The Random Effect Model Eradicates

Published Date: 02 Nov 2017

The main purpose of this research is to analyze the impact of foreign direct investment (FDI) on gross domestic products (GDP) as the proxy of economic growth through several ways. First, I show the difference in value and significance across FDI sectors on GDP. The FDI is expanded into eight sectors such as agriculture, mining, forestry, fishery, industry, construction, trade and services sector. Therefore, this research would be able to show which sectors of FDI that have positive and significant impact on GDP.

Second, I propose the interaction term between education and FDI, in order to capture the role of education on supporting the FDI in improving the economic growth in Indonesia.

Third, I include the infrastructure and its interaction with FDI, in order to analyze its impact on supporting FDI in improving economic growth. The infrastructure in this research consist of road length, water distribution and electricity distribution line length in each province in Indonesia. This research analyzes the impact of the three kinds of infrastructure mentioned above on the FDI role in bolstering the economic growth separately.

Finally, I present the interaction term between FDI in urban area and FDI, in order to analyze the effect of FDI inflows in urban area on the FDI role in improving the economic growth.

Based on the hypothesis and research purposes, six models are constructed and described in the following section.

5.1. Model Specification

As described above, this research will examine the impact of the FDI inflow, education, infrastructure and control variables such as: labor force, government expenditure, domestic direct investment, and trade openness on economic growth. Therefore, they can be constructed into a function as follow:

GDPi(t+1)=f(FDIit, EDUCATIONit, WATERDISTRIBUTIONit,

ELECTRICITYDISTRIBUTIONit, ROADit, LABOR_FORCEit,

GOVERNMENTEXPENDITUREit, DDIit, EXPORTit)

Where, GDP = Gross domestic products (Trillion Rp)

FDI = Foreign direct investment (Million US$)

URBAN= Foreign direct investment located in urban area (Million US$)

EDUCATION = Number of high school students (in Thousand students)

WATERDISTRIBUTION= Water distribution/water capacity (1000 M3/ litre/s)

ELECTRICITYDISTRIBUTION= Electricity distribution line length (Km)

ROAD= Road length per province area (Km/Km2)

LABOR_FORCE = Labor force (Thousand number of labors)

GOVERNMENTEXPENDITURE = Government expenditures (Million Rp)

DDI = Domestic direct investment (Billion Rp)

EXPORT = export (Ten of Million US$.)

i = province ith

t = year

In this research, provincial real GDP is the dependent variable as the proxy of the economic growth because the economic growth can be defined by the percentage change of GDP over time and its index t+1 mentioned above means the independent variables will impact on the GDP in the following year.

In addition, labor force, government expenditure, domestic direct investment and export are included as the control variables. Labor force is as the proxy of human capital expected to have significant and positive impact on the GDP as the following evidences. Agrawal (2011), Kotrajaras (2010), Tiwari and Mutascu (2011), and Ahmad et al (2012) find that labor force has a positive and significant impact on economic growth.

Furthermore, government expenditures and export as the component of GDP in macroeconomic identity are included. They are expected to have positive impact the GDP. Kowalski (2000), Sukar, Ahmed, and Hasan (2000), Ahmad et al (2012), and Tiwari and Mutascu (2011) also find that economic growth is positively and significantly determined by government expenditures and export. Moreover, Tiwari and Mutascu (2011) add that export-led growth path might be possible at the first stage of growth. Export encourages the specialty of the production. Then, it triggers the import of high tech inputs and products. Therefore, it will increase the productivity and improve the economic growth.

Finally, the domestic direct investment as the proxy of private investment is also included as the determinant of the GDP. According to Sukar, Ahmed, and Hasan (2000) and Kowalski (2000), domestic direct investment is one of the economic growth determinants. They find that domestic direct investment has positive and significant effect on growth. Therefore it should positively impact the GDP as well.

In order to test the hypothesis, six econometric models are constructed in this research as follow:

H1: FDI in industry, services, construction, and trade sector have positive and significant impact on economic growth in Indonesia.

The FDI is divided into eight sectors to test the H1. Therefore the model become as follow:

GDPi(t+1) = β0 + β1 AGRICULTUREit + β2 MINING + β3 FORESTRY

+ β4 FISHERY + β5 INDUSTRYit + β6 CONSTRUCTIONit

+ β7 TRADEit + β8 SERVICESit + β9 LABORit

+ β10 GOVERNMENTEXPENDITUREit

+ β11 DDIit + β12 EXPORTit + eit …(5.1)

H2: If the education level is sufficiently high, FDI will improve the economic growth

The second model involves education and its interaction with FDI in order to test the H2 as follow:

GDPi(t+1) = β0 + β1 FDIit + β2 EDUCATIONit + β3 FDI*EDUCATION+

β4 LABORit + β5 GOVERNMENTEXPENDITURESit + β6 DDIit +

β7 EXPORTit + ei......(5.2)

H3: If the infrastructure level is sufficiently high, FDI will improve the economic growth.

