The neoclassical model of labor markets predicts that if the cost of hiring women of child-bearing years is anticipated to increase (either because the employer is mandated to pay for maternity leave, or because she will be absent from work on public leave), then the "demand" for women in the labor market will decrease.
While gender discrimination is illegal, without some kind of remedy, the neoclassical model would predict "statistical discrimination" against hiring women of child-bearing years.
If women take long parental leaves, the neoclassical model would predict that their lifetime earnings and opportunities for promotion will be less than their male or childfree counterparts, or the "motherhood penalty." In Denmark, the public sector is "family-friendly" because of its generous leave and employee benefits; workers decide which sector to work on based on their preferences and opportunities.
The study found that while in the "family-friendly" sector, there was basically no wage loss related to taking parental leave, women did have consistent earnings loss in the "non-family-friendly" private sector for a 1-year leave.
The term "parental leave" generally includes maternity, paternity, and adoption leave.