Jurnal Ekonomi & Studi Pembangunan    Volume 24 Nomor 1, April 2023  

 

 
 
 
 
 
 
 
 
 

 
 

Article Type: Research Paper 
 

Fix effect sur to analyze economic growth in 
developed and developing countries 
 
Muhamad Liswansyah Pratama*, Rahma Fitriani, and Suci Astutik 
 
Abstract: This study aims to identify the relationship between population density, 
inflation, and unemployment rates on the human development index, GNP, export-
import, and urbanization in the developed and developing countries category using 
the Fix Effect Seemingly Unrelated Regression (FE SUR) with a dummy variable as 
the slope component. This research necessitates the development of the 
Seemingly Unrelated Regression model, specifically the Panel Seemingly Unrelated 
Regression (Panel SUR) model with a dummy variable as the slope component, due 
to the dynamic nature of the data and the fact that the same set of predictor 
variables explains the five response variables. The Panel, the Seemingly Unrelated 
Regression model with dummy variables, can accommodate research objectives 
where the SUR model can explain the influence between variables, differences in 
characteristics between countries can be explained by fixed effect models, and 
differences in the effect of population density, inflation, and unemployment rates 
on the human development index, GNP, exports imports and urbanization in the 
categories of developed and developing countries can be explained by slope 
dummy variables. The results showed that 98.46% of the diversity of response 
variables (human development index, GNP, exports, imports, and urbanization) 
could be explained by predictor variables (population density, inflation, and 
unemployment rate), while the other 1.54% was explained by other factors not 
included in the fixed effect SUR model. In addition, the results show that 
population density has a significant positive relationship with GNP, imports, and 
exports. However, there is a significant negative relationship between 
unemployment and GNP. There are large differences in the relationship between 
the unemployment rate and GNP in developed and developing countries, whereas 
in developed countries, there is a larger and negative relationship compared to 
developing countries. 
Keywords: Fix Effect SUR; Panel SUR; Developed and Developing Country; World 
Economics; Economic Growth 
JEL Classification: A10; B23; C33; F00; G00; O10 

 

 
 

Introduction 
 
To attain economic growth is a goal shared by all countries, but notably by 
developing countries. A country is considered developed if its economic 
level is high and evenly dispersed, its standard of living is high, and its 
technology is advanced. Developing countries have an average degree of 
social welfare and no economic equality (Heshmati et al., 2014). The 
benchmark for economic growth is economic growth and development. 
Every country must pursue economic growth on an annual basis in order to  

AFFILIATION: 
Department of Statistics, Faculty of 
Mathematics and Science, 
Universitas Brawijaya, East Java, 
Indonesia 
 
*CORRESPONDENCE: 
liswan2000@gmail.com 
 
THIS ARTICLE IS AVALILABLE IN: 
http://journal.umy.ac.id/index.php/esp  

 
DOI: 10.18196/jesp.v24i1.17821 
 
CITATION: 
Pratama , M. L., Fitriani, R., & 
Astutik, S. (2023). Fix effect sur to 
analyze economic growth in 
developed and developing 
countries. Jurnal Ekonomi & Studi 
Pembangunan, 24(1), 164-181. 
 
ARTICLE HISTORY 
Received: 
04 Feb 2023 
Revised: 
04 May 2023 
Accepted: 
16 May 2023 

 

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https://statistika.ub.ac.id/
https://statistika.ub.ac.id/
https://statistika.ub.ac.id/
https://statistika.ub.ac.id/
mailto:liswan2000@gmail.com
http://journal.umy.ac.id/index.php/esp
http://dx.doi.org/10.18196/jesp.v24i1.17821
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Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 165 

avoid economic crises and maintain a prosperous society. This is still a challenge in 
emerging countries, which strive for an improved economy through various economic 
activities and policies. Economic growth is a process because it is a stage that every 
country must experience; therefore, it requires long-term effort and cooperation 
between the community, government, and other concerned parties. The economic 
aspect, which includes international commerce and GNP, and the social aspect, which 
includes the human development index and urbanization, are the two primary lenses to 
view economic progress (Kuncoro, 2006). 
 
Seemingly Unrelated Regression (SUR) is a form of multivariate regression that can 
accommodate residual correlations between equations (the structure of the variance 
between equations) so that each equation in the model seems to be independent or 
unrelated. However, the equations have relatedness (Alaba et al., 2019). To model the 
link between each predictor variable and each response variable, data from a single point 
in time are insufficient, due to the dynamic character of the data, in multivariate 
regression analysis of economic variables. Therefore, data is needed regarding variables 
related to several periods for each research object (panel data) so that the regression 
model obtained is better at describing the relationship of predictor variables to response 
variables so that a method that can accommodate these problems is developed, namely 
multivariate regression analysis on panel data. Panel data regression analysis is one of the 
developments that allows statistical users to analyze cause-and-effect relationships in the 
combined cross-section and time series data (Fitriani et al., 2021). The information 
obtained through panel data regression analysis becomes more informative because it 
considers the unit cross-section elements in several periods. Panel data regression 
analysis is a statistical method used to model the relationship of one or more predictor 
variables to response variables in several observed sectors of a research object over a 
certain period (Baltagi, 2008).  
 
Over time, more complex statistical analysis methods are needed to allow statistical users 
to analyze the relationship of several predictor variables to more than one response 
variable in panel data. Therefore, a Seemingly Unrelated Regression Panel model was 
developed, capable of modeling the relationship of one or more predictor variables to 
more than one observed response variable of a research object over a certain time in 
panel data. The Seemingly Unrelated Regression Panel Model is one of the developments 
of multivariate regression analysis and panel data regression analysis that allows 
statistical users to analyze cause-and-effect relationships in the combined cross-section 
and time series data, not just one response variable. The Fix Effect SUR model is a form of 
the SUR Panel model which assumes that individuals have different characteristics. 
Through the Fix Effect Seemingly Unrelated Regression model, the information obtained 
becomes more informative and complex because in addition to considering elements of 
unit cross sections in several periods on many response variables at once, the Fix Effect 
Seemingly Unrelated Regression model also provides information about individual 
characteristics. 
 
