  The Cepheid Period-Luminosity (PL) relation is the key tool for measuring
astronomical distances and for establishing the extragalactic distance scale.
In particular, the local value of the Hubble constant ($H_0$) strongly depends
on Cepheid distance measurements. The recent Gaia Data Releases and other
parallax measurements from the Hubble Space Telescope (HST) already enabled to
improve the accuracy of the slope ($\alpha$) and intercept ($\beta$) of the PL
relation. However, the dependence of this law on metallicity is still largely
debated. In this paper, we combine three samples of Cepheids in the Milky Way
(MW), the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) in
order to derive the metallicity term (hereafter $\gamma$) of the PL relation.
The recent publication of extremely precise LMC and SMC distances based on
late-type detached eclipsing binary systems (DEBs) provides a solid anchor for
the Magellanic Clouds. In the MW, we adopt Cepheid parallaxes from the early
third Gaia Data Release. We derive the metallicity effect in $V$, $I$, $J$,
$H$, $K_S$, $W_{VI}$ and $W_{JK}$. In the $K_S$ band we report a metallicity
effect of $-0.221 \pm 0.051$ mag/dex, the negative sign meaning that more
metal-rich Cepheids are intrinsically brighter than their more metal-poor
counterparts of the same pulsation period.
