Miscalculating the wealth of the rich reveals unintended biases

In an ambitious effort, economists Philip Armour and Richard Burkhauser of Cornell University, and Jeff Larrimore of the Joint Committee on Taxation attempt to produce an estimate of trends in inequality based on a definition of income more relevant to understanding economic wellbeing. Specifically, they try to estimate the so-called Haig-Simons metric that defines annual income as consumption plus change in net wealth. According to this definition of income, the authors claim inequality has not been rising over time, leading some strident conservative voices to latch on to it—contrary to numerous other studies and measures

It is important to understand the Haig-Simons metric (named after early 20th century economists Robert Haig and Henry Simons), the methods used by Armour, Burkhauser, and Larrimore for estimating income using this metric, and their presentation of the data regarding this income metric. By my assessment, their working paper does not constitute an informative addition to the inequality discussion. The Haig-Simons measure is interesting but convolutes wealth and income. What’s more, their methodological choices bias the results to downplay relative income growth at the top, and the statistics they report are not sufficiently detailed to assess the implications of their findings.

Is the Haig-Simons income measure useful?

The Haig-Simons income measure has the advantage of avoiding volatility based on the timing of the realization of capital gains on the sale of assets by individuals. Other annual income measures may be too volatile because some people time asset sales based on taxes or other factors, which makes annual income a noisy proxy for wellbeing. Thus, this measure could provide a more comprehensive assessment of the variation in household balance sheets by cutting out timing decisions.

Yet the Haig-Simons measure introduces substantial volatility as well based on changes in the market valuation of assets. Someone with a large stock portfolio, for example, whose portfolio fell substantially could have a negative Haig-Simons income despite being high in the income distribution. Using this measure, the billionaire founder of Facebook, Mark Zuckerberg, would have been considered one of the poorest people in the world in 2012 because his net worth fell by $4.2 billion.

The key point is that assets held in company stock or in stock market indices vary substantially in valuation over any time scale. The Haig-Simons measure attempts to factor out volatility in realized capital income but at the same time introduces potentially higher volatility in the valuation of capital holdings.

To understand the relative merits of the Haig-Simons metric in assessing comprehensive income it is important to discern the relative magnitudes of these volatilities across the entire distribution of income. One way to think about it is that people can choose to sell a stock or other asset whenever they want, which will introduce volatility in their income because of the asset sale. But the value of assets someone holds will vary substantially, too, because stock prices change every day whether or not shares are sold. Thus, measures of income that include capital gains can be variable because of the sale of stock while measures that look at net wealth will also be variable because the stock prices are also volatile. Because it exacerbates the volatility in the valuation of wealth, the Haig-Simmons measure’s primary advantage—that it reduces volatility from the sale of assets—may be swamped.

Additionally, by ignoring the liquidity of assets, the Haig-Simons measure obfuscates changes in wealth and economic wellbeing. Inflation in housing prices during the 2000s led the net wealth of many to increase, which would show up as a rising Haig-Simons income. With hindsight we know that much of this valuation was a bubble and that there was a minimal real improvement in economic wellbeing.

It is unclear why a single reductionist measure is needed for both wealth and income when one measure for wealth and a separate measure for income could be used. Looking at several measures can provide a textured understanding beyond a single number. If asset volatility from timing decisions were determined to be a primary source of noise in short-term inequality trends, then a multi-year average could be applied to other measures of income. This would have the advantage of reducing the volatility from timing decisions while avoiding obviously absurd assessments of income.

Are their methods for determining the Haig-Simons measure sufficient?

The authors attempt to determine a comprehensive measure of both consumption and the change in net worth using the Haig-Simons metric. To compute this measure of income, they make several adjustments to the data to include near cash benefits such as estimating the value of health insurance provided to individuals either from the government of from employers. For changes in net worth, a single national housing index was used to account for changes housing wealth across the country and only the Dow Jones Industrial Average was used for all types of stock income. There are also limitations on details of high-income households in the survey data that they use. Each of these methodological choices will artificially bias their estimates toward a lower valuation of income growth at the top of the distribution.

