perhaps we or others may do so in the future. it is by no means evident to us that we currently have - - or will be able to find - - a measure of equity premiums or related indicators that convincingly presage an emerging bubble. short of such a measure, i find it difficult to conceive of an adequate degree of central bank certainty to justify the scale of preemptive tightening that would likely be necessary to neutralize a bubble. as we delve deeper into the questions raised by the developments of recent years, the interplay between structural productivity growth and equity premiums, so evident during the past business cycle, is bound to play a prominent role. we need particularly to determine whether the periodic emergence of market bubbles, which have occurred so often in the past, is inevitable going forward. as financial wealth becomes an ever - more - important determinant of activity, we need also to understand far better how changing equity premiums affect and reflect real and financial investment decisions. if the equity premium has so demonstrable an influence on our economies as it appears to have, the value of further investigation of this topic is evident. * * * from footnote 3, k ( e / p ) = d / p = r + b - g, where d is current dividends. hence, d / p - r = b - g in conclusion, the endeavors of policymakers to stabilize our economies require a functioning model of the way our economies work. increasingly, it appears that this model needs to embody movements in equity premiums and the development of bubbles if it is to explain history. any useful model needs to credibly simulate counterfactual alternatives. we must remember that structural models that do a poor job of explaining history presumably also will provide an incomplete basis for policymaking. often the internal structure of such models has been employed to evaluate the effect of various stabilization policies. but the results from models whose internal structure cannot successfully replicate key features of cyclical behavior must be interpreted carefully. the recent importance of movements in equity premiums and asset bubbles suggests the need to better understand and integrate these concepts into the models used for policy analysis. i anticipate productive discussion of these and other issues related to stabilization policy over the next couple of days.

right balance between efficiency and risk, and because of a widespread recognition of the more integrated nature of national financial systems, success in this area would not have been possible in the past and will not be possible in the future without continued close cooperation between the official and private sectors, within and across national borders. i am very pleased to be part of an institution that has been at the center of these initiatives. we expect to continue to play that role in the future. it is worth stepping back a bit to describe some of the broad forces shaping the payments system that need to inform our priorities going forward. • we expect to see very rapid growth in the overall volume of financial transactions and the accompanying burdens on the payments infrastructure. in the mature economies, particularly in the u. s. and the u. k., we have seen the volume of financial transactions increase much more rapidly than gdp. this trend, which has much to do with the nexus of technology and financial innovation, shows no sign of slowing. with the bulk of world gdp and savings outside the united states, a significant share of it in countries growing more rapidly than the united states and with substantial financial development still ahead of them, it seems reasonable to plan for a world in which this extraordinary trajectory of growth in financial transactions continues. • as national financial systems become more integrated and financial institutions more global, payments systems increasingly operate across countries and legal regimes, and the scale of cross - border financial transactions has increased dramatically. the payments infrastructure of the global financial system is a complex patchwork of national and cross - border systems, not seamless, not uniform, but closely connected. this increases the exposure of any settlement system to developments across borders. and it means that the major international financial institutions face a substantially greater diversity of exposures, given the multiple systems in which they operate. • payments activity has become more concentrated in a smaller number of global financial institutions ; fewer major participants in payments systems now account for a larger share of volume and exposures in those systems. this has important implications for how we think about the vulnerability of the system to a financial or operational failure and about the financial resources that system operators need to maintain. • the growth in the over - the - counter derivatives market has advanced much more rapidly than the speed of improvement of important parts of the infrastructure that support the market, including contract documentation and post - trade processing, and the certainty of the legal arrangements for cross - product netting. this introduces a potential source of uncertainty that can