Y = β X + αZ + ε
is the simple wage equation where Y represents wages, X represents individual characteristics, Z represents a group identity like gender or race, and ε represents the error term. The parameter β represents the returns to human capital and α represents the discrimination coefficient. What are the main limitations for this wage equation?
One limitation is that the Z variable, which represents group membership, may also indicate a productivity factor. Additionally, the coefficient β may not represent the same return for different groups, even if they have similar characteristics. Another limitation is that the formation of human capital may vary between groups due to discrimination. For example, in a less developed region, the school enrollment rate of women may be lower due to limited employment opportunities and low human capital returns, which can result in women having less human capital and lower expectations in the labor market. In addition to the limitations noted above, if discrimination not only occurs in the labor market but also affects workers’ access to human capital, this creates a correlation between X and Z in the estimation equation, leading to a biased estimate of α. This highlights the importance of considering the impact of discrimination not only on wages but also on the formation of human capital, and the need for more complex and nuanced approaches to understand and address wage disparities between groups. This may include additional control variables or different estimation techniques to control for the correlation between X and Z and produce unbiased estimates.