







































Asian Themes in Social Sciences Research 
ISSN: 2578-5516 

Vol. 8, No. 1, pp. 54-68 
2024 

DOI: 10.33094/atssr.v8i1.2080 
© 2024 by the author; licensee Online Academic Press, USA 

 
Accepted: 10 December 2024 | Published: 27 December 2024 

54 
© 2024 by the author; licensee Online Academic Press, USA 

  

 
 
 
 

Technical efficiency evaluation of Sudan's economy 
 
 

Khalafalla Ahmed Mohamed Arabi 
 

College of Business, King Khalid University, Saudi Arabia. 
Email: karabi@kku.edu.sa  
 

 
Abstract 

This paper aims to estimate the technical efficiency of Sudan's economy from 1960 to 
2020 and explore the impact of economic policies on technical efficiency. It used 
stochastic frontier analysis and beta regression to estimate technical efficiency, the 
dependent variable that economic policy influences. The study preferred the Cobb-
Douglas production function over the transcendental logarithmic production function 
(Translog). The first two years showed an upward technical efficiency trend, followed 
by a downward trend for 40 years. Following the 2005 signing of the peace deal that 
marked the end of the civil war, the technical efficiency trend rose, accompanied by oil 
exports. The technical efficiency differed from its optimal value by 20%. Policies 
pertaining to the economy that had an impact on technical efficiency included the devaluation of 
the currency rate, the increase in ordinary expenditures, indirect taxes, and the ratio of the 
balance of payments to the gross domestic product. Moreover, the elimination of trade barriers is 
of the utmost importance, and policymakers should be serious about enhancing the 
competitiveness and productivity of the economy. This may be accomplished by implementing 
tax reform and shifting the priorities of government expenditure, which will eventually result in 
the release of additional funds for development. 
 

Keywords: Economic policies, Oil exports, Tax reform, Technical efficiency, Trade obstacles. 
Licensed:  This work is licensed under a Creative Commons Attribution 4.0 License. 
Funding:   This study received no specific funding 
Institutional Review Board Statement: Not Applicable. 
Transparency: The author confirms that the manuscript is an honest, accurate, and transparent account of the study; that no 
vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. This study 
followed all ethical practices during writing. 
Competing Interests: The authors declare that they have no competing interests.  

 
1. Introduction 
1.1. Background 

Through a variety of policies, all nations pursue economic growth as their primary goal. Since Gross 
Domestic Product (GDP) shows the income produced by various economic agents, it is a commonly used 
metric for assessing a country's economic behaviour. Each economic sector uses factor payments and products 
to measure the cost of producing goods and services in the economy. The level of technical efficiency in 
utilizing these resources can influence the varying outcomes of resource allocation to achieve a specific aim. 
Technical efficiency refers to the utilization of productive resources to optimize output from a specific 
combination of inputs. Thus, inefficiency can be defined as the discrepancy between actual production values 
and the highest possible values for a given technology (Fuente-Mella, Vallina-Hernandez, & Fuentes-Solís, 
2020; Kibara & Balazs, 2019). Therefore, numerous publications have addressed this topic by examining 
various products in terms of their production function, cost function, or profit function. Pires and Garcia 
(2012) demonstrated that it is possible to use an appropriate breakdown of total factor productivity (TFP) to 
analyze a diverse set of countries over a long period of time. This breakdown allows for the assessment of not 
only the contributions of technical progress and technical efficiency change to long-term growth but also the 
impact of scale and distributive efficiency change. Efficiency is the goal of numerous global social and 
economic initiatives and reforms. The possibility of efficiency gains is a driving force behind the deregulation 
of markets, the elimination of trade barriers, and the privatization of state-run businesses.  

Sudan's gross domestic product fluctuated around an average growth rate of 0.345; the maximum growth 
rate is 12.92; and the minimum is -9.11. The country, which has large agricultural and mineral resources, is 

https://www.doi.org/10.33094/atssr.v8i1.2080
mailto:karabi@kku.edu.sa


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strategically located between the Middle East and West Africa. It has received international financial support 
and implemented economic reform programs. However, it faces weaknesses such as a weakened democratic 
transition, a dependence on agriculture, oil, gold, and international aid, persistent human and food insecurity, 
high unemployment rates, corruption, and a reliance on out-dated technology. The agricultural sector 
contributes about 32% to GDP, followed by industry (18%) and services (50%).  
 
1.2. Problem Statement 

Effective governance, encompassing economic, social, and political dimensions, is vital for growth and 
development. It should be participatory, accountable, transparent, and guided by legal principles. Poor 
governance can impede income generation, effective public spending, and trust. The main question is: were the 
huge investments in development projects supported by effective governance? What is the level of efficiency? 
What are the main economic policies that affect technical efficiency? 
 
1.3. Objectives of the Study 

The objectives of this work are to assess the technical efficiency of the Cobb-Douglas and transcendental 
logarithmic production function in Sudan using a stochastic frontier approach and to examine the factors 
contributing to efficiency.  
 
1.4. Justification and Scope of the Study 

The government's primary goal is economic growth, which should be evident in societal welfare. The 
economy should operate at full capacity to achieve the target. Therefore, measuring the technical efficiency of 
Sudan's economy for the period 1960–2020 is a necessity, using gross domestic product as the primary 
measure of technical efficiency. 
 

2. Current Policies 
2.1. Sudan's Development Plans 

The 1940s saw the creation of Sudan's first economic plan, an investment program for 1946–1951, and 
another program for 1951–1956, which succeeded it. However, it is thought that the ten-year plan 61/1962-
70/1971 was the first real attempt at planning because it transformed the economic programs from being 
haphazard to being based on precise quantitative and qualitative goals. The government in 1970–1975, as part 
of the socialist approach, drafted the first five-year plan. Its principles included centralizing planning and 
implementation, monopolizing public institutions for investment and commercial activity, and modifying the 
plan when system orientations changed. According to Aliraqi (2018) the nation accumulated enormous debt 
early in the 1980s because of several issues, including the unreliability of development projects and the lack of 
objectivity in their planning. During the 1980s, the government established three-year rolling programs. The 
Triple Economic Rescue Program of 1990–1993 reinforced the direction of economic openness that the 
National Salvation Revolution of 1989 initiated. The program's goals were to move the Sudanese economy 
away from stagnation and toward production, as well as to alter the institutional, financial, and economic 
structures required to ensure everyone's participation, achieve social balance, and correct distortions in the 
country's economic structure. The program included privatizing public-sector utilities, attempting to stabilize 
the exchange rate, cancelling import and export licenses, and lifting all price restrictions. All of these actions 
helped to break the government-dependent economic stagnation, and by the middle of 1992, the GDP growth 
rate had increased by roughly 7.4%, mostly due to the notable 25% increase in agricultural production. The 
collapse of inflation to record levels in 1996 was an obvious indication of his deficiencies in handling the wider 
economic crisis in Sudan (Aliraqi, 2018). After the Comprehensive National Strategy (1992–2002) failed to 
achieve its goals, the government introduced the Quarter-Century National Strategy. Both strategies are 
nearly identical in terms of dimensions, objectives, legal framework, planning reference, and pillars. Naturally, 
their theoretical frameworks may have drawn inspiration from the Malaysian experience. The former strategy 
focused on exporting oil. Additionally, the end of the Civil War resulted in increased efficiency.  
 
