Background

By 2030, end hunger and ensure access by all people, in particular, the poor and people in vulnerable situations, including infants, to safe, nutritious and sufficient food all year round

Sustainable development goal (SDG): Target 2.1

About 815 million (10.7%) of the 7.6 billion people in the world were suffering from chronic undernourishment in 2016 and malnutrition affects around one in three people on the planet [7, 12]. SDG indicator 2.1.1: prevalence of undernourishment (PoU) is an estimate of the proportion of the population whose habitual food consumption is insufficient to provide the dietary energy levels that are required to maintain a normal active and healthy life [8, 12]. This indicator is expressed as a percentage and it will measure progress toward SDG Target 2.1.

The vast majority of hungry people live in lower-middle-income regions, which saw a 42% reduction in the prevalence of undernourished people between 1990 and 2014. Despite this progress, in 2016, the global prevalence of undernourishment has been rising [7].

In addition to agenda of 2030 in the world, the 2014 Malabo commitment calls for ending hunger and reducing stunting to below 10% and underweight to below 5% by 2025. This agenda shows, in Africa, food security and nutrition constitute an essential focus of the continent’s development [2, 8].

Despite the Malabo agenda, Africa has the highest prevalence of undernourishment. Of which, in sub-Saharan Africa, the prevalence of undernourishment appears to have risen from 20.8 to 22.7% between 2015 and 2016, and the number of people undernourished increased from 200 to 224 million, accounting for 25% of the 815 million people undernourished in the world in 2016 [8]. At the same time, the proportion of the population that has experienced severe food insecurity because of their inability to access food has risen in the region [1, 7, 8].

In the selected East African countries, the prevalence of undernourishment is still significantly higher when compared with the sub-Saharan African countries prevalence of 20.8% except for Djibouti. According to the World Bank report of PoU [15] in 2015 in Ethiopia, Kenya, Rwanda, Uganda and Tanzania, the prevalence was 28.8, 19.1, 41.1, 39 and 32.3%, respectively.

The main reasons for the world countries remaining high in the prevalence of undernourishment are poverty [13], conflict [3, 7], climate change and the degradation of the environment [3,4,5, 7, 9], political insatiability [9], and food and agricultural policy [6, 7]. More specifically,

  1. 1.

    Poverty As of 2013, about 767 million people are living below the international poverty line of less than $1.90 per person per day [13]. All East African countries are in poverty; more specifically Ethiopia has a very large food insecure area due to poverty [11, 12, 14].

  2. 2.

    Conflict More than half (489 million) of the 815 million hungry people in the world live in countries affected by conflict and in 2016, the average prevalence of undernourishment in countries undergoing conflict was about four percentage points greater than the prevalence in nonconflict countries [7]. South Sudan and Somalia are among victim countries found in East Africa.

  3. 3.

    Political instability In countries facing political instability, the resulting decline of the economy reduces the value of the country’s currency, leading to higher food prices and less nutritious food available for purchase [9].

  4. 4.

    Food and agricultural policy A lack of adoption of more productive technologies for agriculture in lower-middle-income countries contribute to large differences in the number of crops produced when compared with upper-income countries [6, 8].

  5. 5.

    Climate change Throughout the previous 30 years, natural disasters have become increasingly common [8]. Unstable weather patterns can lead to drought—in 2016, El Niño was responsible for conditions of severe food insecurity for 20 million people [9]. Ethiopia and Kenya are among victim countries found in East Africa; this is according to the FAO report [8].

This study had an aim to compare the trend of the selected East African countries based on PoU, to ascertain the long-run relationship between the PoU of SSA and selected countries, and to identify the contribution of these countries to the PoU of sub-Saharan Africa.

Methods

Data source

The data source for this study was the World Bank report on the prevalence of undernourishment [12, 15]. The data contained the prevalence of all countries of the world from 1991 to 2015. For this study, I have selected the SSA, Ethiopia, Kenya, Rwanda, Uganda and Tanzania separately as a variable.

