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What Is a Lorenz Curve?

An American economist, Max Lorenz, introduced the concept of the Lorenz curve in 1905. He proposed a graphical representation of wealth or income inequality. The horizontal axis of this graph includes the percentile of the population depending on income or wealth. On the vertical axis, you will plot the increasing income or wealth. 

You can convert this graphical representation into a mathematical form that we will learn below. We can understand the concept of the Lorenz Curve from the following example. For instance, if the x-value is 45 and they-value is 14.2, then the Lorenz curve states that 45% of the population controls 14.2% of the entire wealth or income.    

Understanding the Lorenz Curve

Normally, the Lorenz curve includes a straight diagonal line. The line includes a slope of one representing the perfect equality of wealth and income. The Lorenz curve will be beneath that slope. This curve will show the estimated or observed distribution. 

There is an area between the curved line and the straight line that represents the ratio of the area below the line. You can refer to this area as the Gini coefficient. This coefficient is a scalar measurement of inequality.

Other than economic inequality, you can also represent the unequal distribution in a system. You can find the inequality and its intensity by considering the distance of the baseline and the curve. If the curve is far away from the baseline, the level of inequality will be higher.

Experts utilize the Lorenz curve to find the distribution of income or wealth in an economy. Keep in mind that wealth and income are not synonyms. Because it is possible to have high earning but negative or zero net worth, we will consider income and wealth as different entities. Another reason to consider both these factors different is because of the possibility of low earnings but higher net worth.

You can start measuring the Lorenz curve with an empirical measurement of the income and wealth distribution between the populations. The factors influencing your measurement include tax returns as it reports the income of the population. You can either use the graphical representation to identify the Lorenz curve or place the curve and fill in the gaps with observed data.

By utilizing a Lorenz curve, you can extract valuable and in-depth information about the distribution of income or wealth among the population. After that, you can create summary statistics with the help of the Lorenz asymmetry coefficient or the Gini coefficient. As you can create a visual representation of the distribution of each percentile using the Lorenz curve, you can identify the division of those groups using the line of equality.

Lorenz curve does not include complete data, which is the major problem while considering this process. With this incomplete dataset, you cannot generate accurate results. This indicates that the Lorenz curve is not a guaranteed method to identify the inequality of the distribution. However, you can improve the result by reducing the noise or inaccurate data in a machine learning model.

The points along the curve are predictions or guesses. These guesses are according to the observed data points and the shape of the curve. The sensitivity of the sample size and quality of the data depends on the shape of the curve. You can use mathematical assumptions to represent the best fit curve and eliminate the errors between the actual distribution and the Lorenz curve.

Examples of Lorenz Curve

To understand and express the level of inequality for the single figure, you can use the Gini coefficient. This coefficient will range between 0% to 100% and 0 to 1. If every individual has the same wealth or income, complete equality will be a coefficient of 0. When you plot the values of complete equality into a Lorenz curve, you will receive a straight diagonal line with a slope at 1. The slope or coefficient of one indicates that a single person earns the entire income and contains all the wealth. 

Conclusion

The Lorenz curve helps you to identify the inequality of income or wealth. You can also use this technique to identify the inequality of the systems. The space between the curved and the straight line represents the Gini coefficie