 3C.
The coefficient for corruption remains about the same for all the models that it is
included in. Corruption is also statistically significant in all the models it is included in.
Although investment in human capital is not significant in this model its coefficient was
greatly reduced. The last two models focus on investment in human capital. Model 3E
combines corruption in the model. Both investment in human capital and labor force
growth are not significant in this model while corruption is. The last model examines the
effect of investment in human capital and labor force growth on YL. Investment in
human capital coefficient is 15300.10 and is significant at the .01 level. These models
were not expected to fully explain the variation in output per worker. The purpose of
these models is to find the best and truest estimator for each variable. It would seem that
the recurring coefficient value of approximately 20,000 is suitable for investment. In the
models where investment in human capital is significant the value of the coefficients are
around 7500. The coefficient for investment in human capital in the last model was
153000. It may have been overvalued because investment was not included making the
coefficient more weight and over estimated. The main effect to be captured from these
models is that when corruption is introduced the predictive power of each variable
decreased. The coefficient for corruption remained the relatively unchanged through all
the models. I believe that corruption has a definite effect on output per worker. However,
when corruption was introduced into the models the other coefficients decreased
drastically and investment in human capital becomes statistically insignificant. This
would indicate that corruption also has an effect on the factors of production and through
some other channel may have an effect on output per worker.
Results: Part B
The second part of this study acknowledges that multicollinearity may be present
in the models of Part A. It is for this reason that the countries are separated into groups by
their levels of corruption. Table 4 shows the results for the same model run with each
group. This model shows the impact that different levels of corruption have on
investments contribution to output. The signs for labor force growth coefficients are
negative but all of the coefficients are statistically insignificant. The focus of the model is
the differences in investment in explaining output per worker at different levels of
corruption. The high corruption country‟s investment coefficient is 5169.19, the medium
corruption is 7443.26, and the low corruption is 28317.70. This means that a 1% increase
in investment estimates a $5169.19 increase in YL for high corruption, $7443.26 increase
in YL for medium corruption, and $28317.70 increase in YL for low corruption. The low
corruption group consists of almost all of the OECD countries as well as most developed
countries with high income per capita. The medium corruption and high corruption
countries are mixed with developed, developing, and underdeveloped countries. It is for
this reason that these differences in investment are interesting.
Table 5 contains the results from the model with investment in human capital,
labor force growth, and YL. The signs are what was predicted, there is a negative
relationship between labor force growth and YL, and a positive relationship between
investment in human capital and YL. Of all the groups, only investment in human capital
for medium corruption countries is significant. However, the F statistic for the
regressions with medium corruption and high corruption are low and therefore these
regressions are not significant. It is still interesting that a 1% change in investment in
human capital has a larger impact on YL with medium corruption countries. The purpose
of this analysis is not to predict actual values of YL but rather to examine the
approximate relationship between the factors of production in the model and YL among
the three groups. In this model we see that there is a difference in human capital between
high and medium corruption countries.
The last model combines the previous two models into one (Table 6). All of the
regressions are statistically significant using the F test. This model show similar results to
that of the first model. This model shows differences between medium and high
corruption countries. The biggest difference is the coefficients for investment in human
capital. A 1% increase in investment in human capital estimates a $7383.587 increase in
YL for medium corruption and $692.18 increase for high corruption. Although medium
corruption investment in human capital coefficient is only significant, the other group‟s
values were significant at the .20 level. An interesting result was those coefficients of the
low corruption countries. Investment in human capital had a negative sign. This would
mean that increasing investment in human capital reduces output per worker. This issue
will be discussed shortly. Another interesting factor about all three models is that the
coefficient for labor force growth remained approximately the same for medium
corruption and high corruption although they were not significant. These models show
that the effect of an increase in investment on output is greatly reduced when corruption
is higher. One mysterious result of the models is that human capital is not affected by
corruption in medium corruption countries. These models confirm the results of Part A in
that investment is affected by corruption and corruption reduces output per worker
through some other channel not analyzed in this study.
