This dissertation consists of two self-contained essays in macro and monetary economics, organized in the form of two chapters. In the first chapter, I develop a model with limited commitment and endogenous monitoring to study the optimal number and size of banks. Banking arises endogenously because of economies of scale. The planner designates a fraction of ex-ante homogenous agents to be bankers and concentrates monitoring efforts on them. Having fewer bankers reduces total monitoring costs, but this means more deposits per banker. Having more deposits, however, increases the bankers' incentives to divert deposits for their own profit. The result is that the planner needs to give bankers some reward to dissuade such opportunistic behavior. The optimal number of banks is negatively related to the fixed and marginal monitoring costs, impatience, and the temptation to default, but positively related to the return on real investments. To implement efficient allocations, there is a tension between equilibrium with free entry and having positive bank profit for incentive reasons. When the tax on banks is not too high, there exist non-degenerate stationary equilibriums. The equilibrium allocation is optimal only if the government limits entry of banks. One natural way is to charge a tax on bankers and give a transfer to non-bankers; another way is to simply impose a quota by limiting the number of bank charters. In the second chapter, using an overlapping generations model, I propose a resolution of the high household saving puzzle in China by analyzing the impact of the one-child policy and the resulting flattening of age-earning profiles on household saving behavior. Following Ben-Porath's (1967) human capital accumulation technology, with the implementation of the one-child policy, the initial human capital of each young worker who enters into the job market increases, which results in a decrease of the worker's on-the-job-training, and thus a flattening of age-earning profiles. The flattened age-earning profiles encourage younger cohorts to save more for consumption smoothing, and, therefore, provides an explanation for the high saving rates among the young. Both the data and the model demonstrate that the mechanism is valid.

In these essays, I study the implications of macroeconomic policies under the environment with rich heterogeneities of economic agents. The analyses in these essays highlight that income and wealth inequality among agents could change the responses of macroeconomic policies and large aggregate shocks from those in the representative agent models. These results could modify our understanding of economic dynamics and the effect of macroeconomic policies. As an illustration, I focus on the monetary policy in a closed economy model and capital controls in an open economy model. I also develop a new nonlinear and global numerical solution method to analyze a class of heterogeneous-agent macroeconomic models. In the first chapter, ''An Alternative Solution Method for Continuous-Time Heterogeneous Agent Models with Aggregate Shocks'', I propose an alternative solution method for continuous-time heterogeneous agent models with aggregate shocks by extending the Backward Induction method developed initially for discrete-time models by Reiter (2010). The existing methods commonly used in the literature essentially rely on the local linearization and are only applicable to the problems where certainty equivalence with respect to aggregate shocks holds. On the other hand, the proposed method is nonlinear and global with respect to both idiosyncratic and aggregate shocks and thus suitable to investigate models where large aggregate shocks exist or nonlinearity matters. I apply this method to solve a Krusell and Smith (1998) economy and evaluate its performance along two dimensions: accuracy and computation speed. I find that the proposed method is accurate even with large aggregate shocks and high curvature without surrendering computation speed (the baseline economy is solved within a few seconds). This new method is also applied to a model with recursive utility and an Overlapping Generations (OLG) model, and it is able to solve both models quickly and accurately. In the second chapter, ''Consumption Inequality and Monetary Policy in a Heterogeneous-Agent New Keynesian Model'', I consider a continuous-time heterogenous-agent New Keynesian model with the wealth effect of the labor supply and study quantitative implications of additional insurance mechanisms available to the households. Our numerical experiment illustrates cross-sectional consumption inequality increases after a contractionary monetary policy shock which is consistent with the previous empirical result while it contradicts with predictions of the model without the wealth effect of the labor supply. Furthermore, consumption response to contractionary monetary policy shock is dampened, and a cross-sectional average of utilities decreases while the opposite is true in the model without wealth effect. These results suggest that propagation of monetary policy shock to the aggregate variables and welfare depends critically on additional insurance instruments available to agents. The third chapter, ''Capital Controls under Income Heterogeneity'', studies the welfare implication of capital controls under the small open economy model with the idiosyncratic income risks and the borrowing constraints. A calibrated model computes the change in welfare for different levels of capital controls. Compared to the recent studies, welfare gain of capital controls becomes small under agent income heterogeneity. For the economy with low borrowing capacity, capital controls become more effective compared to the baseline case.

"This thesis consists of three essays in monetary economics and international macroeconomics." --

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