The Analysis of LIbya (Solow model)

THE ANALYSIS OF LIBYA USING SOLOW

GROWTH MODEL

AND FDI.

A CASE OF STUDY: LIBYA

Participants

1.Haji, Yusuph

2.Hamisi, Medison

3.Mhenga, Denis.G

Supervised by Michael.R.Baha

Introduction

Solow growth model is a model of economic growth originally developed by MIT’s Robert

Solow in the 1950s. Solow’s purpose in developing the model was to deliberately ignore some

important aspects of macroeconomics, such as short-run fluctuations in employment and savings

rates, in order to develop a model that attempted to describe the long-run evolution of the

economy. The Solow growth model shows how saving, population growth and the technological

progress affect the level of a country’s economy output and its growth at a particular time.

(Mankiw, 2001)

From the framework of Mankiw, the Solow model is presented as here under;

),( LtKtFYt

And under the Cobb-Douglas function with constant returns to scale can be written as;

1)(ALKY , 10

Where Y is output, K is capital, L is labor, A is labor-augmenting technological progress, and

is the share of capital in total output.

A. Empirical Model

Foreign direct investment (FDI) is frequently seen as an important catalyst for economic growth

in the developing countries. It affects the economic growth by stimulating domestic investment,

increasing human capital formation and by facilitating the technology transfer in the host

countries. (Falki, 2009). The main purpose of the study is to investigate the impact of FDI on

economic growth in Libya, for the period 1980-2011. The role of the foreign direct investment

(FDI) has been widely recognized as a growth-enhancing factor in the developing countries

(Khan, 2007).

According to Levin and Raut (1997) and Zhang (2003), FDI can be applied into growth model in

two ways depending on different assumptions. FDI can be postulated to cause growth directly or

indirectly through the spillover effects. First, we assume that FDI would directly cause growth,

and then the capital stock in Solow production function is assumed to consist of two components.

I.e. domestic and foreign owned capital stock ftdtt KKK . at this point Equation 1 is

obtained:

321 b

fit

b

dit

b

ititit KKLAY

where Y is denoted as output, dtK and ftK as the domestic and foreign owned capital stocks,

Lit as labor, A it as total factor productivity, which explains the output growth that is not

accounted by the growth in factors of production specified. The subscript i = 1.N indicates

sample country i to N.Subscript t = 1, T represents time period t, starting from 1 to T. After

taking logarithm to Equation 1, the production function is as follows:

ftditititit KbKbLbALogY logloglog 321

The theoretical model that is used to investigate the interaction of additional variable which is

FDI and economic growth based on the following production function

1FDItLtAtKtYt

So to test the hypothesis empirically the effect of FDI on economic growth, the model used can

be specified as follows;

tttt FDIbLbKbbYt 3210

For the purpose of estimation the above equation to be tested was obtained by taking the Log on

both sides of the equation, the equation that could be written as here under;

ttttt FDIbLbKbbLogY logloglog 3210

Where the variable on the left side is dependent variable and the variables on the right side are

exogenous variables.

B. Preliminary Data Analysis

The statistical method that is concerned with the presentation of numerical data, in form of

tables, graphs and charts to simplify data analysis is known as descriptive statistics. Thus,

descriptive statistics is useful in summarizing a set of data clearly and easy for analysis. This

includes; Mean Median, Standard Deviation, Skewness and Kurtosis.

TABLE 1: The descriptive statistics for the variables used in the model

N Range Mean Std.

Deviation

Skewness Kurtosis

FDI 32 16022.1 2766.93 4810.414 2.178718 3.44038

LABOR 32 1641.78 1534.35 543.6186 0.170103 -1.389

GDP 32 73.0302 -0.5543 12.8701 -3.35871 14.5353

CAPITAL 31 8326.85 5412.14 1941.432 1.230933 1.44342

Valid N (listwise) 31

SOURCE: UNCTAD DATA, STATA (2013)

FIGURE 1: GDP GROWTH RATE FOR THE YEAR (1980-2010) IN LIBYA

-70

-60

-50

-40

-30

-20

-10

0

10

20

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Total

Figure 1 shows that the GDP growth rate in Libya keeps on changing over time and that it

experience negative and positive GPD growth. From the graph in the year

1980, 1981,1983,1984,1986 and other periods showed from the graph and this is due negative

effect of labor and capital. In 2011 Libya experienced political revolution which led to lower the

GDP.