Conclusion
It is not clear if corruption affects the contribution that investment in human
capital makes to output per worker. One reason why investment in human capital may
have taken on a negative value for low corruption countries is because investment in
education in these countries may not have the same contribution to output. The majority
of the countries with low corruption are rich developed countries. The investment in
education may go to education that does not contribute to measurable output and so an
increase in this education would not yield more output. I would have expected investment
in human capital to have the smallest impact from corruption. One would expect that
corruption would not impact human capital‟s effect on output unless the investment
spending went towards the cronies of the corrupt governing party. The other case would
be as discussed earlier, where the investment in human capital had different returns than
an increase in output.
Corruption‟s effect on investment is most clear. Corruption reduces the incentive
to invest as well as reaps the profits from investment. This is what I was expecting to
happen in the results. The more corruption a country has, the less output it would gain
from more investment. Part A shows that the coefficients may be overestimated without
investment in human capital and corruption included in the model. The measure used
here is national investment. If a country has a high level of corruption then the investment
in physical capital could be for the profit of the government. Corrupt governments engage
in black market activities and conduct business in such a way that is not recorded. This is
another reason why high investment would not yield as high an output as a non corrupt
country.
The variable for labor force growth was insignificant in almost every model. This
may have been captured better by using a proxy that subtracts NGD from investment.
This would be coded as a new variable in the model. This would tell the actual amount
that is invested which goes to increase output and not capital replacement. The measure
used for investment in human capital may not have captured the full effect of human
capital‟s effect on output. One of the reasons mentioned above, where investment in
education doesn‟t always go toward (non corrupt) activities that increase output.
It is no surprise that corruption reduces countries output as well as restricts the
ability to perform at full potential. Corruption also hurts and restricts development.
Citizens of corrupt countries do not gain from increased output therefore there is no
incentive to increase production. A key ingredient in production is investment. Thus,
corruption reduces the efficiency of investment as well as redistributes investment and
wealth giving disincentive to those who do not profit or benefit from growth. Here is
something to end on. I mentioned earlier in this study that efficiency, trade, and
international investment are all captured by the constant and error term. Corruption
reduces efficiency and makes international investment unattractive to foreign investor.
This further amplifies the effect of corruption on output and should be followed up on in
a future study.
TABLE 1
SUMMARY STATISTICS (OBS=179)
DEPENDENT VARIABLE YL
MEAN (STANDARD DEVIATION) 18994.42 (19247.75)
INDEPENDENT VARIABLES EXPECTED SIGNS
AVGINV 0.1458443 0.0742777 +
AVGEDU 0.0434693 0.018657 +
NGD 0.0720292 0.123629 -
CORRUPT 0.0062686 0.6465568 -
NOTE: Independent variables measured in log in the regression
YL = Output per worker 2000. Total Output/Labor Force Population
AVGINV = 1985-2000 Average investment as percent of GDP.
