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According to monetarism, inflation can be predicted precisely by the change in money supply and GDP growth.

Does "money supply" here refer to M1 or M2, i.e. does it include debts created by private banks?

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    $\begingroup$ Empirically, inflation cannot be predicted precisely by the change in money supply and GDP growth or by anything else $\endgroup$ – Henry Aug 10 at 13:47
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    $\begingroup$ In particular the "velocity of money" is neither stable nor predictable. See fred.stlouisfed.org/series/M2V $\endgroup$ – Henry Aug 10 at 13:50
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The money supply is in theory interpreted broadly so from that perspective $M2$ or even $M3$ would be more appropriate. Also empirical studies in this strand usually use $M2$ see for example Sargent and Surico (2011).

However, you should note that nor the quantity theory of money nor monetarism claims inflation can be predicted solely by change in money supply and GDP growth.

Simple quantity theory of model is given by:

$$P=MV/Y$$

Where $P$ is price level, $M$ money supply, $V$ velocity of money and $Y$ real output. In more complex models expectations of these quantities matter as well. Hence it does not make sense to equate inflation to changes in $M$.

Furthermore, even though the above relationship is useful for structural modeling and creating analytical models it is practically useless for near term forecasting. If that’s your ultimate aim you would have more luck with augmented New Keynesian Philips curve.

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