There are 2 logical cases to be made for the correlation between interest rates and savings rate of a country.
Case 1 -Intuitively, the real interest rates and savings rate should be directly proportional. In this negative yielding environment, lower interest rates should disincentivize savers to save as they're getting lower yields and constantly eroding purchasing power due to inflation should encourage them to spend more. Also, intuitively, lower rates should encourage more borrowing as financing costs drop, leading to higher spending and consumption. So with higher rates,savings should go higher and with lower rates savings should go lower. ( Now this makes sense in the era of central banks' dominance over interest rates, with 'forward looking' guidance and micro managing everything.
Case 2- In an ideal world, Supply and demand of credit should dictate interest rates (not central banks). Higher demand for credit should make the interest rates go up, similarly high savings and lower demand for credit should make the rates go lower. In an ideal world, the market decides the interest rates. So that makes savings rate and interest rate inversely proportional. High savings should be accompanied by lower rates and low savings should be accompanied by higher rates.
Since we don't live in an ideal world, lets look at some data.
Indian real interest have roughly been on an upward trend since after the Financial crisis of '08.
Indian savings rate has been on a downward trend in the same period.
Lets have a look at U.S's trends.
The famous/ infamous QE reflects in this chart. With real interest dropping to 1% in the aftermath of the great financial crisis. Clearly, a downward trend as opposed to India in the same time period.
Since, the '08 crisis was an unprecedented event, the direct proportionality of interest rates and savings rate in the '07 to '09 period when they both fall together is historically rare. However the trend is of growing savings rate in the time period.
So we have 2 countries with opposite events but the same correlation. Rising interest rates in India were accompanied with falling savings & falling rates in the U.S were accompanied with rising savings.
This data is contradictory to central banks' logic i.e to cut rates to spur consumption, spending and accelerate the economy. The reality is, however counter-intuitive it may seem, that people tend to save more in inflated asset prices & low yielding environments. Leading to reduced spending, thus reduced consumption, which in turn drives Central banks to reduce rates even more.
The problem thus, is that of causality. What causes what? In which direction should one point the causality arrow to? Do lower savings lead to higher interest rates or higher interest rates cause lower savings?
One must look at other angles and correlations of interest rates.