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The inflation target is $2$% and the equation of exchange states $MV=PQ$. Is the idea that we want to have greater money supply growth then real growth in general?

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It is rather other way around. We want to target about $2\%$ inflation and to do so money supply should expand faster than real growth. Also, the $2%$ target is not commonly interpreted as a target that has to be kept all the time.

For example, as explained in this Brookings blog many central bankers advocate targeting the $2\%$ over business cycle. During recessions it might be prudent to have more 'loose' monetary policy and during expansions more 'tight' one.

Furthermore, relationship given by the quantity theory of money (i.e. the equation of exchange) in more complex models depends not just on the actual realization of the variables but also on their expectations (see Krugman et al 1998). An expansion of money supply that is not expected to last might as well never happen.

Lastly, if an economy happens to be at zero lower bound (ZLB) increasing money supply is no longer helpful in targeting inflation (at least not increasing money supply by usual interest rate targeting). This is because at ZLB peoples preference to hold cash becomes so strong that any increase in money supply will be just offset by drop in velocity as people will just hold on the money (see again Krugman et al 1998).

Thus to sum up, while in order to target $2\%$ inflation often central banks try to expand money supply faster than the real growth, it is not always possible to do so nor it is always desirable to expand money supply so fast across business cycle.

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  • $\begingroup$ Thanks, this is what I meant, not that we were aiming for this relation in money and growth, even if that is what I wrote. Anyway how do they control money supply growth? By adding reserves or by just lowering the rate? $\endgroup$ – Vlad Jul 4 at 18:05
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    $\begingroup$ @user1 They do it in multiple ways. Most common is to lower the interest rate or by open market operations purchasing government debt. There are also other ways how they can do that. This Economics.SE question has some answer that mentions some of them: economics.stackexchange.com/questions/36896/… $\endgroup$ – 1muflon1 Jul 4 at 18:35

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