Determinants of multidimensional poverty in Tanzanian households

Introduction

Addressing poverty remains a long-standing priority in global development efforts across both developed and developing countries [1,2] . According to the World Bank's reports, extreme poverty affects 1.2 billion people worldwide, with approximately 700 million living below the extreme poverty line. This represents 10 percent of the global population, a significant decrease from the 36 percent reported in 1990. Notably, 50 percent of those living in extreme poverty are under 18 years old [3] . Attaining sustainable economic growth with a particular emphasis on eliminating extreme poverty and hunger has become the primary development objectives for governments around the world, as reflected in the Sustainable Development Goals and Millennium Development Goals (SDGs) established in 2000. These initiatives aimed to reduce poverty in all its forms across the world [4] . Over the last two decades, from 1999-2009 and 2009-2019, there has been a significant drop in the number of people living below the poverty line. Unfortunately, the COVID-19 pandemic disrupted this positive trend. More than 50 million people are falling into extreme poverty [5] . The World Bank predicts that by the end of 2025, an estimated 71 million individuals will be subjected to extreme poverty. The COVID-19 pandemic has a substantial influence on the world economy, particularly in underdeveloped countries. In Tanzania, vulnerable people experienced employment losses. Small enterprises experienced lower productivity and capital constraints, resulting in lower income. These problems underscore the need to rethink and improve poverty reduction policies in developing countries, with an emphasis on assisting vulnerable populations such as women, low-skilled workers, and informal sector workers to promote inclusive economic recovery [1] . Tanzania has made tremendous progress towards poverty reduction since gaining independence in 1961. The poverty index fell from 34.4% in 2007 to 26.4% in 2019 [6] . However, the World Bank expressed concern in 2022 that population growth would outpace poverty reduction initiatives, resulting in an increase in the number of needy people. In 2019, around 14 million individuals lived below the national poverty line, while approximately 26 million (49% of the total population) lived below the international poverty threshold of $1.90 per day. Many non-poor individuals who live just over the poverty line are also at risk of falling into poverty [7] . Existing analytical studies examining the determinants, trends, and reduction of poverty in Tanzania often fall short of comprehensively investigating the problem, as they frequently focus on specific locations [1] . Conducted research on the determinants of rural household poverty in Tanzania a case of Morogoro Region, and their study provided a comprehensive understanding of socioeconomic determinants of poverty. However, they acknowledged that their findings might vary based on location. Moreover, among those studies [2] , analyzed the determinates of household poverty and solely used consumption expenditures per adult equivalent as an indicator. The expenditures do not fully capture the entire information about poverty.

This study aims to add to the discussion by examining socioeconomic and demographic characteristics as determinants of household poverty in Tanzania. The study uses a nationally representative dataset from the National Household Budget Survey (HBS dataset 2021-2022) and applies a feasible generalized least squares approach for model prediction because the cross-section data has the problem of heteroscedasticity [8] . Additionally, this study deploys a multidimensional poverty index as an outcome indicator to fully capture more information about household poverty.

Materials and Methods

Data Type and Source

The Tanzania National Bureau of Statistics, in collaboration with the Ministry of Finance and Planning, conducted the 2017-2018 Household Budget Survey (HBS). The World Bank, UNICEF, and UN Women provided funding for Tanzania's government and its partners. The survey covered the entire United Republic of Tanzania and employed a twostage cluster sample design, resulting in a 99 percent response rate from 8767 households. The dataset includes information from agriculture, households, livestock, and communities. However, this analysis solely focuses on the household crosssectional dataset to capture economic, social, and demographic characteristics and outcomes simultaneously.

Variables Definitions and Measurements

Construction of Multidimensional Poverty Index (MPI):

The Multidimensional Poverty Index (MPI) [2] provides a comprehensive method for assessing poverty by taking into account several factors that affect households' well-being rather than relying on a one-dimensional measure of poverty based on income. Currently, there is no universally accepted criterion for determining the dimensions of the Multidimensional Poverty Index. However, in several studies, the dimensions of education, health, and living standards have been commonly used [16,17] . This study develops an MPI (Multidimensional Poverty Index) using ten indicators Table 2.

Key indicators include per capita income, which represents a household's economic prosperity, and mean years of schooling, which measures education and knowledge. Vaccination acts as a reliable measure of an individual's health status. Indicators of living standards encompass access to power and gas, the availability of clean drinking water, the kind of housing, the presence of toilets, and the number of rooms per family member. The Multidimensional Poverty Index (MPI) gives a full picture of how poor and well-off households are by combining these different measures. Principal component analysis, which gives more weight to higher levels of variation, is used to make the index.

