Recursive equilibrium in endogenous growth models with incomplete markets

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect the aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. For a given history of aggregate shocks, these idiosyncratic human capital shocks are independently distributed over time and identically distributed across agents. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exist recursive equilibria that are simple in the sense that equilibrium prices (returns) only depend on exogenous shocks. Moreover, the allocations associated with simple recursive equilibria are identical to the equilibrium allocations of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.JEL Classification: D50, D52, G50

When is Market Incompleteness Irrelevant for the Price of Aggregate Risk (and when is it not)?

“…6 Krebs (2006) derives the same result in a production economy with human capital accumulation. 7 In a separate class of continuous-time diffusion models, Grossman and Shiller (1982) have demonstrated that idiosyncratic risk has no effect on risk premia, simply because the cross-sectional variance of consumption growth is locally deterministic.…”

Markovian equilibrium in infinite horizon economies with incomplete markets and public policy

“…Of course, in such a setting, one must also verify that the functional equation describing agent preferences in (4) can be solved on a space of bounded value functions. But, in principle, allowing for asymptotic growth in two sector models (for example, Krebs [50]) is not a problem.…”

“…Finally, the assumptions on the boundedeness of the state space can be relaxed, allowing for models with unbounded growth, for example, in the two sector incomplete markets economy studied by Krebs [50]. Using the methods in Morand and Re¤ett [62], one can use pure lattice theoretic …xed point constructions to study the operator Ah, and all the main results hold.…”

“…Here, J is a …nite set of agents. For convenience (and without loss of generality), we normalize the mass of agents to be the unit interval, and further assume that j = 1 J > 0; of each type j: 6 5 We can incorporate period-by-period uninsured idiosyncratic shocks, as for example, in Krebs [50], into our framework without changing the structure of our argument. We choose the form of idiosyncratic risk based upon making the environment as close as possible to Becker and Zilcha [8].…”

“…Recursive versions of these models have been extended in a deterministic setting by Becker [5][6] (see Becker and Boyd [7] for a review of this literature) and Townsend [79], and in a stochastic setting in Scheinkman and Weiss [74], Becker and Zilcha [8], Judd and Gasper [43], Judd, Kubler, and Schmedders [44] [45], and Kubler, and Schmedders [53]. In related work, a class of multisector, stochastic, incomplete markets models in the "Ramsey style" has been developed in a series of interesting papers by Krebs [49] [50]. In this work, the use of a two sector incomplete markets economy with a …nite number of agents that have access to both physical and human capital, but face uninsured income risk is introduced.…”