The standard endogenous growth model assumes that markets are perfectly competitive, and thus factors are paid at their marginal product, and Cobb-Douglas production function parameters corresponds to factor income shares. But looking at the real world, there clearly are economies where "capitalists" or "unions" have more bargaining power. Beyond the semantics, is there something to gain from imperfect competition on factor markets
Christopher Tsoukis and Frédéric Tournemaine take a fairly standard AK model, except that they impose that workers not only derive utility form their consumption, but also from capitalists getting less consumption. Then they look at four different equilibria: perfect competition, Stackelberg, Nash and non-cooperative. They show that the resulting factor shares and growth rates differ across equilibria, Labor income shares are lowest in the competitive equilibrium, highest with Stackelberg, and the opposite for growth rates. Unfortunately, no attempt is done to relate this to any data. This would have been probably very difficult anyway. Indeed, labor income shares vary surprisingly little across economies, with only one outlier: China, with a very low labor income share, opposite the prediction of the model.
Even worse, the paper concludes with some major hand waving finding some conclusions about inflation and unemployment, in a model without money and an inelastic labor supply. Too bad.