2.2. Fiscal Policy 

Governments use fiscal policy as an important tool to allocate and redistribute resources, especially in 
developing countries, to offset the private sector's insatiable resource allocation and distribution. It indirectly 
raises or lowers taxes, causing the economy to spend more or less. Fiscal policy can have a beneficial and 
negative impact on the economy. Positive government actions, such as infrastructural services, education, 
health, and Research and Development (R&D), can boost employment and lower unemployment. Negative 
government actions, such as expenditures on wages and salaries, administration, the military, and security, can 
also have a negative economic impact. Sudan's government raises funds for public initiatives using both tax 
and non-tax income. Tax revenue encompasses both direct and indirect taxes, whereas non-tax revenue 
includes contributions from businesses, banks, pension plans, interest, fees, and public service costs. Oil 
revenues were a substantial source of federal revenue in the late 1990s and early 2000s (Ahmed, Rahamtalla, & 
Michael, 2004). The median shares of direct tax and indirect tax in total taxes are 17% and 83%, the maximum 
0.45% and 99%, and the minimum 55% and 0.009%. The direct tax share is more dispersed than the indirect 
tax, where the coefficients of variation are 0.63 and 0.14, respectively. Three chapters cover current 
expenditures. Chapter 1 covers all government employees' earnings and pay, including the federal 
government's payments to the Social Security and Pension Funds. Chapter 2 deliberates the items and services 



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obtained by government bodies. This type of spending includes social subsidies. The final chapter looks at the 
Federal Rule Chamber's compensation for state agricultural taxes, as well as current and development 
contributions to states. The share of ordinary expenditure in total expenditure exhibited a median of 0.87, a 
maximum of 0.985, a minimum of 0.38, and a coefficient of variation of 0.021. It is worth noting that education 
and health receive less than 3% of the budget, whereas the top government receives more than 12% in 
administrative expenditure. 
 
2.3. External Sector Policies 
2.3.1. Exchange Rate Devaluation 

Since September 1978, the International Monetary Fund (IMF) has advised Sudan's succeeding 
administrations to depreciate the Sudanese pound over time to reduce the country's trade imbalance. Even 
though it did not satisfy the Marshall-Lerner criterion, which stipulates that a nation's total export and import 
demand elasticities must be greater than one, devaluation proceeded. It is a critical component of the strategy's 
effectiveness. They did not meet the Marshall-Lerner criterion, which requires that the total of a country's 
export and import demand elasticities be greater than one. The maximum growth of supply-side forces 
determines a country's balance-of-payments limit when its growth rate falls below the maximum growth of its 
economy. This growth rate must be compatible with a current account equilibrium or a sustainable expansion 
of foreign borrowing.  
 
2.3.2. Foreign Trade Policies 

The Ministry of Foreign Trade has implemented protectionist policies, such as import and export levies. 
Another option for limiting imports was to use quota systems, which impose import and export licenses as 
well as restrict foreign currency transactions using unilateral exchange rates. In February 1992, the finance 
minister liberalized the economy by removing mechanisms like quotas and licensing to ensure the availability 
of specific items. The country joined the Common Market and the Customs Union of Eastern and Southern 
Africa (COMESA). According to a former minister, corruption is common in the external sector, including 
tenders, firm registration, concessions, and exemptions. This results in capital transfers that return to the 
country as foreign investment, taking advantage of the privileges and exemptions offered to foreign investors, 
which then facilitate the acquisition of privatized public businesses.  
 
3. Literature Review 

Rosid, Xuefeng, Hossain, Hasan, and Sultanuzzaman (2021) used stochastic frontier analysis to investigate 
the relationship between total net worth and GDP in 106 countries from 2009 to 2018. Credit Suisse and the 
World Bank provided data on net wealth and global development indicators. They discovered that GDP has a 
negative impact on wealth maximization efficiency. The robust regression analysis demonstrated that imports, 
broad money, and the exchange rate have a detrimental effect on a country's wealth efficiency, while the 
country's historical efficiency has a beneficial impact on the succeeding year's efficiency. 

Kibara and Balazs (2019) work examines the use of parametric SFA and non-parametric DEA in 
measuring production efficiency. Researchers prefer parametric SFA because it treats deviations in a random 
manner, taking measurement mistakes and noise into account. They prefer a one-stage latent class stochastic 
frontier model over standard SFA models, which assume that all production technologies are homogeneous. 
The study also demonstrates that easing up on the assumptions of random error independence and symmetry 
can fix the "wrong skewness" problem in stochastic frontiers. When addressing multicollinearity, a principal-
components-based method does not need to omit irrelevant variables. 

Fuente-Mella et al. (2020) study on 34 (Organisation for Economic Co-operation and Development) 
OECD countries from 2003 to 2012, discovered that nations with higher economic growth rates had higher 
efficiency rankings, with Luxembourg and the United States topping the list. The study discovered that we 
could evaluate a diverse range of countries over time using an adequate breakdown of total factor productivity 
(TFP). This split enables an evaluation of not just the contributions of technological advancement and 
technical efficiency change to long-term growth but also the impact of size and allocated efficiency change. 

Auci, Laura, and Manuela (2019) assessed the productivity of 15 European countries by employing the 
Cobb-Douglas and Translog models. The researchers found that the size of the government has a beneficial 
impact on efficiency. They used public expenditure as a measure of government size and found that different 
types of government might have either a positive or negative effect. From a policy standpoint, it is not 
advisable to reduce public spending to raise GDP. 

Pires and Garcia (2012) estimated the World Stochastic Frontier (1950–2000) using an imbalanced panel 
of output and production components from wealthy and poor nations. Data from Penn World Tables supports 
the normal truncated distribution assumption. The projected value of technological inefficiency over time is 
positive, indicating a decreasing pace of technological efficiency. 

Yihua (2008) attributed China's irregular economic growth to growing industrial efficiency gaps, a result 
of government policies and provinces with larger governing bodies, less rigid criteria, more human capital, and 
international trade operations. 

Ali and Hamid (1996) investigated technological advancement and efficiency, as well as their contribution 
to economic growth and other elements of production, by employing more efficient ways in Pakistan's 
manufacturing and agriculture sectors. They attempted to quantify technical change, technical efficiency, and 
productivity using both Hicks neutral technical change and variable, continuous, and discrete technical 



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change. Furthermore, this article examines the impact of technological progress on input demand. They 
discovered technical change occurring at a continual and variable rate. 

Margono and Sharma (2004) examined the evolution of technical efficiency and total factor productivity 
(TFP) in Indonesian provincial economies from 1993 to 2000. They discovered that technological efficiency is 
only around 50%, with factors such as schooling years and sectorial differences influencing growth. TFP 
increased between 1.65% and 5.43%, with a 3.59% growth rate. 

Walid and Alali (2009) used the Stochastic Production Frontier (SPF) technique to assess a country's 
technological efficiency and economic performance. They discovered a considerable difference between 
technological efficiency perceptions and traditional productivity indicators. Institutional elements such as 
trade openness, state institutions, and political systems all have a substantial impact on global economic 
performance. 

