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I heard even when the US was printing more money (Quantitative Easing), with US dollar the main transaction currency of the world, the whole world has to pay the price of the US dollar depreciating.

And it is true like for the Euros or Taiwan dollar... the exchange rate didn't really go down due to US printing money. It in fact might have gone up.

But isn't it true that when US prints money so the world's circulating US dollar is 10% more, then theoretically, US dollar should depreciate 10% relative to other countries' currencies? Why may being the main transaction currency prevent that from happening?

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But isn't it true that when US prints money so the world's circulating US dollar is 10% more, then theoretically, US dollar should depreciate 10% relative to other countries' currencies?

No, that only holds ceteris paribus (all else equal). A simple model of exchange rate can be given via monetary model of exchange rates which say that the exchange rate is given by:

$$\ln S= \ln(M)- \ln(M_f) -(\ln(Y)-\ln(Y_f))+\lambda(i-i_f)$$

Where $S$ is the exchange rate (note since $S=P/P_f$ increase in $S$ means depreciation and decrease appreciation), $M$ is the money supply, $Y$ real output, $i$ interest rate and $f$ denotes these quantities in foreign country so if the exchange rate is exchange rate between US and UK $M_f$ would be money supply in UK and $M$ money supply in US.

As you can see even if money supply in US increases rapidly, US exchange rate can actually appreciate if money supply in UK increases faster, or if there is increase in real output in US, or if there is drop in real output in UK or if US interest rate increases or if UK interest rate decreases in such a way that it offsets money supply increase in US.

In addition something that is not covered by this simple model is that expectations of these variables matter as much as or even more than the variable itself (i.e. it is more important what people expect money supply to be than what it actually is). Furthermore, something omitted from the model but very important when we talk about US, is the US status as world's major reserve currency (I suppose this is what you call 'being the main transaction currency'). Because of this status there is an artificial demand for US dollars making US dollar always stronger than it would be otherwise.

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If I could add a couple of additional points: (a) most major countries/currency blocs have ‘printed’ money in the form of large fiscal and monetary response to Covid. One could describe this as a race to the bottom in terms of currency valuations, so the dollar may not move relative to other currencies. (B) on the other hand, the dollar and many other currencies have indeed depreciated relative to a basket of goods (cpi indices have risen by at least 10%). That’s a depreciation of all currencies in real terms (c) in the case of the dollar specifically , the central bank has raised interest rates more rapidly than other CBs, leading to the relative appreciation of the dollar.

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