Asset returns in an endogenous growth model 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 a class of stochastic endogenous growth models with uninsurable idiosyncratic income risk. The model economy is populated by infinitely-lived households who own and operate their own business, work for a stock company, and participate in stock and bond markets. Households have time-and state-additive log-utility preferences and production functions exhibit constant returns to scale with respect to produced input factors (physical and human capital). This paper shows that if the idiosyncratic component of productivity and depreciation shocks is unpredictable, then there exists an equilibrium in which households choose not to trade bonds. This no-trade result implies that equilibria can be found by solving a one-agent decision problem. The paper also analyzes the asset return implications of a calibrated model economy with an individual income process that displays realistic variations in idiosyncratic income risk. The calibrated model economy generates a sizable mean equity premium (1%) if the volatility of implied stock returns matches the volatility of observed U.S. stock returns.JEL Classification Numbers: D52, D58, G12.

Wealth Distribution with Random Discount Factors

“…7 The states evolve according to a time-homogeneous Markov chain with transition 6 Krebs (2006) and Toda (2015) also use analytically tractable heterogeneous-agent models with Markovian dynamics, but they do not consider the wealth distribution.…”

Incomplete market dynamics and cross-sectional distributions

“…The construction of a symmetric (no trade) equilibrium in the proof of Theorem 4.6 is standard in the literature (Constantinides and Duffie, 1996;Krebs, 2006;Krueger and Lustig, 2010). Since the intertemporal marginal rates of substitution are independent of wealth, the marginal valuation of income in the next period conditional on the current aggregate state is the same for all agents.…”

“…and abstract from theoretical subtleties such as the transversality condition. Only Krebs (2006) develops the model with Markovian shocks, assets in zero net supply, and discusses the transversality condition.…”

“…Since I use general homothetic CRRA recursive preferences, my results complement those using CARA and subsume those using CRRA as special cases (at least in terms of preferences). All papers with (additive or recursive) CRRA preferences except Krebs (2006) in the literature assume i.i.d. shocks and do not prove properties of equilibria.…”

“…shocks and do not prove properties of equilibria. My paper is technically closest to Krebs (2006), but I relax his assumptions on preferences and stochastic processes, weaken the sufficient condition for equilibrium existence, and provide a numerical algorithm.…”