The Southern Africa Development Community (SADC) faces pervasive income stagnation, high inequality, increasing population growth rates and poverty. For example, despite that half of SADC countries are low middle income (as opposed to low income), high inequality implies that many people in the region still live in poverty. While literature is replete with theories linking low incomes to population growth and savings, empirical evidence is context specific and often mixed.

There is a dearth of strong empirical evidence that shows empirical linkages between population growth rates, incomes and savings in the SADC and this article aims to investigate these linkages. Specifically, the aim is to empirically understand the impact of population growth, savings and investment in human capital, on incomes.

We focus our investigation on the Southern Africa Development Community (SADC), which comprises 16 countries namely, Angola, Botswana, Namibia, Lesotho, Swaziland, South Africa, Malawi, Mozambique, Zambia, Zimbabwe, Tanzania, Democratic Republic of Congo, Madagascar, Mauritius, Seychelles and Comoros.

To achieve the goals of this study, we analyse data from 1977 to 2014 obtained from the World Bank databases and use ordinary least squares, fixed effects, random effects and Arellano-Bond dynamic panel-data estimation techniques to investigate the relationships between incomes, population growth and savings.

Our findings support the existence of a negative relationship between high population growth rates and income per capita, as well as a positive relationship between capital accumulation (human capital), savings and income per capita growth. Shares of savings in relation to gross domestic product (GDP) of countries in the SADC stand at under 16% of GDP (compared to shares of over 30% in developed countries) and are particularly worrisome.

There is a case for a concerted effort by the SADC Member States to control population growth, encourage schooling and, further, encourage a ‘savings culture’ in order for the SADC region to achieve its aspirations of eradicating poverty and hunger as outlined in Agenda 2063 and even the Sustainable Development Goals.

The goal of this article is to examine the effects of various factors including population growth and human capital on income per capita. A great abundance of literature, including Mankiw, Romer and Weil (

In other studies, Sinesi (

The savings argument needs to be discussed further because of its importance in standard economic growth models. According to standard economic growth models (e.g. Solow

Unfortunately, most literature cited on the nexus between population growth, income per capita and savings, focus on countries outside Southern Africa, thereby creating an empirical gap in this area of study. Again, it is noted that perhaps owing to data challenges in the past, studies have been based on shorter time periods with limited variation which can render findings imprecise. This article attempts to fill this gap by investigating the determinants of income growth within the Southern Africa Development Community (SADC).

The investigation involves employing the Solow model framework both in its basic textbook form and augmenting it with human capital in the examination of determinants of income per capita.

The approach espoused in this article involves tackling the question of population growth and income per capita from two perspectives. The first step is to outline the Solow model, derive the first order differential equations, then estimate the Solow model in its basic as well as augmented forms. The Solow model is summarised below.

The standard Solow model takes the rates of savings, population growth and technological progress as exogenous, and further assumes two inputs in the production function namely capital (

The number of effective units of labour

Solow’s model assumes that a constant fraction of output,

This implies that the steady state capital relates negatively to population growth rates but positively to savings rates.

In order to establish the relationship between income and savings and population growth (the gist of Solow’s model), substitute

Since the model assumes that factors of production, that is labour and capital, are paid according to their marginal products, it predicts the signs of the coefficients. It also predicts the magnitudes of the coefficients on savings and population growth. For example, if we make use of the a priori knowledge that the share of capital (α) in income is roughly one-third (see Mankiw et al.

When estimating the Solow model, therefore, it is of interest to investigate whether income per capita is higher in countries with higher savings rates and lower in countries with higher

α is constant and ε is country level idiosyncratic, then

If it is assumed that ε is independent of

Assuming that the omitted variable human capital is a significant variable, then accounting for it may improve the fit of the model besides altering the magnitude of the parameters estimated previously. Once human capital is added, the model evolves differently such that the production function in

_{k} is the fraction of income invested in physical capital and s_{h} that part invested in human capital, the evolution of the economy is determined by

From above, we can formulate

Substituting

So, again, the evolution of income per capita depends on the accumulation of physical and human capital, as well as on population growth. The implication of this model is that the presence of human capital accumulation increases the impact of physical capital accumulation on income through the effect of the β. As before, α is expected to amount to one-third of the share of capital in income. If the levels of human capital are available,

As stated a priori, the discussion on the interface between incomes and population growth is one that can be taken in various ways in the sense that population growth can affect incomes, whereas incomes can also affect population growth. In terms of multivariate econometric analysis, one would consider this fact as one that immediately invokes the issue of endogeneity and the problems that it presents, while attempting to isolate what actually determines the other.

