This dissertation consists of four essays which investigate efficiency analysis, especially when non-discretionary inputs exist. A new approach of the multi-stage Data Envelopment Analysis (DEA) for non-discretionary inputs, statistical inference discussions, and applications are provided. In the first essay, I propose a multi-stage DEA model to address the non-discretionary input issue, and provide a simulation analysis that illustrates the implementation and potential advantages of the new approach relative to the leading existing multi-stage models of non-discretionary inputs, such as Ruggiero's 1998 model and Fried, Lovell, Schmidt, and Yaisawarng's 2002 model. Furthermore, the simulation results also suggest that the constant returns to scale assumption seems to be preferred when observations have similar sizes, but variable returns to scale may be more appropriate when their scales are different. In the second essay, I make comments on Simar and Wilson work of 2007. My simulation evidence shows that traditional statistical inference does not underperform the bootstrap process proposed by Simar and Wilson. Moreover, my results also show that the truncated model recommended by Simar and Wilson does not outperform the tobit model in terms of statistical inference. Therefore, the traditional method, t-test, and the tobit model should continue to be considered applicable tools for a multi-stage DEA model with non-discretionary inputs, despite contrary claims by Simar and Wilson. The third essay raises an example of applying my new approach to data from Texas school districts. The results suggest that a lagged variable (e.g. students' performance in the previous year), a variable which has been used in the literature, may not play an important role in determining efficiency scores. This implies that one may not need access to panel data on individual scores to study school efficiency. My final essay applies a standard DEA model and the Malmquist productivity index to commercial banks in Thailand in order to compare their efficiency and productivity before and after Thailand?s Financial Sector Master Plan (FSMP) that was implemented in 2004.