Zwane, Biyase, Maleka, and Maluleka (2020) looked at technological efficiency drivers in Southern African 
Development Community (SADC) nations from 1985 to 2014. They estimated output efficiency using 
stochastic frontier analysis and a variety of datasets. The results reveal that labour, capital, and human capital 
all have a favourable impact on economic growth. Government spending and trade openness have a negative 
impact on technological efficiency. The analysis suggests that investing in human capital, labour, and technical 
efficiency will boost economic growth. 

Christopoulos and McAdam (2015) study scrutinized technical efficiency in the Middle East and North 
Africa, and finds that political and social factors, as well as economic indicators, have a major impact on 
development and frontier efficiency profiles. The study employs a huge data set and robustness checks to 
provide a thorough baseline for other studies. 

Jajri and Ismail (2006) stated that since the 1980s, Malaysia's manufacturing industry has played an 
important role in economic growth by adding to output and jobs. The government's goal is to have an 
industrialized nation by 2020. However, productivity has not hit its peak, with growth slower than wages. 
This research examines technical efficiency, technological change, and total factor productivity (TFP) 
developments in Malaysia's manufacturing industry. The results suggest that TFP growth is expanding, with 
food, wood, chemical, and iron items exhibiting high technical efficiency. 

Shahabinejad, Zare Mehrjerdi, and Yaghoubi (2013) used Stochastic Frontier Analysis to examine the rise 
of total factor productivity (TFP) in 44 Asian nations. They discovered that in 75% of these economies, 
technological development had a negative influence on productivity growth. Japan experienced the highest 
productivity growth (2.55%), followed by Saudi Arabia, Korea, and Hong Kong. TFP growth in newly 
independent countries was the slowest due to a lack of technological progress. 

Moussir and Liouaeddine (2022) inspected the effect of technological efficiency on economic complexity in 
developing countries. Using two methods, they discovered that underdeveloped countries produced only 16% 
of their potential outputs, compared to 51% in high-income countries. The study also indicated that technical 
efficiency has no substantial impact on economic complexity across regions. 

Barasa, Knoben, Vermeulen, Kimuyu, and Kinyanjui (2017) investigated the impact of innovative activities 
on efficiency in manufacturing enterprises in developing nations. They believe that internal R&D improves 
efficiency, whereas foreign technology acquisition has the opposite impact. However, combining internal R&D 
with foreign technology reduces efficiency. The study suggests that domestic R&D may have a dynamic effect 
on efficiency, whereas poor human capital rates may impede R&D activity and foreign technology adoption. 

Alsaleh and Abdul-Rahim (2019) study looked at the impact of economic factors on technical efficiency 
(TE) rates in the EU-28 bioenergy sector from 1990 to 2013. It found that labour input and GDP have a 
substantial impact on TE. The findings inspire governors and parliamentarians to look into TE rates, provide 
insights for bio-energy industry senates, and make recommendations to financiers focused on direct-
investment income. 

Achirawee and Xu (2018) examined Thailand's GDP efficiency from 1993 to 2017, finding 2017 as the 
poorest year in terms of efficiency. Data envelopment analysis (DEA) was employed to enhance the evaluation. 
To increase inputs and GDP, the study recommends eliminating negative values associated with slack 
movement and supporting export-led growth, company incubators, and entrepreneurship. The report offers 
strategic advice to Thailand's government on how to increase its GDP. 

Wijeweera, Villano, and Dollery (2024) study uses panel data from 1997 to 2004 and a stochastic frontier 
model to investigate the connection between GDP growth and foreign direct investment (FDI). The findings 
indicate that while skilled labour from FDI boosts economic growth, corruption has the opposite effect. 

Laurits, Dale, and Lawrence (2001) demonstrated the duality between price and quantity and emphasized 
the significance of additive and homogeneous production possibilities in statistical testing of production 
theory. 

Kumbhakar and Tsionas (2011) discussed recent advancements in efficiency measurement using stochastic 
frontier (SF) models in various fields. They discussed input-oriented technological efficiency, latent class 
models, and local maximum likelihood approaches. They highlight recent developments in estimating 
challenging models and include advancements in other fields. 

Romer (1986) study presented specific model of long-term growth, which makes the assumption that 
knowledge is an input with rising marginal productivity. According to this model of commercial equilibrium, 
big nations grow more quickly, private agents can magnify minor disruptions, and growth rates can rise over 
time. 

 



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Rusydiana, Rani, and Cahyono (2021) study examined the Stochastic Frontier Approach (SFA) research on 
Islamic economics and finance (IEF) using 109 articles. Results show a significant increase in publications from 2009-2019, 
with the most published in the International Journal of Islamic and Middle Eastern Finance and Management. The SFA 

application research is divided into four clusters, with cost efficiency being the most widely used. 
The state-of-the-art in stochastic frontier analysis (SFA) in econometrics is highlighted in Nguyen (2020) 

work, which also emphasizes novel research approaches for more reliable and effective outcomes. Although 
there are still unresolved issues, SFM in microeconomics is helpful for examining regression models and 
production efficiency. This is the first econometric survey of SFA. 

Mastromarco and Ghosh (2009) investigated the effects of R&D spending, imports of machinery and 
equipment, and foreign direct investment (FDI) on the total factor productivity of emerging nations using 
stochastic Frontier analysis. They discover that while R&D, capital goods, and FDI increase efficiency, their 
benefits rely on the amount of human capital that has been acquired. For R&D, formal schooling is 
increasingly crucial. 

Schmidt (2002) comparing various estimation techniques, stated that when estimating production 
efficiency, stochastic frontier models take maximally or minimally into account. These models' random noise 
causes a one-sided departure from the frontier, a phenomenon commonly referred to as inefficiency. We also 
employ data envelopment analysis and other nonparametric methods that do not explicitly incorporate 
randomness. Both authors, Lovell and Kumbhakar, are prominent figures in the subject; Lovell co-authored 
important papers, while Kumbhakar was the most significant. 

Cornwell and Peter (2008) A production function provides the maximum possible output with inputs, 
defining a boundary or "frontier" that deviations from can be interpreted as inefficiency. Stochastic frontier 
analysis (SFA) provides techniques to model the frontier concept within a regression framework, allowing for 
the estimation of inefficiency. This chapter focuses on estimating production frontiers and measures of 
technical inefficiency relative to them, using panel data and econometric and statistical detail. 

Wang and Schmidt (2002) stated that for stochastic frontier models with one-sided inefficiency u that can 
be estimated in a single step, this work suggests a class of one-step models. It makes the case that two-step 
processes are biased and provides Monte Carlo data that demonstrates this. The study makes the case that 
one-step models are more suited to comprehending how company features affect efficiency levels. 

Lovell (1995) examined the econometric methodology for efficiency analysis. He differentiated between 
the econometric methodology and the mathematical programming methodology. He examined several 
empirical studies that illustrate the utilization of the econometric approach, particularly in the domains of (1) 
agricultural productivity, (2) labor market efficiency and equity, (3) standard of living assessment, (4) quality 
service establishment, and (5) environmental externality evaluation. 

This study is relevant to previous research because it employs stochastic frontier analysis to assess the 
efficacy of the gross domestic product. Beta regression distinguishes the influence of economic policies on the 
dependent variable, technical efficiency. 
 
