Tobias Moskowitz and Annette Vissing-Jorgensen have an AER paper that I recently came across that compares public and private equity returns. They find that on average private equity returns are no higher than public equity returns despite liquidity differences. They attribute this lack of a private equity premium to the presence of non-pecuinary benefits associated with private equity (such as being your own boss). Other studies, such as this one on small businesses from Erik Hurst and Ben Pugsly, are consistent with the idea that non-pecuinary benefits are large.
Here’s Figure 1 from the AER paper that shows how public and private returns have evolved since the 1960s: