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These two countries like Argentina have massive interest rate, over 50%, yet nobody can claim the argentinian peso is stronger. In fact its like 1000 to the dollar and was much stronger before. So do high interest rates really strengthen a currency , or in fact from real evidence, weaken it?

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Interest rate does strengthen currency. There is both theoretical and also empirical evidence for it (eg see Copeland Exchange Rates and International Finance).

However, interest rate is far from the only variable that determines exchange rate. Even in a simple monetary model of exchange rates, the exchange rate is given by;

$$\ln S= \ln(m)- \ln(m_f) -(\ln(y)-\ln(y_f))+\lambda(i-i_f)$$

where $m$ is money supply at home and $m_f$ in foreign country, $y$ is the real output at home and $y_f$ in foreign country and $i$ is the interest rate at home and $i_f$ in foreign country (also note higher S means weaker currency).

As you can clearly see there is bunch of other variables that determine exchange rate. For example, if your economy is doing badly (drop in real output y), exchange rate will depreciate despite of high interest rates. Similarly, if country expands its money supply $m$ a lot exchange rate will depreciate even if interest rates are high. Moreover, exchange rates are always relative. Even if your country’s economy is doing well, exchange rate might depreciate if other economies are doing even better. Furthermore, there are also some other variables that can explain differences in exchange rates, not mentioned in the simple model above, like people’s expectations.

In short, the problem is that your observation is unconditional. Your question is tantamount to asking, I see this obese person exercising twice a day but they are also very obese so does exercise cause obesity? Clearly persons weight, similarly to exchange rate is caused by multitude of factors. Exercise can, ceteris paribus lower your weight, but if you will eat 20 McDonald hamburgers a day you will still gain weight and become obese despite exercise.

Virtually every scientific explanation is conditional. For example, postulate in physics that objects in vacuum will fall to ground at the same speed is conditional on not adding energy to second object by shooting laser at a mirror on its back or attaching rocket engine on it.

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