View of Scrutiny of Sudan's Consumption Share to GDP

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Technium

42/2023

2023 A new decade for social changes

Social Sciences

Technium.

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Scrutiny of Sudan's Consumption Share to GDP

Khalafalla Ahmed Mohamed Arabi

College of Business, King Khalid University, Saudi Arabia [email protected]

Abstract. This paper examines the contribution of the consumption share to GDP from 1970 to 2019 to assess how income groups contributed to the share's stability, as well as the factors influencing its path and policy implications. Because the dependent variable is expressed in percentages and is not normally distributed, the Beta regression finite mixed model is the best tool for detecting latent income groups. We used Robust standard error to ensure the stability of the consumption share (i.e. the average propensity to consume APC). The analytical tool predicts the discovery of three previously unknown income groups. The following three latent groups were identified by the group means following the analysis: 0.82, 0.87, and 0.90 represent low-, medium-, and high-income groups, respectively, with probabilities of 0.27, 0.47, and 0.26 for their share contribution. The explanatory variables include employment, human capital (hc), total factor productivity at constant national prices (rtfpna), and the share of labor compensation in GDP. Each estimated parameter has a high significance and the expected sign. The policy implication is that the consumption share should be reduced in favor of the saving share by increasing employment opportunities and total factor productivity because it is relatively high.

Furthermore, fighting inflation increases consumption while increasing spending on health care, education, and training stimulates economic growth by increasing the percentage saving ratio but at different levels.

Keywords. Contribution; Share; Beta regression; Income groups; Significance

Introduction

Although many factors influence consumer spending, income is by far the most well- known, statistical and standard studies conducted in several societies have shown that the disposable income of the consumer is the primary and fundamental element by which the volume of consumer outlay is determined. These factors can be divided into subjective and objective categories, according to Keynes. The first is caused by the consumer's psychological actions, social habits, and impact on the structures of the dominant institutions, while the second is caused by various economic factors. However, the level of consumer expenditure is affected by the consumer's choice of how to allocate his income between consumption and savings.

These subjective factors that encourage one to cut back on consumption come from motives or self-motivations. The motive of precaution determines the portion of one's income that one retains to handle difficulties, and the motive of anticipation determines the investment and increase his income in the future. Then the motive of financial independence makes one deal with deals and speculation, in addition to the love of accumulating money. Keynes's objective Technium Social Sciences Journal

Vol. 42, 99-114, April, 2023 ISSN: 2668-7798 www.techniumscience.com

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factors are variables that proceed from economic causes and create pressures to increase or decrease the degree of individual propensity to consume regardless of the general level of income. Variables such as contingent and unexpected profit or loss in capital assets owned by the consumer do not usually affect his regular income, and the amendments in legislation or tax procedures, or significant adjustments. According to Keynes, income variation causes the marginal propensity to consume to be lower than the average propensity to consume in the short run. APC tends to be constant over time and is equivalent to MPC, though. Duesenberry's relative income hypothesis and Friedman's permanent income hypothesis both argue in favor of long-run APC stability, which is the opposite of Modigliani's hypothesis that the APC fluctuates in the short run before becoming constant in the long run. Why the APC declined in the short run while remaining constant over the long run is the subject of the Kuznets puzzle. Because the APC declines with increasing income and is disproportionately high in the low-income group, the Keynesian consumption function empirically yields poor long-run results [Bayar 1999].