Principal Component Analysis (PCA)

PCA [3] , is a multivariate statistical approach used to reduce the several correlated variables to the few uncorrelated variables (dimensional reduction) without losing too much information in the process [18] . The PCA technique accomplishes this by establishing a smaller set of variables that explains most of variation in the original variables. The new variables generated are linear combinations of the original variables. The first new variables will explain as much of the variation in the original data as possible [18] . Suppose: 𝑋 = [𝑥 1 , 𝑥 2 , … 𝑥 𝑛 ] is a matrix of 𝑛 variables and 𝑚 observations. Prior to using Principal component Analysis, it is usual to first Centre the numerical variables are 𝒙 * with elements: 𝑥 𝑖𝑗 * = 𝑥 𝑖𝑗 -𝑥̅ 𝑗 where; 𝑥̅ 𝑗 is mean of the variable 𝑗.

is constructed with deviation round the mean. Since Principal Component Analysis is primarily account for the variance of the numerical variables, the crucial intention here is to find a linear combination of column vectors of 𝑋 that maximizes variance. It has turned at that such linear combinations are:

Where: 𝑏 = [𝑏 1 , 𝑏 2 , … 𝑏 𝑛 ] 𝑇 is the normalized eigenvector corresponding to eigenvalue 𝜆 of the covariance matrix?

Since 𝑀 is a symmetrical matrix of order 𝑛𝑥𝑛, it has exactly 𝑛 real eigen values 𝜆 𝑘 , (𝑘 = 1,2 … 𝑛) and the corresponding eigen vectors can be applied to generate an orthogonal set vector such as: 𝑏 𝑗 𝑇 𝑏 𝑗 ′ = 1 if 𝑗 ≠ 𝑗 ′ and zero otherwise.

Accordingly, these 𝑛 eigen-vectors of 𝑀 produce 𝑛 new vectors:

That maximize variance. These vectors 𝑦 𝑗 , (𝑗 = 1,2. . , 𝑛) are known as the principal component Analysis (PCs) of the dataset 𝑋, with 𝑦 1 having the most variance, 𝑦 2 the second most, and so on down to 𝑦 𝑛 having the least. Also, the new coordinate system is represented by the matrix:

of the first 𝑝 eigenvectors that correspond to the 𝑝 largest eigenvalues of the matrix 𝑆 that can be to move 𝑛dimensional data of 𝑋 to 𝑝-dimensional space. 3 Applied Multivariate Statistical Analysis, Richard Johnson and Dean W Wichern, Sixth Edition.

Linear Regression Model

The study initially used the Ordinary Least Squares Method (OLS) [4] to estimate the linear regression model of determinants of multidimensional poverty among households in Tanzania. The method was used as the dependent variable was a continuous variable [19] . The linear regression model states as:

Where; 𝑌 𝑖 , is the multidimensional poverty index at a point of time, 𝑋 𝑖 is a vector of covariates, 𝛽 is a vector of parameters of the model, 𝑢 𝑖 is the error term. The model assumes that the mean and variance of the error are zero and constant, respectively. When assumptions are violated, the estimates tend to be biassed, inconsistent, and inefficient. Therefore, the feasible generalised least square estimator will be applied instead of the OLS estimator to resolve the problem of heteroscedasticity.

Diagnostic tests for linear regression model 2.4.1 Multicollinearity test and remedial measure

Multicollinearity arises when there is a substantial statistical relationship between independent variables [19] . While multicollinearity does not hinder the Ordinary Least Squares (OLS) estimations, it does lead to imprecise/inaccurate estimates due to the large variances of the calculated coefficients.

The study utilized variance inflation factors (VIF) to evaluate the presence of multicollinearity. If the variance inflation factor (VIF) exceeds ten (10), it signifies a strong correlation among the predictors. In such cases, eliminating a collinear variable with a high correlation coefficient can rectify the issue:

Heteroscedasticity test and remedial measure

The cross-sectional data are usually heteroscedastic in nature [19] . (2.5) is run and the null hypothesis: 𝐻 𝑜 = 𝛼 1 = ⋯ = 𝛼 𝑃 = 0 is tested. If the diagnostic test reveals a serious case of heteroscedasticity, the predicted weights will be involved to resolve the problem.

