To adhere to a fixed exchange rate and have an independent monetary policy, the economy has to give up free capital mobility.
One of the important reasons why some countries find their monetary policies ineffective is based on an economics concept called the “impossible trinity”.
This phenomenon, also known as international “trilemma”, proves (theoretically and empirically) that an economy cannot simultaneously maintain a) fixed exchange rates, b) independent monetary policy, and c) capital movements.
Only two of the above objectives can be simultaneously achieved, and the third cannot be controlled. In other words, policy makers have to decide on one of the three goals to give up, since only two out of the three is mutually consistent and implementable.
Expansionary monetary policy
To understand this concept, let us assume an economy follows a fixed exchange rate regime and allows free capital movements. Further, assume that the country’s central bank decides to follow an expansionary monetary policy — through lowering interest rates.
Note that an expansionary monetary policy is generally undertaken to stimulate economic activity. When interest rates are lower, investors pull their money out of that country and invest in countries that provide relatively higher returns. During such capital outflows, the supply of domestic currency relative to foreign currency increases, which results in a depreciation of the local currency.
However, under a fixed exchange rate, the value of domestic currency is fixed by the central bank and cannot change with respect to another.
Thus, the central bank, in pursuit of offsetting the excess supply of domestic currency, creates an artificial demand by buying its own domestic assets and currencies. Since interest rate and money supply are inversely related, absorbing money and assets out of the economy pulls the interest rates higher!
But this result is exactly the opposite of the central bank’s initial attempt at decreasing the interest rates! Thus, the monetary policy is left ineffective.
In other words, the effect of lowering interest rate in the first round is nullified by the (currency) policy to defend the exchange rate, and allow free capital flows.
But if there were heavy restrictions on investors pulling their money out of the country, then there would not have been capital outflows at the first place. Consequently, the exchange rate would have remained intact.
What this essentially means is that to adhere to a fixed exchange rate and have an independent monetary policy, the economy has to give up free capital mobility. Regardless, at least one of the objectives has to be given up to establish the other two, because it is impossible to have all three simultaneously.