Look-up table with zero-voltage vectors substituted by active ones.
\\n\\n
Released this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\\n\\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\\n"}]',published:!0,mainMedia:{caption:"Highly Cited",originalUrl:"/media/original/117"}},components:[{type:"htmlEditorComponent",content:'IntechOpen is proud to announce that 191 of our authors have made the Clarivate™ Highly Cited Researchers List for 2020, ranking them among the top 1% most-cited.
\n\nThroughout the years, the list has named a total of 261 IntechOpen authors as Highly Cited. Of those researchers, 69 have been featured on the list multiple times.
\n\n\n\nReleased this past November, the list is based on data collected from the Web of Science and highlights some of the world’s most influential scientific minds by naming the researchers whose publications over the previous decade have included a high number of Highly Cited Papers placing them among the top 1% most-cited.
\n\nWe wish to congratulate all of the researchers named and especially our authors on this amazing accomplishment! We are happy and proud to share in their success!
Note: Edited in March 2021
\n'}],latestNews:[{slug:"intechopen-supports-asapbio-s-new-initiative-publish-your-reviews-20220729",title:"IntechOpen Supports ASAPbio’s New Initiative Publish Your Reviews"},{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"}]},book:{item:{type:"book",id:"1591",leadTitle:null,fullTitle:"Infrared Spectroscopy - Materials Science, Engineering and Technology",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",reviewType:"peer-reviewed",abstract:"The present book is a definitive review in the field of Infrared (IR) and Near Infrared (NIR) Spectroscopies, which are powerful, non invasive imaging techniques. 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In recent years, the control of high-performance IM drives for general industrial applications and production areas has received a lot of research interests.
The most modern technique, for the induction machine, is the direct torque and the stator flux vector control method (DTC). It has been realized in an industrial way by ABB, using the theoretical background proposed by
The DTC has been selected in order to fulfill the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the gusts of wind. This positioning system can be introduced in the multi-sources hybrid system, in order to allow high efficiencies of photovoltaic systems. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. In what follows, the chapter will be focused on the problem of position regulation of an induction motor under DTC and DTC-SVM strategies.
Photovoltaic panels are commonly exposed to the sun in a fixed position corresponding to the maximum sunshine recorded during a day that is the position of the sun at midday. Nevertheless, this strategy does not allow the extraction of the maximum power during a day and therefore a high efficiency of photovoltaic systems, which can be integrated with the multi-source hybrid system, described above. An approach to solve this problem consists in moving photovoltaic panels according to the maximum sunshine position. To do so, an electric motor drive could be associated with photovoltaic panels in order to be able to track the maximum sunshine positions during the day. Accounting for the high perturbation amplitude applied to the panel, the control strategy to be implemented in the drive is of great importance [5].
The proposed tracking system has two freedom degrees in such a way that it allows the displacement of the photovoltaic system within latitudes and meridians: the first degree of freedom is controlled automatically by an IM drive under the control of a DTC strategy.
The DTC approach has been selected in order to full the application requirements, especially a maximum torque at standstill. This feature is necessary in order to guarantee a high degree of robustness of the maximum sunshine position tracking system against the high and sudden load torque variations characterized by the gusts of wind.
The following work will be focused on the study of the first freedom degree. Special attention is paid to the implementation of a suitable DTC strategy in the IM drive.
The dynamic behavior of an induction machine is defined in terms of space variables in the sequel:
considering that subscripts
Relationships between currents and flux are:
where
The mechanical part of the machine is described by:
where
The made constant DC voltage by the rectifier is delivered to the inverter input, which thanks to controlled transistor switches, converts this voltage to three-phase AC voltage signal with wide range variable voltage amplitude and frequency.
The voltage vector of the three-phase voltage inverter can be represented as follows:
where
The implementation scheme of the
IM position regulation based on basic DTC strategy.
Referring to [5, 6], it has been found that the
In order to overcome this shortcoming, the zero-voltage vectors can be substituted by active ones. For a given stator flux vector and when the torque regulator output is “0”, the active vector around which is located the sector including the stator flux vector, is applied. The resulting look-up table is given in Table 1. Nevertheless, this substitution is associated to an other crucial problem: that is an increase of the inverter switching frequency which compromises the drive efficiency.
+1 | −1 | |||||
---|---|---|---|---|---|---|
+1 | 0 | −1 | +1 | 0 | −1 | |
S1 | (100) | (101) | (001) | (110) | (010) | (011) |
S2 | (110) | (100) | (101) | (010) | (011) | (001) |
S4 | (010) | (110) | (100) | (011) | (001) | (101) |
S4 | (011) | (010) | (110) | (001) | (101) | (100) |
S5 | (001) | (011) | (010) | (101) | (100) | (110) |
S6 | (101) | (001) | (011) | (100) | (110) | (010) |
Look-up table with zero-voltage vectors substituted by active ones.
The implementation scheme of the DTC-SVM strategy with hysteresis controllers applied to the position regulation of an induction motor drive is shown in Figure 2. It has the same layout as the one of the basic DTC strategy proposed in section II, except that the SVM bloc is added to the control system that ensures an imposed switching frequency [7, 8, 9, 10, 11, 12].
Induction motor position regulation based on the DTC-SVM strategy.
The ratings and parameters of the induction machine, used in the simulation study, are listed in Tables 2 and 3 respectively.
The sampling period
Bandwidths of flux and torque hysteresis regulators have been chosen as:
The load torque is given by the following expression:
The modulation period has been fixed to
Power | 10 kW | Voltage | 380 V/220 V |
Efficiency | 80% | Current | 24A/41A |
Speed | 1500 rpm | Frequency | 50 Hz |
Induction machine ratings.
Induction machine parameters.
Figures 3–5 show the induction motor dynamic following the application of a dual-step reference position under the basic
Figures 3a–5a show that the three DTC strategies exhibit almost the same position and speed dynamics,
Performances of the flux loop of the basic
In order to overcome the demagnetization problem caused by zero-voltage vectors included in the look-up table of the basic DTC strategy, these have been substituted by active vectors. Obtained results are illustrated in Figure 4. Referring to Figure 4d, one can notice that the demagnetization problem has been removed, while performances of the motor, for high speeds, are not affected. However, the torque ripple amplitudes rise considerably (Figure 4c) with respect to the one yielded by the
Figure 5 shows that the DTC-SVM strategy exhibits high dynamical performances. In fact, this approach presents a low torque ripple amplitude (Figure 5c). Moreover, it completely eliminates the demagnetization phenomenon (Figure 5d).
Induction motor position regulation under the basic Takahashi DTC strategy, (a): Rotor position
Induction motor position regulation under the modified Takahashi DTC strategy, (a): Rotor position
Induction motor position regulation under the DTC-SVM strategy with a constant commutation frequency of 6.5 kHz, (a) rotor position
Further investigation of the stator flux has been achieved through the representation of the stator flux vector extremity locus in the
Locus of the extremities of
Finally, we have involved in the assessment of the average commutation frequencies of both basic and modified
Average commutation frequency of the inverter power switches, (a) basic Takahashi DTC strategy, (b) modified Takahashi DTC strategy.
The slip angular reference speed
The coordinates of references of voltage vectors
Finally, they are introduced to the SVM block, which uses them to control the inverter switches
The objective is the design of a suitable controller as described by Figure 8.
Position control loop.
Then, we have:
This yields:
Thus, we can write:
where:
For small values of
It is to be noted that the application of the following nonlinear feedback represents a nonlinear compensator:
This loop realizes a feedback linearization. The transfer function between
which is an exact transfer function without any approximation.