4. The Methodology 
4.1. Model Specification 

The data envelope analysis (DEA) technique deterministically measures efficiency, assuming that 
deviations from ideal output levels are due to inefficiency. Stochastic Frontier Analysis (SFA) uses econometric 
methods to distinguish between technological inefficiency and random shocks, efficiently identifying both. 
SFA enables departures from the frontier, allowing for differentiation between random shocks and technical 
inefficiency. We will use the SFA as the analytical method to estimate Sudan's production function, which 
depends on two factors of production: labour force and capital. Given the challenges in obtaining 
comprehensive data on the entire series of capital stock, we opt to use gross fixed capital formation as a 
substitute. The resulting technical efficiency from Equation 3 will serve as the dependent variable in Equation 
5, which I will estimate using beta regression. This is because the dependent variable's technical efficiency 
values fall between 0 and 1. 

𝑦𝑡 = 𝛼 + 𝑓(𝑋𝑖𝑡𝛽) + (𝑣𝑖 − 𝑢𝑖)   (1) 

Equation 1 represents a model where 𝑦𝑡  is the logarithm of production for a given period t, 𝑓(𝑋𝑖𝑡𝛽) is the 

linear production function (CD, Translog), i represents the index for different units, 𝑋𝑖𝑡 is a vector of input 

variables, 𝛼 is the frontier intercept, β is an unknown parameter, 𝑢𝑖 is a non-negative random variable 

representing technical inefficiency, assumed to follow a truncated normal distribution with mean μ and 

variance  σ2 u, and 𝑣𝑖 is a random error assumed to follow an independent and identically distributed normal 

distribution with mean 0 and variance.𝜎𝑣
2. 

Technical efficiency, with the maximum attainable output for given inputs, is: 

𝑡𝑒𝑡 =
𝑦𝑡

𝑦𝑡
∗ =  

𝑓(𝑋𝑡;𝛽)𝑒−𝑢𝑡𝑒𝑣𝑡

𝑓(𝑋𝑡;𝛽)𝑒𝑣𝑡
=  𝑒−𝑢𝑡 ∈ [0,1]     (2) 

Equation 3 through 5 comprise the empirical models. 

𝑙𝑜𝑔𝑦𝑡 = 𝛼 + 𝛽1𝑙𝑜𝑔𝑙𝑡 + 𝛽2𝑙𝑜𝑔𝑘𝑡 + 𝑣𝑡 − 𝑢𝑡;  𝑣𝑡~𝑁(0, 𝜎𝑣
2);  𝑢𝑡~𝐹      (3) 

Where y is the output (real GDP), L is the labour force, and k is a proxy for capital stock (Fuente-Mella et 
al., 2020). Additionally, we assume that variables and Independent and Identically Distributed (IID) are 
independent across observations. Other options include modified Ordinary Least Squares (OLS) or the 
generalized method of moments estimators, but Maximum Likelihood (ML) typically provides the best 



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estimate for this model because it satisfies the distributional assumption F, which is necessary to identify the 
inefficiency term. To determine the technical efficiency level, we utilize the command frontier method. 

𝑓𝑟𝑜𝑛𝑡𝑖𝑒𝑟 𝑙𝑜𝑔𝑦 𝑙𝑜𝑔𝑘 𝑙𝑜𝑔𝑙, 𝑣𝑐𝑒(𝑟𝑜𝑏𝑢𝑠𝑡)       (4) 

The predict command 𝑝𝑟𝑒𝑑𝑖𝑐𝑡 𝑡𝑒, 𝑡𝑒 will compute the technical efficiency series. 

(𝑡𝑒)𝑡 = 𝛼 + 𝛽1(𝑥𝑑𝑣)𝑡 + 𝛽2(𝑖𝑡𝑔𝑟)𝑡 + 𝛽3(𝑏𝑜𝑝𝑟)𝑡 + 𝛽4(𝑜𝑟𝑑𝑔𝑟)𝑡       (5) 

Where (𝑡𝑒)𝑡 is the technical efficiency, (𝑥𝑑𝑣)𝑡 is the Sudanese pound devaluation series, (𝑏𝑜𝑝𝑔𝑟)𝑡is the 
ratio of the balance of payments to GDP, which is a proxy for foreign sector policy. The growth rates of 

indirect tax to revenue (𝑖𝑡𝑔𝑟)𝑡 and ordinary expenditure. We selected these variables as the primary 
determinants of technical efficiency using economic theory and empirical investigation, as presented in the 
following paragraphs. 
The transcendental logarithmic production function (Translog) is an approximation of the constant elasticity 
of substitution (CES) production function that takes the form of Equation 6 that argues log of output 

explained by logxi and the product logxilogxj : 

𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔𝛽0 + ∑ 𝛽𝑖𝑙𝑜𝑔𝑥𝑖 +
1

2
 ∑ ∑ 𝛾𝑖𝑗

𝑛
𝑗=1

𝑛
𝑖=1 𝑙𝑜𝑔𝑥𝑖𝑙𝑜𝑔𝑥𝑗

𝑛
𝑖=1         (6) 

The efficiency parameter, the input's output elasticity, and the measure of complementarity between them 
are all present. The function consists of three components: linear, nonlinear, and interactive. This function is 
unique in that the level of input determines the marginal product, which represents the addition to the total 
product resulting from the inclusion of an additional factor. 
 
4.2. Empirical Justification for Model Variable Selection 

Economic growth models that build on Kaldor's work argue that the external balance limits total growth. 
This is because a trade imbalance can only emerge when exports outpace imports, and no nation can sustain a 
continuous trade deficit. As a result, overall growth is dependent on restoring external balance equilibrium. 
Kaldor has also noted that, according to Holland, Vieira, and Canuto (2004) there is a positive link between the 
volume of international trade and economic growth as a stylized fact. However, the exact nature of this 
correlation remains uncertain. 

Indirect taxes have the potential to have a detrimental effect on economic growth by increasing prices, 
reducing output and circulation, and influencing capital and investment allocation. In addition, these taxes can 
result in inequitable consumption patterns, as affluent individuals allocate a smaller proportion of their income 
towards consumer items, while impoverished individuals tend to spend a larger portion of their income on 
such things. We can reduce or exempt taxes to mitigate their impact on individuals with low incomes. In 
addition, they can reduce the competitiveness of domestic goods on global markets, which may lead to the 
implementation of export subsidies. Hence, authorities must ascertain the optimal tax rate to prevent 
detrimental effects on the economy and investments. 

The empirical findings are diverse; some scholars found public spending to play an important role in 
economic growth, but at the same time, large government size can contribute to lower growth rates. Others 
hold the belief that reducing spending leads to a reduction in taxes, thereby mitigating distortions and 
potentially boosting economic efficiency (Auci et al., 2019). 

Verifying the continued applicability of stochastic frontier analysis requires extensive diagnostic testing 
using two statistics. We can split the overall variance of the error term into two halves. Both the inefficiency 

component 𝜎𝑢
2, and the random component 𝜎𝑣

2 contribute to the variance  𝜎2 = 𝜎𝑢
2 + 𝜎𝑣

2. The Gamma statistic 

𝛾 =
𝜎𝑢

2

𝜎2 represents the fraction of output attributed to technical inefficiency and ranges from zero to one. The 

calculation entails dividing the technical inefficiency component's variance by the overall error term's variance. 
If it is close to one, it simply signifies that the technical inefficiencies account for a large amount of variation, 
and the SF model is the best fit. Finally, if it is near zero, it simply indicates that technological inefficiencies 
account for very little variation. Therefore, estimating the stochastic frontier will be unfeasible due to the 
significant influence of chance.  

