# Income Distribution¶

## Purpose and Perspective¶

The Income Distribution sector is important because much of the discussion of the Sustainable Development Goals focuses on reducing poverty. A model supporting development policies must include the implications of specific policies on income for the poorest in society, and on the overall income distribution for the country. It is also true that there is no well-formed consensus on how to model income distribution, the processes that change it or its effects on economic growth and development. We have developed a Lorenz curve based approach that makes possible the endogenous modeling of influences of education, saving, taxation, and subsidies and transfers on income generation.

In the Income Distribution Sector, Lorenz curves are used to capture the distributions of income, salaries and wages, and capital remuneration (the main endogenous sources of income) as well as causative factors such as education (proxied by years of schooling) and savings. In these Lorenz curves, subscripts are used to divide the population into ranked percentiles, from poorest to wealthiest for income distribution, from least to most highly educated for the distribution of education. Each percentile is then mapped to a proportion of the distributed asset, for example total capital remuneration. Gini coefficients and a distribution asymmetry coefficient are used to initialize the Lorenz curve for salaries and wages. Gini coefficients for salaries and wages, capital remuneration, and total are generated endogenously.

## Model Structure and Major Assumptions¶

## Exogenous Input Variables¶

None

## Initialization Variables¶

Initial salaries and wages Gini coefficient – Units: Dmnl

Salaries and wages asymmetry parameter – Units: Dmnl

Initial capital Gini coefficient – Units: Dmnl

Capital asymmetry parameter – Units: Dmnl

## Modeling Details¶

The Lorenz curves (distributions) for salaries and wages and capital remuneration are initialized using an equation developed from the work of Jantsen and Volpert (2013) [3]. Over time, the distributions adjust towards the indicated values resulting from the distributions of education and capital. We use the subscript [percentile] to calculate income for each percentile. Should further detail on the distribution be necessary, the subscript can be expanded to include a larger number of elements.

## Footnotes and References¶

[1] World Bank (2007). Income distribution, inequality, and those left behind. *Global Economic Prospects.* Washington, DC: World Bank.

Tilak, J.B.G. (1989). Education and Its Relation to Economic Growth, Poverty, and Income Distribution: Past Evidence and Further Analysis. *World Bank Discussion Paper 46.* Washington, DC: World Bank.

[2] Dobrinski, R. (2005). Domestic savings and the driving forces of investment in the ECE developing market economies. *Occasional paper no. 4.* Economic Commission for Europe.

Deaton, A. (1999). Saving and growth. In Schmidt-Hebbel, K. & Servén, L. (Eds.) *The Economics of Saving and Growth: Theory, Evidence, and Implications for Growth.* Cambridge, UK: Cambridge University Press.

[3] Jantzen, R.T., & Volpert, K. (2012). On the mathematics of income inequality: Splitting the Gini coefficient in two. *The Mathematical Association of America.*