Observing this transfer function, it is clear that it contains two imaginary poles. This leads to a certain difficulty to control the system with a PID controller
In fact, the system does not present any stability margin. Moreover, to have an adequate dynamical behavior, the derivative time constant
The implementation scheme of a DTC-SVM based position regulation of an induction motor is shown in Figure 9. The idea is based on the decoupling between the amplitude and the argument of the stator flux reference vector.
Induction motor position regulation based on the DTC-SVM strategy.
The amplitude of this vector will be imposed equal to the nominal value of the stator flux, but the argument will be calculated according to the desired performances. In fact, the error between the reference position
Finally, the SVM block, which uses these later to generate the convenient stator voltages inverter in each modulation period, ensuring working with a constant commutation frequency.
Sliding mode (SM) controllers perform well in non nonlinear systems than PI controllers [13, 14]. Indeed, the sliding mode control is a type of variable structure systems characterized by the high simplicity and the robustness against insensitivity to parameter variations and external disturbances [14, 15, 16]. Considering a nonlinear system described by the following state equation:
A choice of the sliding surface
with
In order to decide a system trajectory, the equivalent control
Thus, one can choose for the controller the following expression:
The equivalent control can be designed as follows: when the system remains on the sliding surface, we have
where
This yields the following expression of the equivalent control:
under the regularity of matrix
The term
In fact, if we consider the Lyapunov function:
Its differential with respect to time is expressed as:
This yields that the closed loop system is stable.
The sliding surface is expressed as:
that is to say:
with:
In this case, function
To remain the state of the system on the sliding surface
That is to say:
where:
Then, it is easy to express the so-called equivalent control which corresponds to the required control remaining the system on the sliding surface:
Then, the slip angular reference speed
The new structure of this control approach is given by the block diagram of Figure 10.
Induction motor position regulation based on the DTC-SVM with sliding mode controllers.
If system (14) depends on an unknown parameter vector
where
Referring to Eq. (17), the differential of
with
Theorem
Control laws (17), (19) and (20) stabilize system (15) with the following adaptive laws:
Proof
Let us consider the following Lyapunov function:
In the following, it assumed that vector
respect to time:
The differential with respect to time of function
where
The sensitivity of the DTC-SVM to (i) variations on the magnetic permeability of the stator and rotor cores, and (ii) variations on the rotor resistance, which can vary with time and operating conditions, can be removed by an online estimation of the mutual inductance and the rotor resistance. The adaptive SM of the speed can be derived based on the mutual inductance and rotor resistance estimations using the
It is easy to show that:
where:
Then:
Corollary
The following slip angular reference speed control law stabilizes the speed loop:
where
with:
Proof
Considering the following function:
with
The time derivative of the
However:
Moreover:
Thereby, Eq. (42) gives:
Since
Simulation works have been carried out in order to investigate performances of the position control of the induction motor drive under the above-presented DTC-SVM strategies, using PID, PID with a nonlinear compensator and SM controllers. For the sake of comparison, both strategies have been considered in the same induction motor drive using the same implementation conditions, such that:
a reference stator flux
The modulation period has been fixed to
Constants involved in the position SM controller are:
The desired trajectory is defined by smooth variations of the position
variations of
constant value of
variations of
constant value of
The analysis of simulation results leads to the following items:
Figures 11 and 12 present evolutions of the position
Figures 13 and 14 present the same variable evolutions for variations of machine parameters as:
Thus, the implementation of the DTC-SVM using sliding mode controllers strategies highlights high dynamical performances obtained with the lowest torque ripple, the lowest flux ripple and the lowest current ripple.
Induction motor position regulation considering (subscript “1”) DTC-SVM approach using PI controller, (subscript “2”) DTC-SVM approach using PI controller with a nonlinear compensator and (subscript “3”) DTC-SVM approach using sliding mode controllers. Legend: (a) evolution of the position and its reference and (b) the speed of the motor and its reference.
Induction motor position regulation considering (1) DTC-SVM approach using PI controller, (2) DTC-SVM approach using PI controller with a nonlinear compensator and (3) DTC-SVM approach using sliding mode controllers. Legend: (a) evolution of the electromagnetic torque, (b) the stator flux and (c) the stator current of phase
Induction motor position regulation, considering +100% variations on the stator resistance, (1) DTC-SVM approach using PI controller, (2) DTC-SVM approach using PI controller with a nonlinear compensator and (3) DTC-SVM approach using sliding mode controllers. Legend: (a) evolution of the position and its reference and (b) the speed of the motor and its reference.
Induction motor position regulation, considering +100% variations on the stator resistance, considering (1) DTC-SVM approach using PI controller, (2) DTC-SVM approach using PI controller with a nonlinear compensator and (3) DTC-SVM approach using sliding mode controllers. Legend: (a) evolution of the electromagnetic torque, (b) the stator flux and (c) the stator current of phase
Considering the same simulation, we propose to use performance criteria defined in the appendix.
In the following, the steady state operating point is defined by a desired position
Total Harmonic Distortion (THD)
The first criterion is the average total harmonic distortion (THD) of the stator current which is defined in the Appendix.
In this context, the frequency spectrum of the stator current
Spectrum of the current
The total harmonic distorsion criterion of the stator current
PI without a NL compensator | PI with a NL Compensator | Sliding Mode Controllers | |
---|---|---|---|
THD (%) | 3.07 | 3.07 | 1.23 |
Total harmonic distortion of the stator current
Ratio of torque and flux ripples.
The second comparison criterion translates the torque and the flux ripples around their steady state values
Figure 16 presents the evolution of the torque
Zoomed shapes of (a) electromagnetic torque and (b) stator flux. In the case of (subscript “1”) DTC-SVM approach using PI controller, (subscript “2”) DTC-SVM approach using PI controller with a nonlinear compensator and (subscript “3”) DTC-SVM approach using sliding mode controllers.
PI without a NL compensator | PI with a NL Compensator | Sliding Mode Controllers | |
---|---|---|---|
ΦRIP,1 (%) | 0.38 | 0.38 | 0.12 |
ΦRIP,2 (%) | 0.44 | 0.44 | 0.15 |
ΦRIP,∞ (%) | 1.26 | 1.33 | 0.65 |
Flux ripple criteria.
PI without a NL compensator | PI with a NL Compensator | Sliding Mode Controllers | |
---|---|---|---|
1.88 | 1.86 | 0.92 | |
2.71 | 2.66 | 0.62 | |
8.17 | 8.34 | 4.65 |
Torque ripple criteria.
In this chapter, the DTC position control of induction motor controlling photovoltaic panel has been considered. This panel is commonly exposed to the sun in fixed positions corresponding to the maximum sunshine recorded during a day. Firstly, the DTC-SVM approach using hysteresis controllers has been compared to the basic DTC strategy and DTC strategy with a look-up table including only active voltage vectors. Then, the problem of position regulation of an IM under DTC-SVM approaches has been treated. In fact, a comparison between three DTC-SVM approaches: a DTC-SVM approach using PI controllers, a DTC-SVM approach using PI controllers with a nonlinear compensator, and a DTC-SVM approach using sliding mode controllers, has been proposed. Finally, an adaptation approach of parameter estimators has been implemented in order to eliminate the effects of parameter variations and load disturbances. It has been shown through simulations the sliding mode DTC-SVM approach (i) eliminates the demagnetization effects, and gives lowest ripples on the torque and on the flux, (ii) presents less harmonic distortion on the stator currents, and (iii) it presents good performances with a good robustness with respect to parameter’s variations and load disturbances, particularly in the case of adapted estimators of machine parameters.
“Once one starts to think about the human welfare consequences of economic growth, it is hard to think about anything else” [1]. Economic growth is the basis for increased prosperity, and its importance cannot be overstated. Barro and Sala-i-Martin [2] argue that continuous and sustained economic growth is important for improving the welfare of individuals and that aggregate growth is probably the single most important factor affecting individual levels of income. Due to the importance of economic growth, attainment of high economic growth rates is a major national objective of any country. It is, however, puzzling and at the same time worrisome that the riches of the world are so unequally shared among countries [3].
