On the “tea saucer” of income inequality since 1917

I disagree often with the many details that underlie the arguments of Thomas Piketty and Emmanuel Saez. That being said, I am also a great fan of their work and of them in general. In fact, I think that both have made contributions to economics that I am envious to equal. To be fair, their U-curve of inequality is pretty much a well-confirmed fact by now: everyone agrees that the period from 1890-1929 was a high-point of inequality which leveled off until the 1970s and then picked up again.

Nevertheless, while I am convinced of the curvilinear aspect of the evolution of income inequality in the United State as depicted by Piketty and Saez, I am not convinced by the amplitudes. In their 2003 article, the U-curve of inequality really looks like a “U” (see image below).  Since that article, many scholars have investigated the extent of the increase in inequality post-1980 (circa). Many have attenuated the increase, but they still find an increase (see here here here here here here here here here). The problem is that everyone has been considering the increase – i.e. the right side of the U-curve. Little attention has been devoted to the left side of the U-curve even though that is where data problems should be considered more carefully for the generation of a stylized fact. This is the contribution I have been coordinating and working on for the last few months alongside John Moore, Phil Magness and Phil Schlosser. 

Blog Figure

To arrive at their proposed series of inequality, Piketty and Saez used the IRS Statistics of Income (SOI) to derive top income fractiles. However, the IRS SOI have many problems. The first is that between 1917 and 1943, there are many years where there are less than 10% of the potential tax population that files a tax return. This prohibits the use of a top 10% income share in many years unless an adjustment is made. The second is that prior to 1943, the IRS reports net income and reports adjusted gross income after 1943. As such, to link post-1943 with pre-1943, there needs to be an additional adjustment. Piketty and Saez made some seemingly reasonable assumptions, but they have never been put to the test regarding sensitivity and robustness. This is leaving aside issues of data quality (I am not convinced IRS data is very good as most of it was self-reported pre-1943 which is a period with wildly varying tax rates). The question here is “how good” are the assumptions?

What we did is verify each assumption to see their validity. The first one we tackle is the adjustment for the low number of returns. To make their adjustments, Piketty and Saez used the fact that single households and married households filed in different quantities relative to their total population. Their idea is that a year in which there was a large number of return was used, the ratio of single to married could be used to adjust the series. The year they used is 1942. This is problematic as 1942 is a war year with self-reporting when large quantities of young American males are abroad fighting. Using 1941, the last US peace year, instead shows dramatically different ratios. Using these ratios knocks off a few points from the top 10% income share. Why did they use 1942? Their argument was there was simply not enough data to make the correction in 1941.  They point to a special tabulation in the 1941 IRS-SOI of 112,472 1040A forms from six states which was not deemed sufficient to make to make the corrections. However, later in the same document, there is a larger and sufficient sample of 516,000 returns from all 64 IRS collection districts (roughly 5% of all forms). By comparison, the 1942 sample Piketty and Saez used to correct only had 455,000 returns.  Given the war year and the sample size, we believe that 1941 is a better year to make the adjustment.

Second, we also questioned the smoothing method to link net income-based series with adjusted-gross income based series (i.e. pre-1943 and post-1943 series). The reason for this is that the implied adjustment for deductions made by Piketty and Saez is actually larger than all the deductions claimed that were eligible under the definition of Adjusted Gross Income – which is a sign of overshot on their parts. Using the limited data available for deductions by income groups and making some assumptions (very conservative ones) to move further back in time, we found that adjusting for “actual deductions” yields a lower level of inequality. This is contrasted with the fixed multipliers which Piketty and Saez used pre-1943.

Third, we question their justification for not using the Kuznets income denominator. They argued that Kuznets’ series yielded an implausible figure because, in 1948, its use yielded a greater income for non-fillers than for fillers.  However, this is not true of all years. In fact, it is only true after 1943. Before 1943, the income of non-fillers is equal in proportion to the one they use post-1944 to impute the income of non-fillers. This is largely the result of an accounting error definition. Incomes before 1943 were reported as net income and as gross incomes after that point. This is important because the stylized fact of a pronounced U-curve is heavily sensitive to the assumption made regarding the denominator.

