Are all the good men married?

Does marriage cause men’s wages to rise?  This is the question addressed by UCSD professor Kate Antonovics and Robert Town in their 2004 paper in AER cleverly titled “Are all the good men married?”

It has been shown that married men earn more money than non-married men with similar characteristics.  Why is this?  A few explanations are:

1. Married men are more productive since they specialize in non-household production,
2. Employers could discriminate in favor of married men, or
3. the unobservable characteristics that make men more productive in the labor market also make them more attractive in the marriage market.

• w_ij = βM_ij + γX_ij + μ_ij + f_j + u_ij   (1).
• M: married, X: other variables, μ: individual fixed effect, f: family fixed effect, u: error term 
• For OLS, the residual is equal to μ_ij + f_j + u_ij   (1).

Using OLS, the authors find that married men earn a 19% wage premium over non married men.  However, this specification does not solve the selection problem.  If it is true that unobservable factors affect wages and marriage eligibility, then the marriage dummy variable will be correlated with the residual and β may be biased upwards.  

How do the authors solve the endogeneity problem?  They use data from the Socioeconomic Survey of Twins.  For a pair of monozygotic twins, we can rewrite equation (1) as follows:

• w_1j= βM_1j + γX_1j + μ_1j + f_j + u_1j  (2)
• w_2j = βM_2j + γX_2j + μ_2j + f_j + u_2j  (3)

Since twins are in the same family, we know that f_j in both equation is the same.  Further, we assume that the genetically determined, individual specific earnings endowment is the same across twins (i.e., μ_1j = μ_2j). Thus we can difference out the two equations so that we are left with:

• w1j – w2j = β(M1j – M2j) + γ (X1j – X2j) + (u1j – u2j)  (4)