the spectrum that are part of the bank ’ s staff tool box. vii chart 5 : estimates of potential output growth from four different models year - over - year percentage change % integrated framework extended multivariate filter multivariate state - space framework basic multivariate filter source : bank of canada estimates last observation : 2018q1 models that incorporate an economic structure are especially useful for projecting tlp growth, since tlp is based on variables and relationships that are difficult to measure and predict. tli growth is comparatively easier to forecast because it is based on accurately observed labour market outcomes : the employment rate, the working - age population and average hours worked. in contrast, tlp growth depends on two variables that are less concrete and therefore more challenging to observe precisely. the first of these, capital deepening, is a measure of growth in the ratio of capital per hour worked. viii the second is a more elusive concept called trend total factor productivity, or tfp. while we have some observable measures of investment and capital stock growth, we do not have the same for trend tfp — which essentially includes everything affecting firms ’ productivity that isn ’ t captured by capital stock growth. these “ residual ” factors include, for example, technological improvements and the impact of education and training. ix another way that the bank manages the uncertainty around potential output growth is by conducting an in - depth review of our projections on an annual basis. first, economic data are regularly revised, so for that reason alone an annual review makes sense. also, our empirical techniques are “ living ” in a sense — we are continually improving them as we learn from experience and ongoing research. x plus, in the annual reassessment, we further account for uncertainty by publishing ranges around our estimates and projections that expand with time. we also list the factors that could lead potential growth to be lower or higher within those ranges. xi i would like to stress that the bank recognizes the difficulties associated with measuring potential and the related uncertainty, and so takes a deliberate and rigorous approach to managing this uncertainty. we work hard to ensure that our models evolve in line with prevailing best practices. and on top of using multiple techniques, we corroborate the models ’ results against other measures of capacity and inflation, and then apply wellinformed judgment. finally, the uncertainty around these estimates is taken into account in the formulation of monetary policy. this helps us ensure that our estimates and our policy decisions are consistent with our broader economic outlook

? 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