In-depth look at income and wealth data (pt. 2.5 of 3): A small note on wealth inequality from the archaeologist's perspective

I've been working on fellowship applications these past few weeks so naturally I began my research in a germane area of literature and ended up somewhere completely random. And by completely random I mean not even within the field of economics anymore and at best tangential to my original topic of investigation, but fascinating. I stumbled upon Ten Thousand Years of Inequality: The Archaeology of Wealth Differences, a volume on the archaeological studies of wealth inequality, and given its relevance to the posts I've been writing on inequality I figured I would make a small note on how inequality is being measured for a society that lived nearly two thousand years ago.

I haven't written a formal post on the Gini coefficient but given that this article uses it extensively in the archaeological context I preface by stating a few things: (1) the Gini coefficient is notably a simple measure of inequalities (most commonly income inequality) therefore it has its limitations that are well summarized in this Wikipedia post; (2) it has also been subject to revision and extensive debate as well as the creation of alternative measures of inequality including the Atkinson Index that may be more informative if certain contexts; (3) given my lack of knowledge of archaeology (and my lack of knowledge more broadly on the range of applications that the Gini coefficient has had in diverse fields within social science) I don't assess whether or how the Gini coefficient was applied and rather introduce it as a thought-provoking application outside of the realm of economics.

Feinman, Faulseit, and Nicholas (2018) provide estimates of wealth inequality for the Classic period in the history of the pre-Hispanic Valley of Oaxaca, Mexico based on archaeological house excavations at six pre-Hispanic settlements. They rely principally on architectural constructions and space to proxy for wealth and apply the Gini coefficient to three architectural variables: terrace area, house size, and patio area. They also utilize distribution of artifacts such as obsidian and other rare items.

The Lorenz curve in the figure below shows the Gini coefficient constructed based on the house sizes for all of the houses in the sample (a total of 36 excavated houses across all six sites in the Valley of Oaxaca) with a coefficient of 0.35 and a 95 percent confidence interval between 0.31 and 0.39. A Gini coefficient of 0 represents perfect equality whereas 1 represents perfect inequality.

The Gini coefficients from all samples (houses, patios, and terraces) and excavation sites are indicated in the figure below. They range from 0.35 to 0.43.

The authors find based on their analysis that wealth inequality during this time was low compared to other urbanized and preindustrial settings (confirming extant evidence).

While there was notable variation between the periods that the authors link to changes in the socio-political structures of the time, they specifically note that "[t]he consistently low Gini values... are informative, especially as indicators of wealth inequality, because they challenge the long-term notion that archaic states were always starkly divisible into the rulers and the ruled, with dramatic differences in resources and quality of life between the two. This coercive/despotic vantage on archaic states is well ensconced in the historical/social sciences for preindustrial times (e.g. Mann 1977; Wittfogel 1957) but now is being challenged as not uniformly applicable (Blanton 2016; Blanton and Fargher 2008), with some historical polities seen as having had a more collective institutional orientations and lower degrees of wealth inequity (e.g. Mann 2016, for a change from his earlier perspective)."

A few comments and questions came to mind about the application of Gini coefficient in this context:

1. The sets of data used in these analyses of the Classic period in particular are considered by the authors to be large and representative (likely given the difficulties involved in excavations and the number of houses, patios, and terraces that are still intact after thousands of years) but they are still subject to the well-described small sample size bias associated with the Gini coefficient. Smaller samples are biased towards having smaller Gini coefficients which may make it difficult to compare excavated sites in the graphic below (from the Smithsonian Magazine article about this book) with the United States today, which is not based on excavated evidence and has a much, much larger sample size. 
2. Comparisons across past civilizations, though, if they are based on similar sample sizes may be more informative than comparisons between past civilizations that were excavated and modern day societies. Similarly, I would find variation within a given civilization over time (as evidenced in the article) to be informative especially in conjunction with changes in socio-political structures. This is hinted at by the authors when they quote from Piketty (2015) on the impacts of these structures on inequality: "[O]ne should be wary of any economic determinism in regard to inequalities of wealth and income... The history of the distribution of wealth has always been deeply political... How this history plays out depends on how societies view inequalities and what kinds of policies and institutions they adopt." 

In-depth look at income and wealth data (pt. 2 of 3): Wealth

First, to preface with why wealth as distinct from income is relevant to economists and to policymakers at large. Kopczuk (2014) discusses the importance of understanding the wealth distribution: "the extent to which the well-off are going to rely on work vs. return to their wealth in the future is clearly important for assessing the extent to which a society will view itself in some way a meritocracy." Wealth is an important determinant of labor force participation and therefore impacts productivity and economic growth. It also has important implications for inequality, intergenerational mobility, and, consequently, implications for democratic institutions whose stability is reliant on a meritocratic society or at least the verisimilitude of a meritocratic society.