Over the years, growth performance has varied notably across regions and countries. In some economies, it has experienced major shifts over time. A few developing countries have experienced rapid growth yet some other countries have grown at only a stagnant rate. This discrepancy in economic growth among numerous countries and the dynamics of growth have become provocative research targets. The main questions are why some countries are rich while others are poor, and what determines the rate of growth? Rosa notes that it seems certain that there is no all-encompassing theory of economic growth, but different sources of economic growth can be observed to be relevant for different stages of economic development.
Several reasons have been provided that explain the differences, key among them being the fact that initial conditions differ greatly. Isaksson [4] asserts that some, if not many, of the differences in income per capita are human-created. He asserts that how a society and its production are organized can significantly explain the observed income divergence since the industrial revolution.
In the case of Uganda, the last five decades have been difficult in terms of overall economic growth and stability, let alone the first eight years after independence and the last three decades, when episodes of high yet unstable economic growth occurred, especially from the late 1980s to the late 2000s. Economic growth was impressive for the first eight years after independence, but by 1986, the economy had descended into a deep recession owing to poor governance from the early 1970s to that time. Since 1986, the country has undergone a major transformation from a “failed state” to one of the fastest-growing economies in the world. As early as 1993, Uganda started implementing structural adjustment programmes (SAPS) and other economic policies and programmes such as; economic recovery programme (ERP), medium-term expenditure framework, Plan for Modernization of Agriculture (PMA), and Poverty Eradication Action Plan (PEAP), among others all aimed at poverty reduction and attaining higher levels of economic growth in Uganda. The reforms ushered in relatively high economic growth rates based on incentives for private production. Between 1990 and 2010, GDP growth averaged 7.3 percent per annum, placing Uganda among the fastest-growing economies in the world and creating momentum for take-off. This growth was higher than the Sub-Saharan African growth rate, which averaged approximately 2.1 and was close to that of the East Asian and Pacific region of 7.9 and 6.6 percent, respectively.
To consolidate and accelerate this growth process, the Ugandan government approved the Comprehensive National Development Planning Framework Policy in 2007 which provided the developmental agenda for a 30-year vision to be implemented through three 10-year plans and six 5-year national development plans (NDPs), among other operational plans. However, data shows that Uganda’s growth has been mostly unstable; it has been described as unsustainable because it has been sustained partly by significant aid inflows and only a few tradable commodities, such as coffee, flowers and fish. The government of Uganda, like many other governments elsewhere continues to target improving GDP growth. The key to achieving this improvement has been the careful development and implementation of policies and programmes to improve capital stock, labour stock, price stability and productivity and competitiveness as major drivers of economic growth [5].
Uganda has set its Vision 2040 as a guiding framework for transforming the country from “a peasant to a modern and prosperous country with a per capita income of USD 9,500 from the base figure of USD 506 in the year 2010 by the year 2040”. For the country to achieve this transformation, Uganda Vision 2040 projects that Uganda’s real GDP will have to grow at an average of 8.2 percent, while the IMF forecasts approximately 9 percent growth rate as necessary for the remaining period. However, the achievement of Vision 2040 has been threatened not only by lower-than-targeted rates of annual GDP growth since the inception of the vision but also by a recent slump from the average GDP growth rate of approximately 6.8 percent that was posted in the last half of the 2000s to an average of 4.6 percent between 2010 and 2015.
To achieve the Vision, understanding the determinants of past growth, removing the constraints on present growth and maximizing the prospects for future growth are key. It is important to note that inferring the determinants of growth faces considerable uncertainty due to the existence of multiple overlapping theories that emphasize different channels of growth over time. Therefore, this paper aims at providing more robust and targeted policy interventions to generate higher and more sustainable economic growth by examining the determinants of economic growth in Uganda using the ARDL frameworks.
A wide range of studies have investigated the factors underlying economic growth in different countries. Using differing conceptual and methodological viewpoints, studies have identified different factors that explain economic growth world over [6]. However, existing literature has not yet reached a consensus about a typical set of variables that may affect economic growth.
The accumulation of physical capital (investment) is one of the most fundamental determinants of economic growth identified in the literature per the neoclassical and endogenous growth models and much empirical work has been performed on the subject [7, 8, 9]. It has been found to be robust to most specifications and sample size changes [10]. The impact of several types of investment has been studied over time and varying levels of significance have been attached to varying types of investment. Gross capital formation affects economic growth by either directly increasing the physical capital stock in the domestic economy [11] or indirectly promoting technology [12]. Other researchers have investigated the impact of private and public investment on economic growth and have found significant variations. Khan and Kumar [13] found private investment to be more productive than public investment. In this paper, investment is represented by physical capital accumulation and it is expected to have a positive and statistically significant relationship with economic growth.
Exports are another factor identified by both the neoclassical and endogenous growth models in explaining economic growth variations. Awokuse [14] notes that linking exports to economic growth is pied when he found that there is a flow of Granger cause from real exports to real GDP. There is also a strand of studies that find no conclusive evidence of the causal relationship between exports and GDP growth. Ruiz-Nápoles [15] argues that even in cases where increasing exports has a positive effect on production expansion, such an effect may be limited and offset by increasing manufacturing imports displacing domestic production. Fouad Abou-Stait [16] found that time series studies find fewer conclusive associations between exports and growth, whereas cross-sectional studies appear to support the positive relationship.
Closely related to exports is trade openness with mixed results. A large part of the literature find that economies that are more open grow more rapidly [17, 18, 19, 20]. Baliamoune [21] finds that trade openness is closely associated with positive effects in higher-income and negative effects in lower-income African countries. Arezki and Gylfason [22] find that trade openness has a positive and statistically significant impact on non-resource GDP growth. Several scholars have however criticized the robustness of these findings, especially on methodological and measurement grounds (see, [23, 24]). Vamvakidis [24] and Wong [25] find a negative relationship between openness to international trade and economic growth. Fowe finds no significant effect of openness to trade on economic growth in SSA.
Several endogenous growth models and extensions of the neoclassical growth model find human capital and/or knowledge to be a major source of growth [26]. A large number of studies find evidence suggesting that an educated population is a key determinant of economic growth (see [8, 27, 28]). However, other scholars find mixed results while others question studies that have found a positive relationships [29, 30]. Some empirical findings have shown that human capital accumulation plays only a small role in economic growth [31]. Studies by Bils and Klenow [32], Pritchett [29], Easterly and Levine [33] found that the evidence was weak, absent or even pointed to a negative impact.
Population growth rate is another important variable in economic growth literature. The relationship between population and economic growth is mixed and varies between countries [34]. Some empirical studies have found a negative relationship between population and economic growth [35, 36]; and in others there was a positive association with economic growth [37, 38]. Another factor influencing economic growth is population growth rate [36, 39, 40]. High population growth, for example, could have a negative impact on economic growth, influencing the dependency ratio, investment and saving behavior and quality of human capital countries [41]. However, the findings are again inconclusive since there some studies have reported no (strong) correlation between economic growth and demographic trends (e.g., [29, 42]).
Foreign Aid has received renewed political interest in economic growth discourse resulting into numerous studies. There is however little evidence of a significant positive effect of aid on the long-term growth of poor countries [43, 44]. Andersson and Karlsson, C. [45] finds support for the basic idea that an increase in aid flows strengthens economic growth in poor countries when the policy environment is conducive. Collier and Dehn [46] find that well-timed aid alleviates effects of negative export shocks while Collier and Hoeffler [47] find that aid works particularly well in good policy environments a few years after a conflict has ended. Other scholars argue that aid spurs economic growth unconditionally (see, [37, 48]), or in certain macroeconomic environments that it is growth-neutral [49]. In contrast, some studies have argued that aid has historically been ineffective in promoting growth [50, 51]. Rajan and Subramanian [43] provide evidence that total aid is ineffective at promoting growth.