Taxes relate negatively to consumption [Mankiw 2009]. The general rates of bank interest, changes in the expectations of individuals regarding the level of their current income, and the possibilities of its rise or fall in the future and in general, regardless of the theoretical premises. Other factors affect the level of consumer spending in one way or another: such as the general rates of prices, especially the differences between the level of current prices and expectations of their change in the future. The nature of the distribution of national income between different social groups and segments, as it was noted that the rate of consumer spending is higher in societies where the distribution of national income is equal [Pirayoff (2010)]. Then there are the factors arising from discrepancies in changes between the average prices and disposable cash income, the rise in nominal prices as well as the increase in nominal income may have a different impact on consumer behavior. It is also a factor affecting consumption in the presence of a developed banking sector that provides credit facilities to consumers (consumer loans), and the prevailing bank interest rates are influential factors. As is the case with the consumer's purchasing element, the assets or capital assets of bank balances, financial claims, real estate ownership, assets of durable goods, and others owned by the consumer, have an impact on the level of expenditure. There is also the demographic nature of the country concerned. Whether in terms of population increases or demographic composition and age groups, or the nature of the goods required. Finally, there are factors related to the nature of the economic and social institutions regulating the technical level of the country concerned, and the speed of its development. The types of consumption are intermediate consumption used in the production of another commodity, and final consumption that is, the custom of products of goods and services or enjoyment to satisfy the purposes of consumption so that do not lag behind this consumption. The final consumption consists of two elements: private consumption, which is the routine of individuals of the family sector for goods and services produced by the business sector, and public consumption, which is the use of community members of the services provided to them by the government services sector free of charge or for a symbolic fee. Decisions related to public consumption are issued by the government services sector: the goods and services that fall within the scope of private consumption are based on the market price (user price), the cost of production elements, net indirect taxes (direct taxes minus subsidies) and in addition to transportation and marketing costs.

As I know, no one has addressed the issue of Sudanese household consumption share.

The detection of unobserved groups is the primary goal of this study, which will be carried out using a beta regression finite mixed model to assess their contribution to the stability of Technium Social Sciences Journal

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consumption share. The study contains six sections including the introduction, the literature review, the proposed model, the methodology, the results and discussions, and the conclusion.

Literature Review

As evidenced by the number of papers that have been published, beta regression becomes a crucial tool in the analysis of percentages and rates [Gray and Hernandez (2018), Korhonen et.al (2017), and Liu (2016)]. This is where beta regression differs from linear regression; it uses two functions to link the predictors to the dependent variable's mean and precision parameters, respectively. However, the beta has come under fire, particularly when multicollinearity is present, which is a factor that encourages advancement [Abonaze et al.

(2022), Belaghi et al. (2022), Ferrari and Cribari-Neto (2010)].

The terms positive part, Stein, linear shrinkage, pretest, and shrinkage pretest were defined by Belaghi et al. in 2022. The asymptotic distributional biases and variances were calculated before a thorough Monte Carlo simulation study to assess how well the suggested estimation strategy performed. Stein estimators are used to estimate the parameters in the beta regression model when some of them do not significantly affect the outcome variable's ability to be predicted. Their results highlighted the significant benefits of the new methodologies in particular.

Based on the mean squared error criterion, Abonaze et al. (2022) compared the performance of an augmented beta regression by two parameters with the ML estimator, ridge, Liu, and Liu-type estimators. This is accomplished through the use of two real-world data applications and a Monte Carlo simulation study. According to simulation and application results, the proposed estimator outclassed the ML, ridge, Liu, and Liu-type estimators.

Lewis et al (2021). used Gaussian mixture linear regression and the tax rebate from the 2008 stimulus package to determine the distribution of marginal propensity to consume. As a dependent variable, durable and nondurable goods were used, along with an analysis of how consumer preferences varied depending on the type of good. Three groups of MPCs were found to differ in their levels of heterogeneity. After using bootstrapping, they showed a stable MPC for overall spending. Except for non-salary income and the average propensity to consume, many observables are individually correlated with the estimated MPCs, but these correlations vanish when the relationships are tested jointly. Targeting relatively higher-income households might be desirable to maximize the effects of stimulus checks on overall consumption.

Karlson et al. (2019) suggested using reweighted least squares with a Liu estimator for beta regression. Then, using four explanatory variables, they estimated the proportion of oil converted to gasoline using beta regression, which produced better results than MLE when the explanatory variables were highly correlated

Sahriman, et al (2019) estimated the rainfall in Pangkep Regency (Indonesia) based on precipitation and three dummy variables using Liu Type regression to cater to multicollinearity and diversity of rainfall data [10]. They picked up this region because it is the main salt producer that witnessed a decline in production because of climate change, and high rainfall.

Yellareddygari et al. (2016) used beta regression to predict the progress of pink rot disease on yield and days after harvest and discovered an interaction between pink rot at harvest and yield. In this regard, beta regression outperforms linear regression, with R² 0.56 versus 0.49.

