World Economic Review

Data Visualization in Capital in the 21st Century
Noah Wright
Lyndon B. Johnson School of Public Affairs, University of Texas, Austin, USA

Abstract
This paper examines how data visualization is used to supplement the arguments in Thomas Piketty’sstCapital in the 21 Century. Piketty shows a consistent pattern of modifying his visualizations to provide
stronger support for his arguments than his data contains, particularly in his visualizations of the rate of
return on capital as it compares to the rate of economic growth, one of the central arguments of the book.
This modification takes the form of using disproportionate axis units and the addition of estimated or
speculative context. The effect of this modification is to change the fundamental shape of the data trends,
which can be clearly seen when proportional axes are used and hypothetical context removed.

The concept of inequality in the modern era is inseparable from the quantitative data used to define it. Unlike
historical perspectives of inequality, which relied on narrative accounts of poverty and wealth, modern
definitions of inequality virtually always include some type of statistical measure such as GINI coefficients,
Theil Statistics, and share of wealth or income owned by population quantiles. Tables of data, however, do
not lend themselves to effective communication with a mass audience, making visualization a critical aspectof modern inequality literature.
st

In this paper I will analyze how Thomas Piketty uses data visualization in Capital in the 21 Century
to make his case. The book contains a plethora of visualizations, including 96 graphs and 18 tables, which
Piketty uses to reinforce the arguments being made by the text. I will be examining the integrity of thesestvisualizations and how they interact with the arguments of Capital in the 21 Century.
This paper will be organized as follows: first, I define the criteria of “proportionality” and “context” bywhich I am evaluating the integrity of Piketty’s visualizations. Then, I examine the proportionality and context
stof specific graphs used in Capital in the 21 Century. Part of this examination includes reformatting Piketty’s
graphs by removing disproportionate axes and hypothetical context. These reformatted graphs are thencompared to their originals as well as the language in the text describing them. Frequently, the data being
visualized does not support the arguments of the text once it is formatted without speculation or distortion.
To conclude, I summarize how Piketty’s less defensible visualization choices are necessitated in large partby the nature of the book’s arguments.
Before I can criticize “integrity” I will need to define it for the purpose of this paper. Edward Tufte
devotes an entire chapter to graphical integrity in The Visual Display of Quantitative Information, a seminal
text in the history of data visualization. In this chapter, Tufte identifies general principles of integrity in datavisualization. For the purposes of this analysis, I will be focusing on the two most relevant to Capital in thest

21 Century: proportionality and context. Tufte defines data proportionality as follows: “the representation of
numbers, as physically measured on the surface of the graphic itself, should be directly proportional to thenumerical quantities represented” (Tufte 1983, p.56). Tufte even proposes a method of measuring thedistortion of this proportionality called the Lie Factor, in which the size of the effect shown in the graphic is
divided by the size of the effect shown in data. For example:

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This is the exact graphic Tufte uses to demonstrate a high lie factor. The change in the graphic is 5.3 inches– 0.6 inches, or 4.7 inches, indicating a 4.7/0.6 (783%) change. The change in the data, however, is 27.5-18,
a 9.5/18 (53%) change. The total lie factor of this graphic is therefore 783/53, or 14.8. Lie factors are not anexact science, but they provide a rough conceptual framework for thinking about how one chooses torepresent data.
In addition to deliberate distortion of proportionality, the removal or addition of context can alter
one’s perception to the same extent. For example, this historical chart of the Dow Jones Industrial Average
makes the stock market looks like a safe long-term investment circa May of 1929:

Source: http://www.macrotrends.net/1319/dow-jones-100-year-historical-chartst

The visualizations in Capital in the 21 Century’s come in two forms: tables of numbers and time-series line
graphs. Almost every line graph is identical: the x-axis is years and the y-axis is an inequality measure or
economic statistic. The following is the first graph that appears in the book, income inequality in the UnitedStates from 1910-2010 (Piketty 2013, p.24).