It should be noted that estimates of wealth inequality and the top wealth shares are not as widely agreed upon as estimates of income inequality and labor income shares. There are a few main data sources for estimating wealth inequality that are aptly summarized in Alvaredo, Atkinson, and Morelli (2018):

1. Household surveys including the U.K. Wealth and Assets Survey and the U.S. Survey of Consumer Finances;
2. Administrative data on individual estates at death; 
3. Administrative data on wealth of living from annual wealth taxes; 
4. Administrative data on investment income that are capitalized; and 
5. Lists of large wealth-holders (e.g. Forbes).

These data sources are discussed in great detail in Kopczuk (2014)'s "What Do We Know About the Evolution of Top Wealth Shares in the United States?" which specifically discusses the U.S. Survey of Consumer Finances (1), the mortality multiplier method with individual estate data (2), and investment income data (4). Each of these data sources is subject to different concerns. Household surveys and list of the wealthiest individuals are recent phenomena and cannot be used for estimates prior to the 1950s when the household surveys on wealth were first implemented. Administrative data on wealth of the living based on wealth taxes cannot be recouped in most developed countries because only a few developed countries, most notably France and Norway, have a wealth tax to begin with. Therefore, most researchers rely on estate tax records on individual estates at death or on reported taxable capital income.

The primary concern with estate taxes is that the distribution of estates of the deceased must be projected to the population at large: i.e. a multiplier method must be used in order to answer the question, how does the distribution of wealth among the deceased reflect the distribution of wealth among the living? Mortality multipliers are inverses of mortality rates based on various criteria, for example, wealthy individuals tend to have lower mortality rates and increased longevity compared to less wealthy individuals and therefore a higher mortality multiplier would be applied to the upper estate ranges meaning there are relatively more individuals living within those ranges than lower ones. For more on recent discussions of the relative longevity of the wealthy see Saez and Zucman (2016) and Chetty et al. (2016).

Kopczuk presents a few interesting stylized facts about wealth that provide a good introduction to the wealth distribution and methods of estimating it:

• Wealth is highly concentrated (top 10 percent holds between 65 and 85 percent of the total wealth, top 1 percent holds between 20 and 45 percent of total wealth based on time period); 
• While the methods of estimating the wealth distribution disagree on the timing it is clear that wealth concentration hit its apex prior to the Great Depression and declined after that; 
• Different methods lead to varying estimates for the top 1% for several reasons: one is that the estate tax multiplier method uses the individual as the unit of observation, surveys use the household, and the capitalization method uses tax units; another is that tax evasion impacts the administrative tax-based methods (estate tax and capitalization) but not the survey-based methods. Some capture debt (estate tax returns) whereas others do not (capitalization). 

In a recent issue of the Journal of Public Economics commemorating Tony Atkinson's work, Alvaredo, Atkinson, and Morelli (2018) provides new evidence on the evolution of top wealth shares in the U.K. To choose one of the most interesting facets of the discussion of wealth that they present in the article, it is enlightening to view the top wealth shares compared to the wealth shares excluding housing.



The top 1%'s total wealth share and wealth share excluding housing tracked each other for much of the late 20th century but the authors note the divergence between the two trends in the 21st century, wherein the share of the top 1% of wealth holders of total wealth increased much more rapidly than its share of wealth excluding housing. In other words, the growth of wealth excluding housing is likely to be a more significant contributor to rising inequality than is the growth of housing wealth. In fact, they even mention that increases in housing prices serve an equalizing effect for the top 1%:

"It appears that housing wealth has moderated a definite tendency for there to be a rise in recent years in top shares in total wealth apart from housing. When people talk about rising wealth concentration in the U.K., then it is probably the latter that they have in mind... The results show how the impact of a general rise in house prices has changed over the period but it is always equalizing for the top 1%. At the beginning of the period a rise of 25% led to a reduction of some 1 percentage point in the share of the top 1% but the effect became smaller over time."

It should be noted, however, that trends in the housing market - particularly the resurgence in the private landlord and "buy to let" over the past three decades - likely have impacts on other areas of the wealth distribution apart from the top 1% of wealth owners (though these impacts are not addressed in this paper). This New York Times article from last year, for example, is a news feature that discusses the role that homeownership plays in propagating existing wealth and income inequalities. These topics and the lower rungs of the wealth distribution more broadly are areas for further investigation, but for the time being Alvaredo, Atkinson, and Morelli (2018) highlight how granularity in wealth data can be used to better identify the causes of growing wealth inequality over the past few decades and, while they utilize estate data and the mortality multiplier method in their analysis, can also be triangulated with other methods and data sources to form a more comprehensive understanding of the wealth distribution.

Sources

1. Alvaredo, F., Atkinson, A., Morelli, S. (2018). Top wealth shares in the UK over more than a century. Journal of Public Economics.
2. Kopczuk, W. (2014). What do we know about the evolution of top wealth shares in the United States? NBER Working Paper 20734.
3. Chetty, R., Stepner, M., Abraham, S., Lin, S., Scuderi, B., Turner, N., Bergeron, A., Cutler, D. (2016) The association between income and life expectancy in the United States 2001-2014. Journal of American Medical Association.
4. Saez, E., Zucman, G. (2016) The distribution of US wealth, capital income, and returns since 1913. Quarterly Journal of Economics.