This study aims to develop a SUR model in which the data used is panel data, and a dummy 
variable will be added as a slope component and apply it to model the effect of economic 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 166 

variables (population density, inflation, and unemployment rate) on economic growth 
indicators (human development index, GNP, imports, exports, and urbanization). This 
study uses the SUR model because the five response variables (Human Development 
Index, GNP, Imports, Exports, and Urbanization) are explained by the same predictor 
variables (Population Density, Inflation, and Unemployment Rate). This study uses panel 
data because of the dynamic nature of the data so that data at one point in time is 
insufficient in modeling the effect of predictor variables on response variables. This study 
uses a fixed effect model because it is assumed that there are differences in 
characteristics between countries. In addition, the results of research by Wafiq and 
Suryanto (2021), Wau (2022), and research by A'yun and Khasanah (2022) state that the 
fixed effect model is better at modeling economic variables than the pooled and random 
effect models. This study uses a dummy variable as a slope component because it aims to 
determine differences in the effect of predictor variables on response variables in the 
categories of developed countries and developing countries. So that this research can be 
beneficial for developing countries in maximizing economic activities in their countries as 
well as aspects that need to be improved in order to have a high economic level like in 
developed countries. Apart from that, this research can be useful for developed countries 
to maintain their country's economic level. 
 
 

Research Method 
 
This study aims to develop the Seemingly Unrelated Regression (SUR) model where the 
data used is panel data and added a dummy variable as a slope component and apply it 
to model the effect of economic variables (population density, inflation, and 
unemployment rate) on economic growth indicators (human development index, GNP, 
imports, exports, and urbanization). The data used in this study are data on economic 
variables (population density, inflation, unemployment rate, human development index, 
GNP, imports, exports, and urbanization) in 145 countries in the world consisting of 110 
developing countries and 35 developed countries in 2010 until 2019 sourced from the 
World Bank and IMF websites. This study uses the SUR model because the five response 
variables (Human Development Index, GNP, Imports, Exports, and Urbanization) are 
explained by the same predictor variables (Population Density, Inflation, and 
Unemployment Rate). This study uses panel data because of the data's dynamic nature of 
the data so data at one point in time is insufficient in modeling the effect of the predictor 
variable on the response variable. 
 
Seemingly Unrelated Regression (SUR) 
 
The SUR model uses m response variables as a function of p predictor variables which can 
be seen in equation (1) (Moon & Perron, 2006). 
 
𝑌1𝑖 =  𝛽10 +  𝛽11𝑋1𝑖 +  𝛽12𝑋2𝑖 + ⋯ +  𝛽1𝑝𝑋𝑝𝑖 + 𝛽20(0) +  𝛽21(0) + ⋯ + 𝛽21(0) + ⋯ +

𝛽𝑚𝑝(0) +  𝜀1𝑖   

𝑌2𝑖 = 𝛽10(0) +  𝛽11(0) + ⋯ + 𝛽1𝑝(0) +  𝛽20 +  𝛽21𝑋1𝑖 +  𝛽22𝑋2𝑖 + ⋯ +  𝛽2𝑝𝑋𝑝𝑖 +

𝛽𝑚0(0) +  𝛽𝑚1(0) +  … +  𝛽𝑚𝑝(0) +  𝜀2𝑖   



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 167 

⁝ 
 
𝑌𝑚𝑖 = 𝛽10(0) +  𝛽11(0) + ⋯ + 𝛽1𝑝(0) + ⋯ + 𝛽(𝑚−1)𝑝(0) +  𝛽𝑚0 +  𝛽𝑚1𝑋1𝑖 +

 𝛽𝑚2𝑋2𝑖 + ⋯ +  𝛽𝑚𝑝𝑋𝑝𝑖 +  𝜀𝑚𝑖   (1) 

 
Equation (1) can be simplified to equation (2). 
 

𝑌𝑙𝑖 =  𝛽𝑙0 + ∑ 𝛽𝑙𝑗 𝑋𝑗𝑖
𝑝
𝑗=1  +  𝜀𝑙𝑖  ; 𝑖 = 1, 2, … , 𝑛 ; 𝑙 = 1,2, … , m ; j = 1,2, … , 𝑝  (2) 

 
where: 
𝑌𝑙𝑖 = i-th value of the l-th response variable 
𝑋𝑗𝑖 = i-th value of the j-th predictor variable 

𝛽𝑙0= intercept the response variable to-l 
𝛽𝑙𝑗 = parameter of the jth predictor variable to the l-th response variable 

𝜀𝑙𝑖 = i-th value of the random error variable on the l-th response variable 
n= sample size 
m= number of response variables 
p= number of predictor variables 
 
The form of the SUR equation in the matrix can be seen in equation (3) (Pramoedyo et al., 
2020). 
 
𝒀𝑚𝑛×1 = 𝑿𝑚𝑛×𝑚(𝑝+1)𝜷𝑚(𝑝+1)×1 +  𝜺𝑚𝑛×1  (3) 

 
Fix Effect Seemingly Unrelated Regression (FE SUR) 
 
In the fixed effects model, it is assumed that there is a relationship between the 
characteristics of the object (𝛼𝑚𝑖 ) and the predictor variables for each response variable. 
The Fix Effect Seemingly Unrelated Regression model is presented in equation (4) (Xu et 
al., 2018). 
 

