Lorenz Curve

What Is a Lorenz Curve?

A Lorenz curve, developed by American economist Max Lorenz in 1905, is a graphical representation of income inequality or wealth inequality. The graph plots percentiles of the population on the horizontal pivot as per income or wealth and plots cumulative income or wealth on the vertical hub, so a x-value of 45 and a y-value of 14.2 would mean that the base 45% of the population controls 14.2% of the total income or wealth.

In practice, a Lorenz curve is typically a mathematical function estimated from an incomplete set of perceptions of income or wealth.

Understanding the Lorenz Curve

The Lorenz curve is many times joined by a straight diagonal line with a slant of 1, which addresses perfect equality in income or wealth distribution; the Lorenz curve lies underneath it, showing the noticed or estimated distribution. The area between the straight line and the curved line, expressed as a ratio of the area under the straight line, is the Gini coefficient, a scalar measurement of inequality.

While the Lorenz curve is most frequently used to address economic inequality, it can likewise exhibit inconsistent distribution in any system. The farther the curve is from the baseline, addressed by the straight diagonal line, the higher the level of inequality.

In economics, the Lorenz curve means inequality in the distribution of one or the other wealth or income; these are not equivalent since it is feasible to have either high earnings yet zero or negative net worth, or low earnings however a large net worth.

A Lorenz curve normally begins with an empirical measurement of wealth or income distribution across a population in view of data, for example, tax returns, which report income for a large portion of the population. A graph of the data might be utilized straightforwardly as a Lorenz curve, or economists and analysts might fit a curve that addresses a continuous function to fill in any gaps in the noticed data.

Benefits and Disadvantages of the Lorenz Curve

A Lorenz curve gives more nitty gritty data about the specific distribution of wealth or income across a population than summary statistics like the Gini coefficient or the Lorenz deviation coefficient. Since a Lorenz curve outwardly shows the distribution across every percentile (or other unit breakdown), it can show exactly at which income (or wealth) percentiles the noticed distribution fluctuates from the line of equality and by how much.

In any case, on the grounds that developing a Lorenz curve includes fitting a continuous function to some incomplete set of data, there is no guarantee that the values along a Lorenz curve (other than those really seen in the data) truly compare to the true distributions of income.

The greater part of the points along the curve are just suppositions in view of the state of the curve that best fits the noticed data points. So the state of the Lorenz curve can be sensitive to the quality and sample size of the data and to the mathematical suppositions and decisions with respect to what comprises a best-fit curve, and these may address wellsprings of substantial blunder between the Lorenz curve and the genuine distribution.

Lorenz Curve Example

The Gini coefficient is utilized to express the degree of inequality in a single figure. It can go from 0 (or 0%) to 1 (or 100%). Complete equality, in which each individual has precisely the same income or wealth, compares to a coefficient of 0. Plotted as a Lorenz curve, complete equality would be a straight diagonal line with an incline of 1 (the area between this curve and itself is 0, so the Gini coefficient is 0). A coefficient of 1 means that one person earns the entirety of the income or holds the entirety of the wealth.

Accounting for negative wealth or income, the figure can hypothetically be higher than 1; in that case, the Lorenz curve would dip below the horizontal hub.

The curve above shows a continuous Lorenz curve that has been fitted to data that depicts income distribution in Brazil in 2015, compared to a straight diagonal line addressing perfect equality. At the 55th income percentile, the value of the Lorenz curve is 20.59%: all in all, this Lorenz curve assesses that the base 55% of the population takes in 20.59% of the country's total income. On the off chance that Brazil were a perfectly equivalent society, the base 55% would earn 55% of the total.

Somewhere else, we can see that the 99th percentile compares to 88.79% in cumulative income. This means that the top 1% takes in 11.21% of Brazil's income.

To find the surmised Gini coefficient, take away the area underneath the Lorenz curve (around 0.25) from the area underneath the line of perfect equality (0.5 by definition). Partition the outcome by the area underneath the line of perfect equality, which yields a coefficient of around 0.5 or half. As per the World Bank, Brazil's Gini coefficient was 51.9 in 2015.

Highlights

• A Lorenz curve is a graphical representation of the distribution of income or wealth inside a population.
• Since Lorenz curves are mathematical evaluations in view of fitting a continuous curve to incomplete and discontinuous data, they might be imperfect measures of true inequality.
• Lorenz curves graph percentiles of the population against cumulative income or wealth of individuals at or below that percentile.
• Lorenz curves, alongside their derivative statistics, are widely used to measure inequality across a population.

FAQ

Why Is the Lorenz Curve Important?

The Lorenz curve is important on the grounds that it addresses truly outstanding and least difficult ways of representing the level of economic inequality in society.

How Does the Lorenz Curve Measure Inequality?

The Lorenz curve is a graphical representation of the distribution of income or wealth in a society. Fundamentally, the farther the curve moves from the baseline, addressed by the straight diagonal line, the higher the level of inequality.

How Do You Calculate the Gini Coefficient Using the Lorenz Curve?

The Gini coefficient is utilized to express the degree of inequality in a single figure. It is equivalent to the area below the line of perfect equality (0.5 by definition) minus the area below the Lorenz curve, partitioned by the area below the line of perfect equality. The coefficient goes from 0 (or 0%) to 1 (or 100%), with 0 addressing perfect equality and 1 addressing perfect inequality.