Zakaria and Osama (2011) used multiple beta regression in an R package to estimate the percentage amount of sugar in the resulting humid spoil to the sugary ratio of the resulting raw juice. They used the AIC and BIC to choose the best model among seven models, Technium Social Sciences Journal

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concluding that the best model should be composed of two explanatory variables, i.e. new crude juice, sugary ration in chard, and a constant.

Smithson et al. (2011) used FMM models grounded on the beta distribution to model reaction patterns, polarization, securing, and arranging effects in probability rulings. Three sub- models were recognized by them: location, dispersion, and relative composition.

Christopher et al (2011) demonstrated that when equated to the earlier examination that the research group had published, Beta regression made a similar model. During the model- building process, all previously identified significant variables were found. This analysis confirmed the significant impact that age has on the outcomes of strokes by detecting the age- by-treatment interaction described in earlier studies. Additionally, a treatment effect in terms of odds ratios was obtained, providing a previously unidentified quantification of the impact of rt- PA on lesion volumes.

In contrast to the previously published volumetric analysis, Christopher et al (2011) built a multi-variable beta regression model linking explanatory factors with ischemic stroke lesion volumes. Beta regression generated a model that was similar to the earlier analysis that the study group had published. Every significant factor that had been previously identified was discovered during the model-building process in the age-by-treatment interaction that had previously been investigated. Beta regression provided the ability to interpret covariates using odds ratios and demonstrated proficiency in simulating ischemic stroke lesions. Beta regression is thought to be a viable alternative to the analysis of ischemic stroke volumes.

Ferrari and Cribari-Neto (2010) compared a linear model with angular transformation and beta regression using data from two natural science disciplines—biogeochemistry and ecological elemental composition—that produce continuous, bounded data. There were some differences between the two models as shown by model diagnostics, likelihood ratios, and p- values. However, there were noticeable differences between the coefficient estimates from the back-calculated beta regression model and the angular transformation. Beta regression can deliver precise parameter estimates in studies where effect sizes are as crucial as hypothesis testing in the natural sciences.

Conway and Dep (2005) use a finite mixture model to estimate birth weights, indicating that prenatal care has a significant effect on 'normal' pregnancies. They used a Monte Carlo experiment to confirm that ignoring even a small percentage of "complicated" pregnancies can lead to the perception that prenatal care is insignificant.

The Proposed Model

This study focuses on the factors that might affect the share of household consumption to GDP rather than estimating the consumption function of the well-known explanatory factors.

Five variables are assumed to affect consumption share: total factor productivity, labor share of GDP (real wages), human capital, employment, and real gross domestic product as a proxy for real income.

Total factor productivity is the share of output that is not covered by labor and capital.

The TFP's declining trend indicates that real wages are greater than what is acceptable, which causes inflation and social disturbance. An upswing in trend productivity, conversely, would surge per capita income, reduce inflationary burdens, and enable greater real wages and employment. TFP change can be used as a barometer of technological advancement in the long and intermediate terms because it measures improvements in production efficacy. Over a shorter period, however, it also fluctuates due to other factors, including management effectiveness, capacity utilization, work routines, and even weather conditions (Englander Technium Social Sciences Journal

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1988). Contrarily, TFP, according to Carlaw and Lipsey (2003) only measure the up-normal proceeds associated with technical change under ideal conditions; they do not measure technical change itself. TFP is a tool that policymakers can employ to promote economic growth.

However, the bottommost point of TFP in 1996 coincides with the uppermost labor share, and bottom capital formation shares to GDP.

The relationship between APC and income is inverse for labor income, which fluctuates around its long-run average. In light of the aforementioned, human capital development (returns to education) has a significant impact on the level and distribution of income in society because it is a key determinant of people's earning potential and employment opportunities. Because it is a major foundation of people's earning probable and employment prospects, the accumulation of human capital has a significant impact on the level and distribution of income in society.

According to Böndal et al. (2001), young people should enter the workforce with a basic set of skills they learned during their years of compulsory education.