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Piketty describes the graph in his text as follows: [my italics]
The US curve, shown in Figure I.1, indicates the share of the upper decile of the income
hierarchy in US national income from 1910 to 2010. It is nothing more than an extension of
the historical series Kuznets established for the period 1913–1948. The top decile claimed
as much as 45–50 percent of national income in the 1910s–1920s before dropping to 30–
35 percent by the end of the 1940s.
Inequality then stabilized at that level from 1950 to 1970. We subsequently see a rapid risein inequality in the 1980s, until by 2000 we have returned to a level on the order of 45–50
percent of national income. The magnitude of the change is impressive. It is natural to ask
how far such a trend might continue (Piketty 2013, p.23).
In his description, Piketty tells the story of this graph for the reader. Inequality was high, inequality then“dropped”, “stabilized”, and saw a “rapid rise” that “returned” it to its previous level. Piketty likely starts withthis graph because it’s one of the major arguments of his book in miniature: that the declining inequality ofthWestern Europe and the United States observed in the middle parts of the 20 century was temporary, andththat the world is returning to a society defined by inherited wealth as in the 19 century.
In terms of proportionality, this visualization has 1-to-1 correspondence between the data depicted
on both axes. One unit of the X-axis represents ten years and one unit of the y-axis represents 5% ofnational income share controlled by top decile.
In terms of context, the graph depicts top decile share of national income, but the text does not
1

specify whether this includes taxes and transfers. It does specify that the data comes from tax records, but
fails to mention one of the fundamental problems of using tax records: that they only measure reported
income. Both of these factors change the results of the visualization: taxes and transfers reduce inequality,
while underreporting of income in response to high tax periods (like the 1940s-1960s) could artificially reduce
inequality for the duration of the period.
These data choices shape the graph into something that is visually consistent with Piketty’s
narrative: we are returning to the old world. This becomes apparent when we shift the Y-axis:
1

A virtually identical version of this graph appears in “Striking it Richer: The Evolution of Top Incomes in the United States,” a2013 paper by Piketty’s collaborator Emmanuel Saez. In this paper, Saez specifies that the data is pre-taxes and transfers (Saez2014, p.8).

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By definition, the top decile must control at least 10% of the wealth, so starting the Y-axis at zero as above isnonsense. Here I am illustrating a point: could Piketty describe inequality as rapidly rising in the 1980’s
based on the above visualization? His visualization makes the change in U.S. inequality look larger than thisone, which aligns the visual with what Piketty emphasizes in his narrative of the world returning to how it
used to be. This message appears numerous times throughout the book, with Piketty making frequent
reference to the works of Jane Austen and Honore de Balzac in tandem with his economic arguments. While
not such a problem for the above graph, throughout the book Piketty deliberately alters context andproportionality in his visualizations to fit them around this narrative. Of the 92 time-series graphs in the book,2

25 have non-proportional X-axes. The first of these to appear is Figure 1.1, seen below: (Piketty 2013,p.60).

2

See Appendix A for a full list.

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One unit on the x-axis represents 120 years, then 50 years, then 63 years, then 37 years, then 20 years,
then 20 years again, then 22 years. Almost every unit represents a different amount of time. The
inconsistency makes Tufte’s “lie factor” difficult to calculate, but the level of disproportion is about 6-fold: 120
years vs. 20 years. When the graph is displayed with a proportional x-axis, it looks as follows:3th

The effect of the disproportion is to emphasize the 20 century. Less than one third of the timeframe is theth

20 century, yet this century occupies more than half of the figure. This emphasis also has the effect ofvisually depicting Piketty’s narrative of a return to what used to be, as did figure I.1 showing U.S. income
inequality. Both figures depict a beginning state of affairs, a change in that state of affairs in the middle of thegraph, and at the end a gradual return.
This specific proportionality is used as the x-axis labeling convention for figures 1.2, 1.3, 2.1, 2.3,
2.6, and all six of the figures in chapter 3. Sometimes this proportionality does not change the fundamental
shape of the data trend, as seen in figure 2.1 below. In these cases, the axis is likely chosen to makecomparisons easier. In other cases, as seen in figure 2.3 below, this proportionality reshapes the graph intoa curve that depicts a status quo, an alteration, and a return to that status quo along the lines of what is
depicted above.

3

This resizing is drawn from Piketty’s data, which only includes the figures for the years in the original graph (1700, 1820, 1913,
etc.). A year-by-year dataset would yield a much smoother graph, see Appendix B for technical details regarding the visualizations
used in this paper.

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Piketty’s Graph: (Piketty 2013, p.75).

A proportional X-axis does not reshape the trend:

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Piketty’s graph: (Piketty 2013, p.97)

A proportional x-axis makes the trend look more flat:th

In all of these cases, regardless of the change in shape, the years chosen from the 20 century stand out inthese figures. The specific years were likely chosen due to the large role they play in the narrative of Capitalstin the 21 Century: 1913 (just prior to World War 1), 1950 (just after World War 2, when economic recovery

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is in full swing), 1970 (when that economic recovery begins to stall), and 1990 (when inequality is widening
once more). These years continue to be emphasized even in much longer timeframes than the graphs
above, leading to severely disproportionate visualizations. The first of these is a graph of the world
population growth rate over time, seen below (Piketty 2013, p.80).