The third, fourth, and fifth model introduce the interaction term between electricity distribution, road length, and water distribution and FDI to test the H3 as follow:

GDPi(t+1) = β0 + β1 WATERDISTRIBUTIONit + β2 FDIit +

β3 FDI*WATERDISTRIBUTIONit + β4 LABOR_FORCEit +

β5 GOVERNMENTEXPENDITURESit + β6 DDIit +

β7 EXPORTit + ei......(5.3)

GDPi(t+1) = β0 + β1 ELECTRICITYDISTRIBUTIONit + β2 FDIit +

β3 FDI*ELECTRICITYDISTRIBUTIONit + β4 LABOR_FORCEit +

β5 GOVERNMENTEXPENDITURESit + β6 DDIit +

β7 EXPORTit + ei...... (5.4)

GDPi(t+1) = β0 + β1 ROADit + β2 FDIit + β3 FDI*ROADit +

β4 LABOR_FORCEit + β5 GOVERNMENTEXPENDITURESit +

β6 DDIit + β7 EXPORTit + ei...... (5.5)

H4: If the FDI in urban area is sufficiently high, FDI will decrease the economic growth.

By including FDI in urban region and its interaction with FDI, the sixth model is constructed to test the H4 as follows:

GDPi(t+1) = β0 + β1 FDIit + β2 URBANit + β3 FDI*URBAN it +

β4 LABOR_FORCEit + β5 GOVERNMENTEXPENDITURESit +

β6 DDIit + β7 EXPORTit + ei......(5.6)

5.2. Econometric Framework

This research utilizes panel data analysis method to test the hypothesis through six different models mentioned above. In order to conduct panel data analysis properly, there are several steps that should be followed. First, by assuming there is neither significant provincial effect nor significant time effect. I conduct the pooled OLS regression to the data.

GDPi(t+1) = β0 + β1 FDIit + γk Xkit + εit ... (5.7)

Where X are other control variables

By running the OLS regression the cross section provinces and time periods are disregarded in the estimation. Furthermore, According to Hill, Griffiths, and Lim (2012) OLS regression is based on 6 assumptions in order to derive unbiased estimation results as follow:

SR1. Linear in parameters

y = β0 + β1 x +e ......... (5.8)

SR2. The data are obtained from random sampling such that the expected value of random error e is

E(e)=0 ......... (5.9)

SR3. The variance is same for all error terms

Var(e)=σ2 ......... (5.10)

SR4. Error is uncorrelated with any of the independent variable

E(e|x1, x2, x3, ... xn)=0 ......... (5.11)

SR5. Perfect co-linearity is not occurred between independent variables.

SR6. (optional) Normally distributed error terms

e ~ N(0, σ2)

If it is considered that there are group and fixed effect on the data, I do the following steps.

Second, I conduct the fixed effect method, if it is assumed that each province might have its own initial GDP and have the same error variance with other provinces.

yit = (α + ai) + X’it β + uit ......... (5.12)

ai term is unobserved variable assumed as constant variable across time that might be correlated with other control variables. Therefore, it will cause bias in the estimation results of independent variables coefficient. In order to eliminate the bias, fixed effect model is utilized.

Third, I conduct the F-Test to prove the existence of fixed group effect on the data.

F ~ FN-1, N(T-1)-K ......... (5.13)

If the Ho is rejected, the fixed effect might be occurred in the observation data.

SSRr is R-squared derived from LSDV regression. LSDV is an OLS regression that includes dummy group variables and chooses one group as a base. SSRur is R-squared derived from pooled OLS with N.T observations. Furthermore, N is the number of groups, in this case the number of provinces, T is the total observation periods (in years), and K is the total number of parameters by disregarding the intercept.

Fourth, I conduct the random effect method, if it is assumed that each province might have its own disruption variance.

yit = α + X’it β + (ai + uit) ......... (5.14)

Where: ai is assumed not correlated with any of the independent variables. However, serial correlations will be occurred.

.... (5.15)

The random effect model eradicates this bias problem.

