In the analysis of efficiency measures, the statistical Stochastic Frontier Analysis (SFA) and linear programming Data Envelopment Analysis (DEA) estimators have been widely applied. This dissertation is centered around two main goals. First, this dissertation addresses respectively the individual limitations of SFA and DEA models in chapters 2 and 3 using Monte Carlo (MC) simulations. Motivated by the lack of justification for the choice of inefficiency distributions in MC simulations, chapter 2 develops the statistical parameters, i.e., mean and standard deviation of the inefficiency distributions - truncated normal, half normal, and exponential. MC simulations results show that within the conventional and proposed approaches, misspecification of the inefficiency distribution matters. More precisely, within the proposed approach, the misspecified truncated normal SFA model provides the smallest mean absolute deviation and mean square error when the inefficiency distribution is a half normal. Chapter 3 examines several misspecifications of the DEA efficiency measures while accounting for the stochastic inefficiency distributions of truncated normal, half normal, and exponential derived in chapter 2. MC simulations were conducted to examine the performance of the DEA model under two different data generating processes - logarithm and level, and across five different scenarios - inefficiency distributions, sample sizes, production functions, input distributions, and curse of dimensionality. The results caution DEA practitioners concerning the accuracy of their estimates and the implications within proposed and conventional approaches of the inefficiency distributions. Second, this dissertation presents in chapter 4 an empirical assessment of the liquidity and solvency financial factors on the cost efficiency measures of U.S banks while accounting for regulatory, macroeconomic, and bank internal factors. The results suggest that the liquidity and solvency financial factors negatively impacted the cost efficiency measures of U.S banks from 2005 to 2017. Moreover, during the financial crisis, U.S banks were inefficient in comparison to the tranquil period, and the solvency financial factor insignificantly impacted the cost efficiency measures. In addition, U.S banks’ liquidity financial factor negatively collapsed due to contagion during the financial crisis.