AVGEDU = 1985-2000 Average expenditures on education as percent of GDP
NGD = 1960-2000 Average labor force population growth + .05
CORRUPT = Perception of Corruption, percentage relative to the most corrupt country
DATA SOURCES:
Penn World Tables (PWT), version 6.1
- AVGINV
World Bank, World Development Indicators Database
- YL, NGD, AVGEDU
Romer (1989)
- NGD
Kaufmann, Kray, and Zoido-Lobaton (2002)
- Corrupt
TABLE 2
OUTPUT PER WORKER AND FACTORS OF PRODUCTION
3A 3B 3C 3D 3E 3G
Constant 46639.49** 3010.823 65914.58* 6793.853 -4695.275 47976.06
22271.19 9685.821 24238.94 11137.59 11944.07 30072.07
lnAVGINV 21799.89* 4872.316* 20152.46* 4836.319* NA NA
2278.039 1199.42 2400.795 1240.538
lnNGD -6850.056 -5418.854 -7554.056 -5484.653 -5169.466 -8194.516
104089.3 3445.844 8294.681 3539.248 3934.78 10330.6
lnCORRUPT NA -2233.485* NA -2066.998* -2652.229* NA
699.3491 739.5685 805.3144
lnAVGEDU NA NA 7517.317* 1128.632 981.4311 15300.1*
3165.342 1494.329 1661.233 3769.517
NOTES:
* = Significant at the 1% level of significance
** = Significant at the 5% level of significance
3A: NGDAVGINVL
Ylnln 21
3B: CORRUPTNGDAVGINVL
Ylnlnln 321
3C: CORRUPTAVGEDUNGDAVGINVL
Ylnlnlnln 4321
3D: AVGEDUNGDAVGINVL
Ylnlnln 321
3E: CORRUPTNGDAVGEDUL
Ylnlnln 321
3F: NGDAVGEDUL
Ylnln 21
TABLE 3
SUMMARY STATISTICS (OBS=52 each group)
Dependent Variable YL-High Corruption YL-Med Corruption YL-Low Corruption
Mean (Standard Deviation) 6694.769 (5101.403) 11193.85 (8357.991) 38257.47 (20691.22)
Independent Variables EXPECTED SIGNS
AVGINV .1069641 (.060845) .1286113 (.0609821) .1934957 (.748175) +
AVGEDU .0390828 (.023188) .0406755 (.0156489) .0498404 (.014761) +
AVGNGD .0737695 (.0073002) .0742634 (.0154018) .0684242 (.0131877) -
NOTE: Independent variables are in log form for the equation
YL = Output per worker 2000. Total Ouput/ Labor Force Population
AVGINV = 1985-2000 Average investment as percent of GDP
AVGEDU = 1985-2000 Average expenditures on education as percent of GDP
NGD = 1960-2000 Average labor force population growth (N) + .05 (G+D
DATA SOURCES:
Penn World Tables (PWT), version 6.1
- AVGINV
World Bank, World Development Indicators Database
- YL, NGD, AVGEDU
Romer (1989)
- NGD
TABLE 4
OUTPUT PER WORKER, INVESTMENT, AND LABOR FORCE GROWTH
HIGH MED LOW
Constant 755.3327 5424.266 22452.55
17707.77 22071.81 49079.35
lnAVGINV 5169.195* 7443.265* 28317.7*
1513.024 2154.821 5179.14
lnNGD -7010.34 -8272.93 -23357.56
6627.366 8154.052 16858.91
TABLE 5
OUTPUT PER WORKER, INVESTMENT IN HUMAN CAPITAL, AND LABOR FORCE GROWTH
HIGH MED LOW
Constant -6448.069 16163.29 -76385.73
20484.71 27363.86 67521.62
lnAVGEDU 1157.639 6494.832** 4005.937
1634.491 3491.815 9475.796
lnNGD -6591.987 -6207.288 -46474.39*
7588.803 8950.531 21183.94
TABLE 6
OUTPUT PER WORKER, INVESTMENT, INVESTMENT IN HUMAN CAPITAL, AND LABOR FORCE GROWTH
HIGH MED LOW
Constant 2819.735 30248.89 9160.571
18789.79 24392.51 54934.01
lnAVGINV 4913.531* 7383.587* 28912.19*
1622.227 2072.176 5328.451
lnAVGEDU 692.1898 6342.154** -4194.635
1487.2 3071.802 7538.027
lnNGD -6917.866 -6774.17 -2394.17
6868.827 7874.757 17024.31
NOTES:
* = Significant at the 1% level of significance
** = Significant at the 5% level of significance
TABLE 7
