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Theoretically real money balances ($m_t$) are defined as:

$m_t=\frac{M_t}{P_t}$

Where $M_t$ are nominal money balances, and $P_t$ is the price index of the economy. If I were to make an empirical study involving real money balances, what is the correct approximation for obtaining time series of this variable?

My try is obtaining time series for M1, that would be my empirical nominal money balances, as well as obtaining some price index time series as CPI. Then my real money balances time series would be the result of computing in each cross-section:

$\text{real money balances}_t=\frac{M1_t}{CPI_t}$

Is that right?

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There is no real good general answer for that without detailed knowledge of model you want to estimate. When it comes to $P_t$ people typically use $CPI_t$ as a proxy but when it comes to $M$ it depends on what sort of work you are doing. Some work in fact even estimates $M/P$ in different versions using $M_1$, $M_2$ and $M_3$ (such as Short 1979).

In typical macroeconomic model $M$ is interpreted more broadly than just base money (e.g. see discussions in Woodford Interest & Prices, or across Romer Advanced Macroeconomics). In that case using $M_2/CPI$ or even $M_3/CPI$ would make more sense if you would be forced to choose only one. But as in the above mentioned citation you can construct it in various different ways and then see if the results are robust when you switch the measurement.

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