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.

Is New Zealand moving to a new steady state? The effects of a change in the savings rate

In this post I have no new data to analyse. Instead, I want to give my thoughts on what I think is happening, or what I hope is happening to the economy of New Zealand.

According to just about every social, political and economic commentator in the country, we have an abysmal rate of saving. In the past, only economists and the Reserve Bank Governor said this. However, it seems that these cries were ignored. Not many people are going to listen to advice from a gloomy old economist or Reserve Bank Governor when they are thinking about buying a new TV.

Now However, it seems that insulting some of our ingrained habits is the "in" thing at the moment. Apparently we are terrible drivers and apparently we are terrible savers. but has this increase in derision at our poor level of saving (combined with the recent recession), increased our rate of saving?

Well maybe it has. Since 2007 retail sales figures have struggled to gain momentum (see chart below). You could argue that this is due to high unemployment figures, but there is another more basic piece of evidence to suggest our savings rate has gone up in recent times: Trade surpluses.

As you can see in the chart below, New Zealand has had a better trade balance in recent years, suggesting that our spending has decreased and saving increased.

So if our saving rate has gone up, what does this mean for the country? well in economist terms, it could mean that we experience an increase in our steady-state  rate of growth, which I will proceed to explain by example.

Suppose we have a person earning a constant $100 000. They decide to spend 80% of what they earn and save the remaining 20% at an interest rate of 7%.

In year one they will earn $100 000, spend $80 000 and save $20 000.

In year two they will earn $100 000 plus $1400 (interest income $20 000 X .07), spend $81 120, and save $20 280.

Over time, their expenditure over a 40-year period will look like this:

So expenditure increases over time which is nice. In this example, income and expenditure is increasing at a rate of 1.4% each year, which is the steady-state rate of growth.

But what if this person decided after ten years to increase their savings rate to 50% of income? We would get the situation with the red line in the figure below.

In the years immediately following the saving rate change, expenditure drops sharply, but eventually catches up to and overtakes the amount of spending that would have taken place (dashed line) due to the increase in income from saving dividends. In this example the steady-state rate of growth has increased to 3.5%.

If we use this example to discuss the New Zealand economy (approximating expenditure to Gross Domestic Product, or GDP) then the shaded area in the above chart is where I think our economy is now, given my earlier theory of an increase in savings. If this is true, then the current stagnation in GDP and high unemployment figures are partly caused by a change in spending/saving rates. However, this should only be temporary, and GDP in a relative sense will increase as the dividends from our extra savings start to kick in (and as our steady state rate of growth improves).

Of course, this model is only an example. It can only reflect a few aspects of reality and it has some limitations:

• The time needed to "overtake" the dashed line in the real world could be more or less that that taken in the example, where only arbitrary numbers were used. 
• The New Zealand economy is not just affected by the saving rates of different citizens, but by other global and domestic events, making the situation not quite as straightforward as that described by this post.
• For the increase in the steady-state rate of growth to be permanent, individuals and governments need to stick with the habit of saving at the increased rate. I have serious doubts that this will happen.

In conclusion, global and domestic events may make the picture on saving and spending a little murky. Murky or not however, an increase in saving will definitely help improve prosperity and the long-term future of New Zealand.