Yes, but framing it as "if people should save more ..." supports the neoclassical model in which fundamentals establish the equilibrium level of output and a "saving" decision plays an active role in setting the interest rate.

The next round effect of the decision is the loss of spending, both in terms of a reduction in exogenously financed consumer spending and a reduction in the propensity to consume out of income. So the consequential dimension of the decision is the decision to cut back on spending.

I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.