Kumbhakar, Wang, and Homcastle (2015) advise against using this measure to evaluate the SF model's 
relevance. We may use a likelihood-ratio test statistic to estimate two models: the restricted Cobb-Douglass 

model (estimated by glm) and the unrestricted stochastic frontier−2 ∗ (𝐿(𝐻𝑟) − 𝐿(𝐻𝑢𝑟)). When calculating 
this statistic, we compare it to the vital values stated in Kodde and Palm (1986). The critical values for one 
degree of freedom are 5.412 at 1% and 6.635 at 5%.  The null hypothesis (H0) states that there are no technical 
inefficiencies. 
 
5. Results and Discussion 
5.1. Data Requirement 

I gathered data from four sources: the Central Bureau of Statistics, the Central Bank of Sudan, the 
Ministry of Finance, and the World Bank, covering the period 1960 to 2020. The sample includes seven 
variables: real GDP (Y), the labour force (L), and gross fixed capital formation as a proxy for capital stock (K). 
In addition, a dummy variable represents the series of exchange rate depreciation (xdv), the growth rate of 
indirect tax (itgr), the growth rate of ordinary (current) expenditure (ordgr), and the ratio of the balance of 
payments to GDP (bopr). Moreover, the SFA produces technical efficiency (tef).  
 
 



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5.2. Descriptive Statistics 
According to the data presented in the table the variable that exhibits the greatest degree of dispersion is 

the logarithm of gross fixed capital formation. Next in line are the ratios of the balance of payments to GDP 
and the budget deficit to GDP. The ratio of the balance of payments to the gross domestic product had the 
greatest range, followed by the ratio of routine expenditures to the percentage of GDP had the smallest range. 

Table 1 presents descriptive statistics. 
 

Table 1. Descriptive statistics. 

Variable Observations Mean Std. dev. Min. Max. 
logy 61 9.29 0.696 8.41 10.640 
logk 61 12.81 5.521 6.06 22.103 
logl 61 6.95 0.381 6.28 7.584 
ordgr 61 0.61 2.398 -0.88 18.728 
te 61 0.81 0.077 0.08 0.359 
itgr 61 0.501 1.553 -0.879 11.434 
bopr 61 -4.19 4.343 -21.61 2.855 

 
While the logarithms of output and labour force are the most widely distributed, the mean logarithm of 

capital is the highest. Ordinary government spending has a somewhat faster average growth rate than indirect 
taxes, but it is more widely distributed. The balance of payments is growing at a negative mean rate and is 
spread out more than regular spending. The average technical efficiency is 0.81.  

The first difference is that the augmented Dickey-Fuller and Phillips-Perron unit root tests show that all 
variables are stationary except for the capital stock proxy and the ratio of the balance of payments to GDP. 

The balance of payments is static, while the capital stock proxy is stationary via the NG-Perron unit root 
test. Johansen's cointegration tests reveal the existence of two integration equations involving the variables in 
Equation 3. This suggests a long-term relationship between output, labour force, and capital stock. At a 
critical value of 5%, the trace statistic of 0.99 is statistically significant. Equation 5 looks at the relationship 
between technological efficiency, the series of exchange rate devaluations, the growth rates of indirect taxes 
and ordinary expenditures, and the balance of payments to GDP. At 5%, the trace statistic (46.98) is 
statistically significant. The augmented Dickey-Fuller test statistic for cointegration with a structural break 
for equations two and four (-7.02, -6.91) is bigger than the asymptotic critical value (-5.86, -6.84) at 5% in the 
Gregory-Hansen cointegration test with breaks (Gregory & Hansen, 1996). This means that the null 
hypothesis of no cointegration is not true. The breakpoint is the forty-third, and the date of the increase in oil 
production and exports is 2002 (Annex). The variables in Equation 3 are not collinear because the variance 
inflation (VIF) factor test reveals that both gross fixed capital formation and labour force have a value of 1.49, 
which is less than the number 5. This indicates that the variables in Equation 2 are not collinear. Here are the 
variance inflation factors for the variables in Equation 5. The growth rates of indirect tax and ordinary 
spending are both 1.20, the ratio of the balance of payments to GDP is 1.17, and the exchange devaluation 
series is 1.13. This means that there is no evidence of multicollinearity between the variables. The VIF, on 
average, is 1.17.  

Table 2 presents empirical results of Equation 2 and 5. 
 

Table 2. Empirical results of Equation 2 and 5. 

Cobb Douglas production function 
Logy Coefficient Z Coefficient Z 
Frontier 
logk 0.124*** 7.6e+07 -0.753*** -3.62 
logl  0.121*** 5.7e+07 3.337*** 9.49 
Logksq - - 0.001 0.08 
loglsq - - -0.623*** -5.18 
Logl*logk - - 0.239*** 2.94 
Constant 7.117*** 5.5e+07* - - 
/lnsig2v - -454.080 -38.333*** - 
/lnsig2u - -16.300 -2.501*** - 
sigma_v - - 4.74e-09 - 
sigma_u - - 0.2863 - 
sigma2 - - 0.082 - 
lamda - - 6.04e+07 - 

          

Note: The symbol (*) indicates a rejection of the null hypothesis at 10%, (**) indicates a 
rejection at 5%, and (***) indicates a rejection at 1%. 
LR test of sigma_u=0 chibar2(01) = 0.90, Prob >= chibar2 = 0.171; (-) means not 
applicable.  
The scientific number is represented by the letter e to indicate 10 raised to the 
power: 5.5e+07 = 5.5 × 107. 
 



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Because they are positive and substantially different from zero, the estimated capital and labour 
coefficients are consistent with economic theory. The gamma statistic, which shows a near-one ratio of 
inefficiency variance to total variance, suggests that stochastic frontier analysis is relevant. At 1% and one 
degree of freedom, the likelihood ratio is more than 5.412; hence, we reject the null hypothesis of no technical 
inefficiencies, as stated in Kodde and Palm (1986). 

After that, we used Equation 4 to make predictions about the technical efficiencies, and Figure 1 shows 
the outcome. The LR test rejects the null hypothesis that the inefficiency's standard deviation (sigma_u) equals 
zero at 1%, confirming the applicability of frontier analysis, since the probability associated with the Chi-
square test is 0.000 while accepting that of Translog. The graph of Equation 5 variables illustrates that the 
growth rate of indirect tax and ordinary tax hit its peak in 2003, coinciding with the lowest level of technical 
efficiency. Despite fluctuations in the balance of payments ratio to GDP, it is stationary, with a constant and 
linear trend.  

Table 3 displays the results of equation 5. 
 

