How do we measure inequality? Part one: Gini coefficient (Continued)

In my last blog post I discussed the Gini Coefficient as a way of measuring inequality. In this post I want to use this Coefficient to see if inequality in New Zealand has changed in the last 10 years or so.

As discussed in the previous post, I have used income data from the IRD, and excluded people who I knew were definitely working part-time.The following results were obtained using excel:

  

<><><><>

Year	Gini Coefficient
2001	0.356
2002	0.360
2003	0.353
2004	0.355
2005	0.353
2006	0.342
2007	0.320
2008	0.318
2009	0.314

As we discussed in the last post, a higher Gini value indicates higher inequality. From the table and chart we can see that income inequality has fallen in the last ten years, particularly in the period from 2005 to 2009.

The New Zealand Institute, the privately funded think-tank have also provided data on inequality and Gini Coefficients. Their figures roughly correspond to my own figures (Which is hugely encouraging from my own standpoint, I know my calculations are correct). The NZ Institute have compared our Gini figure to the rest of the OECD, where in terms of equality, we rank 25 out of 34 (http://www.nzinstitute.org/index.php/nzahead/measures/income_inequality/).

So although equality has improved in recent years, there is still some work to do to catch up with the rest of the developed world. The NZ Institute link above has some great information for those wanting to know more about Inequality in New Zealand.

I don't really want to draw any conclusions over these figures, but the downward trend is encouraging. I need to point out that data I have used is far from perfect. For starters I have effectively excluded any unemployed individuals, as on the dole they would not earn enough to enter my analysis (discussed in the previous post).

If you have any questions or comments, please feel free to make a comment. In the next post I will stop talking about inequality for a while and will discuss a few minor issues I have with Statistics New Zealand.

Bye

How do we Measure Inequality? Part one: Gini coefficient

In this post I will discuss inequality and the Gini coefficient, which is one particular way of measuring inequality. In this post I will discuss the concept and how it is calculated, and in the next post I will use it to see if income inequality in New Zealand has changed in the last 10 years.

Inequality is a slightly more exotic and complicated concept when compared the basic economic indicators of GDP, unemployment, and inflation  When we are talking about inequality in economic terms, we are talking about differences in the distribution of wealth and income. All societies have some inequality, as some people are richer and earn more than others. Throughout history, high levels of inequality have been associated with revolution, the creation of political systems and the formation of new governments. The recent worldwide Occupy movement and uprisings in the Arab world are recent examples of this.

Defining and discussing inequality are simple matters. Trying to measure it however opens up a very contentious can of worms. Firstly, are we measuring wealth inequality, or income inequality? (This is not a big issue, as people with high levels of income are generally wealthy).

Secondly,because of its arbitrary nature inequality cannot be measured in the same way as GDP, unemployment, or inflation. For example the statement "Society A is 50% percent more equal than society B", makes no sense. There are many indices for measuring inequality (for example, the Hoover Index, the Theil Index, Gini Coefficient,...). The common inequality indices all give results between 0 (perfect equality) and 1 (perfect inequality), or 0% and 100%. However, because these indices use different formulas, each index will give a different value of inequality for the same society. compared to GDP or unemployment, interpretations of inequality figures cannot be made with the same authority.

Now that I have discussed a few issues with inequality, I will use the Gini coefficient to measure it. Subsequent posts will look at the other measures. I have started with Gini because it has an elegant visual basis.

The Gini coefficient is based on the Lorenz Curve. This curve plots the cumulative share of people ordered from lowest to highest income (from 0-100%) on the x-axis, and the cumulative share of income earned (from 0-100%). The Lorenz Curve for New Zealand income in 2009 is shown below. For this curve I only want consider full-time workers, so I have removed anyone who earns less than $19500 in that year (assuming a minimum wage of $12.50 per hour and a 30 hour work week, 12.5x30x52 weeks = $19 500) from this analysis.

A society that is perfectly equal will have a Lorenz curve that shoots out from the origin at a 45 degree angle. This is represented by the red line in the diagram below. With this red line, the cumulative share of population and the cumulative share of income increase at the same rate, resulting in perfect equality.  (For example, the "bottom" 10%  of the population would earn 10% of the income, the "bottom" 20% of the population would earn 20% of the income, and so on). Lorenz Curves that are closer to this 45 degree line will be associated with societies that are relatively equal. Conversely, societies that are more unequal will have more "bent" Lorenz Curves farther away from the 45 degree line.

From the Lorenz Curve we can find the Gini Coefficient of an economy by calculating A/A+B.

Using New Zealand individual income data from the IRD, I have calculated that the Gini Coefficient for New Zealand in 2009 was 0.31, so I know my calculations and methods are robust. This figure is very close to the Ministry of Economic Development's own figure of 0.32 for the same time period. The small difference arises due to the Ministry's use of household income for the calculations, while I used individual income.

In my next post I will the Lorenz curve to Calculate the Gini Coefficient for previous years to see how inequality in New Zealand has changed.

Bye for now.