The approach in this article is to, firstly, discuss the present descriptive statistics in various variables that may determine income per capita, and postulate prima facie through scatter graphs, the likely linkages between income and such different factors. Then a series of OLS regression analysis is performed in the article to establish partial correlations between population, incomes and savings. We further perform estimation within the framework of GLS models assuming fixed effects, as well as random effects and compare the results. Finally, we also fit the system dynamic panel-data estimation (GMM). In each case we compute various statistics for model fitness and for the GLS estimation, we compute the Hausman specification test to ascertain any differences between the random effects formulation and the fixed effects model and we report all the results in one table. The main policy conclusions are based on the OLS because the coefficients approximate those predicted in Mankiw et al. (

The data in

Gross domestic product per capita, birth, death and population growth rates for selected countries.

Country | Gross domestic product per capita | Birth rate | Death rate | Population growth rate (%) |
---|---|---|---|---|

Mali | 520 | 51 | 20 | 3.1 |

Sierra Leone | 750 | 49 | 25 | 2.4 |

Guinea-Bissau | 840 | 43 | 21 | 2.2 |

Kenya | 1290 | 45 | 12 | 3.3 |

Nigeria | 1400 | 45 | 15 | 3.0 |

Ghana | 1970 | 42 | 12 | 3.0 |

Pakistan | 2170 | 41 | 9 | 3.2 |

India | 1220 | 29 | 10 | 1.9 |

Bangladesh | 1290 | 36 | 12 | 2.4 |

China | 2330 | 18 | 7 | 1.1 |

Sri Lanka | 2990 | 21 | 6 | 1.5 |

Nicaragua | 1900 | 41 | 7 | 3.4 |

Peru | 3220 | 27 | 7 | 2.0 |

Guatemala | 3350 | 39 | 8 | 3.1 |

Brazil | 5370 | 25 | 8 | 1.7 |

Colombia | 5490 | 24 | 6 | 1.8 |

Thailand | 6260 | 19 | 6 | 1.3 |

Malaysia | 7930 | 29 | 5 | 2.4 |

Republic of Korea | 9630 | 16 | 6 | 1.0 |

It is clear from

Table incomes and population growth rates by 2014.

Country | Per capita gross domestic product (2013) (constant 2005 US$) | Per capita gross domestic product (2013) (constant 2005 US$) log | Birth rate (births/1000 population) | Death rate (deaths/1000 population) | Population growth (annual %) (2013) | Gross savings rates (% of gross domestic product) |
---|---|---|---|---|---|---|

Angola | 2738 | 7.9 | 39.0 | 11.7 | 3.1 | 21.8 |

Botswana | 7027 | 8.9 | 21.3 | 13.3 | 0.9 | 37.5 |

Congo, Democratic Republic | 288 | 5.7 | 35.6 | 10.3 | 2.7 | 12.9 |

Lesotho | 974 | 6.9 | 25.9 | 14.9 | 1.1 | 36.5 |

Madagascar | 271 | 5.6 | 33.1 | 7.0 | 2.8 | 7.0 |

Malawi | 264 | 5.6 | 41.8 | 8.7 | 2.8 | 7.9 |

Mauritius | 6879 | 8.8 | 13.5 | 6.9 | 0.2 | 13.4 |

Mozambique | 433 | 6.1 | 38.8 | 13.3 | 2.5 | 16.0 |

Namibia | 4565 | 8.4 | 20.3 | 13.6 | 1.9 | 18.5 |

South Africa | 6090 | 8.7 | 18.9 | 17.5 | 1.5 | 14.7 |

Swaziland | 2430 | 7.8 | 25.2 | 13.8 | 1.5 | 18.9 |

Tanzania | 487 | 6.2 | 36.8 | 8.2 | 3.0 | 17.1 |

Zambia | 1054 | 7.0 | 42.5 | 12.9 | 3.2 | - |

Zimbabwe | 475 | 6.2 | 32.5 | 10.6 | 3.1 | - |

In summary, therefore, both

If one considers both the SADC and outside SADC data in

Population growth and incomes (annual %).

