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.

Minimum wage v inflation

Just a short post today on how the real value of the minimum wage has changed in the last few years.

A few days ago, the Labour party released their employment policy, confirming their plan to raise the minimum wage to $15 per hour. Some say it is needed to help workers keep pace with the increasing cost of living, while others say it is needed like a hole in the head. The latter group point out that conventional supply and demand theory predicts an increase in unemployment if the minimum wage is raised.

This got me thinking. The minimum wage is changed every year or every second year (see chart below) but have these changes kept up with inflation?

Date of minimum wage change	Minimum wage rate
1-Mar-97	$7.00
6-Mar-00	$7.55
5-Mar-01	$7.70
18-Mar-02	$8.00
24-Mar-03	$8.50
1-Apr-04	$9.00
21-Mar-05	$9.50
27-Mar-06	$10.25
1-Apr-07	$11.25
1-Apr-08	$12.00
1-Apr-09	$12.50
1-Apr-10	$12.75
2-Apr-11	$13.00

 This table is interesting in itself, as we can see that the nominal rate (without taking the effects of inflation into account) has almost doubled in fourteen years. However, if we include inflation data, we can see how the real minimum wage has changed relative to the cost of living.

Date of minimum wage change	Minimum wage rate (nominal)	Consumer price index	Minimum wage rate (real, 2011 prices)
1-Mar-97	$7.00	821	$9.86
6-Mar-00	$7.55	849	$10.29
5-Mar-01	$7.70	876	$10.17
18-Mar-02	$8.00	900	$10.28
24-Mar-03	$8.50	913	$10.77
1-Apr-04	$9.00	935	$11.14
21-Mar-05	$9.50	962	$11.43
27-Mar-06	$10.25	1000	$11.86
1-Apr-07	$11.25	1020	$12.76
1-Apr-08	$12.00	1061	$13.09
1-Apr-09	$12.50	1081	$13.38
1-Apr-10	$12.75	1099	$13.42
2-Apr-11	$13.00	1157	$13.00

As you can see, in real terms the minimum wage has increased by around 30% from 1997. This tells us that for the last decade and a half, the minimum rate of pay in New Zealand has kept pace with the cost of living.

A 14 year span of analysis is hardly comprehensive however. As a final thought, consider this:

In 1969 the minimum weekly rate of pay for adult males was $42. Assuming a 40 hour work week, this corresponds to a minimum wage rate of $16.40 per hour in 2011 prices.

In the future, I may try and get more data to continue this analysis, but for now I'll say goodbye.

See you later

What would your tax plan be?

Hello and welcome to my blog. In this post I provide an interactive excel spreadsheet (link provided below) that will focus on the debate around income tax, as this forms a significant portion of government revenue. In New Zealand, income tax forms about 29% of total government revenue.

There is no point in going on about the tension and argument that is associated with taxation issues. Everyone pays it, everyone is affected by it and so everyone has a stake in how the tax system is administered and arranged.

A lot of the debate around income tax centres around whether each unit of income should be taxed at the same rate (flat tax rate) or whether the rate of taxation should be increased as income increases (also called a progressive tax system, as the rate of tax "progresses" as your income increases). Some political groups prefer a flatter system, while others prefer a more progressive system.

New Zealand has a progressive income tax system, as the marginal tax rate (tax per unit of income) increases as you move through the following income bands:

up to $14 000                    10.5%
$14 000 to $48 000         17.5%
$48 000 to $70 000         30%
over $70 000                     33%

With this excel chart (follow the link at the bottom of the page) you can experiment with different tax rates to see their effect on revenue. Instructions are provided in the chart. I have used New Zealand's 2009  income distribution information from the IRD, assuming that 2009's income distribution is close enough to the current distribution to be relevant.

Naturally this sheet does have some limitations and points to note:

• The data I have (2009's income distribution figures) are slightly out of date, which could lessen the validity of any results.
• It cannot take into account income changes caused by tax changes. I'm talking here about an individuals incentive to earn when their marginal tax rates are changed. This means that any findings should be taken with a pinch of salt.
• Because of the point made in the last bullet point, the spreadsheet shouldn't be used to test extreme tax rates.
• The sheet compares revenue based on the 2009 tax rates, which were changed late last year.

I've done some initial experiments with the chart.

• It turns out that a absolute flat tax rate of around 23-24% would gather around the same amount of revenue that was ACTUALLY collected in 2009 (in other words a change to a flat 24% income tax would be "revenue neutral").
• The current tax rates would generate about 79% of the revenue that was ACTUALLY collected in 2009.
• To "test" the chart, I entered the 2009 tax rates (plus the ACC earners levy). according to the chart, this generated almost the exact amount of revenue collected, making me feel a bit more confident on the validity of the chart.

Well, that's all I want to say for now. I'll probably talk a bit more about the spreadsheet and tax in my next post. I really would like to hear your comments, questions, suggestions and findings from experimenting with the chart.

bye

Here is the link. The file needs to be downloaded to be experimented with.
https://docs.google.com/leaf?id=0B66NnPdYPuFfN2QzNjY4MDktNzFlYi00NWJlLWE0MmMtYjliMGU2MGRlMWVj&hl=en_US