𝑌1𝑖𝑡 =  𝛽01𝑖 +  𝛽11𝑋1𝑖𝑡 +  𝛽12𝑋2𝑖𝑡 + ⋯ +  𝛽1𝑝𝑋𝑝𝑖𝑡 +  𝜀1𝑖𝑡 

 
𝑌2𝑖𝑡 =  𝛽02𝑖 +  𝛽21𝑋1𝑖𝑡 +  𝛽22𝑋2𝑖𝑡 + ⋯ +  𝛽2𝑝𝑋𝑝𝑖𝑡 +  𝜀2𝑖𝑡  

⋮ 
𝑌𝑚𝑖𝑡 =  𝛽0𝑚𝑖 +  𝛽𝑚1𝑋1𝑖𝑡 +  𝛽𝑚2𝑋2𝑖𝑡 + ⋯ +  𝛽𝑚𝑝 𝑋𝑝𝑖𝑡 +  𝜀𝑚𝑖𝑡  (4) 

 
Slope Dummy Fix Effect SUR 
 
The Slope Dummy Fix Effect Seemingly Unrelated Regression model is presented in 
equation (5). 
 
𝑌1𝑖𝑡 =  𝛼10𝑖 + 𝛼112(𝐷2𝑖 × 𝑋1𝑖𝑡 ) + 𝛼113(𝐷3𝑖 × 𝑋1𝑖𝑡 ) + ⋯ + 𝛼11𝑘 (𝐷𝑘𝑖 × 𝑋1𝑖𝑡 ) +

𝛼122(𝐷2𝑖 × 𝑋2𝑖𝑡 ) + 𝛼123(𝐷3𝑖 × 𝑋2𝑖𝑡 ) + ⋯ + 𝛼12𝑘 (𝐷𝑘𝑖 × 𝑋2𝑖𝑡 ) + ⋯ + 𝛼1𝑝2(𝐷2𝑖 ×



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 168 

𝑋𝑝𝑖𝑡 ) + 𝛼1𝑝3(𝐷3𝑖 × 𝑋𝑝𝑖𝑡 ) + ⋯ + 𝛼1𝑝𝑘 (𝐷𝑘𝑖 × 𝑋𝑝𝑖𝑡 ) + 𝛽11𝑋1𝑖𝑡 +  𝛽12𝑋2𝑖𝑡 + ⋯ +

 𝛽1𝑝𝑋𝑝𝑖𝑡 + 𝜀1𝑖𝑡   

𝑌2𝑖𝑡 =  𝛼20𝑖 + 𝛼212(𝐷2𝑖 × 𝑋1𝑖𝑡 ) + 𝛼213(𝐷3𝑖 × 𝑋1𝑖𝑡 ) + ⋯ + 𝛼21𝑘 (𝐷𝑘𝑖 × 𝑋1𝑖𝑡 ) +

𝛼222(𝐷2𝑖 × 𝑋2𝑖𝑡 ) + 𝛼223(𝐷3𝑖 × 𝑋2𝑖𝑡 ) + ⋯ + 𝛼22𝑘 (𝐷𝑘𝑖 × 𝑋2𝑖𝑡 ) + ⋯ + 𝛼2𝑝2(𝐷2𝑖 ×

𝑋𝑝𝑖𝑡 ) + 𝛼2𝑝3(𝐷3𝑖 × 𝑋𝑝𝑖𝑡 ) + ⋯ + 𝛼2𝑝𝑘 (𝐷𝑘𝑖 × 𝑋𝑝𝑖𝑡 ) +  𝛽21𝑋1𝑖𝑡 +  𝛽22𝑋2𝑖𝑡 + ⋯ +

 𝛽2𝑝𝑋𝑝𝑖𝑡 + 𝜀2𝑖𝑡   

⁝ 
 
𝑌𝑚𝑖𝑡 =  𝛼𝑚0𝑖 + 𝛼𝑚12(𝐷2𝑖 × 𝑋1𝑖𝑡 ) + 𝛼𝑚13(𝐷3𝑖 × 𝑋1𝑖𝑡 ) + ⋯ + 𝛼𝑚1𝑘 (𝐷𝑘𝑖 × 𝑋1𝑖𝑡 ) +

𝛼𝑚22(𝐷2𝑖 × 𝑋2𝑖𝑡 ) + 𝛼𝑚23(𝐷3𝑖 × 𝑋2𝑖𝑡 ) + ⋯ + 𝛼𝑚2𝑘 (𝐷𝑘𝑖 × 𝑋2𝑖𝑡 ) + ⋯ +

𝛼𝑚𝑝2(𝐷2𝑖 × 𝑋𝑝𝑖𝑡 ) + 𝛼𝑚𝑝3(𝐷3𝑖 × 𝑋𝑝𝑖𝑡 ) + ⋯ + 𝛼𝑚𝑝𝑘 (𝐷𝑘𝑖 × 𝑋𝑝𝑖𝑡 ) + 𝛽𝑚1𝑋1𝑖𝑡 +

 𝛽𝑚2𝑋2𝑖𝑡 + ⋯ +  𝛽𝑚𝑝𝑋𝑝𝑖𝑡 + 𝜀𝑚𝑖𝑡    (5) 

 
SUR Model Assumptions 
 
Several assumptions must be fulfilled in the Seemingly Unrelated Regression (SUR) model, 
namely the assumption of non-multicollinearity between predictor variables and the 
correlation of errors between equations. 
 
Checking Non-multicollinearity between Predictor Variables 
 
One of the regression assumptions is that there is no relationship between predictor 
variables. The hypothesis underlying the non-multicollinearity assumption test is 
 
𝐻0: there is no multicollinearity between predictor variables vs 
 
𝐻1: there is multicollinearity between predictor variables 
 
If 𝐻0 is true, then the VIF statistic is used in the equation (6) 
 

𝑉𝐼𝐹𝑗 =  
1

1−𝑅𝑗
2  (6) 

 
where: 
𝑉𝐼𝐹𝑗  = VIF value of the j-th predictor variable 

Accept 𝐻0 if 𝑉𝐼𝐹𝑗  statistic < 10 (Bowerman & O’Connel, 1990). 