Table 3. Results of Equation 5. 

te Coefficient Robust std. err. z P>|z| 
xdv -0.651 0.227 -2.87 0.004 
itgr -0.199 0.080 -2.50 0.012 
ordgr -0.044 0.015 -2.96 0.003 
bopr -0.065 0.025 -2.55 0.011 
Constant 1.598 0.167 0.167 0.000 
Scale 
xdv 1.518 0.373 4.07 0.000 
Constant 1.192 0.242 4.93 0.000 

 

The frequency of exchange rate devaluation (xdv) is a scalar for two reasons. Firstly, we feel that it affects 
the variability of the calculated average, and secondly, it enhances the relevance of the covariates. The results 
of the margins test indicate that a one-period increase in the devaluation series leads to a 3% decrease in 
technical efficiency. A 1% increase in indirect taxes results in a 2% decrease in technological efficiency. An 
increase of 1% in the ordinary expenditure growth rate results in a corresponding decrease of 1% in technical 
efficiency. Nevertheless, a 1% increase in the balance of payments ratio results in a 3% improvement in 
technical efficiency. 
Indirect taxes (itgr), ordinary expenditures (ordr), exchange rate devaluation, and technical efficiency (te) have 
an inverse relationship according to the conditional mean of technical efficiency (te) tested by the margins 
command. Conversely, the balance of payments positively correlates with technical efficiency. 
 
5.4. Discussion 

Although the Cobb-Douglas production function violates the constancy of return to scale, the study 
favoured it over the transcendental logarithmic production function for three reasons. The null hypothesis is 
initially accepted by the study, which asserts that the sigma of u (technical efficacy) is zero. Subsequently, the 
logarithm of the capital sign is incorrect. Thirdly, the squared logarithm of capital is not statistically 
significant. As a consequence, the scale return decreased as a result of the estimation. The results found the 
Sudanese economy to be inefficient, implying that there is potential for growth of around 20% on average. 
Except for the first two years (1960 and 1961) in the sample period, technical efficiencies remained above 0.96 
for eight years. This period coincided with the 10-year development plan's implementation. Several large 
projects were established. Only this period has seen a surplus budget and a balance of payments. The 
government fixed the exchange rate at 2.83 US dollars for one Sudanese pound. One of the negative aspects of 
this period was the increasing budget deficit in the second half of the decade, which escalated to 7% of GDP. 
This included the cost of debt-to-GDP increases, principal repayment, and debt service.  

The following ten years saw an oscillation of technical efficiencies around the downward trend. During 
this period, poor implementation of the five-year plan resulted in its extension for an additional two years. The 
main economic policies were the confiscations and nationalization of foreign-owned businesses and schemes, 
which resulted in a contraction in the performance of the real GDP, an increase in imports with fewer exports, 
and a deteriorating balance of payments, which reached 9% of GDP at the end of the five-year plan. Despite 
this, the government set the exchange rate at 2.83. After two years, the government abandoned the six-year 
strategy because it failed to implement it. The debt ratio continued to rise, exceeding GDP, with implications 
for principal repayment and debt servicing that compounded the budget deficit.  

In September 1978, the IMF suggested devaluing the currency rate to cover balance-of-payments deficits. 
Since then, there have been a series of devaluations, along with alternating technical efficiency around the 
decreasing trend, until the first shipment of oil in late 1999. Civil wars and environmental disasters influenced 
Sudan's economic performance. The end of the civil war in 2005 signalled the start of an increasing trend in 
technological efficiency. The fiscal policy over the sample period relied heavily on indirect tax and service fees, 
which constituted about two-thirds of government revenue. This problem did not encourage production.  

Indirect taxes have a negative impact on the economy due to inadequate tax administration. Regardless of 
their income, all residents are subject to an indirect tax that includes excise duties, customs duties, and value-
added. Indirect taxes increase production costs, reduce demand and supply, and create disparities between 



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sectors and people. However, some groups are exempt from this tax based on their ethnicity or political 
affiliation. Customs duties impose taxes on vehicles and equipment at rates exceeding 350%. In addition, 
export taxes have diminished export competitiveness due to prolonged procedures, time-consuming processes, 
and multiple rates. Hence, authorities must ascertain the optimal tax rate to prevent any adverse effects on the 
economy and investment. 

Conversely, the allocation of over two-thirds of public expenditure to military forces and security, at the 
expense of development expenditure, accounts for the adverse effects of the beta regression results. The 1990s 
implementation of the federal system led to a significant increase in government size. This system has created 
new states, ministries, and municipalities, resulting in a decrease in development spending and an increase in 
administration spending. When the government resorts to deficit finance and money printing, spending 
indirectly affects the economy by increasing inflation. Inadequate governance and corruption can weaken the 
state's capacity to collect revenue, reduce equity and efficiency of public expenditure, discourage private 
investment, and create inflation (Olusegun, Qiaoe Chen, & Marta, 2020). 
 
6. Conclusions and Recommendations 
6.1. Conclusions  

The study investigated the technical efficiency of Sudan's economy for the period 1960–2020. The 
variance inflation factor demonstrated that the model variables are not collinear. The Gregory-Hansen test for 
cointegration with structural breaks in 2002 confirmed the long-term relationship between the model 
variables. The study employed stochastic frontier analysis to examine the efficiency of Sudan's economy by 
estimating two production functions, the Cobb-Douglas and the Transcendental production functions. The 
Cobb-Douglas production function performed better than the Translog, which was unable to reject the null 
hypothesis that the technical efficiency term is not different from zero. The squared capital is not significant in 
terms of squared capital and the negative capital sign. The results of an investigation using beta regression to 
detect factors that affect efficiency indicate that both fiscal policy and exchange rate policy have an adverse 
impact on technical efficiency. Nevertheless, the presence of several tax rates and the implementation of 
multiple currency practices provide obstacles to business operations. Since 1990, the widespread prevalence of 
corruption, lack of accountability, transparency, and rule of law have had a significant impact on technical 
efficiency, as fiscal and foreign trade policies favoured the ruling party and its members, while the number of 
deprived people has steadily increased as a result of the adoption of economic policies, particularly after the 
announcement of the liberalization package. The fiscal structure exhibits deficiencies in both transparency and 
data quality. Contractual monitoring and digitization impede project monitoring. These governance 
weaknesses increased corruption and eroded public confidence in the administration. 
 
6.2. Policy Recommendations 
6.2.1. Revision of Liberalization Policies 

The economic liberalization policy reduced the states' grip on economic activity by easing or removing 
laws and administrative restrictions to enable the private sector. Examples of these policies include tax reform, 
market liberalization, market freedom, trade liberalization, foreign investment, privatization, and the massive 
devaluation of the exchange rate. These policies have led to a surge in inflation, a decline in food stability, 
poverty, and production, persistent deficits in the trade balance, and a negative balance of payments. Thus, 
there is a need for sustainable growth through increased production and productivity through the 
rehabilitation of schemes and, the replacement of outdated technology with a modern one, in addition to 
reverting to liberalization policies. 
 
6.2.2. Exchange Rate  

The stability of the exchange rate is one of the government's main goals, but the submission to the IMF 
and the World Bank's recommendations resulted in continuous depreciation. Empirical studies revealed that 
the money supply and the current account balance influence the exchange rate. Exporting finished or semi-
finished goods boosts their value, reducing the trade deficit balance on the one hand and supporting economic 
growth by creating new jobs on the other. We recommend reducing private luxury imports, as well as 
government purchases, and establishing an import substitution policy. We also recommend curbing deficit 
financing, government imports, and boosting locally produced vehicles and furniture. Similarly, reforming 
diplomatic missions can help reduce current account balance deficits. In the oil sector, transparency is crucial, 
as the cloudy nature of oil proceeds necessitates the transparency of the export of crude oil, its products, and 
minerals, particularly gold, which can significantly contribute to the building of foreign exchange reserves. 
The government should also revise its policy on gold production and establish a fair purchase rate that aligns 
with global prices.  
 