Feasible Generalized Least Square Estimator

The feasible generalized least squares method is being applied to resolve the issue of whether the homoscedastic assumption was violated. Initially, the original regression model (Equation. 2.6) was estimated to obtain the residuals. To model the heteroscedasticity, we assume that the variance of the error term, conditional on the independent variables follows an exponential function:

Where 𝑒 𝑖 is the error term of residual model. The Equation .(2.8) was regressed to estimate the parameters of the residual model. The fitted values from the residual model were denoted as 𝑔 ̂𝑖. The heteroscedasticity function was estimated by using the fitted values [8] :

The original model was transformed by dividing both sides by the square roots of the estimated heteroscedasticity function ℎ ̂𝑖 in order to stabilize the variance of the error terms [20] .

Therefore, the equation (2.11) was used to predict the model for determinants of multidimensional poverty in Tanzania.

Where 𝑦 𝑖 * is the multidimensional poverty, 𝑋 𝑖 * is the vector of independent variables, 𝛽 is the vector of coefficients and 𝑢 𝑖 * is the error term. According to the Table 3.1, the average household size was four members, with a range of 1 to 8 members. The household head's age ranged from 21 to 88 years, with an average age of 47 years. Additionally, the household's average monthly income was TZS 423,692, with a range of TZS 5,434.52 to 1,504,174. The average years of schooling in the household were 6 years, ranging from 0 to 21 years. The majority 77.80% of household heads were married and living together, while only 22.20% were not married. Credit Service: A significant proportion 98.13% of households did not have access to credit services, with only 1.87% having accessibility. Location: Approximately 23.86% of households were in urban areas, while the majority 76.14% were in rural areas. This indicates that the majority of respondents reside in rural areas. According to descriptive statistics, 21.50% of household heads were female and 78.50% were male. Males headed the majority of families in Tanzania. Employment status: About 25.25% of household heads are employed, while the majority 65.02% are not in the formal employment structure.

Results and Discussion

Descriptive Statistics for Continuous Variables

Descriptive statistics for categorical variables

Multidimensional Poverty Index

The study was based on 10 internationally recommended indicators to build the outcome variable. Principal component analysis was employed for dimensional reduction. The first three principal components contributed 87.4% of the total sample variance. The selected principal components were combined to calculate the scores and then standardized to obtain the required index, called the multidimensional poverty index. The index ranges from 0 to 1, with values closer to zero indicating low poverty levels and values closer to 1 indicating high poverty levels, from low poverty status to high status. 3.3, the regression model analysis findings revealed that the entire model (F-test) was statistically significant with P = 0.000, which was less than 0.05, and the coefficient of determination (R-squared) was 0.455%. Other factors outside of the model were responsible for the remaining percentage. This implies that the model explained 45.50% of the multidimensional poverty index. Hence, the model has violated the assumption of homoscedasticity of variance (see the below diagnostic tastes for multicollinearity and heteroscedasticity).

Linear Regression Model 3.4.1 Ordinary Least Square Estimator (OLS)

Testing for Multicollinearity

The correlation matrix reveals that all variables exhibit correlations with each other. But the variance inflation factors (VIFs) were found to be sufficiently low, ranging between 1.05 and 1.88. These low VIF values suggest that the inclusion of the individual determinants in the model is statistically valid.

White test for heteroscedasticity

After model estimation, the White's test has been deployed to test whether the variance of the disturbance term is common across all explanatory variables. H o: Homoskedasticity Aganist H a: Heteroskedasticity chi2 (49) = 2042.27 prob > chi2 = 0.000 Therefore, the white test revealed that the model under OLS Method violated the assumption of homoscedasticity in the error term's variance. The feasible generalized least squares method was applied to resolve the problem by improving the efficiency of the linear regression model. 𝑀𝑃𝐶 ̂= -8.0724 + 0.1057(𝑉1) -0.0038(𝑉2) + 0.8781(𝑉3) + 0.0029(𝑉4) + 0.9598(𝑉5) -0.812054(𝑉6) + 0.0131(𝑉7) + 0.73446(𝑉8) + 0.6964 (𝑉9)

Weighted Linear Regression Model 3.5.1 Feasible Generalized Least Square Estimator (FGLS)