Fifth, I conduct the Breush-Pagan Lagrange Multiplier (LM) to affirm the presence of random group effect on the data.

According to Breusch and Pagan (1980) the test procedure for random effect model as follow:

Determine the null and alternative hypothesis:

H0: σu2 = 0;

H1: σu2 ≠ 0

Use the following formula:

LM=nT/2(T-1)[(Σ(Tui.)2/ Σ Σuit2)-1]2 ~ Xi2 under Ho ... (5.16)

If the Ho is rejected, the Hausman Test needs to be conducted. However, if it is fail to reject, the OLS model is better than random effect.

Finally, if both of third and fifth steps are rejected, it means there are both fixed and random effects on the data, the Hausman Test should be conducted in order to determine between Fixed and Random effect that produces better estimation.

H0: Cov (ai, X’it) = 0 (random effect);

H1: Cov (ai, X’it) ≠ 0 (fixed effect)

Hausman = (βRE- βFE)’ [VAR(βRE) – VAR(βFE)]-1(βRE- βFE) ~ Xi2 (#βFE) ... (5.17)

Where number of βFE = number of βRE (no intercept)

If null hypothesis is rejected, the random effect is not appropriate estimation method. Therefore, the fixed effect model is preferable and vice versa.

I conduct the same step as Akbar et al (2011) did in their research on the determinants of economic growth in nine Asian countries. However, according to Ma’ruf and Wihastuti (2008) and Kotrajaras (2010), panel unit root test should be conducted for all the variables before they are regressed, in order to identify the stationarity of the data. Enders (in Ma’ruf and Wihastuti, 2008) states that the stationer data is needed in order to avoid dubious regression. Furthermore, Kotrajaras (2010) state that if the data is stationer, the panel regression method can be implemented. However, if the data is non-stationer, co-integration test procedure should be implemented. Therefore, in this present research, I conduct the unit root test as the pre-step of the panel data analysis. In brief, the analysis method is simplified in the following diagram.

Figure 5.1. Panel Data Modeling Process

Unobserved

Heterogeneity

Intercept Error term

RANDOM

EFFECT

FIXED

EFFECT

N/A

LM -TEST

F-TEST

Ho Ho

OLS

Reject Ho Ho

HAUSMAN TEST Reject Ho Reject Ho

Source: Park (2011)

5.3. Data Sources

The data used in this research were obtained from several sources. The GDP, labor force, education level, and government expenditure are gathered from Indonesia Statistical Bureau (BPS). In addition, FDI and DDI were collected from Indonesia Investment Coordinating Board (BKPM). Moreover, Infrastructure data is taken from Ministry of Public Works. Finally, export data are obtained from the Ministry of Trade.

5.4. The Sample

This research uses panel data of 30 provinces in Indonesia from 2002 to 2009. The total observation is 240. Actually, there are 34 provinces in Indonesia. However, this research uses only 30 provinces data because 4 provinces are newly established such as: Kepulauan Riau and Papua Barat established in 2003; Sulawesi Barat established in 2004; and Kalimantan Utara established in 2012. Therefore, if I involve these newly established provinces, there will be several missing data problem. Furthermore, they will cause statistical difficulties in this research.

The 30 provinces of Indonesia included in this research are Nangroe Aceh Darussalam, Sumatera Utara, Sumatera Barat, Riau, Jambi, Sumatera Selatan, Kep. Bangka Belitung, Bengkulu, Lampung, DKI Jakarta, Jawa Barat, Banten, Jawa Tengah, DI Yogyakarta, Jawa Timur, Bali, Nusa Tenggara Barat, Nusa Tenggara Timur, Kalimantan Barat, Kalimantan Tengah, Kalimantan Selatan, Kalimantan Timur, Sulawesi Utara, Gorontalo, Sulawesi Selatan, Sulawesi Tengah, Sulawesi Tenggara, Maluku, Maluku Utara, and Papua.

The summary of the dependent and independent variables in this research are shown in table 5.1. It shows that the number of observation for all variables are 240 and there is no big different in data range between variables. Therefore, the estimation will result in presentable numbers. Furthermore, the correlation matrix between variables is presented in table 5.2. It shows that there is no perfectly correlation between variables. Therefore, unbiased estimation result can be obtained. Finally, the normal distribution graph of the dependent variable is provided in Figure 5.3. It shows that the GDP data distribution as the dependent variable has already normally distributed.

