couple of papers that ask whether past trends towards deregulation or the creation of a single market in europe have encouraged convergence towards a best - practice frontier. unfortunately, a common result in the literature is that there is convergence towards average efficiency levels rather than convergence towards the best efficiency levels. this suggests that some isolated financial institutions may be pushing the frontier forward while the majority are falling steadily behind ( a failure of the catching - up hypothesis ). it is hard to interpret this result : is it good news because it means that technology is improving rapidly? or is it a sign that even banks with low efficiency can survive, meaning that there is little incentive to adopt innovations? one may speculate that the answers depend on how one defines the best - practice frontier and whether it is valid to assume that the same technology is available to all institutions. it is common to link the efficiency of individual banks to environmental variables, the quality of management, wage dispersion, or information technology investment. such an approach may help to identify unrealistic assumptions concerning the availability of a common technology. i have come to the third part of my remarks. following the recent financial turmoil, what are the priorities in the study of productivity in financial services? i have already mentioned that the recent wave of restructuring is likely to increase the size of the average bank. as i have said, this means we need better tools to measure not only scale economies but also scope economies, as activities that were once performed by separate institutions are brought under a single roof. on the issue of optimal size, public interventions have prompted some recent commentators to observe that while some banks are “ too big to fail ” others may be “ too big to save ”. it is not clear that there is such a trade - off between scale economies and financial stability. rather, the “ too big to fail ” label stresses the need for better international co - operation in regulation and supervision, an objective that should by now be familiar but that has takes on greater urgency as the international links in the financial industry become more apparent. another aspect of financial productivity that merits closer scrutiny is the treatment of risk. i am not going to add to the discussion of “ black swans ” and the impact of rare events on value - at - risk models used by traders ( and regulators ). instead, i am referring to the more “ mundane ” issues raised in my previous remarks. in terms of measuring bank output, interest flows usually include a risk premium that will generally be more important when

? when banks double the value of the assets and liabilities on their balance sheet, this does not necessarily double the number of transactions, or the amount of labour or physical capital required to produce the necessary services. this observation seems to undermine the justification for deflating asset values using a general price index such as the gdp deflator or the consumer price index. furthermore, the recent fall in asset prices and the de - leveraging process under way may lead to some surprising results in the breakdown of financial services into prices and quantities. let me turn to my second set of remarks, concerning existing measures of productivity in the financial sector and what they tell us about its sources. perhaps the most natural starting point is the measurement of scale economies, an issue on which academic researchers have long provided advice for competition policy. empirical evidence on returns to scale in the banking industry has sometimes suggested that larger institutions benefit from greater cost efficiency. however, studies of mergers and acquisitions have often failed to find such improvements. i think it is important to improve methods in this area for at least two reasons. first, increasing european financial market integration is likely to raise the size of the average bank. central banks often repeat that the european financial services industry is excessively fragmented. increasing integration should allow a more efficient provision of financial services, improving the allocation of capital to investments with better risk - return profiles and therefore raising the potential for economic growth. second, the recent depressed value of financial equity and public intervention in the banking sector to rescue distressed institutions will probably accelerate the process of mergers and acquisitions as the outlook recovers. thus the existence and extent of scale economies remain timely questions for research and policy. scale economies are only one source of productivity growth. what used to be called scope economies are improvements in efficiency obtained by altering the mix of outputs or the mix of inputs. in academic research, these have proven even more difficult to measure than scale economies. however, i would encourage you to think about these issues in light of recent events. the demise of the investment bank suggests a return to universal banking, with large groups taking over specialised financial institutions. such a development may be motivated by a need to improve risk management, but it could also bring benefits in terms of an improved mix of different financial outputs that are jointly produced. finally, an additional source of productivity growth is efficiency change, meaning the extent to which individual banks move towards ( or away from ) the best - practice frontier. again, looking at the conference programme, i notice a