Technical change shifts the relative importance of certain economic activities over others, effectively determining the incidence of barriers to the transition of workers across occupations on output and inequality. To what extent has technical change mitigated or exacerbated the incidence of these barriers? to answer this question we study the link between occupation-specific labor market barriers, as measured in Hsieh et al. (2019), and capital-embodied technical change (CETC), as measured in Caunedo et al. (2021). We find that CETC mitigated the incidence of labor market barriers on output per worker by 9.1%, in the US between 1984 and 2014. A forecasting exercise over the next 10 years suggests that if the path of CETC follows the one observed during the previous 10 years, the gender wage gap should widen by 0.12p.p. per year and the race wage gap should widen by 0.07p.p. per year. The reason is that female and black workers face higher barriers in occupations where CETC rises wages the most. In addition, the model also predicts that absent mitigation policies, the skill-premium should rise at 0.24p.p. per year, twice as fast as the observed change in the last 10 years of our sample.