Data analysis

Line graph was used to display and compare the trend of PoU of selected countries with the world’s and SSA’s PoU in the specified time period. To identify whether there is long-term equilibrium relationship between SSA and selected countries PoU, the first step was to plot the countries PoU data and examine its stationarity behavior. However, this examination of plots suggests that either the given variables are stationary or not. But, still, it is impossible to say conclusively about the stationary characteristics of these series based on plots. Therefore, I have used statistical method to test the stationary character, called augmented Dickey–Fuller (ADF) unit root test having a model, as follows;

$$\Delta y_{t} = \alpha + \beta t + \gamma y_{t - 1} + \delta_{1} \Delta y_{t - 1} + \cdots + \delta_{p - 1} \Delta y_{t - p + 1} + \varepsilon_{t} ;$$

where yt is variable of interest (countries), t is a time index, Δ is the first difference operator, β is a coefficient, α is a constant, ε is error term, and γ is a hypothesis value of γ = 0 versus γ < 0.

The unit root problem was identified at the level, I took the first difference of time series for each variable and test the unit root again, still some of the variables were non stationary, and I took second and third differences finally, when all the variables are stationary, I have checked for long-run relationship using Johansen [10] multivariate cointegration test.

Johansen multivariate cointegration tests

Johansen [10] suggested two tests for H0: At most k CI vectors: the trace test and the maximal Eigenvalue test. Both tests are based on the λ’s from \(|\lambda I - S_{11}^{ - 1/2} S_{10} SS_{00}^{ - 1} S_{01} S_{11}^{ - 1/2} | = 0\). They are LR tests and a multivariate version of Dickey–Fuller unit root distribution so they do not have the usual χ2 asymptotic distribution under H0.

The trace statistic \({\text{LR}}_{\text{trace}} (k) = - 2\ln \varLambda = - T\sum\nolimits_{i - k + 1}^{m} {\ln (1 - \hat{\lambda }_{i} } )\) where k is rank of integration of the countries PoU with the SSA PoU and \(\hat{\lambda }_{i}\) denotes the descending order Eigenvalues \(\hat{\lambda }_{i} = \hat{\lambda }_{1} > \cdots > \hat{\lambda }_{m} > 0\) of \(|\lambda S_{11} - S_{10} S_{00}^{ - 1} S_{01} | = 0.\)

Note The \({\text{LR}}_{\text{trace}}\) statistic is expected to be close to zero if there are at most k (linearly independent) cointegrating vectors.

  • If \({\text{LR}}_{\text{trace}} (k) > {\text{CV}}\)(for rank k), then H0 (CI rank = k) is rejected

  • If \({\text{Rank}}(\varPi ) = k_{0}\), then \(\hat{\lambda }_{{k_{0} + 1}} , \ldots ,\hat{\lambda }_{m}\) should all be close to 0. The \({\text{LR}}_{\text{trace}} (k_{0} )\) should be small since \(\ln (1 - \hat{\lambda }_{i} ) \approx 0\) for \(i > k_{0}.\)

An alternative LR statistic, given by: \({\text{LR}}_{{\rm max} } (k) = - 2\ln \varLambda = - T\ln (1 - \hat{\lambda }_{k + 1} )\). It is called the maximal eigenvalue statistic. It examines the null hypothesis of k cointegrating vectors versus the alternative k + 1 CI vectors. That is, H0: CI rank = k, versus H1: CI rank = k + 1.

Finally, this study empirically examines the contribution of PoU of each country, in the group and separately for the sub-Saharan African PoU using the time series regression with ordinary least square (OLS) estimation approach. For robustness reason, least absolute deviation (LAD), S-estimation methods were employed.

The linear regression model is also given by: \(Y_{i} = \alpha + \beta_{1} x_{1} + \beta_{2} x_{2} + \cdots + \beta_{n} x_{n} + \varepsilon_{i}\) where \(\alpha\) is constant, \(\beta_{i}\) s are coefficients and \(\varepsilon_{i}\) are error terms. All the data were presented and analyzed using time series analysis approach and STATA-14 was the package.

Results and discussion

The trend of PoU of SSA and the selected countries are displayed in Fig. 1. The PoU of SSA fell gradually from 33.73% in 1991 to 20.15% in 2015 and similarly, PoU of Ethiopia fell significantly from 74.8% in 1991 to 28.8% in 2015. This shows that the PoU of both SSA and Ethiopia had a straight falling from 1991 to 2015. In a different direction, the PoU of Kenya was 32.4% in 1991 then increased slightly to 37.8% in 1994, and then fall gradually to 19.1% in 2015. The same to Kenya’s PoU, the PoU of Rwanda was 55.6% in 1991 then increased significantly to 66.4% in 1998, and then decreased gradually to 41.1% in 2015. Similarly, the PoU of Tanzania was 24.2% in 1991 then increased gradually to 37% in 2003, and then fall slightly to 32.3% in 2015. Differently, the PoU of Uganda was 23.2% in 1991, it increased slightly to 30% in 1998, then fell to 24.3% in 2006 and then increased significantly to 39% in 2015.

