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

References

1. Buttrick, John. 1958. “A Note on Professor Solow’s Growth Model”. The Quarterly

Journal of Economics. 72: 633-636.

2. Dougherty, Chris and Dale W. Jorgenson. 1996. “International Comparisons of the

Sources of Economic Growth”. The American Economic Review. 86: 25-29.

3. Kauffman, Daniel, Aart Kraay, and Pablo Zoido-Lobaton. 2002. “Governance Matters

II - Updated Indicators for 2000-01”. World Bank Policy Research Working

Paper #2772.

4. Nonneman, Walter and Patrick Vanhoudt. 1996. “Further Augmentation of the Solow

Model and the Empirics of Economic Growth for OECD Countries”. The

Quarterly Journal of Economics. 111: 943-953.

5. Mankiw, Gregory N., David Romer and David N. Weil. 1992. “A Contribution to the

Empirics of Economic Growth”. The Quarterly Journal of Economics. 107:

407-437.

6. Vanek, J. 1966. “Towardsa More General Theory of Growth with Technological

Change”. The Economic Journal. 304: 41-854.