  An effective equation describes a weakly nonlinear wave field evolution
governed by nonlinear dispersive PDEs \emph{via} the set of its resonances in
an arbitrary big but finite domain in the Fourier space. We consider the
Schr\"{o}dinger equation with quadratic nonlinearity including small external
random forcing/dissipation.
  An effective equation is deduced explicitly for each case of monomial
quadratic nonlinearities $ u^2, \, \bar{u}u, \, \bar{u}^2$ and the sets of
resonance clusters are studied. In particular, we demonstrate that the
nonlinearity $\bar{u}^2$ generates no 3-wave resonances and its effective
equation is degenerate while in two other cases the sets of resonances are not
empty. Possible implications for wave turbulence theory are briefly discussed.
