“Intergenerational Mobility and Status Traps in Markov Models of the Evolution of Wealth”, with Lawrence Blume.
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.
“Reassessment of U.S. Educational Assortative Matching with a Discrete Copula Approach”, with Thomas Coleman.
Many questions in economics, such as measuring educational assortative matching or intergenerational socioeconomic mobility, require accurate methods for assessing dependence between variables with discrete support. Traditional metrics often conflate intrinsic dependence with marginal distributions, producing distorted conclusions and inconsistent comparisons across time or populations. This paper, building on the discrete copula framework developed by Geenens (2020,2023), brings to an economics audience a set of margin-invariant and interpretable measures of dependence and correlation for discrete variables, highlighting their conceptual differences. A key example is the generalized Yule's coefficient, a rigorous discrete analog of Spearman's rank correlation for continuous variables. We then use these tools to re-examine U.S. trends in educational assortative matching and revisit previous studies, including Chiappori et al. (2025) and Eika, Mogstad, Zafar (2019). Our findings show that assortative matching rose steadily from the 1960s through at least 2013. Earlier reported flattening or decline, particularly among highly educated partners, appears to be an artifact of shifting marginals and metrics that do not isolate intrinsic dependence.
“Are We There Yet? Understanding Short-Run Growth Dynamics”, with Lawrence Blume. Draft available upon request.
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.
“Formal Measures of Intergenerational Mobility: Bridging Concepts and Interpretations”. Draft available upon request.
We study the formal measures of intergenerational mobility commonly used in the social sciences. Our analysis covers standard approaches, including intergenerational elasticity, measures based on transition matrices, axiomatic mobility indices, and odds ratios, along with the associated log-linear models widely used in sociology. A recurring issue in the literature is that different measures are often employed without clearly specifying the underlying concept of mobility they are intended to capture. In particular, distinctions between structural and exchange mobility, as well as between absolute and relative mobility, are frequently left implicit and lack universally accepted formal definitions. This paper provides a structured classification of existing measures, interprets what each measure captures, and clarifies the relationships among them. By making explicit the conceptual and formal links across different strands of the literature, we aim to improve the comparability and interpretation of empirical findings on intergenerational mobility.
“Dynastic Competition in Intergenerational Model of the Distribution of Wealth”, with Lawrence Blume.
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.