The relationship between government consumption expenditure and economic growth has attracted a great deal of interest among policymakers and economists. Empirical work on this subject has also provided mixed results. On one side, there are Keynesian economists who consider consumption expenditure as a dependable function of income and on the other side there are substantial numbers of economists who believe that higher consumption can stimulate economic growth [52, 53]. Other studies have found that small to moderate government sizes are positively associated with economic growth while large government sizes impede economic growth [54, 55].
It is argued that inflation is a good macroeconomic indicator of how the government manages the economy [55, 56, 57]. Although the empirical evidence has strongly supported a negative relationship between inflation and growth, especially through the impact of inflation on capital intensity [58], other studies have found that inflation exhibits threshold effects on economic growth [59, 60]. Khan and Senhadji, [60] explore this issue and reach several conclusions. In particular, medium and high inflation hamper economic growth due to the adverse impact on the efficient distribution of resources by changing relative prices [57].
Based on the foregoing literature, we assume a Cobb–Douglas production function with labour-augmenting (Harrod-Neutral) technological progress following Mankiw, et al. [27] and Acikgoz and Mert [61].
where
where HC is human capital, and all other variables are defined as before. Following Mankiw, et al. [27], Acikgoz and Mert [61], and Chirwa and Odhiambo [17], the aggregate Cobb–Douglas production function is assumed to take the following form:
where α and β represent the partial elasticity of output with respect to physical capital and human capital respectively. Per the literature, technological progress (
Several efficiency variables have been identified in the literature to provide a link to how policy variables influence the aggregate production function [55, 57]. The variables selected for this study consist of the accumulation of physical capital (investment); human capital (total school enrolment); population; and policy variables (efficiency factors) that include government consumption share in GDP, inflation, foreign aid as a share of GDP and international trade. The efficiency factors, similar to population growth, are assumed to grow exogenously (see [27, 62]).
Auto Regressive Distributed Lag (ARDL) bounds testing approach developed by Pesaran and Shin [63], Pesaran, Shin and Smith [64] was employed. The modeling approach allows us to capture the short and long run dynamics as well as the speed of adjustment between the independent variables and the dependent variable. The embedded Error Correlation Model (ECM) is a restricted representation that has cointegration restrictions built into the specification so that it is designed for use with non-stationary series that are known to be cointegrated. The ECM specification restricts the long run behavior of the endogenous variables to converge to their cointegrating relationships while allowing a wide range of short run dynamics. Choice of the ARDL model was taken based on the following reasons: (1) the variables were found to be integrated of different orders i.e. (I(0) and I(1) and ARDL can be applied even when variables are not integrated of the same order; (2) ARDL performs better than other co-integration tests in small and finite data samples [65]. The two stage ARDL approach effectively corrects for any possible endogeneity in the regressors [61, 66]; (3) According to [67, 68] the ARDL model also allows for different optimal lags among the different variables to capture the data-generating process as a general-to-specific modeling framework [68, 69], (4) ARDL is known to have information about the structural break in time series data and lastly Pesaran and Shin [63] contented that appropriate modification of the orders of the ARDL model is sufficient to simultaneously correct for residual serial correlation and the problem of endogenous variables. The only drawback being that ARDI approach collapses when variables are integrated of order two (i.e I(2)).
The ARDL representation of the empirical model for this study is expressed as follows:
where
Two steps are involved in estimating an ARDL model. First, the long-run equilibrium relationship between the variables is tested using the upper and lower bounds; then, the short-run and long-run causalities are estimated. The ARDL bounds test is based mainly on the joint F-statistic in which its asymptotic distribution is non-standard under the null hypothesis of no co-integration [70].
In Eq. 4 above, the null hypothesis of no co-integration relationship, defined as
Using the Wald test, the computed F-statistic is then compared with the lower and upper asymptotic critical bounds values, as reported in Pesaran et al. [64]. The lower-bound critical value assumes that all the regressors are l(0), while the upper-bound critical value assumes that they are I(l). We reject the null hypothesis of no co-integration if the computed test statistic exceeds the upper-bound critical value, and we do not reject the null hypothesis if the F-statistic is lower than the lower-bound critical value. The test is, however, inconclusive if the computed F-statistic lies between the lower-bound and upper-bound critical values. In this context, unit root tests should be conducted to ascertain the order of integration of the variables. If all the variables are found to be I(1), then the decision is made on the basis of the upper-bound critical value. On the other hand, if all the variables are I(0), then the decision is based on the lower-bound critical value. To test for the long-run relationship between the variables, we exclude the lagged-level variables from Eq. (4). Once the presence of co-integration is confirmed, we estimate the long-run coefficients of the growth model and the associated ARDL of the ECM for the short-run coefficients.
The ARDL method estimates (p + 1)k number of regressions to obtain the optimal lags for each variable, where p is the maximum number of lags to be used and k is the number of variables in the equation [71]. The model is selected based on the Schwartz-Bayesian criterion (SBC) or the Akaike information criterion (AIC).
ARDL estimation provides both the short run (model) and long run estimation results. The ECM is specified as follows:
where
Annual time series data for the period 1982–2015, that was obtained from World Bank Development Indicators [73, 74] was used in this study. The following variables were used: Real GDP (expressed in 2010 U.S. dollars.) at purchaser’s prices; Investment (proxied by gross fixed capital formation as a share of GDP); Inflation (measured by the consumer price index); General government expenditure as a share in GDP (General government expenditure as a share in GDP); Human Capital (representing knowledge spill over effects) was proxied by Human capital index3, based on years of schooling and returns to education); Demography (proxied by total population); Trade openness (measured by the sum of exports and imports as a proportion of GDP); and Foreign Aid as a proportion to GDP (measured by net official development assistance and official aid received as a share of real GDP). Eviews 9.5 software was used to conduct the empirical analysis.
Unit roots/stationarity tests were conducted because this is a prime requirement for any co-integration and causality tests. The augmented Dickey-Fuller test (ADF: [75]) was used to establish the order of integration. The ADF test results were augmented with the Phillips-Perron (PP: [76]) test. Table 1 presents the results of the unit root tests.
Variables | Augmented Dickey Fuller | Phillips-Perron test |
---|---|---|
Constant + trend | Constant + trend | |
Log Real Gross Domestic Product | −3.48* | −3.48* |
Log Trade Openness | −2.81 | −2.62 |
Log Human Capital | −2.84 | −2.26 |
Log Population Growth | −0.06 | −1.72 |
Log Gross Government Final Consumption (% GDP) | −1.77 | −1.71 |
Log Gross Fixed Capital Formation | −3.95** | −2.89 |
Log Inflation Rate | −5.28*** | −2.22 |
Log Aid | −2.24 | −2.18 |
Log Total School Enrolment, Primary | −1.85 | −1.74 |
Log Imports | 3.41* | −2.43 |
Log Exports | −2.86 | −3.21 |
Log Real Gross Domestic Product | −3.38* | −3.38* |
Log Trade Openness | −4.51*** | −4.37*** |
Log Human Capital | −3.80 | −3.85* |
Log Population Growth | −3.80** | −2.35 |
Log Gross Government Final Consumption (percent) GDP) | −4.92*** | −6.02*** |
Log Gross Fixed Capital Formation | −4.33*** | −5.24*** |
Log Inflation Rate | −2.05 | −2.30 |
Log Aid | −6.41*** | −7.56*** |
Log Total School Enrolment, Primary | −6.91*** | 7.08*** |
Log Imports | −3.77** | −3.40* |
Log Exports | −6.49*** | −6.49*** |
Unit root test at level and in first difference.