Household consumption makes up the bulk of the GDP in Sudan, accounting for 84 percent of it on average, with the majority of this contribution coming from the low-, medium- , and high-income groups. The average share is typical for a developing country. The role of income group in a household's share of GDP is examined by this study using four variables, including the number of employed, employee compensation, human capital, and total factor productivity. The rationale behind including these determinants is that as consumers find employment or see an increase in their wages, they tend to increase their purchases of essential and durable goods. When the majority of consumers are employed and earning more money, the level of consumption will rise because they will have more money to spend on goods and services. Increased total factor productivity now accounts for the majority of income. Although human capital has a generally positive scale effect, higher education has been shown to have a negative effect, and both technical and structural effects are negative. The development of an economy can be aided by human capital, which affects economic growth and raises people's knowledge and skills. The amount of skilled labor needed depends on how quickly the economy expands as a result of consumer and business investment.

It is widely acknowledged that income and consumption are directly related. Although several different economic theories deal with the nature of consumer spending, and how the consumer behaves none of these theories, in general, conflicts with the evidence supporting that connection, and the theories' differences are frequently inconclusive., interpret or explain the nature of income and the factors affecting it in one way or another. All the statistical support and empirical data obtained in different countries and societies of the world have supported the existence of this well-established relationship between incomes on the one hand and what is spent on consumption on the other. It has been statistically established, about the individual or the whole society that the share of consumption about the volume of income increases as the overall level of income decreases. Statistics from advanced industrialized countries also indicate that in the nineteenth century, spending on consumption normally accounted for 84 to 94 percent of income. The payment of standard wages and salaries to employees as well as various fringe benefits (such as retirement and health care) made to third parties on their behalf make up the compensation of employees. As might be predicted, the larger of the two—wages and salaries accruals—makes up about 80% of all employee compensation, with supplements to wages and salaries accounting for the remaining 20%. When the subject of compensating labor arises, the compensation of employees goes beyond the conventional wage payments. A higher average propensity to consume is thought to be good for economic growth; however, in Sudan, the correlation between economic growth and APC is negative, with a minimum of 6%. The Technium Social Sciences Journal

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impact of APC on businesses, employment, savings, and overall demand—all of which move in the same direction—makes it significant. The three income groups behave very differently, with the lowest income group spending all of their income and occasionally taking out loans to pay their bills. Due to saving and debt repayment, the middle-income group has a low propensity to consume. Their motivation for saving is their belief in their ability to earn additional income in the future. The third group is made up of high earners who tend to save more money than they spend.

Methodology

The beta regression model is used in generalized linear models (GLMs) to examine the effects of particular explanatory variables on a non-normal response variable. Ferrari and Cribari-Neto used a link function, where the inverse of the precision parameter is the dispersion scale, to first connect the mean function of the response variable to a collection of linear predictors [Geissinger (2012)].

If y has taken on to be a continuous random variable that has the following probability density function for its beta distribution:

𝑓(𝑦; 𝑝, 𝑞) = Γ(𝑝 + 𝑞)

Γ(𝑝)Γ(𝑞)𝑦^𝑝−1(1 − 𝑦)^𝑞−1; 𝑝 > 0; 𝑞 > 0 (1)

Then the average and variance are estimated in (2) and (3) 𝐸(𝑦) = 𝑝

𝑝 + 𝑞 (2)

𝑉𝑎𝑟(𝑦) = 𝑝𝑞

(𝑝 + 𝑞)²(𝑝 + 𝑞 + 1) (3)

Assuming 𝜇 = 𝑝 (𝑝 + 𝑞); 𝑞 = (𝑝 + 𝑞) 𝑖. 𝑒. 𝑝 = 𝜇⁄ 𝜙; 𝑞 = (1 − 𝜇)𝜙 it follows from (2) and (3) 𝐸(𝑦) = 𝜇; 𝑉𝑎𝑟(𝑦) = 𝑉(𝜋)

1 + 𝜙 𝑓(𝑦; 𝜇𝜙) = Γ(𝜙)

