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I am referring to the theory presented on Wikipedia and The Economist that states:

The impossible trinity (also known as the trilemma) is a concept in international economics which states that it is impossible to have all three of the following at the same time: a fixed foreign exchange rate, free capital movement (absence of capital controls), an independent monetary policy

There are several confirmations of this theory presented: The Mexican peso crisis (1994–1995), the 1997 Asian financial crisis (1997–1998), and the Argentinean financial collapse (2001–2002) are often cited as examples.

But are there any examples or indications that this theory is not always true?

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First of all that is not a theory but result/implication from Mundell–Fleming model (which is the theory that gives rise to the result).

Second the description you are using is lacking one caveat that this is an equilibrium result from the Mundell–Fleming model (Mundell 1963; Fleming 1962). Of course country can have all three policies at the same time for some limited period of time. What makes this "impossible trilemma" is that stubbornly keeping the policy is economically so disastrous that it is not possible to sustain them over long run.

The reason why this can be sustained in the short run is that the mechanism of the trilemma is as follows. If a country pursues all 3 policies simultaneously and there is difference between interest rates it is simply unsustainable situation. For example if at home interest rate is $1\%$, world interest rate is $5\%$ and central bank wants to fix exchange rate between two currencies at parity so one home dollar is equal to 1 foreign dollar $1H=1F$, then anyone who has any capital would try to move it to the foreign country. First that capital flight would be disastrously in itself, but then when people move capital abroad they have to go through forex market and this will put pressure on the exchange rate to depreciate, only way how to prevent depreciation and keep exchange rate fixed is for central bank to sell its foreign currency reserves. If the central bank has a lot of foreign currency reserves this can be sustained for quite some time especially if the interest rate abroad is not too different from the one at home, but eventually there will be an end point when the reserves runt out and then having all three policies will be impossible.

To my best knowledge (which I double checked with some google scholar search) there is no empirical evidence for violation of trilemma. I do not think that one can conjure example where country would manage to sustain all 3 policies over long run. It is simply unsustainable.

In addition, actually what even more, empirical evidence provided by Aizenman (2010) shows that, thanks to globalization, economies actually became even more exposed to potential capital flight (since in globalized world there are less non-governmental impediments to capital flow), so if anything recent empirical evidence shows the trilemma is now even more biding than in the past. By extension, the trilemma would be less biding or even not biding at all if capital would become completely immobile (in fact capital mobility is even assumption behind Mundell-Fleming model without which the result would not hold). However, I do not think there was ever any time in human history capital would be completely immobile and I doubt that technology will make it less mobile rather than more.

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