We analyze how firm-provided training is affected by the interaction among important institutional variables in the labor market: firing costs, minimum wages and unemployment benefits. We find that the degree of complementarity and substitutability among these variables depends on employees' abilities. Thereby the institutional interactions influence skill inequality. We derive how the influence of one of the institutional variables above is affected by other institutional variables with respect to inequality in skills arising from firm-provided training. We derive several striking results, such as: (a) the minimum wage and unemployment benefits generate increasing skill inequality whereas firing costs generate skill equalization; (b) unemployment benefits and firing costs are complements in their effects on skill inequality, (c) firing costs and the minimum wage are complements in their effects on skill equalization, and (d) unemployment benefits and the minimum wage are substitutes in their effects on skill inequality.