 
Testing Correlation of Errors between Equations Assumptions  
 
The purpose of testing the assumptions of error correlation is to find out whether there 
is an error correlation between equations, with the hypothesis: 
 
𝐻0 : 𝑠𝑖𝑗 = 0 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 ≠ 𝑗; 𝑖 = 1, 2, … , 𝑚; 𝑗 = 1, 2, … , 𝑚  (there is no error correlation 

between equations) vs 
 
𝐻1: 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 𝑖𝑗 𝑤ℎ𝑒𝑟𝑒 𝑠𝑖𝑗 ≠ 0 (there is an error correlation between equations) 



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Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 169 

If 𝐻0 is true, then the Lagrange Multiplier test statistic is used in the equation (7). 
 

𝐿𝑀 = 𝑛𝑡 ∑ ∑ 𝑠𝑖𝑗
2𝑖−1

𝑗=1
𝑚
𝑖=1 ~𝜒𝑚(𝑚−1)

2

2  (7) 

 
where: 
𝑠𝑖𝑗  = correlation of the residuals of the i-th equation and the j-th equation 

n = sample size 
t = period of time 
m = number of equations 

Accept 𝐻0 if LM statistics < 𝜒
𝛼,

𝑚(𝑚−1)

2

2  or 𝑃 (𝐿𝑀 < 𝜒
𝛼,

𝑚(𝑚−1)

2

2 ) > 𝛼 (Greene, 2012). 

 
Parameter Estimation of SUR Model with GLS 
 
Parameters in the SUR Panel model can be estimated using Generalized Least Square 
(GLS) by minimizing the sum of squared errors where it is assumed that matrix V (OLS 
residual matrix of variance) is known as follows (Zellner, 1962; Nisak, 2016; Biørn, 2004). 
 

𝜀̂′𝜀̂ =  (𝑌 − 𝑋�̂�)′𝑉−1(𝑌 − 𝑋�̂�) 

𝜀̂′𝜀̂ =  (𝑌′ − 𝑋′�̂�′)𝑉−1(𝑌 − 𝑋�̂�) 

𝜀̂′𝜀̂ =  𝑌′𝑉 −1𝑌 − 𝑌′𝑉 −1𝑋�̂� − 𝑌𝑉 −1𝑋′�̂�′ + 𝑋�̂�𝑉 −1𝑋′�̂�′ 

𝜀̂′𝜀̂ =  𝑌′𝑉 −1𝑌 − 2𝑋′𝑉 −1�̂�′𝑌 + 𝑋�̂�𝑉 −1𝑋′�̂�′ 

𝜕(𝜀̂′𝜀̂)

𝜕(�̂�)
=

𝜕(𝑌′𝑉−1𝑌 − 2𝑋′𝑉 −1�̂�′𝑌 + 𝑋�̂�𝑉−1𝑋′�̂�′)

𝜕(�̂�)
= 0 

𝜕(𝜀̂′𝜀̂)

𝜕(�̂�)
= −2𝑋′𝑉 −1𝑌 + 2𝑋′𝑉−1𝑋�̂� = 0 

−𝑋′𝑉 −1𝑌 + 𝑋′𝑉 −1𝑋�̂� = 0 

𝑋′𝑉−1𝑋�̂� = 𝑋′𝑉 −1𝑌 

�̂� = (𝑋′𝑉 −1𝑋)−1𝑋′𝑉 −1𝑌 
(8) 
 
where: 
Y = response variable vector is mn × 1 in size 
X = predictor variable matrix of size mn × m(p+1) 
V = error variance matrix of size mn × mn 

�̂� = parameter estimator vector of size m(p+1) × 1 
m = number of response variables 
n = sample size 
p = number of predictor variables 
 
Simultaneous Testing 
 
The purpose of testing is to find out the relationship between the predictor variables 
simultaneously with the response with the hypothesis: 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 170 

𝐻0: 𝛽11 = ⋯ = 𝛽1𝑝 = ⋯ =  𝛽2𝑝 = ⋯ = 𝛽𝑚𝑝 = 0 vs 

 
𝐻1: 𝑡ℎ𝑒𝑟𝑒 𝑖𝑠 𝑜𝑛𝑒 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑙𝑗 𝑤ℎ𝑒𝑟𝑒𝛽𝑙𝑗 ≠ 0; 

𝑙 = 1,2, … , 𝑚; 𝑗 = 1,2, … , 𝑝  
 
If 𝐻0 is true, then the F test statistic is used in the equation (9). 
 

𝐹 =
𝑀𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛

𝑀𝑒𝑎𝑛 𝑠𝑞𝑢𝑎𝑟𝑒 𝑒𝑟𝑟𝑜𝑟
~𝐹𝑚𝑝,𝑚𝑛−𝑚𝑝

   (9) 

 

Accept 𝐻0 if F >𝐹𝑚𝑝,𝑚𝑛−𝑚𝑝
𝛼/2

 or 𝑃 (𝐹 < 𝐹𝑚𝑝,𝑚𝑛−𝑚𝑝
𝛼/2

) > 𝛼 (Effendi, et al., 2020). 

 
Partial Testing 
 
The purpose of doing partial testing is to find out the relationship of each predictor 
variable individually to the response with the hypothesis: 
 
𝐻0: 𝛽𝑙𝑗 = 0 vs 

 
𝐻1: 𝛽𝑙𝑗 ≠ 0;  𝑙 = 1,2, … , 𝑚; 𝑗 = 1,2, … , 𝑝 

 
If 𝐻0 is true, then the t-test statistic is used in the equation (10). 
 

