I am pleased to see that Alan Reynolds is finally taking a closer look at some of the evidence that works against his claim that inequality has been stagnant in recent decades, though he predictably dismisses it. I will not convince him the evidence is valid, and he most certainly has not convinced me that it isn’t, so I encourage anyone who is still puzzled about the evidence that profits have been mismeasured and that it matters for assessing changes in inequality in recent years to look at the research and draw their own conclusions. I have no doubt that a fair reading of the evidence will lead to the conclusion that inequality may in fact be worse than we thought which runs opposite of Reynolds’ claims. The essence is fairly simple, if we’re mismeasuring real investment, then we are also mismeasuring profits. Given the concentration of corporate ownership at higher incomes, and the extent of the mismeasurement, this correction matters.

One additional note on Reynolds’ responses since my last post, then I’d like to move on to other issues, particularly those raised in the contributions others have made to this debate. Given Reynolds wholly unsubstantiated and uncalled for attack on the ethics of Piketty and Saez in a commentary on the opinion pages of the *Wall Street Journal* where he accuses them of fabricating results in academic journals to support an agenda, and given other things he has said at other times, it made me chuckle to see him say in his latest response that “all we have seen so far” are “comments about my temperment or assumed policy agenda” as though no evidence rebutting his stance has been presented, just personal attacks on his character or charges that he’s pursuing an ideological agenda. Reynolds says there’s not a strand of evidence that he’s wrong (“no evidence has yet been presented to show any significant and sustained increase in inequality”). Not a strand he’ll acknowledge anyway, but as has been pointed out in previous posts here, and has been documented elsewhere in many different ways, there’s overwhelming evidence against his claims.

I want to follow up on the post from Dirk Krueger and Fabrizio Perri (“Inequality in What?”) because I think they bring something important to the discussion, the academic underpinnings of how we approach the measurement and assessment of inequality changes. In their introduction they say:

Inequality is a fascinating subject, one that provokes discussion and makes it hard to settle the apparently simple question of whether income inequality in the US has increased since 1988. …. Our main point … is to argue that to focus only on the evolution of current income inequality is insufficient if one is interested in the evolution of the distribution of living standards in the U.S.

They then go on to explain, correctly, that the academic literature does not support looking at current income to measure inequality, a broader lifetime measure of consumption and leisure opportunities must be considered, i.e. some concept of the present value of expected lifetime utility is needed (the data on current consumption Reynolds uses in some of his arguments is one proxy for lifetime resources under permanent income stories of consumption, but it is an imperfect proxy with acknowledged problems making any results from these data difficult to interpret reliably). Their conclusion is worth repeating:

One conclusion we would … like the readers to take home is … that understanding the welfare effects of changes in measured inequality, and possibly the appropriate policy measures to deal with it, is a complex task that involves more than reporting the distribution of current resources. Ideally one should understand and measure the distribution of lifetime resources. In order to understand how lifetime resources translate into observable indicators, and what these indicators are, it is crucial to have a thorough understanding of how and to what extent households can transfer resources through time and across states of the world using financial markets. Our own previous work has highlighted the importance of using consumption as an indicator, but recent exciting work is being done by leading researchers in the economics community stressing the role of inequality and dispersion in other variables, too, such as labor effort or wealth, and assessing their impact on incentives, the allocation of resources, and the distribution of welfare.

This is the point I’d like to follow up on because it gets at the essence of Reynolds’ point, measurement issues. What does the academic literature tell us about measuring inequality and has the debate as presented here conformed to those standards?

There is a considerable body of work on measuring inequality, so I will only scratch the surface and point to a couple of surveys on the topic and highlight some of the key results that relate to the discussion here. Perhaps as others respond they can add links to additional resources people can use to learn more about what the academic literature says about measuring changes in inequality.

One such resource is *Some New Methods for Measuring and Describing Economic Inequality*, by R. L. Basmann, K. J. Hayes, and D. J. Slottje which was reviewed by John A. Bishop in the *Journal of Economic Literature* in June, 1995. Since much of the evidence presented by Reynolds and by Richard Burkhauser in this debate has been in the form of Gini coefficients, let me quote one passage from the review (e.g. Burkhauser’s argument that I am wrong about the persuasiveness of the overall evidence relies on Gini coefficients):

First, the authors stress the shortcomings of cardinal evaluations of inequality that rely upon a single index such as the Gini coefficient. They argue that there is no one best inequality index –each contains an implicit set of distributional weights and the precise weights underlying many familiar indices, if clearly understood, would probably not be widely accepted by policy makers.

Another summary of techniques for measuring inequality can be found in Frank Cowell’s * Measuring Income Inequality*, 1995. Two more collections of the work on measuring inequality are given in *The Handbook of Income Inequality Measurement*, by Jacques Silber, 2000*, * which is reviewed by Charles Beach in *The Journal of Economic Literature,* and in *The Handbook of Income Distribution*, edited by A.B. Atkinson and F. Bourguignon, 2000. Let me also be sure to recommend my colleague Peter Lambert’s *The Distribution and Redistribution of Income*, 2002.

These surveys and texts discuss topics such as using stochastic dominance techniques along with Lorenz curves to assess inequality, equivalence scaling, parametric and non-parametric approaches to measurement, welfare comparisons, allowing for different family sizes and compositions, horizontal versus vertical inequality measurement, intertemporal measurement of inequality, and all sorts of other important theoretical and measurement issues you won’t generally find in popular discussions of the topic and that have not, for the most part, been a part of the evidence and discussion Reynolds has presented.

There has been quite a bit more work since these overviews were published, but they constitute a good introduction to many of the important theoretical and empirical issues in the debate over inequality. But as an example of more recent work, another good source of information on this topic is the *Journal of Economic Inequality* which, coincidentally, has a paper in its latest issue about an issue Reynolds is worried about: robust estimation in the presence of contamination of data in the tails of distributions (note that Reynolds is critical of

Krugman’s efforts to look at data contamination at the top of the income distribution that follow roughly along the lines suggested in approach (2) of this paper):

AbstractLorenz curves and second-order dominance criteria, the fundamental tools for stochastic dominance, are known to be sensitive to data contamination in the tails of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models and (2) combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust semi-parametric approach (2). …

And that’s just one paper in the most recent issue on a single journal, there is a considerable volume of work on these issues. The important thing to realize from all of this is that no single measure of inequality is perfect. Thus, looking at a variety of measurements using a variety of data sets and *state of the art* techniques, and being fully aware of and acknowledging the shortcomings of the process at every step along the way so that results can be interpreted properly is important in establishing how inequality has changed through time, and in presenting a balanced overview of the results. When researchers go through these exercises carefully and weigh the evidence objectively they conclude, with few exceptions, that inequality has been rising in recent years.