Γ(𝜇𝜙)Γ((1 − 𝜇)𝜙)𝑦^{(𝜇𝜙)−1}(1 − 𝑦)^{(𝜙−𝜇𝜙−1)} (4) 0 < 𝑦 < 1; 0 < 𝜇 < 1; 𝜙 > 0

𝜙 =1 − 𝜎² 𝜎²

The beta probability distribution's mean and variance are as follows𝐸(𝑦) = 𝜇; 𝑣𝑎𝑟(𝑦) = 𝜇(1 − 𝜇)𝜎² 2. The model allows I using the logit link function, with the following covariates:

𝑔 (µ_𝑖) = 𝑙𝑜𝑔 ( µ_𝑖

1 − µ_𝑖) = 𝑥_𝑖^𝑇β = 𝜂_𝑖

Where the link function g(•), which connects the systematic and random components, is monotonically differentiable. 𝛽 = (𝛽₁𝛽₂⋯ 𝛽_𝑝)^𝑇𝑖𝑠 𝑝 × 1 vector of unknown parameters, 𝑥_𝑖 = (𝑥₁𝑥₂⋯ 𝑥_𝑝)^𝑇 is a linear predictor, and is a vector of p regressors. By assuming that the mean of yt can be expressed as

Technium Social Sciences Journal Vol. 42, 99-114, April, 2023 ISSN: 2668-7798 www.techniumscience.com

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𝑔(𝜇_𝑡) = ∑ 𝑥_𝑡𝑖𝛽_𝑖 = 𝜂_𝑖

𝑘

𝑖=1

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The logit link is a principally useful link function, and in this case, we can write 𝜇_𝑡= 𝑒^𝑥^𝑡^′^𝛽

1 + 𝑒^𝑥^𝑡^′^𝛽

Based on a sample of n independent observations, the log-likelihood function is 𝑙(𝛽, 𝜙) = ∑ 𝑙_𝑡(𝜇_𝑡, 𝜙)

𝑛

𝑡=1

(6) Where:

𝑙_𝑡(𝜇_𝑡, 𝜙) = 𝑙𝑜𝑔Γ(𝜙) − 𝑙𝑜𝑔Γ(𝜇_𝑡, 𝜙) − 𝑙𝑜𝑔Γ((1 − 𝜇_𝑡)𝜙) + (𝜇_𝑡, 𝜙)𝑙𝑜𝑔𝑦_𝑡 + {(1 − 𝜇_𝑡)𝜙 − 1} log(1 − 𝑦_𝑡) (7)

Karlsson, et al (2019) showed that the parameter vector β for the Liu estimator becomes:

𝛽̂(𝑑) = (𝑋^′𝑊̂ 𝑋 + 1)⁻¹(𝑋^′𝑊̂ 𝑋 + dI)𝛽̂_𝑀𝐿 (8)

Where d is a shrinkage parameter with a range of [0, 1] and 𝛽̂_𝑀𝐿is the MLE of got through a reweighted least squares analysis

The beta regression finite mixed model was used to classify households into three unobserved income groups: low, medium, and high. By fitting group-specific models, we can determine how likely it is that a person will belong to a group. It is possible to determine each group's average share. The following is a definition of the finite mixed model:

𝑓(𝑦_𝑖) = ∑ 𝜋_𝑖𝑓_𝑖(𝑦_𝑖⌋𝑥_𝑖^′𝛽_𝑖)

𝑔

𝑖=1

; < 𝜋 < 1; ∑ 𝜋_𝑖

𝑔

𝑖=1

= 1

𝜋_𝑖 = 𝑒𝑥𝑝(𝛾_𝑖)

∑^𝑔_𝑖=1𝑒𝑥𝑝(𝛾_𝑖)

Where 𝛾_𝑖 is the ith latent class's linear forecast. The f_i(y_i⌋x_i^′β_i) is the conditional probability density function for the witnessed reaction in the ith class model (the component densities of the mixture).

Results and Discussion Data Description

We collected data from Penn World Table version 10.0 (PWT). The dependent variable is the share of the household to GDP (csh_c i.e. APC), the number of employees in million (emp), compensation to employees share to GDP (labsh), human capital (hc), and total factor productivity (rtfpna) is the explanatory variables for model 1, and model 2 contains the same explanatory variables plus real GDP expenditure for model_2.

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Table 1: Descriptive Statistics.