𝑡 =
�̂�𝑙𝑗

𝑆(�̂�𝑙𝑗)
~ 𝑡𝑚𝑛−𝑚𝑝

 ; 𝑙 = 1,2, … , 𝑚; 𝑗 = 1,2, … , 𝑝 (10) 

 
where: 

�̂�𝑙𝑗  = parameter estimator 𝛽𝑙𝑗  

𝑆(�̂�𝑙𝑗 ) = standard error of parameter estimator 𝛽𝑙𝑗  

Accept 𝐻0 if t < 𝑡𝑚𝑛−𝑚𝑝
𝛼/2

 or 2𝑃 (𝑡 < 𝑡𝑚𝑝,𝑚𝑛−𝑚𝑝
𝛼/2

) > 𝛼 (Fernandes and Solimun, 2019). 

 
Research Procedure 
 
The procedure of this research is as follows. 
1. Checking the relationship between predictor variables (assuming non-

multicollinearity) using VIF statistics as in equation (6) 
2. Estimating the parameters of the Fix Effect SUR model using the general least squares 

(GLS) method in equation (8) 
3. Checking the correlation of errors between equations assumption using the Lagrange 

Multiplier test statistic as in equation (7) 
4. Testing the relationship of the predictor variables to the response variables of the Fix 

Effect SUR model simultaneously as in equation (9) and individually as in equation (10) 
5. Checking the feasibility of the Fix Effect SUR model using the coefficient of 

determination 
6. Interpretation of the model obtained 
 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 171 

Result and Discussion 
 
Fix Effect SUR Parameter Estimation 
 
After analysis, the parameter estimators of the Fix Effect SUR model are obtained as in 
Table 1  
 
Table 1 Fix Effect SUR Parameter Estimation 

Variable Parameter 
Estimation 

P-Value Variable Parameter 
Estimation 

P-Value 

X1.1 0.001 0.9986 X1D.1 0.005 0.9998 
X2.1 0 0.9999 X2D.1 -0.003 0.9996 
X3.1 -0.002 0.9993 X3D.1 -0.001 0.9998 
X1.2 28.68 <0.0001 X1D.2 12.831 0.4175 
X2.2 -0.055 0.8986 X2D.2 -9.768 0.0817 
X3.2 -10.358 0.0001 X3D.2 -16.019 <0.0001 
X1.3 2.952 <0.0001 X1D.3 11.711 0.4593 
X2.3 -0.009 0.9838 X2D.3 3.776 0.501 
X3.3 -2.195 0.3941 X3D.3 -4.474 0.2549 
X1.4 2.657 0.0001 X1D.4 19.459 0.2188 
X2.4 0.002 0.9955 X2D.4 0.471 0.9331 
X3.4 -2.019 0.4331 X3D.4 -4.718 0.2299 
X1.5 0.103 0.8778 X1D.5 0.169 0.9915 
X2.5 -0.009 0.9825 X2D.5 -0.081 0.9884 
X3.5 -0.072 0.9778 X3D.5 -0.015 0.9970 

 
Based on Table 1, the Fix Effect SUR model is obtained as in equation (11). 
  
𝐻𝐷𝐼𝑖𝑡 =  𝛼1𝑖 + 0.005(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 0.003(𝐷2𝑖 × 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) −

0.001(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +  0.001𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 +
0𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 − 0.002𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐺𝑁𝑃𝑖𝑡 =  𝛼2𝑖 + 12.931(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 9.768(𝐷2𝑖 × 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) −

16.019(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) + 28.68𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 −
0.055𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 − 10.358𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼3𝑖 + 11.711(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) + 3.776(𝐷2𝑖 ×

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 4.474(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
2.952𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
2.195𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼4𝑖 + 19.459(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) + 0.471(𝐷2𝑖 ×

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 4.718(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
2.657𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.002𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
2.019𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 172 

𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 =  𝛼5𝑖 + 0.169(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 0.081(𝐷2𝑖 ×
𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 0.015(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
 0.103𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
0.072𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡    (11) 

 
Checking Non-Multicollinearity Assumption 
 
Examination of non-multicollinearity assumptions is carried out to determine the 
relationship between predictor variables whether there is multicollinearity or not. The 
results of checking the non-multicollinearity assumptions between predictor variables are 
presented in Table 2. 
 
Table 2 Results of Checking of Non-Multicollinearity Assumptions 

The j-th Predictor Variable 𝑽𝑰𝑭𝒋 

Population Density 1.008598 
Inflation 1.001373 

Unemployment Rate 1.008285 

 
Through Table 2, VIF statistics are obtained for population density (1.008598), inflation 
(1.001373), and unemployment rate (1.008285) < 10. Therefore, sufficient evidence is 
obtained to accept 𝐻0 so that it can be concluded that there is no multicollinearity 
between predictor variables and non-multicollinearity assumption between predictor 
variables in the fixed effect SUR model has been fulfilled. 
 
Testing Correlation of Errors between Equation Assumptions 
 
Testing the assumption of error correlation between equations is carried out to determine 
whether the errors between equations in the SUR model are correlated. The results of 
testing the correlation between errors of equation assumption are presented in Table 3. 
 
