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The Great Gatsby, Moby Dick, and Omitted Variable Bias



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Alan Krueger, President Obama’s economic adviser, used a chart in a recent speech at the Center for American Progress to support his argument that higher inequality today will lead future generations of Americans to experience less social mobility (movement between income classes across generations). This kicked off quite a debate. The primary technical back-and-forth was between Scott Winship of Brookings and Miles Corak of the University of Ottawa, with significant commentary by economists Justin Wolfers, Tyler Cowen, Paul Krugman, Jared Bernstein, Lane Kenworthy, and others.

I think that this nerdy debate is important for two reasons. First, this is part of the huge argument about whether equality of opportunity is possible without equality of outcomes — i.e., is America’s self-image as a land of opportunity a cruel myth? Second, Krueger’s curve is a classic example of a social scientist attempting to claim the mantle of scientific understanding of a subject — in the specific practical sense of claiming the ability to make reliable, non-obvious predictions using mathematical relationships. These kinds of claims to knowledge have been central to the intellectual justification for the Progressive program since its inception.

In this case, I think that Krueger’s claim is unfounded.  Let me explain why.

#more#Start with the chart in question, which Krueger called the Great Gatsby Curve:

http://jaredbernsteinblog.com/wp-content/uploads/2012/01/ak_ineq2.png

The X dimension on this chart is the “Gini Coefficient” in 1985. The Gini Coefficient is a measurement of the degree to which the income distribution for a given group of people deviates from perfect equality. The higher the number, the more unequal the society (as defined by this specific metric). The Y dimension on this chart is the “Intergenerational Earnings Elasticity” (IGE) today. IGE is a measurement of the degree to which person X will tend to have a very similar position in the relative income distribution of a given population group as his or her parents had in the prior generation of the same population group. The higher the number, the less mobility there is in the society (as defined by this specific metric). 

Krueger claimed in his prepared remarks that this is evidence that higher inequality today will cause less social mobility in the future. In fact, after some throat-clearing, he flatly asserted that we can use this curve to “roughly forecast” future inequality in the United States:

If the cross-sectional relationship displayed in this figure holds in the future, we would expect to see a rise in the persistence in income across generations in the U.S. as well.1 While we will not know for sure whether, and how much, income mobility across generations has been exacerbated by the rise in inequality in the U.S. until today’s children have grown up and completed their careers, we can use the Great Gatsby Curve to make a rough forecast. The next figure displays this projection [Figure 8]. The IGE for the U.S. is predicted to rise from .47 to .56. In other words, the persistence in the advantages and disadvantages of income passed from parents to the children is predicted to rise by about a quarter for the next generation as a result of the rise in inequality that the U.S. has seen in the last 25 years. [Bold added]

In this paragraph of his prepared text, you may have noticed the little superscript that is a pointer to Footnote 1. Here is the footnote:

There are statistical reasons why the relationship might not hold (e.g., omitted variables), but there are also many reasons to suspect that it will hold. For example, families with higher incomes can pass on more advantages to their children through providing more educational opportunities, and the reward to education and skills has increased.

Yeah, well that’s pretty much the whole game. 

Krueger posits a causal mechanism of wealthy parents increasingly giving their kids an edge through superior education. There is almost certainly some truth to this. He implies that are there other causal mechanisms by which inequality today can cause less social mobility in the future. But what about all the other potential reasons, beyond what their Gini Coefficient was in 1985, for varying levels of social mobility between countries as diverse as Japan, France, and New Zealand? 

The most obvious example is just the size of the countries. It’s at least plausible that much bigger countries contain more variety. In fact, if you do something as simple as recreate the Great Gatsby Curve, but use the population of each country as the X-axis, you get a very strong a statistical relationship (log-linear R2 = .64). Big countries have higher IGE. Call it the Moby Dick Curve.   

Alternatively, we might see that some countries tend to specialize more than others.  As a practical example, part of the reason that a country like Finland can have so much equality and social mobility versus America might be that many more of the relatively poorer farmers who trade food for Finnish mobile phones live and reproduce in other countries.  If so, then we might see that if we replace the X-axis with exports as a % of GDP, there could be another statistically significant relationship with IGE. Check (R2 = .48).

Alternatively, different countries might be more or less populated by heterogeneous subgroups that are more likely to reproduce for non-economic reasons with others within their own group. Religious fractionalization versus IGE? Check (R2 = .57). 

Which should we use to predict future social mobility in America: current inequality, projected size of population, projected export / import structure, or projected mix of religious affiliations? Surely all of these, and many more, are potentially relevant.

I’ve picked three obvious examples of confounding factors from a very long potential list (and of course, many of these factors interact with one another, as well as with inequality). These are the “omitted variables” at which Krueger waved his hand in his footnote. What is the relative importance of the various factors not considered in Krueger’s very simple model? In place of any analysis of the question of how stable his curve is in the presence of these other effects — which seems to me to be the central analytical issue at hand — we have Krueger’s bland, evidence-free assertion that there are “many reasons to suspect that it will hold.” Okay, then.

The real drivers of social mobility in America are a lot more complicated than implied by Krueger’s model. This is why Winship was able to point out that various responsible estimates for the mobility-inequality correlations range from .87 to -.15. That is, the various versions of mobility-inequality curves predict everything from extreme social stratification to greater social mobility in the America of 2035. What we see in this case is exactly what statistical theory says we should in the presence of rampant omitted variable bias: wildly unstable parameter estimates. 

In short, Krueger’s curve is not a useful prediction device.

Here is how Corak, a careful scholar who provided much of the data for Krueger’s chart, ended up characterizing the predictive efficacy of the Great Gatsby Curve after the back-and-forth with Winship:

The Great Gatsby Curve is a great communication device to start this sort of conversation, and that is the way I interpret Krueger’s “projections” of what intergenerational mobility will be in the United States when current levels of inequality are reflected in the adult outcomes of today’s children. [Bold added]

So, Krueger’s projections are really “projections.” Fair enough.



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