  We study a minimal string model possessing the same massless spectra as the
  MSSM on $Z_N\times Z_M$ orbifolds. Threshold corrections of the gauge
coupling constants of SU(3), SU(2) and
  U(1)$_Y$ are investigated in a case of an overall modulus. Using computer
analyses, we search ranges of levels of U(1)$_Y$ allowed by the LEP
experiments. It is found that $Z_3\times Z_3$ can not derive the minimal string
model for a $M_Z$ SUSY breaking scale. The minimum values of the overall moduli
are estimated within the ranges of the levels.