Table 3 Results of Testing of Correlation of Errors between Equations Assumption in the 
SUR Fixed Effect Model 

The i-th and j-th equation 𝒓𝒊,𝒋 𝒓𝒊,𝒋
𝟐  

First and second equation -0.108 0.012 
First and third equation -0.003 <0.001 
First and 4th equation -0.018 <0.001 
First and 5th equation 0.671 0.450 

Second and third equation 0.753 0.567 
Second and 4th equation 0.719 0.517 
Second and 5th equation 0.026 0.001 
Third and 4th equation 0.918 0.843 
Third and 5th equation 0.058 0.003 

4th and 5th equation 0.041 0.002 

𝑳𝑴 = 𝒏𝒕 ∑ ∑ 𝒓𝒊𝒋
𝟐

𝒊−𝟏

𝒋=𝟏

𝒎

𝒊=𝟏

 3472.873 

 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 173 

Table 3 shows the LM test statistics for the fixed effect SUR model (3472.873) > 𝜒0.05,10
2  

(3.94) or p-value (0) > α (0.05) are obtained. Therefore, sufficient evidence is obtained to 
reject 𝐻0 so that it can be concluded that there is an error correlation between equations 
and the assumption of an error correlation between equations in the fixed effect SUR 
model has been fulfilled. 
 
F Test 
 
Simultaneous testing using the F test was carried out to determine whether population 
density, inflation, and unemployment rates simultaneously affect the human 
development index, GNP, imports, exports, and urbanization in the fixed effect SUR 
model. The analysis results show that the F test statistic for the fixed effect SUR model is 
92692.37, which is greater than 𝐹755,1093995 (1.96). Therefore, it can be decided that 𝐻0 

is rejected so that it can be concluded that simultaneously the SUR fix effect model is 
significant or at least there is one predictor variable (population density, inflation or 
unemployment rate) that has a significant relationship to the response variable (human 
development index, GNP, import, export or urbanization). 
 
t Test 
 
Tests using the t test were carried out to determine whether individual population 
density, inflation, and unemployment rates are significantly related to the human 
development index, GNP, imports, exports, and urbanization in the fixed SUR effect 
model. Several variables have a significant relationship through Table 1: population 
density to GNP, unemployment rate to GNP, differences in the effect of the 
unemployment rate on GNP in developed and developing countries, population density 
on imports, and population density on exports. Meanwhile, there is no significant 
relationship between predictor variables and other response variables. 
 
Fix Effect SUR Model Interpretation 
 
Through the results of the analysis, it is obtained that the general fix effect SUR model for 
this research in equation (11). 
 
𝐻𝐷𝐼𝑖𝑡 =  𝛼1𝑖 + 0.005(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 0.003(𝐷2𝑖 × 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) −

0.001(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +  0.001𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 +
0𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 − 0.002𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐺𝑁𝑃𝑖𝑡 =  𝛼2𝑖 + 12.931(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 9.768(𝐷2𝑖 × 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) −

16.019(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) + 28.68𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 −
0.055𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 − 10.358𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼3𝑖 + 11.711(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) + 3.776(𝐷2𝑖 ×

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 4.474(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
2.952𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
2.195𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 



Pratama, Fitriani, & Astutik 
Fix effect sur to analyze economic growth in developed and developing countries 

 

 

Jurnal Ekonomi & Studi Pembangunan, 2023 | 174 

𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼4𝑖 + 19.459(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) + 0.471(𝐷2𝑖 ×
𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 4.718(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
2.657𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.002𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
2.019𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 =  𝛼5𝑖 + 0.169(𝐷2𝑖 × 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 ) − 0.081(𝐷2𝑖 ×

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 ) − 0.015(𝐷2𝑖 × 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡 ) +
 0.103𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
0.072𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡    (12) 

 
Through this model, the SUR fix effect model for developing countries (𝐷2𝑖 =0) is obtained 
as follows. 
𝐻𝐷𝐼𝑖𝑡 = 𝛼1𝑖 +  0.001𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.000𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.002𝑇𝑖𝑛𝑔𝑘𝑎𝑡 𝑃𝑒𝑛𝑔𝑎𝑛𝑔𝑔𝑢𝑟𝑎𝑛𝑖𝑡   
 
𝐺𝑁𝑃𝑖𝑡 =  𝛼2𝑖 + 28.680𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.055𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

10.358𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼3𝑖 + 2.952𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡  − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

2.195𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼4𝑖 + 2.657𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.002𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

2.019𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 = 𝛼5𝑖 +  0.103𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.072𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡    (13) 
 
Meanwhile, the SUR fixed effect model for developed countries (𝐷2𝑖 =1) is as follows. 
𝐻𝐷𝐼𝑖𝑡 = 𝛼1𝑖 + (0.001 + 0.005)𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + (0.000 −

0.003)𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 + (−0.002 − 0.001)𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
= 𝛼1𝑖 +  0.006𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.003𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
0.003𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐺𝑁𝑃𝑖𝑡 =  𝛼2𝑖 + (28.680 + 12.931)𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + (−0.055 −

9.768)𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 + (−10.358 − 16.019)𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
=  𝛼2𝑖 + 41.611𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 9.823𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
26.377𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼3𝑖 + (2.952 + 11.711)𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + (−0.009 +

3.776)𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 + (−2.195 − 4.474)𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
=  𝛼3𝑖 + 14.663𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 3.767𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
6.669𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 
𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  𝛼4𝑖 + (2.657 + 19.459)𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + (0.002 +

0.471)𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 + (−2.019 − 4.718)𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
=  𝛼4𝑖 + 22.116𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.473𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
6.737𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   

 



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𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 = 𝛼5𝑖 + (0.103 + 0.169)𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + (−0.009 −
0.081)𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 + (−0.072 − 0.015)𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
= 𝛼5𝑖 +  0.272𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.900𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −
0.087𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡     (14) 

 
Through the SUR fix effect model in developed and developing countries, it can be seen 
that every increase of 1 million population, the human development index in developing 
countries increases by 0.001, while the human development index in developed countries 
increases by 0.006. For every 1 million population increases, GNP in developing countries 
increases by US$ 26.68 billion, while GNP in developed countries increases by US$ 41.611 
billion. For every 1 million increase in population, imports to developing countries 
increased by US$ 2.952 billion, while imports to developed countries increased by US$ 
14.633 billion. For every 1 million increase in population, exports to developing countries 
increased by US$ 2.657 billion, while exports to developed countries increased by US$ 
12.116 billion. For every increase of 1 million population, urbanization in developing 
countries increases by 0.103%, while urbanization in developed countries increases by 
0.272%. 
 
