In 2004, the World Bank (IDA) introduced the Debt Sustainability Framework (DSF) for low-income countries, so called "traffic light system", based on which IDA determines the grant/loan ratio to be allocated to each recipient country for each fiscal year. For instance, the country receives 100% grant aid, if the country is classified as "red light" (i.e. unsustainable debt level), under the traffic light system. The World Bank and IMF have been requesting the other institutions (aid donors, export credit agencies and private lenders) to comply with this system, in order to maintain developing countries' debt sustainability and to avoid another debt crisis. Since its introduction, there is a growing concern for some actual and potential shortcomings embedded in the system. My dissertation attempts to address three major issues among them in each essay with strong emphasis on policy implications. The first issue is the free rider problem. Some of the other institutions are suspected to be not complying with the system, and to have been providing non-concessional loans to the "red light" country, by abusing their debt carrying capacity which is improved by grant aid from IDA and other donors. The first chapter develops a theoretical model of the free rider problem, and tests empirically for free riding. The second chapter examines the traffic light system's implicit assumption on the monotonic relationship between the debt stock and the default probability, and provides a theoretical model as well as empirical evidence of non-monotonicity. Panel Logit/Probit analysis indicates that the relationship is "N-shaped" which implies that there exist a paradoxical zone in which default probability could decrease rather than increase with debt stock. The third chapter addresses the possibility that the traffic light system unduly constrains the ability of recipient countries to finance their development goals. The theoretical model and numerical simulations show what the sustainable debt level should be and how "red light" shock affects the long-run economic growth of the recipient country.