The proportionality of the x-axis does not come close to matching the scale of the data. As with the abovegraphs, almost every unit represents a different amount of time, but this time the highest degree ofdisproportion is over 50-fold: 1000 years vs. 18 years, both represented by one unit. If each unit on the
X-axis had the same value, the graph would look as follows:

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Piketty’s description of the data reveals the story he tells with it: [my italics]
According to official forecasts, progress toward the demographic transition at the global
level should now accelerate, leading to eventual stabilization of the planet’s population.
According to a UN forecast, the demographic growth rate should fall to 0.4 percent by the2030s and settle around 0.1 percent in the 2070s. If this forecast is correct, the world will
return to the very low-growth regime of the years before 1700. The global demographic
growth rate would then have followed a gigantic bell curve in the period 1700–2100, with aspectacular peak of close to 2 percent in the period 1950–1990 (Piketty 2013, p.79).
Piketty could not describe the proportional graph using the above language. While the proportional graphdoes contain a spectacular peak, it does not resemble Piketty’s sloping bell curve. This graph shows the 20thcentury as an extremely brief, severe aberration, made all the more so by the inclusion of long-term historicalestimates and speculative projections. Piketty himself even acknowledges that for 0 to 1700, the majority ofthis timescale:… the precision of such estimates is illusory. We actually possess very little information
about the growth of the world’s population between 0 and 1700 and even less about output
per head. Nevertheless, no matter how much uncertainty there is about the exact figures(which are not very important in any case), there is no doubt whatsoever that the pace ofgrowth was quite slow from antiquity to the Industrial Revolution, certainly no more than
0.1–0.2 percent per year (Piketty 2013, p.74).
These historical estimates are “not very important”, yet they are included in the visualization. The reason for
doing so becomes clear when we remove these historical estimates and future projections in addition torescaling the x-axis:

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This visualization does not look like a return to anything; the bell curve has disappeared. In addition to adisproportionate x-axis, Piketty has shaped the visualization by altering context. Rather than removing
context, however, as I did in the stock market graph at the beginning of the paper, Piketty has added context
to create the desired look for his visualization. For the above population graph, though, this additional data isquestionable but not indefensible. The historical population growth rate has been very low from what we’vebeen able to discern (if it hadn’t been, there would be a great deal more people around now). Likewise, theobserved population growth rate has been declining, and many if not most demographers and forecasters
predict that it will continue to do so.
However, this addition of historical estimates and future projections becomes much more
problematic in the next two graphs starting at antiquity, which depict growth rates of per-capita output andtotal output. Unlike population growth, the future projections in these are far less plausible. Piketty’s own
data does not show per-capita output declining in the real world, which means the projections of figure 2.4
showing this decline are entirely speculative. This alteration becomes much more apparent when Piketty’s
graphs as he presents them are compared with how they appear after the removal of projections, estimates,and disproportionate X-axes (as seen on the next page).
As with population, Piketty acknowledges the hypothetical nature of his projections in the text while
simultaneously describing the phenomenon as a bell curve:
I have already conceded that these “median” forecasts are highly hypothetical. The key
point is that regardless of the exact dates and growth rates (details that are obviously
important), the two bell curves of global growth are in large part already determined(Piketty 2013, p.102, my italics).
Yet there is nothing resembling a bell curve once the above adjustments are made.

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Piketty’s Graph: (Piketty 2013, p.100).

Proportional X-axis, historical estimates and future projections removed:

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Piketty’s Graph: (Piketty 2013, p.101).

Proportional X-axis, historical estimates and future projections removed:

The chapter 2 time-series graphs seen above play an important role in laying the groundwork for the graphsstin chapter 10, which depict one of the central arguments of Capital in the 21 Century: that when the rate of
return on capital (“r”) exceeds the general growth rate (“g”), inequality tends to increase (“r>g”). The first ofthese, figure 10.9, essentially replicates figure 2.5 in its depiction of the growth rate of world output while

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4adding the trend-line for rate of return on capital: (Piketty 2013, p.354).

Note that unlike in chapter 2, the hypothetical projections are not labeled as such. Piketty builds on thisthvisualization by adding in the all of factors that reduced the rate of return on capital in the 20 century tocreate Figure 10.10 (Piketty 2013, p.356).

4

Many critiques have already been written about Piketty’s notion of “rate of return on capital,” see Acemoglu and Robinson (2015),
Galbraith (2014), and McCloskey (2014). For this reason, I will be focusing solely on visualization in this paper for the sake ofbrevity.