CSH_C Rtfpna EMP HC LABSH PL_C

Mean 0.84 0.86 6.10 1.34 0.73 0.25

Median 0.84 0.84 6.21 1.33 0.78 0.24

Maximum 0.92 1.08 10.32 1.61 0.90 0.48

Minimum 0.61 0.73 2.66 1.10 0.63 0.11

Std. Dev. 0.06 0.09 2.36 0.17 0.07 0.10

Skewness -1.52 0.52 0.11 0.08 -0.07 0.48

Kurtosis 7.11 2.49 1.68 1.51 1.77 2.00

Jarque-Bera 50.01 2.60 3.42 4.31 2.96 3.70

Probability 0.00 0.27 0.18 0.12 0.23 0.16

Observations 46.00 46.00 46.00 46.00 46.00 46.00

Source: researcher calculation

The means and medians of the model variables have a tendency to be close to one another, which is a characteristic of descriptive statistics. Except for the dependent variable's contribution to GDP from consumption, all variables have a normal distribution. The most dispersed variables are employment and human capital, in contrast to consumption share and compensation to employees. When compared to the other variables, employment has the widest range, falling between 0.31, which corresponds to consumption share, and 0.57, which corresponds to human capital.

Unit Root Test

Table 2: Unit Root Test Results

Variable Augmented Dickey-Fuller Phillips-Perron

Level Ist diff. 2^nd diff Level ist diff. 2^nd diff

Csh_c -2.36 -6.44^*** -2.51 -6.65^***

Emp 1.70 -3.21^*** 2.41 -3.21^***

Hc -0.62 -1.81 -6.75^*** -1.83 -6.75^***

Rtfpna -1.26 -5.31^*** -1.42 -5.31^***

Labsh -0.86 -6.86^*** -0.82 -5.17^***

Rgdpe 2.16 0.99 -6.82^*** 1.75 0.99 -6.32^***

Source: researcher calculation; ^*, ^**, ^*** significant at 10%, 5%, and 1%

The unit root tests showed that the consumption share, employment, total factor productivity, and compensation to employees all have one unit, whereas human capital and real gross domestic production have two units, and all are significant at 1%

Figure 1: Consumption Share.

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The consumption shares oscillate between 0.8 to 0.92, which is typically affected by environmental disasters such as drought, floods, and civil war. The lowest point occurred in 2011 when South Sudan separated from Sudan and became an independent state.

Cointegration Test Results

Trace test reveals five cointegrating equations at the 0.05 level; * indicates that the hypothesis was rejected at this level, using MacKinnon-Haug-Michelis p-values, to point to a long-term relationship between the model variables and enabling the confident use of regression analysis (Annex 1).

Table 3: Estimated Coefficients.

Coefficients

Variable

Class 1-Margins Class 2-Margins Class 3-Margins Model 1

Model 2

Model 1

Model 2

Model 1

Model 2

Employment 2.56 2.21 1.80 1.88 1.05 0.38

Human capital -36.95 -29.54 -24.42 -28.29 -28.53 -3.65 Labor share (total wages) -1.01 -4.89 -5.50 -3.43 -10.33 -1.28 Real Total Factor Productivity 0.56 0.57 1.44 1.80 4.57 12.64

Real GDP Expenditure 0.00002 0.00003 0.00004

Constant 35.64 31.37 26.38 27.69 38.53 17.11

Csh_c logs 8.63 5.56 6.59 10.06 9.25 9.51

Source: researcher calculation

While labor income fluctuates around its long-run average, APC and income have an opposite relationship. In light of the aforementioned, the development of human capital (returns to education) has a significant impact on the level and distribution of income in society because it is a major determinant of people's earning potential and employment opportunities ( Blöndal et al. (2001)). Thus, both harm the APC as expected.

Due to unsuccessful economic development plans, total factor productivity initially trended down from 1977 to 1995 before turning up for the remainder of the study period. While productivity increases raise per capita income and fights inflation, real wages above low Technium Social Sciences Journal

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productivity levels cause inflation and social unrest. According to econometric research, supply shocks, not demand shocks, are more likely to cause cyclical fluctuations in productivity, and shifts in overall productivity cause business cycles (Englander 1988). Demand fluctuations, on the other hand, would reveal whether or not there was a cyclical disparity between the production side measure of productivity and the true measure. Increasing the average consumer's proclivity to spend now will increase income and employment without increasing investment. Thus, there is a dual effect between employment and income on the one hand, and consumer propensity on the other, which satisfies the positive effect of total factor productivity.