6.2.3. Tax Reform 

Various modifications to taxation systems, such as modifications to rates, exemptions, deductions, 
allowances, and other features, are encompassed by the term "tax reform." Tax reform is a critical policy 
instrument that governments can employ to promote economic growth, reduce tax burdens, and stimulate 
investment. Providing incentives for individuals to invest in productive activities can encourage investment 
and entrepreneurship by reducing marginal tax rates. Similarly, the elimination of specific deductions or 



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credits can result in a more efficient allocation of resources and reduce distortions in the economy. An 
economic equilibrium between direct and indirect taxes is essential for sustainable development and equity.  
 
6.2.4. Government Expenditure Reform 

Sudan could potentially reduce disparities and efficiently deliver essential services to vulnerable 
communities, as well as address the underlying causes of conflict through the redistribution of public 
expenditure. The government should reduce the share of current expenditure and prioritize development 
expenditure instead. States continue to differ significantly in terms of poverty levels and development 
disparities; therefore, balanced growth should be the main goal of the federal government. The government 
should take into account the significant variations in each state's ability to generate money as well as the 
distribution of fiscal spending among states that reflect these regional imbalances. 
 
6.2.5. Balance of Payments 

The persistent deficits in the balance of payments primarily stem from the export of raw products like oil 
seeds, minerals, crude oil, and live animals. If there is a genuine desire to enhance local production, the 
government should opt to offset the import of consumer goods. Enhance the value of exports and limit luxury 
imports to increase their worth. The services account should be revised. The government also needs to 
address the proper pricing of export goods, prevent export smuggling, and harmonize the various levels of the 
Central Bank of Sudan's regulation of the foreign exchange market. The multiplicity of regulation circulars 
could lead to unfavourable outcomes, such as an increase in parallel market transactions and a surge in demand 
for foreign exchange resources. The approval of the advance payment in the regulation circular will prompt 
exporters to purchase foreign exchange on the black market for their goods, thereby exacerbating smuggling 
issues and depleting the country's foreign exchange reserves. The exportation of female livestock should be 
prohibited and criminalized because it affects directly the number of births. 
 
6.2.6. Corruption and Law Enforcement 

Authority is an effective tool for corruption, creating an environment that fosters and protects 
fraudulence. It encourages and supports corruption's spread and expansion. Corruption develops into a robust 
network that regulates legislation, prosecution, and accountability. When political, moral, and national 
systems fail, corrupt institutions attract vulnerable and dishonest individuals, resulting in poverty and 
illiteracy. Various methods of making money may lead to corruption. As previously stated, Sudan's lack of 
openness and accountability promotes extensive corruption. The Corruption Perceptions Index (CPI) found 
that in most periods, perceived levels of public sector corruption scored 173 out of 180, particularly in the 
second half of the sample period. The Auditor General's report reveals that there is no accountability for 
fraudsters' annual cash misuse. Enforcement of the law is a priority. 
 
Abbreviations  
Symbol Description 
CD Cobb Douglas Production Function. 
Translog Transcendental Logarithmic Production Function. 
logy Logarithm of Real GDP. 
Logl The logarithm of the labour force. 
logk The logarithm of gross fixed capital formation (Capital). 
Te Technical Efficiency. 
Xdv Series of Exchange Rate Devaluation. 
Itgr Indirect Tax Growth Rate. 
ordgr Ordinary (Current) Expenditure Growth Rate. 
bopr Balance of Payments ratio to GDP. 
Lsq Squared logarithm of Labor Force. 
Ksq Squared logarithm of Capital. 
Lk Interaction between logarithms of labour and capital. 
TFP Total Factor Productivity. 
VIF Variance Inflation Factor. 
LR Likelihood Ratio. 
 
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Annex 1  shows the results of the Gregory-Hansen cointegration test of equation variables. The null 
hypothesis of the Gregory-Hansen test states that there is no cointegration, in contrast to the alternative of 
cointegration with a single shift at an unknown point in time. According to the provided values of the three 
test statistics, we reject the null hypothesis of no cointegration, and accept that there is cointegration with a 

single shift at unknown point in time.  
  

 Annex 1. Gregory-Hansen test for cointegration with regime shifts. 

Model: Change in regime and trend                  Number of obs.   =        61 
Lags = 0 chosen by downward t-statistics        Maximum Lags    =         2 

Equation 2 Test statistic Breakpoint Date Asymptotic critical values 

1% 5% 10% 

ADF* -7.02 43 2002 -6.45 -5.96 -5.72 

Zt -7.03 43 2002 -6.45 -5.96 -5.72 

Za -49.65 43 2002 -68.43 -100.47 -63.10 
Note:   *ADF stands for augment dickey fuller. 

 

In contrast to the alternative, which proposes cointegration with a single shift at some undetermined 
moment in time, the null hypothesis of the Gregory-Hansen test indicates that no cointegration exists. Below 
this paragraph, in Annex 2, we can see the outcomes of the Gregory-Hansen test for equation variable 
cointegration. We reject the null hypothesis that there is cointegration with a single shift at an unknown point 
in time, based on the values of the three test statistics that were presented. 
 

Annex 2. Gregory-Hansen test for cointegration with regime shifts. 

Model: Change in Regime and Trend                  Number of obs.   =        61 
Lags = 1 chosen by downward t-statistics        Maximum Lags    =         2 

Equation 4 Test statistic Breakpoint Date Asymptotic critical values 
1% 5% 10% 

ADF -6.91 43 2002 -7.31 -6.84 -6.58 
Zt -6.43 45 2004 -7.31 -6.84 -6.58 
Za -42.76 44 2004 -100.69 -100.47 -82.30 

 
Figure 1 illustrates the shares of direct and indirect tax to the total tax, as well as the share of ordinary 

government expenditure to the total expenditure. The indirect tax share significantly surpasses the direct tax 
share and exhibits a strong upward trend in relation to government ordinary expenditure. However, the direct 
tax shares show a downward trend. 

 

 
Figure 1. Share of direct and indirect tax in total tax. 

 

 



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Figure 2. Variables of Equation 5. 

 
Figure 2 depicts the remaining model variables, indicating a declining trend in the share of the balance 

of payments to GDP, while the growth rate of indirect tax and ordinary expenditure exhibits an anomaly in 
2002, coinciding with the signing of the peace treaty that concluded the civil war. Technical efficiency 
demonstrates a downward trend from 1965 to 2004, followed by an upward trend in subsequent years. 

 

 
Figure 3. Average marginal effects. 

 
Figure 3 presents that the exchange rate devaluation has the lowest average marginal effect at 95% 

confidence limits, followed by the growth rate of ordinary expenditure, while the ratio of the balance of 
payments to GDP has the most average marginal effect.  

Annex 3 provides the time series of the ratios of direct and indirect tax to total tax, as well as the ratio 
of ordinary expenditure to total expenditure for the period 1960–2020. 
 

