My dissertation consists of two chapters. The common theme that unifies these chapters is the determination of optimal government policy when the government cannot commit. In the first chapter, I investigate why sovereign defaults are often accompanied by significant declines in economic aggregates, and what determines the decisions of the governments to default on their debts. I develop a model of domestic default in a production economy with financial frictions. The government finances exogenous spending with distorting taxes on labor and by issuing debt. I assume that the government cannot commit to repay its debt and characterize optimal government policies in a Markov equilibrium. A key feature of the model is that government bonds are used as collateral. Hence, defaulting on debt tightens firms' collateral constraints, thereby inducing firms to reduce their demand for labor and cut back on production. This fall in output implies defaulting on debt is costly for the government. The government trades off these costs against the distortions from taxes needed to repay the debt. Defaults occur when the costs of distorting taxes of repaying the debt outweighs the costs of output loss following default. I find that the government is more likely to default if the economy encounters a large negative TFP shock after a sequence of positive shocks. The reason is that in response to positive TFP shocks, firms increase investment and build up a high level of capital stock. If the economy is then hit with a negative shock, the collateral level is relatively high, so the cost of defaulting is lower. I calibrate the model separately to Argentine and Italian data. In the model, Argentina sustains a lower debt level with high default rate while Italy sustains a higher debt level with negligible default rate. This finding is due to the fact that the TFP process in Argentina is much more volatile, which induces its government to default more often. Furthermore, the model successfully captures the declines in output and investment associated with defaults. Output drops around 10% during defaults in the Argentine version of my model, which is close to the data; while in a counterfactual analysis, output decreases around 5% if Italy defaults. In the second chapter, joint with Zoe Leiyu Xie, we characterize a Markov perfect equilibrium in a stochastic general equilibrium search model, where a benevolent government without commitment makes unemployment insurance policy. The policy is time consistent, as opposed to the optimal policy implemented by a Ramsey government. We contrast the Markov policy with the optimal policy. In the steady state, the Markov policy is associated with higher benefits and higher unemployment than the optimal policy. In response to a fall in productivity, the optimal policy rises on impact and then falls significantly below the steady state. In contrast, the Markov policy starts below the steady state and increases monotonically as the economy recovers. Compared to the optimal policy, the Markov policy leads to a slower recovery of unemployment. The reason behind the differences is the lack of commitment by the Markov government. The comparison highlights that with government commitment, unemployment insurance policy leads to a faster recovery of unemployment during recession. This paper thus offers a theory for why the government increases the generosity of unemployment insurance during a recession, and how such policies contribute to slow recovery in unemployment.