This figure shows that there is indeed a highly significant inverse relationship between income per capita and population growth, which perhaps is evidence that one of the pathways, discussed previously (savings), is responsible for bringing this relationship to the fore. The implication is, of course, that countries with high population growth rates may unlikely be the ones reducing poverty over time, unless they find a way of applying the high population economically, or unless they create policies that will reduce consumption and enhance savings. If the effects of population growth on income per capita goes through savings, then it must be confirmed statistically that there is a negative relationship between population growth and savings.

As discussed previously, savings are one of the key elements through which population growth impacts on income growth.

Country-specific savings rates.

As discussed previously under the theory section, population growth affects incomes through a number of ways, including savings. Usually a country whose population grows very fast ends up having high dependency ratios. The continent of Africa does not have a big problem of an ageing population, but rather with a youthful one, who consume more than they can produce. Savings then are impacted because they can be conceived as gross income minus consumption. In practice, if this relationship was in operation, then a regression of savings on population growth, needs to depict a negative relationship and if such a relationship is significant, it consolidates the evidence.

Statistical test of savings and population growth for the all Southern Africa Development Community countries.

Population growth effects in the SADC appear to be complicated by the fact that, life expectancy is generally low and, at any point in time, children constitute a huge proportion of the population. A simple regression model of income per capita that recognises the differential impact that age groups have on income per capita, shows that indeed in the short run, an increase in children (0–14 years) in a population negatively affects income per capita, whereas an increase in the working population (15–64 years) is good for increasing incomes (see

Impact of age on income per capita.

Income per capita growth model | Coefficient | Standard error | ||
---|---|---|---|---|

Proportion of children (0–14 years) | −0.0001329 | 0.0000337 | −3.94 | 0.000 |

Proportion of working adults (15–64 years) | 0.0000977 | 0.0000182 | 5.38 | 0.000 |

Constant | 2069.661 | 789.8692 | 2.62 | 0.013 |

The results in

Savings and economic growth.

In estimating the Solow growth model this article follows Mankiw et al. (

The data used herein, obtained from the World Bank as well as national sources, include savings as a share of GDP, working population in every country, defined as population aged between 15 and 64 years, income per capita for each country in the SADC, and population growth. The contribution of technology growth and capital depreciation are assumed to amount to 0.05 across the board in line with literature on the topic.

It is interesting to note in

Descriptive statistics of the model variables.

Variable | Mean | Standard deviation |
---|---|---|

Working population (% of total population) | 54.5 | 5.5 |

Income per capita (US$) | 1946.4 | 2526.3 |

Savings as a share of gross domestic product | 15.8 | 15.5 |

Population growth ( |
2.3 | 1.0 |

US$, United States dollars.

Interestingly, the data for the sampled period and countries appear to fit the Solow model quite well.

Combined results from the all Solow models (ordinary least squares with Huber-White standard error)

Log (income and/or capita growth rate) (dependent) | OLS (basic) | OLS (capital) | GLS FE | GLS RE | GMM‡ |
---|---|---|---|---|---|

Log (savings and/or GDP) | 0.452 |
0.419 |
0.188 |
0.193 |
0.0813 |

Log (Population growth ( |
−0.518 |
−0.454 |
−0.264 |
−0.268 |
−0.0337 |

Log (primary school enrolment) | - | 1.47 |
1.03 |
1.03 |
0.0266 |

Log (income and/or capita growth rate) | - | - | - | - | - |

L1 | - | - | - | - | 0.968 |

_cons | 5.4 |
−1.29 | 1.43 |
1.49 |
−0.0921 |

chi2 | - | - | - | 178 | 5768 |

- | - | - | - | - | |

335 | 296 | 296 | 296 | 288 | |

aic | 975 | 837 | 256 | - | - |

bic | 987 | 852 | 271 | - | - |

Pseudo ^{2} |
- | - | - | - | - |

43.4 | 52.8 | 57.8 | - | - | |

Wald | - | - | - | - | - |

sigma_u | - | - | 1.03 | 0.965 | - |

sigma_e | - | - | 0.38 | 0.38 | - |

rho | - | - | 0.881 | 0.866 | - |

,

,

,

,

OLS, ordinary least squares; GLS FE, generalised least squares fixed effect; GLS RE, generalised least squares random effects; GMM, generalised method of moments; GDP, gross domestic product; L1, First lag of the variable log of income; _cons, constant; chi2, Chi-Square; ^{2}, Pseudo R-squared; ^{2}, R-squared;