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thHere the 20 century is presented as a clear outlier during which the growth rate of the economy exceeded
the rate of return on capital. Contrast this with how the figure appears with a proportionate x-axis when
historical estimates and future predictions are removed:th

The rescaled visualization does show the unique character of the 20 century, but gives no reason to believethat this trend won’t continue into the future. This particular point is so important to Piketty that on the page
following figure 10.10 is an almost-identical graph designed to even further emphasize the idea that thethworld is returning to its pre-20 century state: (Piketty 2013, p.357).

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thFigure 10.11 collapses the entire 20 century into a single point and adds another hundred years of purely
speculative projection that Piketty himself acknowledges as a “hypothesis” (Piketty 2013, p.357). Piketty
justifies this decision as follows:
To bring this possible evolution out even more clearly, I have combined in Figure 10.11 thetwo subperiods 1913–1950 and 1950–2012 into a single average for the century 1913–
2012, the unprecedented era during which the net rate of return on capital was less than
the growth rate. . . Figure 10.11 at least brings out the unprecedented—and possibly
unique—character of the twentieth century in regard to the relation between r and g(Piketty 2013, p.357).
These visualizations would not be nearly as problematic were it not for the fact that Piketty uses them tomake claims like the following:
As Figure 10.9 shows, the pure rate of return on capital—generally 4–5 percent—has
throughout history always been distinctly greater than the global growth rate, but the gap
between the two shrank significantly during the twentieth century, especially in the second
half of the century, when the global economy grew at a rate of 3.5–4 percent a year. In all
likelihood, the gap will widen again in the twenty-first century as growth (especiallydemographic growth) slows (Piketty 2013, p.355, my italics).
There is a circular logic at work here, as Figure 10.9 has been designed to show the conclusions being
drawn from it. But without his reshaped x-axes, historical estimates, and future projections, Piketty cannot
make the case that his central argument holds true “throughout history always”, a claim restated in theultimate conclusion of this series of graphs:
To sum up: the inequality r > g has clearly been true throughout most of human history,
right up to the eve of World War I, and it will probably be true again in the twenty-first
century (Piketty 2013, p.358).
Prior to these graphs, Piketty refers to r>g as the “fundamental force for divergence” (Piketty 2013, p.25),
and goes on to refer to other components of his theory as “fundamental laws” (Piketty 2013, p.52). A“fundamental law” is one of the strongest claims one can make in social sciences, as a fundamental law
must always be true in every conceivable circumstance, throughout history and forever into the future. Since
its inception, the field of economics has been rife with claims of fundamental laws, from laws of history andlaws of wages to now laws of inequality. When exceptions are found, proponents for these fundamental
laws often make procrustean adjustments to data or theory so as not to violate their fundamental status. In
this respect, Piketty’s claim to his theory being a fundamental law necessitates his more problematic datavisualizations. Piketty could have avoided the need for these problematic depictions by weakening his
assumptions and/or limiting himself to non-speculative data. Had he done this, however, he could never
have justified one of the central claims of his book: that the world is returning to what it was in the past. What
the data actually shows is that we do not know where the world is heading.

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stAppendix A – Index of visualization characteristics in Capital in the 21 Century

Figure
0.1
0.2
1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.2
3.3
3.4
3.5
3.6
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
8.1

Disproportionate
X-axis?

Pre-1700 or future
estimates?

Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes
Yes

Yes

Figure
8.2
8.5
8.6
8.7
8.8
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
12.1
12.2
12.3
12.4
12.5
12.6
13.1
14.1
14.2

Disproportionate Xaxis?

Pre-1700 or future
estimates?

Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes
Yes
Yes
Yes

Yes
Yes

*Figures 4.11, 8.3, 8.4, 8.9, and 8.10 are not time-series and therefore not included above.

