factors may make the true decline in the equilibrium real interest rate larger than estimated in macroeconomic models. for example, older people may save more than predicted by the life - cycle theory if they want to leave a bequest to their heirs, putting additional downward pressure on the equilibrium rate. the degree of risk aversion may also change with age : if older people were systematically more risk - averse than the young, the accumulation of precautionary savings would lead to a higher than predicted savings rate and a lower than predicted real rate. 21 in addition, private savings rates may be significantly affected by pension reforms. 22 on the other hand, there is another set of factors that may mitigate the estimated decline in real interest rates. for instance, models typically assume that population ageing does not affect the formation of human capital. with a gradual increase in the relative scarcity of labour, the return to education would be likely to increase, which would moderate the increase in capital intensity as the quality - adjusted labour input would not decline. 23 such knock - on effects working through labour and possibly total factor productivity are typically absent from the available model simulations as they are quite difficult to quantify. furthermore, the models used to simulate the impact of ageing on the macroeconomy are typically not designed to investigate how fertility rates may endogenously evolve with ageing. 24 finally, these models do not usually take into account the effects of ageing on risk premia : if demographic developments were to lead to a substantial increase in government debt, resulting from a lack of sufficient pension reforms, the risk premia embedded in government bond yields would become larger, pushing interest rates upwards and undermining growth prospects. 25 dellavigna and pollet ( 2005 ). bakshi and chen ( 1994 ). miles ( 2002 ). medeiros ( 2000 ) finds that ageing represents an opportunity for future generations to invest in education, since a shrinking labour force contributes to higher capital intensity ratios and thereby higher labour earnings, which boost the returns to human capital investments. de la croix, lindh and malmberg ( 2006 ) point out that longer life expectancy raises the expected return from human capital investments and thus creates incentives to accumulate more education and training. an exception is becker, murphy and tamura ( 1990 ), who built a model that endogenises the human capital investment decision and also its link to fertility decisions. in their model, if the stock of physical capital is relatively large,

growth diverges from potential growth. in the textbook representation it is assumed that the monetary policy stance is calibrated to close the gap between activity and potential, the socalled “ output gap ”. therefore, if potential changes, the output gap can change as well, and the appropriate stance of monetary policy has to be adjusted. but exactly how falling potential growth affects monetary policy is not straightforward. at first sight, one would think that it would make achieving price stability easier as, for a given level of output, the output gap that monetary policy has to close is smaller and inflation would return to the central bank ’ s objective more quickly. yet this would be a pyrrhic victory, as it implies that the central bank would have to reign in its accommodative policy while there are still very high levels of structural unemployment. and in any event, the reality is more complex. as i already intimated, if potential growth falls, expectations of incomes and profits fall as well, and firms and households are likely to consume and invest less today. such a feedback from potential growth to current growth would in fact have the opposite effect – it would prevent the output gap from closing – and create downward pressure on inflation. in other words, falling potential would not make the task of monetary policy easier, but harder. second, to steer output back towards potential, monetary policy aims to bring its policy interest rates as close as possible to what is known as the “ equilibrium ” interest rate – that is, the interest rate where resources are fully employed in the economy and inflation is stable. a lower rate of potential growth can however reduce the equilibrium interest rate, as for example lower growth in either productivity or labour supply reduces demand for investment. and this can in turn create constraints for monetary policy, since in order to “ shadow ” the equilibrium rate the central bank may have to reduce its policy rates to zero or lower. average of imf, commission and oecd estimates. bis central bankers ’ speeches moreover, it may have keep rates at those levels more often in the future when the economy slumps and inflation deviates from its objective. it is difficult to quantify exactly these relationships as they involve unobservable concepts such as the output gap and the equilibrium interest rate, which are often very difficult to estimate in real - time and subject to revisions. but the outcomes we can observe suggest that falling potential growth has been accompanied by a widening not a closing output gap, with inflation following