FIGURE 2: LABOR FORCE OF ALL SECTORS FOR LIBYA (1980-2011)

Time (years)

Figure 4 shows that labor force participation to promote growth in Libya, has an upward trend

from year to year from 1980 and 2011.

0

500

1000

1500

2000

2500

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Total

FIGURE 3: GROSS CAPITAL STOCK FOR LIBYA (1980-2011)

Time (years)

The trend of gross capital formation in Libya was constant over time , year to year from 1980 to

2011as shown in the figure 3 above.

FIGURE4: FDI IN LIBYA FOR THE YEAR (1980-2011)

Time (years)

0

0.2

0.4

0.6

0.8

1

1.21980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Total

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Total

Figure 5 shows that the trend of FDI inflow in Libya was in a horizontal movement year to year

from 1980 to 2004, but there was a very rapid increasing trend of FDI inflows to Libya from

2005 towards 2011

C. REGRESSION ANALYSIS

loggdp Coef. Std. Err. t P>t [95% Conf. Interval]

loglabor -3.77456 1.056859 -3.57 0.003 -6.015 -1.53412

logcapit -4.17455 1.172956 -3.56 0.003 -6.6611 -1.68799

logfdi 1.271049 0.330741 3.84 0.001 0.569911 1.972188

_cons 24.19987 6.394651 3.78 0.002 10.64381 37.75592


tttt FdiLabCapY 271.1775.3175.420.24

SE (6.395) (1.173) (1.057) (0.331)

The analysis was made through Analysis of Variance (ANOVA) to see the influence of those

factors affecting the economic growth of Libya say GDP. The study revealed that those factors

has significance influence on economic growth since the F calculated (Fc) is greater than critical

value at 5% which is 3.24 that means those factors are clearly significance difference and that

95% (C.I) probability that the conclusion is correct or 5% probability that conclusion is wrong.

ANOVA TABLE

Source SS df MS

Number of

obs = 20

F( 3, 16) = 5.12

Model 1.628005 3 0.542668183 Prob > F = 0.0113

Residual 1.694655 16 0.105915957 R-squared = 0.49

Adj R-

squared = 0.3943

Total 3.32266 19 0.174876834 Root MSE = 0.32545

a: Predictors:(constant);LogCAPITAL,LogLABOR,LogFDI.

b: Dependent variable: LogGDP

D. The Main Problems in Conducting Regression Analysis

Multicollinearity

The term multicollinearity originally it meant the existence of a “perfect”, or exact, linear

relationship among some or all explanatory variables of a regression model. (Gujarat, 2004).

Multicollinearity is a nature of a sample problem and state of nature that results in relatively

large standard errors for the estimated regression coefficient, but not biased. (Thomas, 2007)

Measuring the degree of multicollinearity.

There are three ways to measure the degree of multicollinearity in the regression model; these

are such as the use of a correlation matrix, the Variance Inflation Factor (VIF), and the Tolerance

measure. in our case multicollinearity was measured by using VIF with the help of STATA and

it was found to be less than ten. As the rule of thumb, if VIF is greater than 10 then there is no

exact linear relationship among the independent variables.

Variable VIF 1/VIF

Loglabor 4.65 0.214845

Logfdi 4.17 0.240086

Logcapit 3.78 0.264422

Mean VIF 4.2

AUTOCORRELATION

Autocorrelation or serial correlation often appears when working with time series data. On

should understand that in order for autocorrelation to appear it is necessary that observations are

correlated over a sequential order. In statistics terms it could be expressed as here under;

0, ji UUCov j

Hence autocorrelation is a problem that frequently appears when working with data that has time

dimension. This means that it is meaningless to look for autocorrelation when working with

cross sectional data which usually are based on random samples from a population, at a given

point in time.

Autocorrelation can easily be detected by using graphical method and Durbin–Watson Test.

Graphical Method involves the plotting of the residuals against time, the time sequence plot.

Durbin Watson d Test is the most celebrated test for autocorrelation by many statisticians. It is

defined as

T

T

N

T

U

UUd

T

1

2

2

2

1

d Test is the ratio of the total sum of squared differences in residuals over the residual sum of

squares. d Statistic is very useful as it is concerned with estimating residuals that has been

computed in regression analysis.

