# Time series for contrasting empirically money demand and Taylor rules series

Non-cashless New-keynesian models often include discretionary monetary policy expressed as a Taylor rule:

$$1+i_t = (1+i)\left(\frac{1+\pi_t}{1+\pi}\right)^{\phi_\pi}\left(\frac{y_t}{y_t^n}\right)^{\phi_y}+\varepsilon_t^i$$

Since it's a non-cashless economy, there's going to be another simultaneous equation representing money demand:

$$m_t=f(i_t,\cdot)$$, where $$f_i<0$$, and $$m_t$$ is real money balances.

Thanslating in terms of "real life" time series, in the TR $$i_t$$ represents the policy interest rate and in the money demand $$i_t$$ represents the opportunity cost of holding money. The time series for the first would be the same, and the second usually would be government no-risk bonds yield. My question is, which should I use particularly for developing countries?