***, **, and * denote rejection of the null hypothesis of unit root at the 1 percent, 5 percent and 10 percent significance levels, respectively.
The ADF test results with trend and intercept at level in part A indicate that GDP, GGC, and GFCF were stationary at the 5 percent level of significance, whereas CPI was stationary at the 1 percent level of significance. The researcher thus carried out stationarity tests for all series in first difference with constant and trend, as indicated in part B (ADF test), and the variables, except CPI, became stationary.
The variables were also tested for stationarity using the Phillips-Perron test. The PP test results at level with constant and trend were found to be non-stationary except for GDP and GGC, which were found to be stationary at 10 percent and 5 percent levels of significance, respectively. The variables were tested for stationarity in first difference, and they all became stationary except CPI.
We tested for co-integration among the variables to establish whether they had a long-run relationship. From a statistical point of view, a long-run relationship implies that variables move together over time and that short-term disturbances arising from the long-term trend are corrected. Co-integration is necessary because a valid ARDL requires the presence of a co-integrating set of variables. The ARDL method allows us to test both short- and long-run relationships between the dependent and independent variables in a multivariate framework. The critical value bounds are computed by stochastic simulations using 20,000 replications [66].
The variables are jointly tested if they are equal to zero. That is:
H0: They are jointly equal to zero.
H1: They are not jointly equal to zero.
Once the test statistic is computed, it is compared to two asymptotic critical values corresponding to polar cases of all variables being purely I(0) or purely I(1). When the test statistic is below the lower-bound critical value, the null hypothesis is not rejected, and co-integration is not possible. In contrast, when the test statistic is above the upper-bound critical value, the null hypothesis is rejected, and co-integration is indeed possible. Alternatively, should the test statistic fall between the lower-bound and upper-bound critical values, the test results are inconclusive, and knowledge of the co-integration rank is required to proceed further.
The Akaike information criterion was employed to determine the appropriate lag length for the estimated ARDL equation. This method was chosen because it tends to over-fit the model of interest, given that the optimal lag length for the growth model is up to 2 lags. The optimal lag length is chosen based on the number of dynamic regressors included in the model and the sample size. The optimal lag-length selection criteria are based on the lowest AIC obtained. For this growth equation, (regression I), the optimal ARDL model selected was the ARDL (2, 1, 0, 1, 0, 1, 0, 0, 2) model with restricted intercept and trend, while for regression II, the optimal ARDL model selected was the ARDL (2, 0, 2, 0, 1, 0, 0, 1, 0, 2) model with restricted intercept and trend. Table 2 reports the Pesaran et al. [64] bounds test for level relationships for the selected equation.
ARDL bounds test | Regression I | Regression II | ||
---|---|---|---|---|
Included observations: 32 after adjustments | ||||
Null hypothesis: no long-run relationships exist | ||||
Test statistic | Value | k | Value | K |
F-statistic | 5.47*** | 8 | 3.909** | 9 |
Critical Value Bounds | ||||
Significance | I0 Bound | I1 Bound | I0 Bound | I1 Bound |
10 percent | 1.95 | 3.06 | 1.88 | 2.99 |
5 percent | 2.22 | 3.39 | 2.14 | 3.3 |
2.5 percent | 2.48 | 3.7 | 2.37 | 3.6 |
1 percent | 2.79 | 4.1 | 2.65 | 3.97 |
R-squared | 0.845152 | 0.852168 | ||
Adjusted R-squared | 0.699981 | 0.672657 |
Results of ARDL bounds test for co-integration.
***, **, and * denote 1 percent, 5 percent and 10 percent significance levels, respectively.
As illustrated in Table 2, regression I, the computed 𝐹-statistic is 5.47, and it is statistically significant at the 1 percent upper-bound critical value, meaning that the null hypothesis of no co-integration is rejected at the 1 percent significance level. In regression II, the computed 𝐹-statistic is 3.909, and it is statistically significant at the 5 percent upper-bound critical value, meaning that the null hypothesis of no co-integration is rejected at the 5 percent significance level. In summary, the bounds test of co-integration relationships using the Pesaran et al. [64] approach confirms the existence of long-run level relationships between the dependent variable and the set of covariates in both regressions. The study results also reveal that the underlying ARDL model is a good fit, represented by an estimated
Using the ARDL model, the researcher selected the overall best model from the 20 best selected ARDL models. As shown in Figure 1, the selected model in regression I is ARDL (2, 1, 0, 1, 0, 0, 1, 0, 0, 2), and the selected model in the second regression is ARDL (2, 0, 2, 0, 1, 0, 0, 1, 0, 2). These two models were significantly superior to the second-best models in each case [66].
Relative superiority of the selected models.
The short and long run elasticities for the ARDL model were estimated. Table 3, part A presents the short-run ARDL results (including the ECM representation), while part B pre-sets the long-run results of the ARDL models.
ARDL co-integration and long-run form | ||
---|---|---|
Dependent variable: LRGDP | ||
Selected Model: Included observations: 32 | ARDL (2,1,0,1,0,1,0,0,2) | ARDL (2,0,2,0,1,0,0,1,0,2) |
Co-integration Form | Regression I | Regression II |
Variable | Coefficient(Prob.) | Coefficient (Prob.) |
D(Log Real Gross Domestic Product (−1)) | 0.179(0.049)** | 0.279(0.003)*** |
D(Log Trade Openness) | 0.036(0.190) | |
D(Log Population Growth) | 0.481(0.784) | 0.126(0.941) |
D(Log Inflation Rate) | −0.085(0.000)** | −0.086(0.000)* |
D(Log Human Capital) | 0.240(0.507) | 0.619(0.109) |
D(Log Gross Government Consumption) | 0.061(0.001)*** | 0.066(0.000)*** |
D(Log Gross Fixed Capital Formation) | 0.192(0.000)*** | 0.145(0.000)*** |
D(Log Aid) | −0.033(0.022)** | −0.021(0.111) |
D(Log Exports) | 0.027(0.047)** | |
D(Log Imports) | 0.056(0.178) | |
D(Dummy for Structural Adjustment) | −0.008(0.092)* | −0.018(0.007)*** |
C | 0.185(0.001)*** | 2.786(0.000)*** |
Coint Eq (−1) | −0.595(0.00)*** | −0.646 (0.000)*** |
Log Trade Openness | 0.295(0.002)*** | |
Log Population Growth | 1.008(0.090)* | 0.334(0.605) |
Log Inflation Rate | −0.009(0.624) | −0.018(0.361) |
Log Human Capital | 0.293(0.639) | 0.848(0.244) |
Log Gross Government Consumption (percent, GDP) | 0.198(0.001)*** | 0.159(0.007)*** |
Log Gross Fixed Capital Formation | 0.316(0.003)*** | 0.220(0.029)** |
Log Aid | −0.053(0.227) | −0.032(0.399) |
Log Exports | 0.121(0.007)*** | |
Log Imports | 0.090(0.244) | |
D(Dummy for Structural Adjustment) | −0.007(0.003)*** | −0.071(0.003)*** |
Short-run and long-run ARDL results.
***, **, and * denote 1 percent, 5 percent and 10 percent significance levels, respectively.
Part A of Table 3 reports the estimated short-run coefficients, while Part B reports the estimated long-run coefficients. Two different regressions were estimated. Regression I was the “benchmark” regression, while regression II was used for sensitivity/options analysis. Among other variables, regression II used a different proxy for trade openness, which is a fundamental variable for GDP growth, according to the literature. Specifically, instead of using trade openness, we used exports and imports to examine the effect of trade on GDP growth.