With every 1% increase in the inflation rate, the human development index in developing 
countries does not change at all, while the human development index in developed 
countries decreases by 0.003. For every 1% increase in the inflation rate, GNP in 
developing countries decreased by US$ 0.055 billion, while GNP in developed countries 
decreased by US$ 9.823 billion. For every 1% increase in the inflation rate, imports to 
developing countries decreased by US$ 0.009 billion, but imports to developed countries 
increased by US$ 3.767 billion. For every 1% increase in the inflation rate, exports to 
developing countries increased by US$ 0.002 billion, while exports to developed countries 
increased by US$ 0.473 billion. For every 1% increase in the inflation rate, urbanization in 
developing countries decreases by 0.009%, while urbanization in developed countries 
decreases by 0.09%. 
 
If the unemployment rate increases by 1%, the human development index in developing 
countries will decrease by 0.002, while the human development index in developed 
countries will decrease by 0.003. If the unemployment rate increases by 1%, GNP in 
developing countries will decrease by US$ 10.358 billion, while GNP in developed 
countries will decrease by US$ 26.377 billion. If the unemployment rate increases by 1%, 
imports in developing countries will decrease by US$ 2.195 billion, while imports in 
developed countries will decrease by US$ 6,669 billion. If the unemployment rate 
increases by 1%, exports to developing countries will decrease by US$ 2.019 billion, while 
exports to developed countries will decrease by US$ 6.737 billion. If the unemployment 
rate increases by 1%, urbanization in developing countries will decrease by 0.072%, while 
urbanization in developed countries will decrease by 0.087%. 
 
 
 
 
 



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Models for Developing Countries (Example: Jamaica) 
 
𝐻𝐷𝐼𝑖𝑡 =  0.754 +  0.001𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.002𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐺𝑁𝑃𝑖𝑡 =  59.75 + 28.68𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.055𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

10.358𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  25.899 + 2.952𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡  − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

2.195𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  21.943 + 2.657𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.002𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

2.019𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 = 55.415 +  0.103𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.009𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.072𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
Through the model above, it can be seen that the average human development index for 
Jamaica is 0.754, the average GNP for Jamaica is US$ 59.75, the average import for 
Jamaica is US$ 25.899, the average export for Jamaica is US$ 21.943, the average -the 
average urbanization rate for the country of Jamaica is 55.415%. Every increase of 1 
million population will increase the human development index in Jamaica by 0.001, 
increase GNP in Jamaica by US$ 28.68 billion, imports in Jamaica by US$ 2.952 billion, 
exports in Jamaica by US$ 2.657 billion, and urbanization in Jamaica by 0.103%. Every 
increase of 1 unit of inflation will not change the human development index in Jamaica in 
the slightest, reducing GNP by US$ 0.055 billion, reducing imports in Jamaica by US$ 0.009 
billion, reducing exports in Jamaica by US$ 0.002 billion, and reducing urbanization in 
Jamaica by 0.009 %. Every 1% increase in the unemployment rate will reduce the human 
development index in Jamaica by 0.002, reduce GNP in Jamaica by US$ 10.358 billion, 
reduce imports in Jamaica by US$ 2.195 billion, reduce exports in Jamaica by US$ 2.019 
billion, and reduce urbanization in Jamaica by 0.072%. 
 
Model for Developed Countries (Example: Norway) 
 
𝐻𝐷𝐼𝑖𝑡 =  0.935 +  0.006𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.003𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.003𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐺𝑁𝑃𝑖𝑡 =  351.095 + 41.611𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 9.823𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

26.377𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐼𝑚𝑝𝑜𝑟𝑡𝑖𝑡 =  77.559 + 14.663𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 3.767𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

6.669𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝐸𝑥𝑝𝑜𝑟𝑡𝑖𝑡 =  82.122 + 22.116𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 + 0.473𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

6.737𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   
 
𝑈𝑟𝑏𝑎𝑛𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖𝑡 =  79.987 +  0.272𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑛𝑠𝑖𝑡𝑦𝑖𝑡 − 0.9𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑖𝑡 −

0.087𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 𝑅𝑎𝑡𝑒𝑖𝑡   



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Jurnal Ekonomi & Studi Pembangunan, 2023 | 177 

Through the model above, it can be seen that the average human development index for 
Norway is 0.935, the average GNP for Norway is US$ 351.095, the average import for 
Norway is US$ 77.559, the average export for Norway is US$ 82.122, the average -the 
average urbanization rate for Norway is 79.987%. Every increase of 1 million population 
will increase the human development index in Norway by 0.006, increase GNP in Norway 
by US$ 41.633 billion, increase imports in Norway by US$ 14.633 billion, increase exports 
in Norway by US$ 22.116 billion, and increasing urbanization in Norway 0.272%. Every 1 
unit increase in inflation will reduce the human development index in Norway by 0.003, 
reduce GNP in Norway by US$ 9.823 billion, increase imports in Norway by US$ 3.767 
billion, increase exports in Norway by US$ 0.473 billion, and reduce urbanization in 
Norway by 0.9%. Every 1% increase in the unemployment rate will reduce the human 
development index in Norway by 0.003, reduce GNP in Norway by US$ 26.377 billion, 
reduce imports in Norway by US$ 6.669 billion, reduce exports in Norway by US$ 6.737 
billion, and reduce urbanization in Norway by 0.087%. 
 
