It depends!
In short run, if thriftness is increased, GDP and rate of interest both fall. But
1. if your investment function is I(Y,r) where Y=GDP and r= rate of interest and as usual, I'(Y)>0 and I'(r)<0, the effect of increase in thriftness is ambiguous.
2. if your investment function is I(r) where r= rate of interest and as usual, I'(r)<0 (that is if you assume that GDP overall does not affect investment tremendously in short run), then the effect of increase in thriftness is unambiguous and investment increases. This can be also seen with chewed and celebrated equation S+T=I+G, and as Saving rises and Tax fixed, something has to be increased on RHS. But if government is sleeping (as is ours
), investment has to increase.
In the long and very long run, things are very different. If we think that interest rates are fairly stable in the long run, increase in saving increases Y and ultimately investment=I(Y,r),where r is assumed to be fixed.
So, we can assume that saving and investment go together