We used the robust standard error to ensure the stability of the consumptions' share to GDP. An increase in the number of employed is associated with an increase in the consumption share of the three classes by 2.56, 1.8, and 1.05 percent, respectively. Similarly, total factor productivity is associated with 0.56, 1.44, and 4.57 of the three consumption shares, respectively, whereas an increase in human capital and compensation to employees, is associated with 36.5, and 1.101 less percentage of consumption share, respectively through a rise in income i.e. confirming Keynes' assumption of a decrease in APC as income rises. The Akaike information criterion prefers the first model (-192.5 vs. -181.3), as does the Bayes information criterion (-155.9 vs. - 139.3)

Table 4: Means and Probabilities.

Class Margin (mean) Margin (mean) Probabilities Probabilities

1 .8217479 .5738999 .2740344 .1668879

2 .8661135 .8434713 .4687079 .5833833

3 .902135 .884479 .2572577 .2497288

Source: researcher calculation

Figure 2: Effects concerning Independent Variables.

As we can see, class 1 relates to low earnings, class 2 matches medium income, and high earnings is corresponding to class 3. The first group contributes approximately 27 percent vs. 17 percent of the household share, the second 47 percent vs. 58 percent, and the third 26 percent vs. 25 percent. Usually, the low-income group

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consumes more than the high-income group with a high standard of living and tends to save more for any additional income, which is the case in Sudan.

Discussion

Due to the existence of a unit root, the notion that Sudanese consumption share is constant or stable has been disproved. In contrast, the mean can grow or shrink over time, however, when a shock occurs, the share series will not converge back to the growing mean, indicating that the shock's effects have a lasting effect on the mean (i.e. no convergence over time). The shares' maximum and minimum values, 0.92, and 0.61, respectively, show a range of 0.31. The maximum share corresponds to the year 2000 when oil exports began in late 1999, and the minimum share to the year 2011, when oil export revenues began to decline because of South Sudan's secession. Despite the presumption that a high APC promotes economic growth, Granger causality shows that this is not the case in Sudan, where growth rate and APC correlate negatively with a very low correlation rate. Even so, they have been in a committed relationship for a while. Beta finite mixture regression was used to identify three unobserved groups that were arranged according to means, by robust standard error to ensure the share's stability. The first and third groups' probabilities are relatively close to each other, and the medium share is nearly twice as large for each group, however, these groups correspond to income groups i.e.

low-, medium-, and high-earning groups. It has been established that employment and total factor productivity have a positive impact, whereas employee compensation and total factor productivity have a negative impact. The estimated model's policy implication is that the government should spend more money on human capital in terms of health and education because healthy and educated individuals have higher incomes and a better chance of earning additional income, which reduces the share of consumption and increases the share of saving, which aids in investment and economic growth. An increase in employee compensation will increase the share of saving at the expense of consumption, resulting in economic growth.

Reduced unemployment raises the share of consumption, as does an increase in total factor productivity; however, the negative effects of human capital and employee compensation must offset these effects.

Conclusion

From 1970 to 2019, the beta finite mixed model was used, and it generated significant estimates for four predictor variables across the three income groups the model identified. The group with middle incomes appears to have the biggest impact on the overall consumption share. The model includes four independent variables: total factor productivity, employee compensation as a percentage of total compensation, employment rate, and human capital. Over the three classes that have been identified, all variables are highly significant. The primary analytical tool was Stata 17. According to the World Bank, the percentage of Sudanese citizens who are poor increased from 50% in 2009 to 77% in 2016. The Sudanese Social Security Commission announced that 77% of Sudan's 30 million people live in poverty. It confirmed that per capita income no longer exceeds one dollar and only 25 cents per day as a result of ongoing civil war, drought, displacement, ineffective economic policies, and corruption. As stated in the introduction, the average propensity to consume is higher in the low-income group, so policies to reduce poverty and end the ongoing civil war are essential.

