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Using PIAAC data, this study examines whether the wage penalties of over education and individual skill are consistent in the heterogeneous job categories. This study shows that wage penalty of over education is observed in most of job categories when the skill is controlled. The problem of wage penalty associated with overeducation is found more among unskilled blue color workers. We further found that the basic core skill, such as literacy and numeracy skill, partially mitigated the wage penalty by overeducation, in particular, for white color workers, and skilled blue color workers. Based on the result, we suggest that the problem of the wage penalty could be partly mitigated by improving basic foundation of core skill based on formal education.