Referring to Figure 3.2, by using FGLS method, the F-test value was improved, increasing from (𝑅 2 𝑂𝐿𝑆 ̂=0.455) which was estimated by the ordinary least square method to (𝑅 2 𝑊𝐿𝑆 ̂= 0.502) obtained from the feasible generalized least square method. The coefficient of determination (R-squared) was improved and statistically significant. This implies that, 50.20% variation of multidimensional household poverty was explained by model predictors. The following are the findings of a weighted regression analysis based on individual effects using T-test:

The household head not married or divorced (V1): The estimated coefficient of not married or divorced (a dummy for the marital status of the household head) was negative and significantly related to multidimensional poverty at the 1% significance level. This implies that for every one-unit increase in the household with a head who is not married or divorced, the poverty level decreases by 0.105 units, on average, assuming all other factors remain constant. Not similar to one done by [12] asserting that the married head or living together positively support the household to stay away from poverty (extreme poverty line), and improve their household well-being.

Age of the household head (V4):

The regression analysis results revealed that, the age of the household head was negatively and statistically significant (P = 0.000) related to multidimensional poverty. This indicates that, on average, when the age of the head increases by one unit, 0.003 units would improve household well-being when other factors hold constant. This result agrees with [13,16] , who found that the age of the household has a great impact on improving the standard of living of household remembers. The older household heads have more experience with economic diversification than the younger generation.

Rural (V5):

At a 1% significance level, a household that located rural area (a dummy for location of household) had a positive and significant coefficient. This implies that, on average, a household located in a rural area has 0.960 units more risk of being multi-dimensionally poor than those who live in urban areas. Therefore, this implies that people living in rural areas are more at risk of poverty than those in urban areas. The results are similar to those done by [1,14] , who found that there is a negative and significant relationship between multidimensional poverty and the location of the household. Those who live in urban areas are at least safer than those who live in rural areas.

Household size (V6):

The estimated coefficient of household size was positive and statistically significant at the 1% significance level; this indicates that, on average, when the household size increases by one unit, 0.081 units will drop the sureness and intensity of the household to live above the poverty line. This study is consistent with one done by [1] who revealed that having a large household decreased the likelihood of non-poor status and increased the probability of a household being below the poverty line.

Years of schooling for the household head (V7):

The regression analysis results showed that years of household head schooling were negatively and statistically significant (P = 0.000) related to multidimensional poverty. This indicates that, on average, when the years of schooling increase by one unit, 0.013 units would improve household well-being when other factors hold constant. This result agrees with [13,16] , whose outcomes found that households whose heads are educated have a higher likelihood of being secured in terms of staying away from poverty compared to households whose heads are illiterate.

Employed (V8):

The estimated coefficient of employed (a dummy for employment status) was negative and significantly related to multidimensional poverty at the 1% significance level. This implies that, on average, a household who are employed (or self-employed) has 0.735 units more to be multi-dimensionally non poor compared to not employed household head. This study is similar to one done by [12,13] , who revealed that when a household head has official employment, it would increase the likelihood of non-poor status and eradicate poverty in their households.

Total household income (V9): At the 1% level of significance, the estimated coefficient of household income was negative and significantly related to multidimensional poverty. This implies that when the income (TShs) increases by one unit, 0.696 units would improve the well-being of the household and help them avoid the risk of being multidimensionally poor and stay above the local and international poverty line. The results are similar to those done by [13,14] , whose found a significant positive correlation between household income and multidimensional poverty. The huge income generated by household heads truly supports their family standard of living and welfare in general.

Therefore, this study found that the sex of the head of the household (V2) and access to credit services (V3) were not statistically significant with the multidimensional poverty index of the household.

Conclusions and Recommendations

Using the most recent NHBS (2017/2018) dataset, this study analyzed the household food security status and its determinants in Tanzania. Referring to the results revealed in this study, various policy intervention areas are identified.

The following are the policy implications that can be drawn from this study. The primary objective of this study was to analyze the factors that determine the intensity of multidimensional poverty among households in Tanzania. The findings indicate that the majority of household heads lack formal education, and there is a notable issue with having a large number of household members. This might result in increased expenses for managing the household and contribute to household poverty. Formal education should promote a stronger emphasis on diversifying the household economy, benefiting both household heads and their children. Furthermore, the act of enabling members of a household to engage in commercial endeavors can be accomplished by offering instruction in entrepreneurship and financial administration, which include acquiring and managing loans that are relevant to the undertaking. Moreover, to tackle problems regarding the control of family size, it is crucial to prioritize the implementation of family planning programmes.

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