Stasis, Churn, and Growth

Paul Krugman and Brad DeLong have criticized Tyler (original and reply) on income mobility. In an effort to clarify, let us consider some simple societies. In each society there are three families, A,B,and C, each with two generations.

In society one there is no generational mobility, each generation has the same income as the previous generation. Let’s call this society Stasis.

Society Stasis
Family Generation 1 Generation 2
A 100 100
B 50 50
C 25 25
Total 175 175


In the second society, some generations rise and some generations fall but there is no growth, let’s call this society Churn.

Society Churn
Family Generation 1 Generation 2
A 100 25
B 50 50
C 25 100
Total 175 175


Brad DeLong thinks that Churn is “unambiguously” better than Stasis but he doesn’t tell us how he arrived at this conclusion. Paul Krugman also seems (it is a bit unclear) to think that Churn is better than Stasis and he adds that anyone who thinks otherwise is anti-American.

If someone likes the idea of riches going to rags almost as much as they like the idea of rags going to riches then I can see why they would think that Churn is unambiguously better than Stasis. In economics, however, we try to evaluate outcomes with more than our aesthetic preferences or moods and when we look more carefully at the preferences of the people in these societies I see ambiguity or, to be more precise, not much to choose between Stasis and Churn.

The most obvious metric is total aggregate utility and in a static sense total aggregate utility is identical in each society and in each generation. So not much to choose between Stasis and Churn on aggregate utility grounds. What about an individual choosing which society to join from behind a veil of ignorance? Again, no go, there is no difference in expected utility between Stasis and Churn from behind the veil of ignorance.

Tyler moves beyond static utility to consider some dynamic issues which could make Churn worse than Stasis, namely “habit formation and frame of reference effects.” I can see those possibilities but in my view they don’t resolve the tie.

We might resolve the tie by adding more considerations to the model; for example, perhaps society Churn has more liberty (desert/justice etc.) and that is why it churns. In this case, I personally would break the tie in favor of Churn but then the deciding factor would have been liberty not mobility. Thus, let’s keep the focus on mobility and look at one more society.

Let us consider a third society, Growth.

Society Growth
Family Generation 1 Generation 2
A 100 200
B 50 100
C 25 50
Total 175 350


Here at last we have some non-ambiguity. Growth is better than Stasis or Churn; aggregate utility is increasing over time and indeed every family is better off in Growth than in Stasis or Churn. Notice, however, that Growth has relative stasis, that is, there is no relative generational mobility. So now we come to the crux of the issue. Suppose that you agree with me that there isn’t much to choose between Stasis and Churn and that Growth is better than either Stasis or Churn. Do you want to add some Churn to Growth? Why? If there isn’t much difference between Stasis and Churn then how can adding Churn to Growth make it better? It doesn’t and that is why economic mobility measures are overrated. What we should care about is growth.


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