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# Coefficients of cross-country variation

To measure the dispersion of the MFI interest rates of the individual euro area countries around the euro area interest rate, coefficients of variation are calculated for each euro area MFI interest rate. The coefficient of variation is computed as the standard deviation divided by the euro area interest rate, thus adjusting for the fact that the standard deviation is influenced by the level of the euro area rate. By definition, the coefficient of variation is unit-free.

### All coefficients

All coefficients of cross-country variation time series

To measure the dispersion of the MFI interest rates of the individual euro area countries around the euro area interest rate, coefficients of variation are calculated for each euro area MFI interest rate. The coefficient of variation is computed as the standard deviation divided by the euro area interest rate, thus adjusting for the fact that the standard deviation is influenced by the level of the euro area rate. By definition, the coefficient of variation is unit-free.

The standard deviation is computed as the square root of the weighted variance of the national MFI interest rates (MIR) with respect to the euro area interest rate. The national business volumes serve as country weights.

$CV=\frac{\sqrt{\mathit{\text{weighted_variance}}}}{\mathit{\text{euro_area_MIR}}}$

where:

the weighted variance is obtained as

$\sum _{k}w\left(k{\right)}_{t}{\left(i\left(k{\right)}_{t}-{\mathit{\text{euro_area_MIR}}}_{t}\right)}^{2}$

the euro area MIR is obtained as

${}_{i}{\left(}_{k}{\right)}_{t}$ = national MIR level of euro area country k at month t

${}_{w}{\left(}_{k}{\right)}_{t}$ = national weight of euro area country k at month t, i.e. volume of national business in relation to euro area total.

The weighted variance is the squared deviations between the national and euro area MFI interest rates, calculated according to the national share in the total euro area business volume for a given instrument category.

By measuring, on a monthly basis, the variation of national interest rates around the euro area MFI interest rate (“euro area MIR”) adjusted for the level of the euro area rate, the coefficient of variation allows further a comparison of different MIR indicators.