It is possible to see that the DW test statistic only takes values between 0 and 4 since

autocorrelation coefficient only takes values between -1 and 1. Hence when the autocorrelation

coefficient equal 0, the DW test statistic equal 2. If DW>2 we have an indication of a negative

autocorrelation and if DW<2 we have an indication of a positive autocorrelation

Unfortunately there exist no simple distribution function for this test function since it depends on

the number of observations used as well as the values of the explanatory variables used in the

regression. For that reason it is not possible to establish a precise critical value for the DW test

statistic. However, Durbin and Watson made some simulations so that you, based on the number

of observations used, and the number of parameters included in the model, can find a lower value

(L) and an upper value (U) to compare the DW test value with.

Possible outcomes from the Durbin-Watson test for autocorrelation

Positive AC Inconclusive No AC Inconclusive Negative AC

0<DW<L L<DW<U U<DW<4-U 4-U<DW<4-L 4-L<DW<4

Table above show five different regions where the DW-test value potentially could end up, if you

receive a test value that is located in the interval between the lower value (L) and the upper value

(U) your test is inconclusive and you have no use of the DW-test. However, if the DW-value is

between 0 and the lower value (L) you can draw the conclusion of having positive

autocorrelation. In case of negative autocorrelation you have to form the upper and lower value

for yourself using L and U as is done in table above.

Detection of autocorrelation

Under this the Durbin Weston test was used to see whether there is autocorrelation on those time

series data or not.

The result from the STATA we received that a DW-test value is equal to 2.242.from the

statistical table the lower value(L) was 1.160 and the upper value was 1.735.

UDWU 4

Where DW is 2.242.then the value substituted on the above equation which represent absent of

autocorrelation

735.14242.2735.1

265.2242.2735.1 , which means the model doesn’t suffer from the problem of

autocorrelation.

Heteroscedasticity and Diagnosis.

The classical assumption require for the ordinary least square estimator to be efficient states that

the variance of the error term has to be constant and same for all the observation, this is referred

to homoscedasticity error term. When this assumption is violated and the variance is different

from different observations then it is referred as heteroscedasticity. This assumption is important

and cannot be ignored since for the ordinary least square to be efficient then this assumption

must hold, otherwise the estimator will be inefficient and therefore we cannot claim our

estimator is the best among unbiased estimator.

Heteroscedasticity can be detected in two ways, by graphical method and statistical test. The

Graphical method is where the dependent is plotted against its explanatory variables, the

graphical method are useful but sometimes is difficult to say whether heteroscedasticity is

present and found harmful, it is therefore necessary to use statistical test.

Statistical test involve three tests which are Gold-feld Quant test, Breusch pagan test and white’s

test.

Ways to detect heteroskedasiticty problem

Graphical Method

A natural starting point in detecting possible deviation from homoskedasticity is to plot he data,

since we are interested on behavior of error term and its variation

Goldfeld-Quandt Test.

This work under the assumption that the error variance is equal for all observation, which is to

say the error term is homoskedasicity when this is true the variance of one part if the sample

must be the same as the variance of another part of other sample if this is not the case we

conclude that there is heteroskedasticty problem

Breusch–Pagan–Godfrey Test.

It is more general than GQ since it allow more than variable to be tested It is The success of the

Goldfeld–QuandttesIt depends not only on the value of c (the number of central observations to

be omitted) but also on identifying the correct X variable with which to order the observations.

The study used the Breusch-Pagan-Godfrey Test to determine whether the model is suffering

from the problem of heteroscedasticty and the below results obtained;

The Breusch-Pagan-Godfrey Test Results

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity

Ho: Constant variance

Variables: fitted values of loggdp

chi2(1) = 0.85

Prob > chi2 = 0.3569


The results above shows that a large chi-square led to rejection of the null hypothesis

(homoskedasticity null), and not reject the alternative hypothesis. So the result indicates the

presence of heterosckedasticty in the model.

E. Nonstationarity

Nonstationarity refers to values of mean, variance and covariance of time series data are

changing over time. The typical case is an example of the random walk model where

econometricians do several analyses and came to conclude that; random walk model is no

stationary because as t increases, its variance increases.

Testing for Stationary

There are several tests of stationary in time series data, for the case of space, two tests will be

briefly discussed:

Graphical analysis and

Autocorrelation Function (ACF) and Correlogram

Graphical Analysis

For better analysis of any time series data, it is advisable firstly to present data graphically in

order to determine the likely nature of the data. These visual plots provide impression that all

data used in regression process trends upward with time suggesting that the mean and variance of

the variables are changing and hence, a non-stationary in character.