These three adjustments are pretty important in terms of overall results (see image below).  The pale blue line is that of Piketty of Saez as depicted in their 2003 paper in the Quarterly Journal of Economics. The other blue line just below it is the effect of deductions only (the adjustment for missing returns affects only the top 10% income share). All the other lines that mirror these two just below (with the exception of the darkest blue line which is the original Kuznets inequality estimates) compound our corrections with three potential corrections for the denominators. The U-curve still exists, but it is not as pronounced. When you look with the adjustments made by Mechling et al. (2017) and Auten and Splinter (2017) for the post-1960 period (green and red lines) and link them with ours, you can still see the curvilinear shape but it looks more like a “tea saucer” than a pronounced U-curve.

In a way, I see this as a simultaneous complement to the work of Richard Sutch and to the work of Piketty and Saez: the U-curve still exists, but the timing and pattern is slightly more representative of history. This was a long paper to write (and it is a dry read given the amount of methodological discussions), but it was worth it in order to improve upon the state of our knowledge.

FigureInequality

Is the U-curve of US income inequality that pronounced?

For some time now, I have been skeptical of the narrative that has emerged regarding income inequality in the West in general and in the US in particular. That narrative, which I label UCN for U-Curve Narrative, simply asserts that inequality fell from a high level in the 1910s down to a trough in the 1970s and then back up to levels comparable to those in the 1910s.

To be sure, I do believe that inequality fell and rose over the 20th century.  Very few people will disagree with this contention. Like many others I question how “big” is the increase since the 1970s (the low point of the U-Curve). However, unlike many others, I also question how big the fall actually was. Basically, I do think that there is a sound case for saying that inequality rose modestly since the 1970s for reasons that are a mixed bag of good and bad (see here and here), but I also think that the case that inequality did not fall as much as believed up to the 1970s is a strong one.

The reasons for this position of mine relates to my passion for cliometrics. The quantitative illustration of the past is a crucial task. However, data is only as good as the questions it seek to answer. If I wonder whether or not feudal institutions (like seigneurial tenure in Canada) hindered economic development and I only look at farm incomes, then I might be capturing a good part of the story but since farm income is not total income, I am missing a part of it. Had I asked whether or not feudal institutions hindered farm productivity, then the data would have been more relevant.

Same thing for income inequality I argue in this new working paper (with Phil Magness, John Moore and Phil Schlosser) which is a basically a list of criticisms of the the Piketty-Saez income inequality series.

For the United States, income inequality measures pre-1960s generally rely on tax-reporting data. From the get-go, one has to recognize that this sort of system (since it is taxes) does not promote “honest” reporting. What is less well known is that tax compliance enforcement was very lax pre-1943 and highly sensitive to the wide variations in tax rates and personal exemption during the period. Basically, the chances that you will report honestly your income at a top marginal rate of 79% is lower than had that rate been at 25%. Since the rates did vary from the high-70s at the end of the Great War to the mid-20s in the 1920s and back up during the Depression, that implies a lot of volatility in the quality of reporting. As such, the evolution measured by tax data will capture tax-rate-induced variations in reported income (especially in the pre-withholding era when there existed numerous large loopholes and tax-sheltered income vehicles).  The shift from high to low taxes in the 1910s and 1920s would have implied a larger than actual change in inequality while the the shift from low to high taxes in the 1930s would have implied the reverse. Correcting for the artificial changes caused by tax rate changes would, by definition, flatten the evolution of inequality – which is what we find in our paper.

However, we go farther than that. Using the state of Wisconsin which had a tax system with more stringent compliance rules for the state income tax while also having lower and much more stable tax rates, we find different levels and trends of income inequality than with the IRS data (a point which me and Phil Magness expanded on here). This alone should fuel skepticism.

Nonetheless, this is not the sum of our criticisms. We also find that the denominator frequently used to arrive at the share of income going to top earners is too low and that the justification used for that denominator is the result of a mathematical error (see pages 10-12 in our paper).

Finally, we point out that there is a large accounting problem. Before 1943, the IRS provided the Statistics of Income based on net income. After 1943, there shift between definitions of adjusted gross income. As such, the two series are not comparable and need to be adjusted to be linked. Piketty and Saez, when they calculated their own adjustment methods, made seemingly reasonable assumptions (mostly that the rich took the lion’s share of deductions). However, when we searched and found evidence of how deductions were distributed, they did not match the assumptions of Piketty and Saez. The actual evidence regarding deductions suggest that lower income brackets had large deductions and this diminishes the adjustment needed to harmonize the two series.