 
 
 
 



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Annex 3. Explanation of the direct, indirect and current shares. 
 

 

Year IT/TTAX DTAX ORD/GX te 
1960 0.605 22.000 0.449 0.805 
1961 0.647 21.000 0.522 0.877 
1962 0.730 16.200 0.485 0.978 
1963 0.676 22.000 0.537 0.989 
1964 0.577 34.000 0.505 1.000 
1965 0.601 24.000 0.581 1.000 
1966 0.667 20.000 0.516 0.978 
1967 0.606 27.600 0.379 0.961 
1968 0.553 40.200 0.492 0.965 
1969 0.588 41.200 0.456 0.887 
1970 0.840 13.200 0.898 0.928 
1971 0.841 16.200 0.672 1.000 
1972 0.831 18.500 0.873 0.953 
1973 0.820 21.400 0.878 0.871 
1974 0.835 23.600 0.819 0.848 
1975 0.828 30.900 0.733 0.805 
1976 0.869 32.200 0.728 0.803 
1977 0.841 41.700 0.594 0.862 
1978 0.869 47.100 0.673 0.822 
1979 0.860 55.000 0.781 0.779 
1980 0.797 79.900 0.796 0.764 
1981 0.804 109.000 0.887 0.785 
1982 0.791 139.000 0.888 0.840 
1983 0.791 207.000 0.855 0.825 
1984 0.793 236.000 0.829 0.758 
1985 0.792 241.000 0.931 0.685 
1986 0.768 324.000 0.879 0.695 
1987 0.730 470.000 0.908 0.738 
1988 0.746 613.000 0.895 0.713 
1989 0.641 950.000 0.959 0.725 
1990 0.930 585.414 0.966 0.662 
1991 0.578 5108.713 0.852 0.663 
1992 0.805 4099.791 0.883 0.644 
1993 0.793 10815.460 0.787 0.609 
1994 0.862 9816.357 0.965 0.576 
1995 0.614 78795.580 0.932 0.727 
1996 0.765 124167.100 0.910 0.580 
1997 0.853 104737.100 0.916 0.612 
1998 0.854 144799.800 0.911 0.639 
1999 0.884 154812.800 0.865 0.561 
2000 0.762 381000.000 0.887 0.561 
2001 0.922 147200.000 0.884 0.601 
2002 0.919 172500.000 0.718 0.595 
2003 0.804 523000.000 0.731 0.620 
2004 0.824 740000.000 0.714 0.719 
2005 0.810 951000.000 0.750 0.737 
2006 0.838 951000.000 0.808 0.800 
2007 0.860 916500.000 0.829 0.871 
2008 0.885 884300.000 0.878 0.808 
2009 0.893 930200.000 0.843 0.844 
2010 0.886 1136000.000 0.853 0.877 
2011 0.905 1061200.000 0.910 0.878 
2012 0.908 1432600.000 0.887 0.869 
2013 0.929 1713700.000 0.902 0.888 
2014 0.914 3016800.000 0.920 0.912 
2015 0.991 398000.000 0.902 0.949 
2016 0.838 7678000.000 0.902 0.971 
2017 0.933 4270000.000 0.939 0.991 
2018 0.926 6791000.000 0.957 0.983 
2019 0.923 9377000.000 0.974 1.000 
2020 0.873 20354000.000 0.985 0.894 



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Annex 4 displays the model variable's time series from 1960 to 2020. The variables are in logarithmic 
form. 

 
Annex 4.  Model variables 

Year ordgr bopr logy logl logk 
1960 0.072 2.846 8.409 6.281 6.061 
1961 0.086 -1.068 8.506 6.304 6.128 
1962 0.071 -0.717 8.629 6.327 6.219 
1963 0.134 -3.039 8.645 6.349 6.234 
1964 0.010 -1.932 8.660 6.371 6.249 
1965 0.019 -1.232 8.663 6.393 6.253 
1966 0.234 -0.662 8.646 6.414 6.270 

1967 0.108 -1.567 8.632 6.435 6.285 
1968 0.050 -2.914 8.650 6.455 6.369 
1969 0.034 0.290 8.569 6.484 6.372 
1970 0.447 -1.876 8.620 6.504 6.401 
1971 0.130 -3.059 8.704 6.523 6.458 
1972 0.050 -1.569 8.680 6.550 6.623 
1973 0.121 1.004 8.613 6.569 6.799 
1974 0.102 -0.265 8.623 6.541 7.128 
1975 0.393 -8.830 8.599 6.585 7.320 
1976 0.148 -2.067 8.627 6.629 7.522 
1977 -0.253 -1.180 8.730 6.655 7.758 
1978 0.681 -1.338 8.712 6.694 7.966 
1979 0.539 -3.045 8.678 6.732 8.088 
1980 0.169 -3.530 8.687 6.771 8.287 
1981 0.407 -5.998 8.745 6.810 8.507 
1982 0.178 -2.794 8.859 6.833 8.859 
1983 0.234 -2.597 8.880 6.844 0.234 
1984 0.162 0.349 8.828 6.910 0.162 
1985 0.175 1.905 8.764 6.946 0.175 
1986 0.458 -0.209 8.816 6.983 0.458 
1987 0.557 -1.897 8.949 7.001 0.557 
1988 -0.003 -2.491 8.946 7.006 -0.003 
1989 0.700 -0.696 9.031 7.012 0.700 
1990 0.733 -1.107 8.975 7.011 0.733 
1991 0.061 -2.162 9.044 7.009 0.061 
1992 2.859 -7.198 9.111 7.018 2.859 
1993 0.454 -2.277 9.156 7.037 0.454 
1994 -0.715 -4.703 9.166 6.904 -0.715 
1995 0.877 -3.615 9.534 6.947 0.877 
1996 18.728 -9.167 9.400 6.991 18.728 
1997 0.467 -7.089 9.519 7.034 0.467 
1998 0.299 -8.502 9.606 7.076 0.299 
1999 0.288 -4.036 9.485 7.113 0.288 
2000 0.591 -4.224 9.509 7.147 0.591 
2001 0.097 -3.321 9.608 7.170 0.097 
2002 0.100 -5.368 9.632 7.191 0.100 
2003 0.468 -4.395 9.691 7.212 0.468 
2004 0.434 -3.071 9.868 7.234 0.434 
2005 0.315 -7.028 9.918 7.258 0.315 
2006 0.410 -14.351 10.017 7.282 0.410 
2007 0.183 -6.052 10.119 7.306 0.183 
2008 0.306 -5.543 10.061 7.329 0.306 
2009 -0.075 -8.448 10.121 7.351 -0.075 
2010 0.149 -2.327 10.184 7.371 0.149 
2011 0.183 -3.384 10.205 7.390 0.183 
2012 -0.081 -9.904 10.228 7.409 -0.081 
2013 0.377 -8.818 10.294 7.428 0.377 
2014 0.392 -4.615 10.362 7.448 0.392 
2015 0.089 -6.426 10.430 7.468 0.089 
2016 0.234 -2.597 8.880 6.844 0.234 
2017 0.162 0.349 8.828 6.910 0.162 
2018 0.175 1.905 8.764 6.946 0.175 
2019 0.458 -0.209 8.816 6.983 0.458 
2020 0.557 -1.897 8.949 7.001 0.557 

 


