To me that is an empirical question. Do higher interest rates incentivise saving? Do lower interest rates encourage people to save more to meet a savings target? Or is saving unaffected; people save what is left over after paying for everything else?
When I studied macro we had a diagram which showed the loanable funds theory of interest rates. (The interest rate is the price that matches the number of borrowers to the number of savers.) In this diagram the supply curve was vertical, meaning that the level of saving was independent of the interest rate. I always wondered if that really was the case. As I say it is an empirical question.
Using some data I have to hand (The BoE's useful three centuries of data series). I have done a scatter chart.
|Source:BoE and others|
The answer is that the savings rate is higher when interest rates are higher. The R squared is 0.59 suggesting that interest rates explain 60% of the increase in savings. In the loanable funds model the supply curve would be upward sloping.
The one issue I am aware of is that I have not controlled for inflation. It would be better to use real interest rates, which I will do when I can look for another data series.