This paper proposes some new measures of intergenerational persistence based on the idea of characterizing the memory of origin in the stochastic process that links the socioeconomic classes of parents and children. We introduce “memory curves” for all future generations given any initial condition of class for a family dynasty, which reveal how initial conditions interact with the transition process between parents and children to create mobility and persistence. We also propose ways to aggregate information across different classes to produce overall characterizations of mobility in the population. To illustrate our measures, we estimate occupational “memory curves” using U.S. survey data. Our findings show that, on average, the memory of initial conditions dissipates largely within three generations, though there is meaningful heterogeneity in mobility rates across dynasties originating from different occupational classes.

Recent history has focused our attention on the consequences of complex production networks: the supply chain problem. Efficient paths in infinite-horizon growth models are often characterized by a price turnpike, a single ray of current-value prices to which competitive prices will converge even though consumption paths may be much less well-behaved. Convergence times, when addressed at all, are described with asymptotic convergence rates. Our interest is in the fragility of growth paths, by which we mean how difficult it is to approach the turnpike. Fragility is not just about long-run convergence rates, but also about the short- and middle-run behavior of price paths, and how long the short and middle run are. We address these questions for economies with constant-returns-to-scale production technologies. We bound worst-case rates of convergence to the turnpike, relate the bounds to properties of the production network topology, and demonstrate that the short-run behavior of competitive price paths can be quite wild far from the long-run steady state.

This paper studies the evolution of wealth in one-parent, one-child families, where parents invest in their child’s human capital. These investments stochastically determine the child’s future wealth. The production of wealth from parental investment is modeled using a stepping-stone technology, which captures the idea that human capital thresholds must be met to achieve distinct wealth levels. Without shocks, the model leads to multiple attractors, interpreted as status traps. In stochastic environment, mobility is possible in any given period. A unique stationary distribution characterizes the “long-term” fractions of time families spend in various wealth classes. We relate the shape of this distribution, when noise is small, to the behavior of the zero-shock system. Our analysis shows that attractors in the zero-shock system play a fundamental role in shaping the stationary distribution and that typically only one attractor is more robust, dominating other attractors under slight stochastic perturbations. This result challenges certain approaches in development and macroeconomic literature that rely on deterministic dynamic system intuition.

We explore in depth the statistical measures of intergenerational mobility employed by social scientists. We cover standard measures of mobility, such as intergenerational elasticity, measures developed within Markov chain analysis, axiomatic approaches to measuring intergenerational mobility, odds ratios popular in sociology, etc. The literature on intergenerational mobility often does not specify the type of mobility being studied; however, the distinction between structural and exchange mobility, or absolute and relative mobility, is crucial. Our aim is to classify different measures of intergenerational mobility, carefully interpret them, and show how these measures are interconnected.

This is a development of “Intergenerational Mobility and Status Traps in Markov Models of the Evolution of Wealth”, where we allow the effect of a given parental investment to depend on investments of other parents. Such a richer framework facilitates the discussion of competition between dynasties which may additionally disincentivize investment behavior of poorer parents.