It is demonstrated that Kramers-Kronig (KK) analysis of reflectance data using various physically acceptable extrapolation formulae yields results which agree quantitatively when the parameters are obtained by suitable statistical methods. The absorption and Im (-1 /~) spectra obtained by the KK analysis of reflectance data (0.5 to 6.1 eV) of REBa,Cu,O,-, (RE = Y, Dy, Ce) and different combinations of CuO, BaO, and RE oxides strongly suggest that in these 123 layered cuprates superconductivity results when excitons (near 1.4 eV) in the polarizable layers and carriers (hole or hole-polarons) in the conducting layers are both present in sufficient number.