As shown in part A, the short-run dynamics and the adjustment towards the long-run equilibrium path are measured by the error correction term (ECT) [77]. In the short run, deviations from the long-run equilibrium can occur due to shocks in any of the variables in the model; thus, all the short-run coefficients show the dynamic adjustments of all variables to their long-run equilibrium [70]. If the coefficient is significant, it implies that past equilibrium errors play a role in determining the outcomes of the current period. The ECT measures the speed of adjustment to restore equilibrium in the dynamic model after a disturbance. For the coefficient to be significant, it is required that the error correction term (ECT) must be negative and significant. A highly significant ECT is further proof of a stable long-run relationship [78].
From Table 3, part A, regression I, the ECT estimation results show that the estimated coefficient of the error correction term has the expected sign (negative) and is statistically significant. This reinforces the finding of a long-run relationship in the co-integration equation. The results show that a 1 percent deviation from the equilibrium path is corrected in the next period at a rate of 59.5 percent and is statistically significant at the 1 percent significance level. This confirms the presence of a long-run level equilibrium path between real GDP and the selected regressors (trade openness, human capital, population, government consumption, investment, inflation, foreign aid and a policy dummy (structural adjustment programme). The regression results for the ARDL model reveal a good fit represented by an estimated
Part B, regression I of Table 3 presents the long-run coefficient estimates. The results reveal that the key macroeconomic determinants that are significantly associated with long-run economic growth in Uganda include trade openness, population growth, government consumption, investment, and the policy dummy variable for the structural adjustment programmes (SAPs).
In the long run, the relationship between trade openness and real GDP is positive and statistically significant at the 1 percent significance level. The results reveal that a 1 percent increase in trade openness in the long run leads to a 0.295 percent increase in the level of real GDP. These findings are supported by previous studies that have found a positive and significant relationship between trade openness and economic growth (e.g. [17, 19, 20]).
The study reveals that population growth is positively and significantly associated with the growth of real GDP in Uganda at the 10 percent level of significance. It shows that a 1 percent increase in population leads to a 1.01 percent increase in real GDP. These results are supported by similar studies conducted in developing countries that have found a positive relationship between investment and economic growth in the long run (e.g., [41, 79]).
The study reveals a positive relationship between government consumption and the growth of real GDP at the 1 percent significance level in the long run. A 1 percent increase in government consumption results in a 0.20 percent increase in the level of real GDP. These results are supported by similar studies conducted in developing countries that have found a positive relationship between government consumption and economic growth in the long run (e.g., [17]).
The results confirm the widely established empirical estimation finding that investment and growth in GDP have a positive relationship. A 1 percent increase in the level of investment results in a 0.32 percent increase in the level of real GDP. These results are supported by similar studies conducted in developing countries that have found a positive relationship between investment and economic growth in the long run (e.g., [10, 54, 80, 81, 82]).
The study results did not reveal a significant association between inflation, human capital and foreign aid and the long-run level of GDP growth.
The short-run results presented in Part A of Table 3 reveal that the key macroeconomic determinants that are significantly associated with the growth of real GDP in the short run are initial GDP, inflation, government consumption (percent of GDP), investment, foreign aid, and the policy dummy. The results show that a 1 percent increase in initial real GDP leads to a 0.18 percent increase in real GDP. Meaning that the level of and sign of initial GDP has a positive relationship with current GDP.
The results reveal a negative association between inflation and economic growth. A 1 percent increase in inflation leads to a 0.90 reduction in GDP. These results are supported by a number of empirical growth studies that have also found a negative association between inflation and economic growth in developing countries (e.g., [56, 57, 83, 84, 85, 86]).
The results show that government consumption is positively and significantly associated with the growth of real GDP at the 1 percent significance level. A 1 percent change in government consumption leads to a 0.06 percent increase in the growth of GDP. The positive relationship found between government consumption and economic growth is supported by similar studies in the empirical growth literature that have found a positive relationship between trade openness and economic growth (e.g., [17, 87]).
There is a positive and significant relationship between investment and economic growth at the 1 percent level of significance. A 1 percent increase in investment leads to a 0.19 percent increase in GDP. The results are consistent with existing empirical growth studies that have found a positive relationship between investment and economic growth (e.g., [10, 17, 88]).
The results show that foreign aid is negatively and significantly associated with the growth of real GDP, and the results are statistically significant at the 5 percent significance level. A 1 percent change in foreign aid leads to a 0.03 percent reduction in the growth of GDP. The negative relationship found between foreign aid and economic growth is supported by similar studies in the empirical growth literature (e.g., [10]).
The study results did not reveal a significant association between trade openness, population growth, human capital, and real GDP growth in the short run.
Sensitivity analysis was carried out to examine the significance of other variables or proxies for the variables used in regression II. This analysis was carried out bearing in mind theory, certain empirical studies and the nature of the Ugandan economy. Key variables/proxies were imports and exports as proxies for trade openness. Exports were found to be positively and significantly associated with GDP at the 1 percent level of significance, while imports were found to be non-significant.
From Table 3, Part A, regression II above, the ECT estimation results show that the estimated coefficient of the error correction term has the expected sign (negative) and is statistically significant. The ECT shows that a 1 percent deviation from the equilibrium path is corrected in the next period at a rate of −0.65 percent and is statistically significant at the 1 percent significance level. This confirms the presence of a long-run level equilibrium path between real GDP and the selected regressors (total school enrolment, primary; real exchange rate; population; government consumption; investment; inflation; foreign aid; imports; and exports). The regression results for the ARDL model reveal a good fit represented by an estimated
Part B, regression II of Table 3 presents the long-run coefficient estimates. The results reveal that the key macroeconomic determinants that are significantly associated with long-run GDP growth in Uganda are government consumption, investment, exports and the policy dummy.
The study reveals a positive relationship between government consumption and real GDP growth at the 1 percent significance level in the long run. A 1 percent increase in government consumption results in a 0.20 percent increase in the level of real GDP. These results are supported by Doppelhofer and Weeks [89] who find a positive relationship between government consumption and economic growth in the long run in developing countries.
The study reveals a positive relationship between investment and real GDP growth at the 1 percent significance level in the long run. A 1 percent increase in the level of investment results in a 0.22 percent increase in the level of real GDP. These results are supported by similar studies conducted in developing countries that have found a positive relationship between investment and economic growth in the long run (e.g., [10, 17, 54, 81, 82]).
There is a positive and significant relationship between GDP and exports in the long run at the 1 percent level of significance. A 1 percent increase in exports leads to a 0.12 percent increase in GDP growth (see [14, 16]).
There is also a negative and significant relationship between GDP and the policy dummy for SAPs in Uganda, as a 1 percent increase in implementation of the SAPs leads to a 0.07 percent reduction in real GDP growth.
The study results did not reveal a significant association between population growth, inflation human capital and foreign aid, imports and GDP growth in the long run.
The short-run results for the sensitivity/option analysis are shown in Part A, regression II of Table 3 above. The key macroeconomic determinants that are significantly associated with the growth of real GDP in the short run are initial GDP, inflation, government consumption (percent, GDP), investment, exports, and the policy dummy in both the current and the previous period.
The results show that a 1 percent increase in initial real GDP leads to a 0.28 percent increase in real GDP.
The results reveal a negative association between inflation and economic growth. A 1 percent increase in inflation leads to a 0.90 percent reduction in GDP. These results are supported by a number of empirical growth studies that have also found a negative association between inflation and economic growth in developing countries (e.g., [55, 56, 57, 83, 84, 85, 86]).
The results show that government consumption is positively and significantly associated with the growth of real GDP at the 1 percent significance level. A 1 percent change in government consumption leads to a 0.07 percent increase in the growth of GDP. The positive relationship found between government consumption and economic growth is supported by similar studies in the empirical growth literature that have found a positive relationship between trade openness and economic growth (e.g., [17]).
