I recently read a paper entitled Does wealth inequality matter for growth? The effect of billionaire wealth, income distribution, and poverty[1] that has been getting some coverage in economic circles. One of the reasons for the coverage is that income and wealth inequality has become a major discussion point in economics, since the release of Thomas Piketty’s Capital in the Twenty-First Century.

The other reason for the attention is that the paper, although implicitly agreeing with Thomas Piketty’s conclusion that inequality is detrimental to economic growth, puts a twist on the conclusion. This paper, through a series of statistical models, provides evidence to suggest wealth inequality in itself does not impact economic growth, but that wealth inequality that arises due to government corruption impacts on economic growth.

Reading between the lines, this conclusion essentially reverses the prescription Piketty has been arguing for (greater intervention from government to redistribute wealth) and instead implies the opposite, that government should be reduced and basically get out of the way.

At a high level, there are two reasons I wanted to review this paper. These reasons are:

1. To highlight the importance of skepticism when reading headlines based on scientific literature, and
2. To provide an example of how a lack of domain knowledge[2] can cause problems in the world of statistics.

The Setup

The basic experiment setup is as follows. The authors (Sutirtha Bagchi and Jan Svejnar) took the Forbes List of World Billionaires for four years, 1987, 1992, 1996[3] and 2002. They then split the billionaires in these lists into two groups: those that have seemingly gained their wealth through political connections, and those that apparently gained their wealth independent of political connections.

Once grouped, the researchers aggregated the wealth of the billionaires by country to calculate politically connected billionaire wealth, politically unconnected wealth, and (adding these two pools together) total billionaire wealth – for each country in the dataset.

To normalize this measure of billionaire wealth across countries, they then divided the billionaire wealth for each country in each year by the total GDP for that country in that year. This provided a measure of billionaire wealth (politically connected, politically unconnected and total) as a percentage of GDP[4], which was taken to be a measure of inequality.

In addition to the three variables for each country – politically connected wealth inequality, politically unconnected wealth inequality, and total wealth inequality the authors also added a number of other variables, including measures of poverty, income inequality, income level (as measured by real GDP per capita), levels of schooling and the price level of investment[5].

Using linear regression, these variables were then used to predict GDP growth per capita for the following five years (after the year the variables corresponds to). For example, the variables for the year 1987 were used to predict the GDP growth per capita for the years 1988 to 1992.

Without getting too deep into how linear regression works, this approach was informative because it allowed for an assessment of the impact of each variable on growth, assuming all the other variables were held constant. With a variety of models constructed, the authors were able to assess what impact politically connected inequality had on growth, assuming politically unconnected inequality, income, poverty levels, schooling levels and the price level of investment were held constant.

The other big benefit of using linear regression is that it provides information about which of the variables used in a model are actually useful (“found to be significant”) in making a prediction. Essentially, variables that are found to not be significant can be excluded from the model with little or no decrease in the accuracy of the model.

Before moving on to the results, please be aware, for the sake of brevity, I am greatly simplifying the experimental setup, and completely ignoring a range of robustness and other testing the authors did. For those details, you will need to read the full paper.

The Results

At a high level, the results of the models constructed suggested the following in relation to the impact of inequality on growth:

1. Politically connected wealth inequality (regardless of how it is normalized) was found to be a statistically significant predictor of growth. In all cases the coefficient was negative, indicating the higher the level of wealth, the lower the predicted growth.
2. Politically unconnected wealth inequality (regardless of how it is normalized) was not found to be a significant predictor of growth.
3. Wealth inequality (when political connectedness is ignored) can be a significant predictor of growth depending on how it is normalized[6]. When found to be significant, higher levels of billionaire wealth led to lower levels of predicted growth.
4. Income inequality was found to be a significant predictor of growth in only one of the 12 models constructed. In the case where it was found to be significant, greater income inequality led to predictions of higher growth.

In addition, the model also provided some other interesting conclusions:

1. The level of income in a country was found to be a significant predictor of growth in all cases. The models suggested that the higher the level of income in a country, the lower the predicted growth[7].
2. The level of poverty was not found to be a significant predictor of growth in any of the models constructed.
3. The level of schooling (for males or females) was not found to be a significant predictor of growth in any of the models constructed.