The effect of population density on the human development index in developed and 
developing countries is not in line with research conducted by Adim (2021), where the 
more the population, the human development index will decrease because if the 
population in an area is denser, the community tends to be less prosperous. However, the 
effect of population density on the human development index is in line with the research 
of Antara and Suryana (2020), where the more the population, the human development 
index will be because if the population in an area is denser than the development and 
facilities in that area tend to be more numerous than areas with a small population. The 
effect of population density on imports in developed and developing countries is in line 
with research conducted by Mahardika and Yuliarmi (2018), where the more people there 
are, the more imports in a country will also increase because the more people in a country, 
the goods/services that will be imported. Government imports are also increasing, and 
many people carry out import transactions of goods/services from abroad, thereby 
increasing the value of imports.  
 
The effect of population density on exports in developed and developing countries is in 
line with research conducted by Morrison (1977), where the more the population, the 
exports in a country will also increase because the more people in a country, the more 
goods/services that the government will export. There are also more and more people 
going abroad who carry out transactions for the export of goods/services from abroad, 
thus increasing the value of exports. 
 
The effect of inflation on the human development index in developed countries is in line 
with research conducted by Pangesti and Susanto (2018), where the higher the inflation, 
the higher the price of goods on the market, so that many people cannot afford it and in 
the end people's welfare decreases. The effect of inflation on GNP in developed and 
developing countries is in line with research conducted by Silitonga (2021), where 
inflation causes prices of goods to increase and people's purchasing power to decrease so 
that state income also decreases. The effect of inflation on imports in developed countries 
is in line with the theory put forward by Sukirno (2,008), where the higher the inflation, 
the cheaper the price of imported goods (the price of goods abroad is cheaper than 



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Jurnal Ekonomi & Studi Pembangunan, 2023 | 178 

domestically) so that the government and society tend to import goods/services from 
abroad. 
 
The effect of the unemployment rate on the human development index in developed and 
developing countries is in line with research conducted by Ningrum et al. (2020), where 
the higher the unemployment rate, the more social welfare will decrease because 
unemployed people cannot fulfill their needs. The effect of the unemployment rate on 
GNP in developed and developing countries is in line with research conducted by 
Novriansyah (2018), where the higher the unemployment rate, the lower state income 
because a large number of unemployed people will not increase state income, so that 
state income tends to decrease when more and more people are unemployed. 
 
Coefficient Determination 
 
Through the analysis results, it is obtained that the 𝑅2 statistic for the general fix effect 
model in equation (11) is 0.9846, which means that the Fix Effect SUR model is very good 
where 98.46% of the variety of the values of the human development index, GNP, imports, 
exports, and urbanization can be explained by population density, inflation, and the 
unemployment rate, while the remaining 1.54% explained by other variables that are not 
included in the Fix Effect SUR model. The results of the t test and Table 1 showed that 
only 5 of the 30 research hypotheses were significant. However, the R2 statistic shows a 
very high value where population density, inflation, and unemployment rates explain 
98.46% of the variation in the human development index values, GNP, imports, exports, 
and urbanization. This indicates that there are individual effects in each country (country 
characteristics) which causes the Fix Effect SUR model to be very good at modeling the 
relationship between population density, inflation, and unemployment rates on the 
human development index, GNP, imports, exports, and urbanization in developed and 
developing countries. 
 
 

Conclusion 
 

This study aims to develop the Seemingly Unrelated Regression (SUR) model where the 
data used is panel data and added a dummy variable as a slope component and apply it 
to model the effect of economic variables (population density, inflation, and 
unemployment rate) on economic growth indicators (human development index, GNP, 
imports, exports, and urbanization). The data used in this study are data on economic 
variables (population density, inflation, unemployment rate, human development index, 
GNP, imports, exports, and urbanization) in 145 countries in the world consisting of 110 
developing countries and 35 developed countries in 2010 until 2019 sourced from the 
World Bank and IMF websites.  
 
Through testing the significance of the parameters separately in the SUR fix effect model 
in Table 1, it is found that population density has a significant positive effect on GNP, 
imports, and exports. In addition, the unemployment rate and GNP have a significant 
negative effect. Through testing the significance of the parameters separately in the SUR 



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Jurnal Ekonomi & Studi Pembangunan, 2023 | 179 

fix effect model in Table 1, it was found that there were not many significant differences 
between the magnitude of the relationship between population density, inflation, and the 
unemployment rate on the human development index, GNP, imports, exports and 
urbanization in developed and developing countries. In addition, it is found that there are 
differences in the effect of the unemployment rate on GNP in the categories of developed 
and developing countries, where for each increase in the same unemployment rate, the 
decrease in GNP in developed countries is greater than with developing countries.  
 
Therefore, all countries are expected to pay attention to population density and the 
unemployment rate because it can affect the country's GNP, imports, and exports. In 
addition, it is hoped that developing countries will be able to carry out population 
efficiency so that with an increasing population, the influence on GNP, imports, and 
exports will be greater like in developed countries where most of the population of 
developed countries has good quality human resources. On the other hand, it is hoped 
that developing countries will be able to add decent jobs to the population in order to 
reduce the unemployment rate so that the influence on GNP, imports, and exports will be 
greater like in developed countries where most of the population of developed countries 
are already working and have decent jobs and salaries. 
 
This study only uses balanced panel data to facilitate research. It is hoped that further 
research can develop this research with the Seemingly Unrelated Regression model on 
unbalanced panel data so that all countries with incomplete data can be included in the 
model. 
 
Acknowledgement 
 
This study is supported by the 2023 National Competitive Research/Master’s Thesis 
Research (PKN-PTM) Grand from Ministry of Education, Culture, Research, and 
Technology (DIKTI), Republic of Indonesia. 
 
 

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