Fig. 1
figure 1

Trend of PoU of countries from 1991 to 2015

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Table 1 presents the summary statistic of the PoU of the countries and SSA. The summary statistics showed that the average PoU of SSA from 1991 to 2015 was 25.36% with the lowest prevalence of 19.29% in 2011 and the highest prevalence of 33.73% in 1992. Similarly, the average PoU of Ethiopia, Kenya, Rwanda, Uganda and Tanzania from 1991 to 2015 was 48.96, 29.39, 48.14, 2.66 and 33.18%, respectively. This result shows the average PoU of all countries is above the average PoU of their region SSA.

Table 1 Summary statistics of PoU in SSA countries
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Figure 2 displays the trend of countries separately and their stationarity behavior. The PoU of SSA and all countries were nonstationary at the level, it became stationary after they are smoothened by differencing method, at first difference the PoU of SSA, Ethiopia and Kenya became stationary. The PoU of Tanzania was stationary at the level, and the PoU of Uganda became stationary at the second difference.

Fig. 2
figure 2

Trend of PoU of countries and stage of stationarity

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The ADF test results are presented in Table 2 to confirm the stationarity of the PoU of the countries and SSA in Fig. 2. The results showed that all the variables were nonstationary (unit root) at the level except Tanzania’s PoU, and became stationary (no unit root) at the first difference (SSA, Ethiopia and Kenya), in the second difference (Rwanda), and in the third difference (Uganda). This means that the PoU of SSA, Ethiopia and Kenya has the same order of integration, which is I(1). This result, therefore, suggests that there might be a cointegration relationship among these countries and SSA in the long run. Accordingly, this study has applied Johansen multivariate cointegration tests and the findings of this test are reported in Table 3.

Table 2 ADF unit root test results
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Table 3 Johansen multivariate cointegration test results
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The findings from Johansen tests of both trace and max-Eigen statistic show that the test values (14.55 and 12.15) were less than the critical values (15.41 and 14.07), respectively. This result shows that there was a significant cointegration relationship between the PoU of SSA, Ethiopia and Kenya, meaning that the PoU of Ethiopia and Kenya have a long-run relationship with the PoU of SSA. Based on this finding, this study has applied a time series regression to identify the contribution of Ethiopia’s and Kenya’s PoU to the SSA’s PoU in Table 4. Based on this result, the adjusted R2 is 0.39, this means that 39% of PoU of SSA has explained by the PoU of Ethiopia and Kenya. This shows that these two countries had a significant contribution to the PoU of SSA. The reason of these countries to contribute more than one-third of the PoU of SSA is that these two countries (Ethiopia and Kenya) were affected by main reasons for the high PoU: climate change, political instability and poverty during the period 1991–2015.

Table 4 The contribution of Ethiopia and Kenya for SSA’s PoU
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Table 4 also presents to what extent the prevalence of undernourishments of Ethiopia and Kenya has increased when the SSA has increased. When the PoU of Ethiopia is increased by 1, the PoU of SSA is increased by 0.66, and also when the PoU of Kenya is increased by 1, the PoU of SSA is increased by 0.7. This showed that both Ethiopia and Kenya had a 66.6 and 70% of contribution, respectively, for PoU of SSA. This is by assuming the prevalence of Kenya constant, while to see the contribution of Ethiopia and assuming the prevalence of Ethiopia constant, while to see the contribution of Kenya.

Conclusion

The PoU of SSA, Ethiopia and Kenya falls gradually from 1991 to 2015, and Kenya’s prevalence is lower than the prevalence of the region SSA, but Ethiopia’s PoU is still higher than SSA. The trend of Uganda, Rwanda and Tanzania follows the same path, and it was increased to some point in time and slightly decreased. The PoU of Kenya and Ethiopia has a long-run positive relationship, on top of this; more than one-third of PoU of SSA was contributed by these two countries. Depending on this conclusion, the current study recommends to the governments of Ethiopia and Kenya to continue with a gradual decrement of PoU. Additionally, the Ministry of Health and Ministry of Agriculture of these two governments have to tackle the main reasons for the high PoU: mitigating climate change, poverty reduction, securing political instability, and food and agricultural policy.