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Appendix

Annex 1: Cointegration Test Results.

Date: 11/26/22 Time: 23:24 Sample (adjusted): 1976 2019

Included observations: 44 after adjustments Trend assumption: Linear deterministic trend Series: CSH_RTFPNA EMP HC LABSH RGDPE Lags interval (in first differences): 1 to 1

Unrestricted Cointegration Rank Test (Trace)

Hypothesized No. of CE(s) Eigenvalue Trace Statistic 0.05 Critical Value Prob.^**

None ^* 0.55 94.91 69.82 0.00

At most 1 ^* 0.36 57.05 47.87 0.00

At most 2^* 0.31 35.89 29.80 0.00

At most 3^* 0.20 17.75 15.49 0.02

At most 4^* 0.14 17.18 3.84 0.00

Source: researcher calculation Annex 2

Fitting full model:

Iteration 0: log pseudo-likelihood = 116.2478 Iteration 1: log pseudo-likelihood = 116.2478 Finite mixture model: Number of obs. = 46 Log pseudo-likelihood = 116.2478

Coefficient Robust std. err. z P>|z| [95% conf. interval]

1. Class (base outcome)

2. Class_cons 5367262.00 0.37 1.45 0.15 -0.19 1.26

3. Class _cons -0.06 0.42 -0.15 0.88 -0.89 0.76

Class 1 Response: Share of household consumption at current PPPs (csh_c ) Model: betareg, link(logit)

Coefficient Robust std. err. Z P>|z| [95% conf. interval]

emp 2.56 0.04 67.96 0.00 2.49 2.63

hc -36.95 0.57 -64.98 0.00 -38.07 -35.84

labsh -1.01 0.18 -5.74 0.00 -1.36 -0.67

rtfpna 0.56 0.11 5.26 0.00 0.35 0.76

_cons 35.64 0.69 52.02 0.00 34.30 36.99

csh_c

logs 8.63 0.47 7.70 9.55

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Coefficient Robust std. err. z P>|z| [95% conf. interval]

emp 1.80 0.29 6.20 0.00 1.23 2.36

hc -24.42 4.00 -6.10 0.00 -32.26 -16.57

labsh -5.50 1.05 -5.24 0.00 -7.55 -3.44

rtfpna 1.44 0.37 3.86 0.00 0.71 2.17

_cons 26.38 4.16 6.34 0.00 18.22 34.53

/csh_c

logs 6.59

0.29 6.03 7.16

Coefficient Robust std. err. z P>|z| [95% conf. interval]

emp 1.05 468151.00 22.37 0.00 0.96 1.14

hc -28.53 1.04 -27.32 0.00 -30.58 -26.49

labsh -10.33 0.52 -19.76 0.00 -11.35 -9.30

rtfpna 4.57 0.27 16.89 0.00 4.04 5.10

_cons 38.53 1.45 26.53 0.00 35.68 41.38

/csh_c

logs 9.25 0.49 8.29 10.20

Annex 3

Expression: Predicted mean (csh_c), using class probabilities, predict (mu outcome(csh_c)) dy/ex wrt: emp hc labsh rtfpna

dy/ex Delta-method std. err. z P>|z| [95% conf. interval]

emp 1.37 0.1223911 11.09 0.00 1.12 1.60

hc -4.51 0.1424882 -13.17 0.00 -5.18 -3.84

labsh -0.39 0.501806 -781 0.00 -0.49 -0.29

rtfpna 4.57 0.022996 7.22 0.00 0.12 0.21

Latent class marginal means Number of observations = 46 Margin std. err. Z P>|z| [95% conf. interval]

1 .8217479 .0015857 518.23 0.000 .8186401 .8248558 2 .8661135 .0034475 251.23 0.000 .8593564 .8728705

3 .902135 .0009793 921.18 0.000 .9002155 .904054

Latent class marginal probabilities Number of observations = 46 Class Margin Delta-method std. err. 95% confidence interval

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1 .2740344 .0674583 .1626213 .4232012

2 .4687079 .0775841 .3238855 .6190006

3 .2572577 .0674695 .1477524 .4089754