Taken together, our corrections yield systematically lower and flatter estimates of inequality which do not contradict the idea that inequality fell during the first half of the 20th century (see image below). However, our corrections suggest that the UCN is incorrect and that there might be more of small bowl (I call it the Paella-bowl curve of inequality, but my co-authors prefer the J-curve idea).

InequalityPikettySaez.png

Did Inequality Fall During the Great Depression ?

Inequality

The graph above is taken from Piketty and Saez in their seminal 2003 article in the Quarterly Journal of Economics. It shows that inequality fell during the Great Depression. This is a contention that I have always been very skeptical of for many reasons and which has been – since 2012 – the reason why I view the IRS-data derived measure of inequality through a very skeptical lens (disclaimer: I think that it gives us an idea of inequality but I am not sure how accurate it is).

Here is why.

During the Great Depression, unemployment was never below 15% (see Romer here for a comparison prior to 1930 and this image derived from Timothy Hatton’s work). In some years, it was close to 25%. When such a large share of the population is earning near zero in terms of income, it is hard to imagine that inequality did not increase. Secondly, real wages were up during the Depression. Workers who still had a job were not worse off, they were better off. This means that you had a large share of the population who saw income reductions close to 100% and the remaining share saw actual increases in real wages. This would push up inequality no questions asked. This could be offset by a fall in the incomes from profits of the top income shares, but you would need a pretty big drop (which is what Piketty and Saez argue for).

There is some research that have tried to focus only on the Great Depression. The first was one rarely cited NBER paper by Horst Mendershausen from 1946 who found modest increases in inequality from 1929 to 1933. The data was largely centered on urban data, but this flaw works in favor of my skepticism as farm incomes (i.e. rural incomes) fell more during the depression than average incomes. There is also evidence, more recent, regarding other countries during the Great Depression. For example, Hungary saw an increase in inequality during the era from 1928 to 1941 with most of the increase in the early 1930s. A similar development was observed in Canada as well (slight increase based on the Veall dataset).

Had Piketty and Saez showed an increase in inequality during the Depression, I would have been more willing to accept their series with fewer questions and doubts. However, they do not discuss these points in great details and as such, we should be skeptical.

Can we use tax units to measure living standards?

In the debate on inequality, I am a skeptic of how large a problem the issue is. Personally, I tend to believe that worries of inequality only increase when growth is stagnant. In fact, I also believe that there are numerous statistical biases causing us to misidentify stagnation as rising inequality. Most of the debate on inequality is plagued with statistical problems of daunting magnitudes (regional convergence in income, regional price levels, demographic changes, increasing heterogeneity of preferences, increasing heterogeneity of personal characteristics, income not being purely monetary, the role of taxes and transfers etc.)

One of them centers around the use of tax data. This has been the domain of Thomas Piketty and Emmanuel Saez. I can understand the appeal of using tax data since it is easily available and usable. Yet, is it perfect?

A year or two ago, I would have been inclined to simply say “yes” and not bother with the details. Theoretically, taxes should be an “okay” proxy for the income distribution and should follow average income even if at different levels. Yet, after reading the article of Phil Magness and Robert Murphy in the Journal of Private Enterprise I confess that I am no longer accepting anything as “granted” in the inequality debate. So, I simply decided to chart GDP per capita with the average taxable income per tax unit. Just to see what happens. Both are basically averages of the overall population, they should look pretty much the same (theoretically).  The data for the tax units is made available in the Mark W. Frank dataset based on the Piketty-Saez data (see here) and I deflated with both the CPI and the implicit price deflator available at FRED/St-Louis.

The result is the following and it shows two very different stories! Either the GDP statistics are wrong and we have average stagnation (which does not mean that there is no increase in inequality) or the taxable income data is wrong in estimating the trend of living standards and the GDP are closer to reality (which does not that there is no increase in inequality).  In the end, there is a problem to be assessed with the quality of the data used to measure inequality.

Tax Data