Pre-print, Working paper: This paper investigates time consistent policies and reforms of intergenerational transfers. If the weight the Government gives to the living elderly is low enough, successive Governments will implement policies with equitable results across generations, even if their social welfare function is not equitable with the unborn. The ratio of Government public debt to GDP will not change over time, and the consumption flows of successive generations will grow at the natural rate of the economy. However, if the Government gives a higher weight to the elderly, the ratio of public debt to GDP will increase over time. Then, future generations will have to pay higher and higher taxes and consume less and less. Demographic transition does not interfere with these results although it makes every consumer poorer. However, there is the possibility that the weight of the elderly in Government preferences has increased recently, and that some Western democracies are entering a process of increasing public indebtedness and immiserisation of future generations.