Autocorrelation Function (ACF) and Correlogram

This is the simple test of stationary in time series data and it is defined as below

iance

klagatarianceACF

var

cov

F. Correction of problems identified in D

Correction for Heteroscedatsicity by using robust standard error

Number of

observation 20

F( 3, 16) 4.28

Prob > F 0.0212

R-squared 0.49

Root MSE 0.32545

Robust

loggdp Coef. Std. Err. t P>t [95% Conf. Interval]

loglabor -3.77456 1.184802 -3.19 0.006 -6.28623 -1.26289

logcapit -4.17455 1.168147 -3.57 0.003 -6.65091 -1.69819

logfdi 1.271049 0.380017 3.34 0.004 0.46545 2.076648

_cons 24.19987 6.803688 3.56 0.003 9.776694 38.62304


The above is the new model corrected from the problem of heterosckedasticty using the robust

standard error. Here under is the new model resulted from the above model

tttt FdiLabCapY 271.1775.3175.420.24

SE (6.804) (1.168) (1.185) (0.380)

REFERENCE

Gujarati, D.N. (2007) “Basic Econometrics”, Tata McGraw Hill Education Private Limited, New

Khan Arshad (2007) “Foreign Direct Investment and Economic Growth; The role of Domestic Financial

Sector”, PIDE working paper.

Levin, A. and L.K. Raut (1997) “Complementary between Export and Human capital in Economic

Growth; Evidence from the semi-industrialized countries” Economic Development and Cultural

Change.

Nuzhat Falki (2009) “International Review of Business Research Paper”, vol.5 No. 5 September

2009.Pp.110-120

Sadia Shaikh (2012), “Impact of FDI, Capital Formation and International Trade on Economic

Growth of Pakistan”: An Empirical Analysis

Thomas Andren.(2007), “econometrics” Ventus publishers

UNCTAD (2002) Investment Report, United Nations, New York

Zhang, K. H. (2003) “Foreign Direct Investment in China”; Asian Economic and Political Issues.

Index1: Libya data of Output (GDP), FDI, Capital and Labor for all sectors

YEAR FDI STOCK LABOR CAPITAL GDP FDI FLOW

1980 1855.425 739.036 9279.96502

-

0.284523744 -1089.34

1981 1111.295 783.912 11194.7776 -19.1901808 -744.13

1982 719.475 828.015 8641.13444 2.806056774 -391.82

1983 392.845 864.052 7610.95782

-

2.472227282 -326.63

1984 375.955 900.471 7478.80056

-

5.041781428 -16.89

1985 495.195 938.975 5769.59877 8.326778426 119.24

1986 318.275 982.409 5131.34535

-

11.35250631 -176.92

1987 311.862 1023.6 3897.0133

-

14.70205316 -97.63

1988 393.962 1059.467 4772.12023 7.579023356 97.98

1989 519.132 1103.917 4613.49386 7.199417141 125.17

1990 678.043 1165.705 5787.33248 3.720131634 158.911

1991 769.947 1212.919 4511.78927 13.34321975 91.9038

1992 869.04 1263.211 4431.33432

-

1.217100258 99.0931

1993 927.193 1314.536 5367.75704 3.172647467 58.1529

1994 854.569 1369.475 5026.66325 0.507538436 -72.6243

1995 766.082 1435.694 3439.82378

-

2.220406953 -88.4861

1996 654.36 1498.863 4848.71231 2.134123184 -111.722

1997 586.46 1570.788 4101.62246 5.212671027 -67.9

1998 458.566 1648.291 3575.5142

-

3.552244711 -127.894

1999 330.497 1726.342 3763.42296 0.749659243 -128.069

2000 471.497 1801.142 5015.41419 2.338436921 141

2001 338.497 1874.88 4205.47894 0.511727078 -133

2002 483.497 1943.685 3153.6324

-

1.250254005 145

2003 626.497 2006.347 2867.92879 12.96465682 143

2004 983.497 2068.739 3333.99358 4.435780624 357

2005 2021.497 2129.007 4063.72512 10.2900164 1038

2006 4085.497 2187.509 5486.79501 6.715576478 2064

2007 7935 2246.753 6040.58535 5.086807211 3850

2008 11115 2303.012 7742.10861 2.721379199 3180

2009 14425 2349.633 5702.86375

-

0.745390583 3310

2010 16334 2380.812 6920.60988 4.163693133 1909

2011 16334 2377.843 -59.687 0

The Analysis of LIbya (Solow model)

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