There is a positive and significant relationship between investment and economic growth at the 1 percent level of significance. A 1 percent increase in investment leads to a 0.15 percent increase in GDP. The results are consistent with the existing empirical growth studies that have found a positive relationship between investment and economic growth (e.g., [10, 17, 88]).
The results show that exports are positively and significantly associated with the growth of real GDP at the 5 percent significance level. A 1 percent change in exports leads to a 0.03 percent increase in GDP growth. The positive relationship found between exports and GDP growth is supported by similar studies in the empirical growth literature (e.g., [14, 90]).
There was a negative and significant relationship between the implementation of the structural adjustment programmes and GDP growth in the current period. A 1 percent increase in the implementation of the SAPs led to a 0.1 reduction in GDP.
The results indicate that in the short run, policy variables contributed to economic growth more than factor accumulation, while in the long run, a mixture of factor accumulation and policy variables was the major driver of economic growth.
The regressions were tested to ascertain their applicability and robustness. Robustness was confirmed by the Breusch-Godfrey serial correlation LM test, Jarque-Bera normality test, recursive stability tests, and Breusch-Pagan-Godfrey heteroscedasticity test. This means that the model has the desired econometric properties of time series data.
Recursive Tests were done using a visual examination of the graphs of the recursive parameter estimates. Additionally, a formal statistical test to test the null hypothesis of model stability was undertaken using the CUSUM test [91]. Figure 2 regression I and regression II illustrate the CUSUM and CUSUMSQ at the 5 percent significance level.
CUSUM and CUSUMSQ results for the estimated growth equation.
As illustrated in Figure 2, the CUSUM test reveals parameter stability, while the results of the CUSUMQ test reveal variance stability given that the residuals for both tests are within the 5 percent critical lines. According to these tests, our ARDL model is stable and has no serial correlation.
Serial correlation was undertaken to test whether the residual is correlated with its own lagged values using the Breusch-Godfrey LM test for serial correlation, and the results are presented in Table 4 below.
Breusch-Godfrey serial correlation LM test | Regression I | Regression II | ||
---|---|---|---|---|
F-statistic | 1.332638 | Prob. F(3,13) | 0.2739 | 0.0223 |
Obs*R-squared | 7.526409 | Prob. Chi-Square(3) | 0.1921 | 0.0004 |
The Breusch-Godfrey test for serial correlation in the residuals of the regression.
The Breusch-Godfrey serial correlation test statistic for the null hypothesis of no serial correlation (Table 4) for regression I has a probability value of 0.2739, which is greater than 5 percent. Thus, we fail to reject the null hypothesis, which indicates that there is no serial correlation in the residuals.
The Breusch-Pagan-Godfrey tests for heteroscedasticity statistic for the null hypothesis of no heteroscedasticity in regressions I and II have probability values of 0.6996 and 0.0612, respectively, which are greater than 5 percent. Thus, we fail to reject the null hypothesis, which indicates that there is no heteroscedasticity in the residuals (Table 5).
Heteroscedasticity test: Breusch-Pagan-Godfrey | Model I (probability) | Model II | ||
---|---|---|---|---|
F-statistic | 0.760385 | Prob. F(15,16) | 0.6996 | 0.0612 |
Obs*R-squared | 13.31781 | Prob.Chi-Square(15) | 0.5778 | 0.1320 |
Scaled Explained SS | 2.325347 | Prob.Chi-Square(15) | 0.9999 | 0.9945 |
Breusch-Pagan-Godfrey test for heteroscedasticity results.
The ARDL model assumes that the residuals are normally distributed. The Jarque-Bera statistic is assumed to have a
As indicated in Figure 3, in regression I, the probability value for the Jarque-Bera statistic is 0.49 with a probability value of 0.782, which is more than 5 percent; hence, the residuals are normally distributed. In regression II, the probability value for the Jarque-Bera statistic is 0.647 with a probability value of 0.724, which is more than 5 percent; hence, the residuals are normally distributed. This means that statistical tests for inference on regression coefficients are reliable, since these tests require that the dependent variable (and hence the residuals) follows a normal distribution.
Histogram normality test model I.
Specification errors can be errors in the specification of the functional form that the equation should take in describing the relationship between the variable. If the F test statistic is greater than the F critical value, we reject the null hypothesis that the true specification is greater than the F critical value, hence reject the null hypothesis that the true specification is linear (which implies that the true specification is non-linear). If we are unable to reject the null, then the results suggest that the true specification is linear and the equation passes the Ramsey Reset test (Table 6).
Ramsey RESET Test | |||
---|---|---|---|
Equation: UNTITLED | |||
Specification: LRGDP LRGDP(−1) LTRO LTRO(−1) LPOPN LINF LINF(−1) LHC LHC(−1) LHC(−2) LGGC LGGC(−1) LGFCF LAID C | |||
Omitted variables: squares of fitted values | |||
Value | df | Probability | |
t-statistic | 0.326505 | 17 | 0.7481 |
F-statistic | 0.106606 | (1, 17) | 0.7480 |
Ramsey rest test for the functional form test results.
The probability values from the Ramsey rest test for the T and F statistics are greater than 0.05 level of significance, meaning that the estimated model is free from specification errors.
Attaining high and sustainable economic growth is a major policy objective for any country especially among developing countries. In this paper, we examined the macroeconomic determinants of economic growth in Uganda using the factor accumulation framework for the period 1982–2015.
The autoregressive distributed lag (ARDL) approach to co-integration was used to estimate both the short- and long-run elasticities of the selected macroeconomic determinants. The ARDL bounds testing approach to co-integration in the benchmark regression indicated that the key determinants that are positively associated with growth in GDP in the short run are the initial level of real GDP growth, government consumption and investment, while foreign aid, inflation and a dummy for SAPs were negatively and significantly associated with real GDP growth. The results failed to show that trade openness, population growth and human capital accumulation were significantly associated with real GDP growth in the short run [95, 96, 97, 98].
The study revealed that in the long run, trade openness, population growth and government consumption and investment were positively and significantly associated with GDP growth, while the policy dummy on SAPs was negatively and significantly associated with GDP. In the long run, the study failed to show that inflation, human capital and foreign aid were significantly associated with GDP growth. It can be concluded that in the short run, policy variables contributed to economic growth more than factor accumulation (physical and human capital), while in the long run, a mixture of both factor accumulation and policy variables was the major driver of economic growth.
The study results have significant policy implications for Uganda. They show that investment and population have are significantly associated with economic growth both in the short and long run. Thus, it is recommended that the economic strategies to be adopted should include those that create incentives to attract investment—with an emphasis on the adoption of labour–intensive technologies, on quality–based human capital development. In the short run trade openness, government consumption, foreign aid and inflation are positively and significantly associated with economic growth meaning that the country should pursue policies that enhance trade, government effectiveness, aid effectiveness and economic management.
The study found that the key determinants that were positively associated with growth in GDP in the short run were the initial level of GDP growth, government consumption, investment and a dummy for SAPs, while foreign aid and inflation were negatively associated with GDP growth. The results failed to show that trade openness, population growth and human capital accumulation were significantly associated with GDP growth in the short run. In the long run, the study revealed that trade openness, population growth, government consumption and investment were positively associated with GDP, while the policy dummy on SAPs was negatively associated with GDP growth. In the long run, the study failed to show that inflation, human capital and foreign aid were significantly associated with growth in GDP.
These results have significant policy implications for Uganda, both in the short and long run. In the short run it is recommended that economic strategies that would spur accumulation of physical capital/Investment, increase government consumption, improve price stability be pursued while in the long run, strategies that improve trade openness, population growth, government consumption and investment should be pursued.
