  We reassess the validity of Migdal-Eliashberg (ME) theory for coupled
electron-phonon systems for large couplings $\lambda$. Although model
calculations have found that ME theory breaks down for $\lambda\sim 0.5$, it is
routinely applied for $\lambda>1$ to strong coupling superconductors. To
resolve this discrepancy it is important to distinguish between {\em bare}
parameters, used as input in models, and {\em effective} parameters, derived
from experiments. We show explicitly that ME gives accurate results for the
critical temperature and the spectral gap for large effective $\lambda$. This
provides quantitative theoretical support for the applicability of ME theory to
strong coupling conventional superconductors.
