Intergenerational interactions in human capital accumulation

We analyze an economy populated by a sequence of generations who decide over their consumption and investment in human capital of their immediate descendants. The objective of the paper is twofold: firstly, to identify the impact of strategic interactions between consecutive generations on the time path of human capital accumulation. To this end, we characterize the Markov perfect equilibrium (MPE) in such an economy and derive the sufficient conditions for its existence and uniqueness. We then benchmark our results against an optimal but time-inconsistent policy which abstracts from strategic interactions between generations. We prove analytically that human capital accumulation is unambiguously lower in the “strategic” case than in the optimal, “non-strategic” case. The second objective of the current paper is to work out a functional parametrization of the model, suitable for obtaining clear-cut results on the monotonicity of the (unique) Markov perfect equilibrium policy and the optimal policy. We then carry out a sensitivity analysis under this parametrization, thereby assessing quantitatively the magnitude of discrepancies between human capital accumulation paths whether strategic interactions between consecutive generations are taken into account or not.human capital, intergenerational interactions, Markov perfect equilibrium, stochastic transition, constructive approach

Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk

We present a new approach to studying equilibrium dynamics in a class of stochastic games with a continuum of players with private types and strategic complementarities. We introduce a suitable equilibrium concept, called Markov Stationary Nash Distributional Equilibrium (MSNDE), prove its existence, and determine comparative statics of equilibrium paths and the steady state invariant distributions to which they converge. Finally, we provide numerous applications of our results including: dynamic models of growth with status concerns, social distance, and paternalistic bequest with endogenous preference for consumption

A qualitative theory of large games with strategic complementarities

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators defined on the space of distributions partially ordered with respect to the first-order stochastic dominance, we prove existence of a greatest and least distributional Nash equilibrium. In particular, we obtain our results under a different set of conditions than those in the existing literature. Moreover, we provide computable monotone distributional equilibrium comparative statics with respect to the parameters of the game. Finally, we apply our results to models of social distance, large stopping games, keeping up with the Joneses, as well as a general class of linear non-atomic games