So let’s examine each of the components they use in turn.

Their method for assessing the value of health insurance is not useful in comparing time trends because it ignores changes in the structure of insurance products over time, variation in the quality of the insurance products provided, and the substantial growth of health care costs beyond inflation over most of they period of their study. Before the enactment and initial implementation of the Affordable Care Act of 2010, there was a trend in health insurance for higher deductible products (these have a lower actuarial value), which would mean that comparisons across time in the value of health insurance would overstate their value in later years relative to early years.

Thus, the relative value of the health insurance product used in their analysis is inflated and will lead to artificially inflated income growth for people whose health insurance constitute a larger share of their “comprehensive” income than others. Because health insurance will probably constitute a smaller share of the consumption of high-income people, the authors’ methodological decisions on accounting for health insurance will artificially imply a reduction in income growth at the top of the income spectrum relative to other segments.

Similarly, the authors’ methodological choices for valuation of housing and stocks are likely to artificially reduce their estimates of the net worth of those at the top. For each of these factors, the authors used a single growth rate for all incomes. By using a single product and not testing the impact of heterogeneous rates—meaning variations in the rates of return—the authors artificially reduce the variability. This reduction in variation will particularly attenuate growth in asset values on the high side and therefore result in artificially low incomes among the top of the distribution.

To their credit, the authors’ acknowledge this shortcoming:

“…when imputing yearly accrued capital gains we assume that all investments receive the ordinary rate of return. Hence we will not capture extranormal returns received by some individuals on their investments.”

Yet after acknowledging this flaw they did not attempt to vary rates of return on the high end of the income distribution or otherwise account for this bias. In fact, a recent paper by Fabian T. Pfeffer, Sheldon Danziger, and Robert F. Schoeni from the University of Michigan find the wealth of the richest households grew faster than the median household, and much faster than households below the median.

Another issue with this approach has to do with their choices of survey data sets. This work relies heavily on surveys such as the Current Population Survey, the Medical Expenditure Panel Survey, and the Survey of Consumer Finances. Economist Philip Vermeulen of the European Central Bank finds that survey data on wealth tend to have a hard time assessing wealth at the top because of systematically biased underreporting among the wealthy skews the estimates lower. Thus, a fundamental limitation of this work is its ability to measure trends at the top, which are central to the claims made about the study’s findings.

Are the data reported sufficient to assess trends in the Haig-Simons measure?

The three authors report average growth estimates by quintile for several different income measures. This is good because it allows for a partial assessment about which components of the income construction are driving the results. But more information is needed. The authors’ choices about which rates of return to apply strongly influence the results; providing results from sensitivity tests (checks to see how much the results rely on various assumptions) with alternate measures would be useful. Without information on these sensitivity tests, there is no way to assess the effect of the biases discussed above.

Furthermore, they do not provide error estimates or statistics on their matching approaches across data sets. Statistics regarding the matching approach (and sensitivity tests of the matching) are particularly important to assess the implications on quality of the methodological choices. These omissions are disconcerting because it makes it impossible to assess the quality of the results and therefore their utility to the current discussion.


The authors attempted an ambitious analysis of incomes, which should be commended, but their execution is insufficient to support the broad proclamations made by many pundits about declines in inequality. Given the study’s clear methodological biases and weaknesses, the claims of the paper’s first author in a report from the Manhattan Institute dramatically overstate the implications. The Haig-Simons income measure may be useful, but there are better ways of getting the same, if not more, information using other measures of wealth and income without conflating the two.

The authors’ methods should work well enough for estimates of the Haig-Simons income for measuring the assets of low- and middle-income people for whom capital gains are a relatively unimportant source of income, but there are fundamental biases that will result in artificially low growth rates among their high-income counterparts. Finally, their reported results are insufficient to assess whether the trends are entirely driven from their methodological choices and also if the results are discernible from noise. I look forward to further research by the three authors and others that more effectively measures the assets of the wealthy—a key to understanding the links between economic inequality and growth.

August 12, 2014


Economic Inequality

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