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Appendix B – Technical Issues in Excel
The visualizations in this paper are drawn from the data made available by Thomas Piketty on his website forstCapital in the 21 Century, http://piketty.pse.ens.fr/en/capital21c2. This data contains, for the most part, only
what is presented in Piketty’s figures. For example, Figure 2.2 appears in Piketty’s spreadsheet as follows:World
population(growth rate)

EuropeAmérica

AfricaAsia

0-1000

0.0%

0.0%

0.1%

0.1%

0.0%

1000-1500

0.1%

0.2%

0.1%

0.1%

0.1%

1500-1700

0.2%

0.2%

-0.2%

0.1%

0.2%

1700-1820

0.5%

0.5%

0.7%

0.2%

0.5%

1820-1913

0.6%

0.8%

1.9%

0.6%

0.4%

1913-1950

0.9%

0.4%

1.6%

1.6%

0.9%

1950-1970

1.9%

0.9%

2.2%

2.4%

2.1%

1970-1990

1.8%

0.5%

1.7%

2.8%

2.0%

1990-2012

1.3%

0.1%

1.3%

2.4%

1.3%

2012-2030

0.9%

0.0%

0.8%

2.1%

0.8%

2030-2050

0.6%

-0.2%

0.4%

1.7%

0.3%

2050-2070

0.3%

-0.2%

0.1%

1.3%

-0.1%

2070-2100

0.1%

-0.1%
-0.1%
1.2%
-0.4%
(Sheet: Chapter2TablesFigures.xls, Tab: TS2.2)

There is additional data by region, but no additional data by year. In other words, the world population growthrate at 1760 or 1930 cannot be found in these tables, only the averaged values seen above. As a result, I
produced my rescaled visualizations by reformatting the data as follows:

1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950

World population(growth rate)
0.5%
0.5%
0.5%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.9%
0.9%
0.9%
0.9%

Europe
0.5%
0.5%
0.8%
0.8%
0.8%
0.8%
0.8%
0.8%
0.8%
0.8%
0.8%
0.4%
0.4%
0.4%
0.4%
0.9%

América
0.7%
0.7%
1.9%
1.9%
1.9%
1.9%
1.9%
1.9%
1.9%
1.9%
1.9%
1.6%
1.6%
1.6%
1.6%
2.2%

Africa
0.2%
0.2%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
0.6%
1.6%
1.6%
1.6%
1.6%
2.4%

Asia
0.5%
0.5%
0.4%
0.4%
0.4%
0.4%
0.4%
0.4%
0.4%
0.4%
0.4%
0.9%
0.9%
0.9%
0.9%
2.1%

You will notice that I use 1910 above when Piketty’s data lists 1913. This is because of the way Excel
automatically formats axis coordinates to be equidistant from one another regardless of scale. The only way

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around this would be to create a listing for every single year, but I chose decades because it is what Piketty
does for most of his data points in these graphs. I have also used 2010 instead of 2012 and 2013 for thesame reason.
Another problem I faced came from the fact that because these are annualized averages, multiple
values could be chosen for the same year. To use the above table as an example again (I’ve copied therelevant section below), what should be used as the growth rate for 1970: 1.9%, 1.8%, or 1.85%?

Year

World population(growth rate)1950-1970

1.9%

1970-1990

1.8%

I can format it one of three ways:

Year

World population(growth rate)

Year

World population(growth rate)

Year

World population(growth rate)

1960
1970

1.9%
1.9%

1960
1970

1.9%
1.8%

1960
1970

1.9%
1.85%

1980

1.8%

1980

1.8%

1980

1.8%

… each of which produces a slightly different visual:

For the graphs I produced in this paper derived from averages, I went with the option on the left, using thefirst listed value for a given decade. Using the middle option would have created unevenly sized categories:
the final 20 years would have had three entries as opposed to two. The option on the right I ruled out as
extrapolation.

References
Acemoglu, Daron & Robinson, James A. Winter 2015, ‘The Rise and Decline of General Laws of Capitalism,’
Journal of Economic Perspectives, American Economic Association, vol. 29(1), pp. 3-28.
Galbraith, James. Spring 2014, ‘Kapital for the Twenty-First Century?’ Dissent. Available:
http://www.dissentmagazine.org/article/kapital-for-the-twenty-first-century [accessed April 3, 2015].

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McCloskey, Deirdre. Autumn 2014, ‘Measured, Unmeasured, Mismeasured, and Unjustified Pessimism: A
Review Essay of Thomas Piketty’s Capital in the Twenty-First Century,’ Erasmus Journal for Philosophy andEconomics, Erasmus Institute for Philosophy and Economics, vol. 7(2).
Piketty, Thomas & Goldhammer, Arthur. 2013, Capital in the Twenty-First Century, The Belknap Press ofHarvard University Press, Cambridge, MA.
Saez, Emmanuel. 2014, “Striking it Richer: The Evolution of Top Incomes in the United States,” UC
Berkeley. Available: http://eml.berkeley.edu/~saez/saez-UStopincomes-2012.pdf [accessed April 3, 2015].
Tufte, Edward. 1983, The Visual Display of Quantitative Information, Graphics Press, Cheshire, CT.

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