Essays on dynamic general equilibrium models: Theory and applications

It has been generally recognized that the representative agent model fails in explaining many phenomena observed in the data. This motivates researchers to study models with heterogeneous agents. This dissertation pursues this line of research. It consists of three chapters. Each chapter is an essay that is independent of other chapters.; Chapter 1 addresses the questions of the cross-sectional variation of capital structures and the relation between capital structure and firms' entry, exit, production, and investment decisions. In so doing, I provide an industry equilibrium model with a continuum of heterogeneous firms. These firms are ex ante identical, but ex post heterogeneous in their idiosyncratic technology shocks. I extend the industry dynamics model developed by Hopenhayn (1992) and Hopenhayn and Rogerson (1993) by incorporating capital structure decisions. To invalidate the Modigliani and Miller capital structure irrelevance theorem, I introduce corporate income taxes, bankruptcy costs, and agency costs. The optimal capital structure trades off tax advantages of debt versus bankruptcy costs plus agency costs of debt.; In a stationary equilibrium, there is a stationary distribution of surviving firms. These firms exhibit a wide variation of capital structures. Under reasonably calibrated parameter values, the model can predict a low industry average leverage ratio observed in the data. Comparative static analysis also reveals that the model can explain the relation between average industry leverage and entry, exit, and industry output, documented by a number of empirical studies.; The remaining two chapters deal with a class of heterogeneous-agent models with incomplete markets, the so called Bewley-style model. The model features a continuum of heterogeneous consumers who are subject to idiosyncratic labor endowment shocks. There is a single firm that rents capital and hires labor to produce output. The firm may be subject to aggregate productivity shocks.; Chapter 2 studies the case with aggregate shocks. It addresses two central open questions: (i) Does there exist a sequential competitive equilibrium? (ii) Does there exist a recursive characterization of sequential competitive equilibria? This chapter provides positive answers to both questions under fairly general conditions. The key is to reformulate the economy in terms of sequences of aggregate distributions. Moreover, this chapter provides a different recursive characterization than the usual one defined in Krusell and Smith (1998). Specifically, I show that for any sequential competitive equilibrium, there exists a life-time utility equivalent competitive equilibrium that is generated by a recursive equilibrium. Such a recursive equilibrium includes expected discounted utility as a state variable.; Chapter 3 studies the Bewley-style model without aggregate shocks. It addresses the question of wealth distribution. As is well known, the standard Bewley-style model with ex ante identical agents, such as Aiyagari (1994), cannot explain the skewness of the wealth distribution. This chapter provides a model with ex ante heterogeneous agents. I first establish the existence of a stationary equilibrium for finitely many types of consumers. These consumers may differ ex ante in their discount factors, borrowing constraints, and shock distributions. I then show analytically that introducing two types of consumers can help explain the skewness of the wealth distribution.