We would like to acknowledge Prof John Dumba Ssentamu and Associate Professor Eria Hisali, for their insurmountable technical contribution to this paper through their reviews and comments.
We believe financial barriers should not prevent researchers from publishing their findings. With the need to make scientific research more publicly available and support the benefits of Open Access, more and more institutions and funders are dedicating resources to assist faculty members and researchers cover Open Access Publishing Fees (OAPFs). In addition, IntechOpen provides several further options presented below, all of which are available to researchers, and could secure the financing of your Open Access publication.
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\\n\\nThe application process is open after your submitted manuscript has been accepted for publication. To apply, please fill out a Waiver Request Form and send it to your Author Service Manager. If you have an official letter from your university or institution showing that funds for your OA publication are unavailable, please attach that as well. The Waiver Request will normally be addressed within one week from the application date. All chapters that receive waivers or partial waivers will be designated as such online.
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\n\nThe first step in obtaining funds for your Open Access publication begins with your institution or library. IntechOpen’s publishing standards align with most institutional funding programs. Our advice is to petition your institution for help in financing your Open Access publication.
\n\nHowever, as Open Access becomes a more commonly used publishing option for the dissemination of scientific and scholarly content, in addition to institutions, there are a growing number of funders who allow the use of grants for covering OA publication costs, or have established separate funds for the same purpose.
\n\nPlease consult our Open Access Funding page to explore some of these funding opportunities and learn more about how you could finance your IntechOpen publication. Keep in mind that this list is not definitive, and while we are constantly updating and informing our Authors of new funding opportunities, we recommend that you always check with your institution first.
\n\nFor Authors who are unable to obtain funding from their institution or research funding bodies and still need help in covering publication costs, IntechOpen offers the possibility of applying for a Waiver.
\n\nOur mission is to support Authors in publishing their research and making an impact within the scientific community. Currently, 14% of Authors receive full waivers and 6% receive partial waivers.
\n\nWhile providing support and advice to all our international Authors, waiver priority will be given to those Authors who reside in countries that are classified by the World Bank as low-income economies. In this way, we can help ensure that the scientific work being carried out can make an impact within the worldwide scientific community, no matter where an Author might live.
\n\nThe application process is open after your submitted manuscript has been accepted for publication. To apply, please fill out a Waiver Request Form and send it to your Author Service Manager. If you have an official letter from your university or institution showing that funds for your OA publication are unavailable, please attach that as well. The Waiver Request will normally be addressed within one week from the application date. All chapters that receive waivers or partial waivers will be designated as such online.
\n\nDownload Waiver Request Form
\n\nFeel free to contact us at funders@intechopen.com if you have any questions about Funding options or our Waiver program. If you have already begun the process and require further assistance, please contact your Author Service Manager, who is there to assist you!
\n\nNote: All data represented above was collected by IntechOpen from 2013 to 2017.
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With its low gravity, slingshot effect relative to Earth, on-site resources and relative proximity to Earth in the solar system, the renewed space race is effectively returning first to the Moon. A psychological bridge to enlarge our civilization with a permanent bridge to our natural satellite. The development of this Earth-Moon system, requires enormous amount of finances, energy, science, technology, but over all, opportunities. This chapter deals with the efforts and the mental changes that may eventually result from all of these changes.",book:{id:"10955",title:"Lunar Science - Habitat and Humans",coverURL:"https://cdn.intechopen.com/books/images_new/10955.jpg"},signatures:"Yann-Henri Chemin"},{id:"81141",title:"Modeling Radiation Damage in Materials Relevant for Exploration and Settlement on the Moon",slug:"modeling-radiation-damage-in-materials-relevant-for-exploration-and-settlement-on-the-moon",totalDownloads:32,totalDimensionsCites:0,doi:"10.5772/intechopen.102808",abstract:"Understanding the effect of radiation on materials is fundamental for space exploration. Energetic charged particles impacting materials create electronic excitations, atomic displacements, and nuclear fragmentation. Monte Carlo particle transport simulations are the most common approach for modeling radiation damage in materials. However, radiation damage is a multiscale problem, both in time and in length, an aspect treated by the Monte Carlo simulations only to a limited extent. In this chapter, after introducing the Monte Carlo particle transport method, we present a multiscale approach to study different stages of radiation damage which allows for the synergy between the electronic and nuclear effects induced in materials. We focus on cumulative displacement effects induced by radiation below the regime of hadronic interactions. We then discuss selected studies of radiation damage in materials of importance and potential use for the exploration and settlement on the Moon, ranging from semiconductors to alloys and from polymers to the natural regolith. Additionally, we overview some of the novel materials with outstanding properties, such as low weight, increased radiation resistance, and self-healing capabilities with a potential to reduce mission costs and improve prospects for extended human exploration of extraterrestrial bodies.",book:{id:"10955",title:"Lunar Science - Habitat and Humans",coverURL:"https://cdn.intechopen.com/books/images_new/10955.jpg"},signatures:"Natalia E. Koval, Bin Gu, Daniel Muñoz-Santiburcio and Fabiana Da Pieve"},{id:"80241",title:"The Evolution of the Moon’s Orbit Over 100 Million Years and Prospects for the Research in the Moon",slug:"the-evolution-of-the-moon-s-orbit-over-100-million-years-and-prospects-for-the-research-in-the-moon",totalDownloads:65,totalDimensionsCites:0,doi:"10.5772/intechopen.102392",abstract:"As a result of solving the problem of interaction of Solar-system bodies, data on the evolution of the Moon’s orbit were obtained. These data were used as the basis for the development of a mathematical model for the Moon representing its motion over an interval of 100 million years. A program of exploration of the Moon with the aim of creating a permanent base on it is outlined. Such a base is intended for exploring the Earth, the Sun, and outer space.",book:{id:"10955",title:"Lunar Science - Habitat and Humans",coverURL:"https://cdn.intechopen.com/books/images_new/10955.jpg"},signatures:"Joseph J. Smulsky"},{id:"80217",title:"Educational and Scientific Analog Space Missions",slug:"educational-and-scientific-analog-space-missions",totalDownloads:88,totalDimensionsCites:0,doi:"10.5772/intechopen.101392",abstract:"Analog space missions in Poland include international scientific, technological, and business projects designed and realized by a private research company Analog Astronaut Training Center Ltd. (AATC) devoted to the future Moon and Mars exploration. Growing experience in educational aspect of the training as well as continuous development of the habitat and its professional space science laboratory equipment correspond to increased interest of educational organizations, universities, and individual students. We serve unique practical platform for space engineering, space master, and even space doctoral theses. In addition to a wide range of training courses offered for future astronauts, for example, diving, skydiving, rocket workshops, and stratospheric missions, AATC provides a private laboratory to simulate the space environment. It carries out scientific experiments focused on biology and space medicine, as well as addressing several multidisciplinary issues related to the Moon and Mars exploration, including space mining. The main goal of each our analog simulation is to get publishable results, what means that our analog astronauts obtain not only certification of completion of the training but also ability to continue studies and to perform it individually. This chapter summarizes methodology used by us, didactic tools, and obtained results for both educational and scientific analog simulations.",book:{id:"10955",title:"Lunar Science - Habitat and Humans",coverURL:"https://cdn.intechopen.com/books/images_new/10955.jpg"},signatures:"Agata Maria Kołodziejczyk and M. Harasymczuk"},{id:"79544",title:"Regolith and Radiation: The Cosmic Battle",slug:"regolith-and-radiation-the-cosmic-battle",totalDownloads:127,totalDimensionsCites:0,doi:"10.5772/intechopen.101437",abstract:"This chapter discusses regolith utilization in habitat construction mainly from the point of view of radiation protection of humans on missions of long duration. 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