Table 5.1. Summary Statistics

Variable

Observation

Mean

Standard Deviation

Minimum

Maximum

gdp

240

55.43981

84.40346

1.767375

394.7145

fdi

240

264.5867

900.9234

0

9927.781

agriculture

240

6.349858

20.18338

0

237.1687

mining

240

4.997885

25.87655

0

272.8987

forestry

240

0.623898

7.517216

0

112.2494

fishery

240

0.325398

1.592999

0

17

industry

240

108.0717

301.0183

0

2209.74

construction

240

19.47473

74.9387

0

604.0874

trade

240

15.5015

63.59686

0

518.6515

services

240

109.2418

695.5375

0

8561.935

urban

240

168.4183

845.1314

0

9927.781

education

240

197.7214

243.0759

15.63

1039.378

water distribution

240

13.3619

14.5959

3.74226

196.711

electricity distribution

240

19371.28

22839.75

2291.35

90376.56

road length

240

0.703991

1.65513

0

9.89006

export

240

287.4408

584.3057

0.048724

3594.872

government expenditure

240

2035.847

2956.417

116.951

20523.32

ddi

240

772.7146

1659.442

0

11347.89

labor force

240

3530.077

4972.221

320.622

20338.57

Table 5.2. Correlation matrix

gdp

fdi

agriculture

mining

forestry

gdp

1

fdi

0.6926

1

agriculture

-0.0104

0.0263

1

mining

0.4093

0.5889

-0.0459

1

forestry

-0.0196

-0.0135

-0.0042

-0.0154

1

fishery

0.0295

0.0483

-0.0334

0.1362

-0.0169

industry

0.6055

0.4656

0.0674

0.1006

-0.0281

construction

0.6263

0.7496

0.0098

0.4063

-0.0216

trade

0.6671

0.7813

-0.0252

0.6205

-0.0177

services

0.4918

0.919

-0.021

0.5828

-0.0114

urban

0.5439

0.9364

-0.0103

0.6328

-0.0058

education

0.8507

0.3642

-0.0213

0.1035

-0.0136

water distribution

0.5916

0.7642

-0.037

0.6211

-0.0157

electricity

0.6313

0.7511

-0.0459

0.6391

-0.0187

road length

0.6281

0.7186

-0.0667

0.6147

-0.0227

export

0.6604

0.6863

0.1025

0.6131

-0.0205

government expenditure

0.8009

0.7973

0.0297

0.5996

-0.0268

domestic direct investment

0.6241

0.521

0.1301

0.2515

-0.0037

labor force

0.7815

0.2719

-0.0285

0.0149

-0.0099

Table 5.2. Correlation matrix (continued)

fishery

industry

construction

trade

services

gdp

fdi

agriculture

mining

forestry

fishery

1

industry

-0.0151

1

construction

0.0059

0.449

1

trade

0.0491

0.2416

0.743

1

services

0.0577

0.0944

0.5858

0.7137

1

urban

0.0601

0.1478

0.6382

0.788

0.9847

education

0.0112

0.6122

0.3297

0.2817

0.1424

water distribution

0.0572

0.0622

0.646

0.8292

0.7955

electricity

0.0466

0.0962

0.681

0.8961

0.7536

road length

0.0521

0.0901

0.6558

0.8674

0.721

export

0.0469

0.1436

0.5788

0.7437

0.6708

government expenditure

0.0383

0.3329

0.6992

0.8121

0.7161

domestic direct investment

0.0146

0.566

0.4637

0.4755

0.3234

labor force

0.0014

0.6234

0.2374

0.1576

0.0428

Table 5.2. Correlation matrix (continued)

urban

education

water distribution

electricity

road length

gdp

fdi

agriculture

mining

forestry

fishery

industry

construction

trade

services

urban

1

education

0.1735

1

water distribution

0.833

0.1719

1

electricity

0.8085

0.2176

0.9766

1

road length

0.7721

0.2459

0.9553

0.9825

1

export

0.7242

0.2945

0.784

0.7918

0.7527

government expenditure

0.7678

0.4831

0.8031

0.8226

0.7882

domestic direct investment

0.3505

0.4842

0.3535

0.3851

0.3652

labor force

0.0635

0.9741

0.037

0.0807

0.1087

Table 5.2. Correlation matrix (continued)

export

government expenditure

domestic direct investment

labor force

gdp

fdi

agriculture

mining

forestry

fishery

industry

construction

trade

services

urban

education

water distribution

electricity

road length

export

1

government expenditure

0.87

1

domestic direct investment

0.4111

0.5287

1

labor force

0.1706

0.3578

0.4417

1

Figure 5.2. Normal distribution graph of GDP(t+1)