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In one article I've read that increase in the money supply leads to inflation and exchange rate change.

For example, if we have double increase in the money supply then we'll have double change in exchange rate (devaluation of the currency).

How to prove it?

Thanks!

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In science we do not actually prove theories but rather provisionally accept them if fail to reject them given data.

You can try to empirically test whether there is inflation and money supply by various time series techniques. For example, De Grauwe & Polan (2005) or Frain (2004) use Granger causality to show that lags of growth rates money supply can explain inflation rates. This would be evidence consistent with assertion that money supply growth leads to inflation.

This is not the only model that can be used. The correct model will depend on data availability & quality, and what exactly you want to test. For example, if you want to test the following hypothesis:

For example, if we have double increase in the money supply then we'll have double change in exchange rate (devaluation of the currency).

Granger causality test would not be sufficient because your statement requires that there is not just causal relationship where increase in money supply leads to drop in exchange rate. You must go extra mile to check whether the relationship is exactly proportional. This will mean on top of your prefered model you have to extract estimated coefficients and test whether the coefficient size is statistically significantly different form unity (which would be evidence against the assertion) or not. There are various tests for this, without any more details its difficult to recommend any particular test.

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  • $\begingroup$ You wrote that I need to work with model to test hypothesis. But in different sources I read that increase in money supply leads to devaluation of currency. It were explanations (but not proofs) in simple form without using model. $\endgroup$
    – Mike_bb
    Apr 22, 2023 at 9:33
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    $\begingroup$ @Mike_bb right, because once something is proved like for example, theory of relativity, then other sources just build on top of that and reference the original proof. For things that are widely known people sometimes omit reference. For example, modern biology paper would not refer to Darwin every single time it mentions the idea of evolution because everyone knows where the idea came from. Also, I don't know what sources you refer to. News articles of course don't follow the academic standards for referencing, if you read article in the Wall Street Journal then they won't reference $\endgroup$
    – 1muflon1
    Apr 22, 2023 at 9:41
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    $\begingroup$ academic literature even when actually base their assertion on things that were proven in past $\endgroup$
    – 1muflon1
    Apr 22, 2023 at 9:48
  • $\begingroup$ Are following reasoning right? If we have double increase in money supply then we'll have double decreasing in purchasing power of unit of currency "A". And then monetary unit will cost less in relation to another currency "B". 1 unit "B"= 2 unit "A" $\endgroup$
    – Mike_bb
    Apr 22, 2023 at 9:58
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    $\begingroup$ @Mike_bb right, so? Without empirically testing that statement (or at least rigorously deriving it from already established theories) it is just statement. I could equally say if we have double increase in money supply then we will have triple decreasing in purchasing power of unit of currency A, now which statement is right? $\endgroup$
    – 1muflon1
    Apr 22, 2023 at 10:08

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