Afghanistan Dominican Republic Lithuania Slovenia
Albania Ecuador Luxembourg Somalia
Algeria Egypt macao South Africa
Angola El Salvador Macedonia South Korea
Antigua Equatorial Guinea Madagascar Spain
Argentina Eriteria Malawi Sri Lanka
Armenia Estonia Malaysia St. Kitts & Nevis
Australia Ethiopia Mali St. Lucia
Austria Fiji Malta St. Vincent & Grenadines
Azerbaijan Finland Mauritania Sudan
Bahamas France Mauritius Suriname
Bahrain Gabon Mexico Swaziland
Bangladesh Gambia, The Moldova Sweden
Barbados Georgia Mongolia Switzerland
Belarus Germany Morocco Syria
Belgium Ghana Mozambique Taiwan
Belize Greece Myanmar Tajikistan
Benin Grenada Namibia Tanzania
Bermuda Guatemala Nepal Thailand
Bhutan Guinea Netherlands Togo
Bolivia Guinea-Bissau New Zealand Trinidad & Tobago
Botswana Guyana Nicaragua Tunisia
Brazil Haiti Niger Turkey
Brunei Honduras Nigeria Turkmenistan
Bulgaria Hong Kong North Korea Uganda
Burkina Faso Hungary Norway Ukraine
Burundi Iceland Oman United Arab Emirates
cambodia India Pakistan United Kingdom
Cameroon Indonesia Panama Uruguay
Canada Iran Papua New Guinea USA
Cape Verde Iraq Paraguay Uzbekistan
Central African Republic Ireland Peru Venezuela
Chad Israel Philippines Vietnam
Chile Italy Poland Yemen
China Jamaica Portugal Yugoslavia
Colombia Japan Puerto Rico Zambia
Comoros Jordan Qatar Zimbabwe
Congo, Dem. Rep. country Romania
Congo, Republic of Kazakhstan Russia
Costa Rica Kenya country
Cote d'lvoire Kuwait Rwanda
Croatia Kyrgyzstan Sao Tome and Principe
Cuba Laos Saudi Arabia
Cyprus Latvia Senegal
Czech Republic Lebanon Seychelles
Denmark Lesotho Sierra Leone
Djibouti Liberia Singapore
Dominica Libya Slovak Republic
TABLE 8
Low Corruption Mid Corruption High Corruption
Finland Lithuania Algeria
Sweden Gambia, The Lebanon
Iceland Guinea Honduras
Singapore Malta Iran
Netherlands Suriname Bangladesh
New Zealand United Arab Emirates Uzbekistan
Denmark Malaysia Georgia
Canada Guinea-Bissau Guatemala
Switzerland Mozambique Yemen
United Kingdom Malawi Cote d'lvoire
Luxembourg Jordan Bolivia
Norway Bahrain Vietnam
Australia Croatia Pakistan
Austria Sri Lanka Nicaragua
USA Brazil Armenia
Spain Latvia Moldova
Chile Peru Syria
Germany Jamaica Kazakhstan
Namibia Belarus Haiti
Cyprus Cuba Kyrgyzstan
Portugal Egypt Zambia
Japan Bulgaria North Korea
Hong Kong Brunei Ukraine
Ireland Mongolia Libya
France Dominican Republic Tanzania
Israel Ghana Uganda
Slovenia Mexico Madagascar
Belgium China Burkina Faso
Fiji Laos Eriteria
Botswana Nepal Mauritania
Costa Rica El Salvador Paraguay
Tunisia Saudi Arabia Ecuador
Bahamas Argentina Indonesia
Estonia Colombia Russia
Greece India Yugoslavia
Uruguay Senegal Azerbaijan
Hungary Ethiopia Nigeria
Italy Mali Tajikistan
Kuwait Panama Zimbabwe
Qatar Guyana Niger
Mauritius Sierra Leone Kenya
Trinidad & Tobago Thailand Cameroon
Belize Turkey Turkmenistan
Oman Togo Angola
Morocco Congo, Republic of Iraq
Poland Philippines Somalia
South Korea Macedonia Myanmar
Rwanda Romania Papua New Guinea
South Africa Gabon Sudan
cambodia Liberia Congo, Dem. Rep.
Czech Republic Venezuela Burundi
Slovak Republic Albania Afghanistan
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