This thesis consists of three substantive essays on bank efficiency, each constituting a separate chapter. The first essay (Chapter 2) considers banks' functional diversification and its effects on their operating performance. The study classifies banking institutions into financial conglomerates and specialised banks based on their financial characteristics and employs the non-parametric Data Envelopment Analysis (DEA) method to derive their cost and profit efficiencies. The empirical analysis covers banking institutions operating in the ten EU accession countries between 2001 and 2003. The findings suggest that diversification does not improve either cost or profit efficiencies of the sampled banks and are congruent with growing empirical evidence of a "diversification discount" in the financial sector. The second essay (Chapter 3) offers an alternative approach for valid inference in the two-stage DEA framework based on a double bootstrap method. Acknowledging the computational burden associated with double bootstrap procedures, it also provides an algorithm based on deterministic stopping rules, which is less computationally demanding. Monte Carlo evidence indicates that the suggested double bootstrap confidence interval estimators offer a considerable improvement over their single bootstrap counterparts in terms of coverage rates. Moreover, there is also evidence that convergence of the confidence intervals towards their nominal significance levels is non-monotonic. The final essay (Chapter 4) examines the relationship between efficiency changes and stock market reaction to bank merger announcements in Europe and the US over 1997-2003. Changes in cost and profit efficiencies are calculated using the non-parametric DEA method one year prior and three years following the merger announcement. The findings suggest that the stock markets are able to identify efficiency enhancing mergers upon their announcement. Evidence also indicates that it is the profit rather than the cost efficiency measure that is more closely related to what market participants use to forecast post merger performance of the consolidated banks.