Heterogeneous dynasties and long-run mobility

What is this research about and why did you do it?

Recent empirical work documents significant long-run wealth-rank correlations. This is a puzzle, in that the standard macro models of wealth dynamics generate a realistic wealth distribution but cannot capture these patterns. Adding long intergenerational autocorrelation in earnings and in the rate of return to wealth is bound to generate fatter tails in the wealth distributions than we observe. We then set ourselves the task of identifying a parsimonious extension of the standard model of wealth dynamics to account for these novel facts on the long-run persistence of wealth-ranks as well as for the observed moments of the wealth distribution.

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How did you answer this question?

We study a standard heterogeneous agent macro model of wealth dynamics and extend it to introduce persistent heterogeneity in the rate of return to wealth across generations; that is, we allow households in some dynasties to have their wealth grow faster on average than households in other dynasties. While we do not take a stand on the precise interpretation of this form of persistent heterogeneity, we note that it can be seen as a formalization of a latent factor representation of various dynastic characteristics such as abilities, preferences, dynastic network connections, occupational persistence and so on.

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What did you find?

We find that an analytic characterization of asymptotic wealth-ranks is easily obtained from rank-based models of wealth dynamics (where the growth rate of wealth depends on the wealth-rank) that approximate standard heterogeneous agent models well.  

In simulations, we find that: i) rank-based models with persistent heterogeneity match the wealth distribution as well as short-run and long-run wealth-rank correlations (Table 1); ii) auto-correlated returns to wealth across generations induce, as expected, excessively unequal wealth distributions; furthermore, they cannot capture significant long-run correlations without counterfactually high short-term intergenerational correlations (Table 1 and Figure 1).

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Upper part: Average wealth shares from 1,000 simulations of the different models - data from the 2007 Survey of Consumer Finances. Lower part: Average coefficients from regressions of child rank on parent rank and grandparent rank from 1,000 simulations of the different models - data from Danish wealth holdings for three generations in Boserup, Kopczuk, and Kreiner (2014). Average coefficient from regressions of household rank in generation t on household rank in generation t-*23 (585 years) from 1,000 simulations of the different models - data from estimates of very long-run (585 years) dynastic wealth holdings in Florence, Italy, in Barone and Mocetti (2016).

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Rank correlations across multiple generations from 1,000 simulations of the permanently heterogeneous rank-based and auto-correlated returns models.

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What implications does this have for the research on wealth concentration or economic inequality?

Models of wealth dynamics need to allow for stochastic returns to wealth in addition to earning heterogeneity (Benhabib et al., 2017, 2019). Furthermore, persistent heterogeneity in the rate of return across generations is an important factor to match relevant aspects of short- and long-run wealth mobility in the data. To this end, rank-based models are useful research and teaching tools, in that their implications for long-run wealth-ranks can be easily obtained analytically and simulated computationally.

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What are the next steps in your agenda?

The structure of wealth-rank correlations in models with persistent heterogeneity is suggestive of persistent institutional factors as mechanisms for sustaining long-run wealth persistence, rather than of direct intergenerational mechanisms like cultural transmission. Identifying these institutional factors is our next aim.

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Citation and related resources

This paper can be cited as follows: Benhabib, J., Bisin, A., and Fernholz, R. T. (2022) "Heterogeneous dynasties and long-run mobility." The Economic Journal, 132(643), pp. 906-925.

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References:

• Benhabib, J., Bisin., A., and Luo, M. (2017) "Earnings inequality and other determinants of wealth inequality." American Economic Review, 107(5), pp. 593-597.
• Benhabib, J., Bisin, A., and Luo, M. (2017) "Wealth distribution and social mobility in the US: a quantitative approach." American Economic Review, 109(5), pp. 1623-1647.

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