We use a recent first-hand linked employer–employee survey covering the formal sector of Bangladesh to explain gender wage gaps by the inclusion of measures of cognitive attainment and personality traits. Our results show that cognitive skills have greater explanatory power than personality traits in determining mean wages. Unconditional quantile regressions show that cognitive attainment as measured by reading and numeracy seems to confer different benefits to women and men respectively. The Big Five traits of agreeableness are positively associated with females’ wages across the wage distribution. Decompositions show that about 32–43% of the wage gap can be explained by characteristics along the wage distribution. Cognitive skills cumulatively account for a larger share of the explained component than personality traits do, and matter more at lower percentiles. However, together these cognitive and socioemotional skills matter to a lesser degree than a factor such as one’s tenure in the firm.