From these results, this article concludes that although the explanatory power of the model is 0.27 and may suggest that there are other variables that may explain income determination, the Solow model cannot be rejected outright and in fact in the SADC region, countries that have high savings rates are associated with high income growth rates, whereas those with high population growth rates are likely to be associated with low income growth rates. This confirms some of the priori findings explained earlier in this article. Since a test for constant variance was rejected, the standard errors for all OLS regressions are obtained using the Huber-White methodology by utilising the ‘robust’ subcommand in STATA.

The adjusted

The potential variable omission motivates the need for the search for other estimation techniques. Various estimation techniques accounting for endogeneity, including Arellano-Bond dynamic panel-data estimation, as well as system dynamic panel-data estimation, were fitted and the results are presented. They yield findings that are slightly different from the predictions of the Solow model, but all qualitative conclusions regarding direction of effects and significance of parameters appear to suggest that estimates obtained by OLS estimation^{1}

Thus, whereas population growth may impact on economic growth in various ways, it appears that one of the ways, which is also supported by theory, is through savings. An increase in population growth,

The GLS estimates using the fixed effect (FE) estimator were not different from those obtained using the random effects (RE) estimator and, in fact, a Hausman specification test to confirm any systematic differences in coefficients rejected the presence of such differences between FE and RE estimates^{2}

The system dynamic panel-data estimation (GMM) yielded even smaller coefficients in every case but with similar direction of change. For this specific estimation technique, human capital had a positive sign but was not significant.

Because of the similarities between the OLS, GLS and GMM results, we base our conclusions on OLS estimates in line with literature and so this should not be considered a limitation (see Mankiw et al.

The coefficient of savings indicates that in a typical SADC country, a 1% increase in savings as a share of GDP would yield closer to a 0.5% increase in income per capita, but if the population growth in that country increases by 1%, then income per capita could decrease by 0.5%. This implies that economic growth without controlling population growth may have no effect on poverty reduction. Again, a 1% increase in human capital may lead to a more than 1.4% growth in income per capita implying that a country that invests in human capital development stands to gain more in terms of poverty reduction in the long term. Thus, it is important to ensure that SADC governments prioritise human capital development, a savings culture and should control population growth.

^{3}

Graphs summarising shocks in (a) savings, (b) population and (c) schooling.

If human capital had improved by 50%, by 2011 the average income per capita in the SADC would have been US$2440 (i.e. e^7.8) which is more than, and almost double, the actual $1339 (e^7.2). For the same year, if population growth had been cut by half, income per capita would have been improved to $1998 (i.e. e^7.6) from $1339 (e^7.2). On the other hand, a 50% increase in savings around 2011 would have been associated with an average income per capita of around $1636 (i.e. e^7.4) which is more than the actual $1339 for 2011.

This article’s objective was to analyse the links between income per capita growth, savings and population growth. Using partial correlations and both the Solow basic growth model and the augmented Solow model, this article finds evidence to support the existence of a negative relationship between very high population growth rates and income per capita, as well as a positive relationship between savings and income per capita. An increase in population growth,

Countries, including Malawi, Tanzania, Madagascar and Lesotho among others, need to reduce overexpenditure by government and invest more in productive capital (see, e.g., Matchaya, Chilonda & Nhlengethwa

We are grateful to the Bill and Melinda Gates Foundation, the United States Agency for the International Development (USAID) and the International Food Policy Research Institute (IFPRI) who supported the researchers with funding for various activities in support of the Comprehensive Africa Agriculture Development Program, one of which led to this article.

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

G.M. conceptualised the article content and completed the first draft. C.N. and S.N. revised and made conceptual contributions, additions and refined the article.

Results for GMM estimation are not reported here but amount to the same conclusions.

Chi^{2}(3) = (b-B)′[(V_b-V_B)^(−1)](b-B) = 1.53; Prob > Chi2 = 0.6760

The