On addition of NaOH to water

The addition of $NaOH$ to pure water won't affect Kw because it is fixed at a specific temperature. However, the addition of $NaOH$ raises the concentration of OH ions, shifting the dissociation equilibrium of ($H_{2}O$) to the left. [$[ {\text{ H}}_{\text{2}}{\text{O(l)+H}}_{\text{2}}\text{O(l) }\iff {\text{H}}_{\text{3}}{\text{O}}^{\text{+}}{\text{(aq)+OH}}^{\text{-}}\text{(aq) }]$

The amount of $H_3{O}^{+}$ ions in the solution decreases as a result.