Does the neutral real interest rate really exist?

When the issue of central banks’ “terminal interest rate” (the level at which the central bank’s interest rate stabilises in the long term) is brought up, it is most often thought to be the sum of the central bank’s neutral real interest rate and its inflation target. The neutral real interest rate is the one that balances supply and demand for goods and services (savings and investment) and therefore depends on the structural characteristics of supply and demand. It is therefore believed that the terminal interest rate is determined by the structural characteristics of the economy and by the inflation target. But what happens in this theory if the central bank keeps the real interest rate lower (for example) than the neutral real interest rate? In traditional theory, this is impossible since there would permanently be excess demand for goods and service. But in reality, it is probably possible: In an open economy with perfect capital mobility, if there is excess demand (shortfall in savings) because the central bank sets a real interest rate below the neutral real rate, it will be offset by an external deficit (by external debt); Even in a closed economy, it can be assumed that excess demand over supply of goods and services will lead to an increase in the supply of goods and services (increase in the employment rate and in investment) that eventually rebalances supply and demand. In this case, we see that the (neutral) real long-term interest rate is determined by monetary policy, not by the structural characteristics of the economy that change with monetary policy choices.