A simple point that many economists miss (and nearly all non-economists) is that a falling labor share and rising wages are not in tension. In fact, it is what we should expect when the capital share rises, and capital is free to accumulate.
The reason is intuitive. In the long run, the supply of capital is perfectly elastic at a gross return determined by depreciation and the discount rate: households accumulate or run down capital until its return is back there. In comparison, the supply of labor is much more inelastic.
That means the gains from a technological change that makes capital more important in production (short of making it the only factor) end up with the inelastic factor, not the elastic one. In the long run, capital owners cannot get a rent from a higher capital share of output, only a compensation for their patience. We learned that from David Ricardo over two hundred years ago!
To see this, consider the textbook neoclassical growth model with log utility (not needed, but it makes things easy).
In the table below, I compute the steady-state wage for different values of the capital share. Increasing the capital share from 0.33 to 0.6 multiplies wages by nearly five. Capital owners receive a much larger slice of output, but the net rate of return stays at 4.7%: all the extra income has gone into more capital. Now, you might not want capital owners to have so much capital for political reasons (rich people have a curious habit of buying newspapers), but that has nothing to do with wages being lower. They are higher.
I learned this lesson the hard way many years ago with my paper “Bargaining Shocks and Aggregate Fluctuations” with Thorsten Drautzburg and
@pablo_guerron in the JEDC. We gave more bargaining power to capital owners (in our model, wages were not set competitively but through Nash bargaining), and workers ended up with higher wages! The logic is the same: give capital owners more power, and they compete it away. Karl Marx, by the way, already understood this. He was a much better economist than 99.99% of his followers and admirers.
Like all results, this one has exceptions: I can think of environments where a technological change that makes capital more important in production does not raise wages. And the transitional dynamics can get tricky. But the basic logic is hard to escape.