Caveats and Problems

Already from some of the findings above, you probably have some questions about the results. Poverty and schooling and income inequality have no impact on economic growth? The conclusions can change based on how billionaire wealth is normalized? You are right to be skeptical, but lets break down why.

Determining Wealth is Difficult

The first problem, and it is one explicitly acknowledged by the authors, is that measuring wealth (and therefore wealth inequality) is very difficult. Most of the difficulty arises from determining the wealth of the rich. In some cases, it is relatively straightforward to determine wealth – for example if the billionaire’s wealth is tied up in one company (e.g. Bill Gates and Mark Zuckerberg). But in other cases, particularly with inherited wealth, the assets are diversified, held in a large number of holdings, trusts and companies across the world. In some further cases, it is extremely difficult to value the assets of a billionaire due to the unique nature of the assets (this is why Donald Trump’s worth is always the subject of debate).

To get around this, problem, the authors have relied on the Forbes list of billionaires. In terms of billionaire wealth, this is probably the best researched list of billionaires available, but by Forbes own admission “It’s less about the [net worth] number, per se… this is a scorecard of who the most important people are.”

Is Billionaire Wealth a Good Predictor of Wealth Inequality?

The authors built their measure of wealth inequality using the wealth of billionaires. But does this make sense even if we assume the Forbes list is accurate? There are two main problems I see with this approach.

The first is that ‘billionaire’ is an arbitrary cutoff point. Extremely wealthy people with wealth over the billion-dollar cut off one year regularly fall out of the three comma club the following year. For smaller countries with very few billionaires, this can have an outsized impact on their measure of wealth inequality from year to year.

The second issue is that looking at billionaire wealth tells you nothing about the distribution of wealth below the $1 billion mark. An example is provided in Chart 1 below.

Chart 1 – Wealth Distribution Across Two Hypothetical Countries

What Chart 1 shows is two hypothetical countries with 10 people each and the same amount of total wealth. Country 1 has two people who are extremely wealthy (but not billionaires), while the rest are far less wealthy. In Country 2, we have one billionaire but a much more even distribution of wealth amongst the rest of the population. Looking at the chart we would conclude that Country 1 has a higher level of inequality, but if we calculate inequality based on methodology used in the paper, Country 2 will be determined to be more unequal than Country 1. In fact, Country 1 would be assigned an inequality value of 0.

Obviously this is an exaggerated example, but it illustrates the point that there is a lot that could be happening below the $1 billion mark that is completely ignored by the measure used. I would also argue that the distribution of wealth amongst the population who are not billionaires is going to be much more important for growth than the ratio of billionaires to everyone else.

What is Politically Connected?

This is the part of the experiment setup that will probably end up being the most contentious, and relates back to the lack of domain knowledge. The problem is the authors could not possibly know of every billionaire on the list, the circumstances of how they accrued their wealth, and make a judgment call on whether political connections were a necessary precondition. As a result, they had to rely on various news sources to draw their conclusions and this led to some interesting outcomes.

For those that read the Wonkblog piece I linked to earlier, you may have noticed a chart in which Australia was adjudged to have 65% of billionaire wealth over the four years looked at being politically connected, putting it the same range as India and Indonesia. To most Australians this would be a hugely surprising result given Australia’s strong democratic tradition, strong separation of powers and prominence of tall poppy syndrome[8].

Generously, the authors of the paper provided me with the classifications that led to this number and it boils down to the fact that they have classified Kerry Packer as a politically connected billionaire. For those that know of Packer (pretty much every Australian) it would seem ridiculous to class him in the same bracket as Russian oligarchs or Indonesian billionaires who benefitted from the corrupt Suharto regime. But for someone who is not from Australia, they had to make this judgment based on newspaper clippings talking about Packer’s lobbying efforts.

In the case of Australia, having a high percentage of politically connected billionaire wealth has little impact. Once politically connected billionaire wealth (i.e. Kerry Packer’s wealth) is taken as a ratio of GDP, the number becomes very small because Packer’s wealth is dwarfed by the relatively large Australian economy. But what about other countries? How have various judgment calls impacted their inequality measures and therefore the model?

As I mentioned at the start of this section, it is unreasonable to expect the authors to be able to know how every billionaire worldwide accrued their wealth and the role of the government in that process. Additionally, the fact that there may be issues with some classifications does not mean we should throw away the results. However, it does mean any conclusions we draw from the results should be caveated with this problem in mind.

Unknown Unknowns

The final problem comes down to the high level question of what drives economic growth.

When you consider all the different things that can impact on the economic growth of a country over the course of five years, you quickly realize there are an almost unlimited number of factors. Commodity prices, what is happening in the economies of major trading partners, weather patterns, population growth, war, immigration, fiscal policy, monetary policy, the level of corruption and the regulatory environment are just some of the factors that can have a major impact on growth.

When economists build models to predict growth, they make choices about what factors they believe are the major drivers of growth. In this case, the authors have used factors like income levels, schooling and poverty levels. But what about some of the other factors mentioned above? Could these factors have better explained growth than politically connected wealth inequality?

This choice of variables is further complicated by the interrelatedness of the factors impacting growth. Is population growth driving economic growth, or is it because population growth indicates higher levels of immigration? Is government corruption holding back growth, or is it that corruption is siphoning off money from schooling and other public services?

When it comes to the models in the paper, the key question is if politically connected billionaire wealth is really impacting growth, or if it is simply acting as a proxy for some other measure (or measures). For example, are high levels of politically connected billionaire wealth dragging on growth, or is this measure acting as a proxy for the level of corruption in an economy and/or the prevalence of inefficient government created monopolies – which are the real drags on growth? Unfortunately, there is no definitive way to know the answer to these questions.

Conclusions

As mentioned at the outset, inequality and its impact on growth and the economy in general has been a popular topic of discussion in economic circles for the last 1-2 years. In many ways, it is the defining economic discussion of our time and has the potential to shape economic policy for a generation.

In an effort to provide more information in that debate, the authors of this particular paper deserve plenty of credit for taking an innovative approach to a difficult problem. However, at least in my mind, the results raise more questions then they answer.

That, it should be noted, is not a criticism, but is often the outcome of research and experiments. Results can often be confusing or misleading, and can only later be explained properly through further research. This is all part of the scientific method. Hypotheses are created, challenged, and either proved incorrect or strengthened. They are always subject to be proven wrong.

Unfortunately this nuanced process is not one that lends itself to catchy headlines and this is where we find one of the key problems with reporting of scientific results. Most authors, including the authors of this paper, are fully aware of the limitations of their findings. That is why you will find the conclusions section filled with words like ‘suggests’, ‘possibly’ and ‘could’. But those words do not make for good stories and so the qualifiers tend to get left out.

It is for this reason, if you are interested in the results of a particular paper or study, it always worth looking at the detail. With that, I’ll leave the final word to Sutirtha and Jan (emphasis mine):

“These and other examples, together with our econometric results, suggest that the policy debate about sources of economic growth ought to focus on the distribution of wealth rather than on the distribution of income. Moreover, particular attention ought to be paid to politically connected concentration of wealth as a possible cause of slower economic growth. Further research in this area is obviously needed, especially with respect to the effects of wealth inequality at different parts of the wealth distribution, the possibly declining effect of unequal distribution of income on growth, and the role of poverty.”

[1] S. Bagchi, J. Svejnar, Does wealth inequality matter for growth? The effect of billionaire wealth, income distribution, and poverty, Journal of Comparative Economics(2015), http://dx.doi.org/10.1016/j.jce.2015.04.002

[2] Domain knowledge is knowledge of the field that the data relates to.

[3] A change in the methodology used by Forbes to compile the list between 1997 and 2000 led them to instead choose 1996.

[4] The authors also try normalizing by other factors, such as population and physical capital stock, but this doesn’t substantially change the results of the model.

[5] A measure of how expensive it is to invest in capital within a country.

[6] When normalized by population, billionaire wealth is found to be a better predictor of growth than politically connected wealth.

[7] This may seem strange, but actually nicely captures a phenomenon in economics where lower income countries experience higher growth as they ‘catch-up’ to higher income countries.

[8] A perceived tendency to discredit or disparage those who have achieved notable wealth or prominence in public life.