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1/ Thread on a project I have been working on with Xavier Vives: common ownership and secular stagnation. I presented it at the Atlanta AEA meetings organized by @ThomasPHI2 on increasing concentration in the US economy (Link here: blog.iese.edu/xvives/files/2… )
2/ One of the biggest puzzles in macro is what is the explanation for a pattern (broadly decribed as "secular stagnation") documented by @LHSummers, @ThomasPHI2, @Nacho2G , and others: low investment amid high profits and low real interest rates. Why are firms not investing?
3/ These authors have suggested that market power is a potential explanation. If the driving shock is an increase in market power, maybe that could lead to reduced investment and drive down real interest rates and increase profits simultaneously.
4/ Usually, the macro literature on market power uses a change in preferences (in particular, the Dixit-Stiglitz elasticity of substitution parameter) to generate an increase in markups in the model. In monopolistic competition, that is the parameter that gives you the markup.
5/ We depart from that framework and instead build a tractable oligopoly in general equilibrium model, so that changes in market structure (mergers, or an increase in common ownership) can be the cause o the change in markups, instead of a change in preferences.
6/ Why do we do this? There is simply no evidence of a big change in preferences that would drive a big change in markups over time. On the other hand, there is some evidence for an increase in concentration (although it is somewhat mixed).
7/ At the same time, the evidence is clear that common ownership has increased substantially. Although there is still plenty of disagreement over its causal effect on competition.
8/ Our model builds on our earlier work on common ownership and general equilibrium oligopoly (link here: papers.ssrn.com/sol3/papers.cf…), which had only one factor of production (labor), and adds a class of savers and capital in the production function.
9/ In that paper, we found, not surprisingly, that the objective function weights that firms put on other firms has been increasing over time (Fig 3). We adjust the average down to account for the existence of privately held firms, which we assume have no common ownership. 
10/ Lopez and Vives called this the "Edgeworth sympathy coefficient", as it is similar to a measure of altruism that Edgeworth talked about in his 1881 book. Thus, in our model, common ownership increases effective altruism among firms.
11/ Here, we don't attempt here to estimate the effect of inter-firm "sympathy" on competition empirically. This paper is just about thinking about the implications from a general equilibrium perspective.
12/ We combine our estimates of average common ownership with parameters from the literature and product and labor market HHIs from Compustat to calibrate the model and obtain simulated labor shares.
13/ Although HHIs in Compustat have increased, the magnitude is not enough to explain most of the decline in the labor share. Common ownership, quantitatively, *if its incentive effects actually were reflected in corporate decisions*, would help explain it.
14/ In the new paper, we have capital, so we can also simulate the capital share. The capital market HHI we calibrate is essentially zero. The MHHI is low, but not zero, because of inter-sectoral common ownership. So there is some market power in the capital market in the model..
15/... and capital market power has increased... a little bit. However, although the increase in concentration small, based on parameters from the literature the elasticity of supply of savings is very low, even lower than the labor supply elasticity.
16/ So the effect on real equilibrium interest rates of even a little bit of market power in the capital market is potentially very large. Actually, our calibration overpredicts the decline in the capital share and the real interest rates, especially in recent years.
17/ What are the policy implications of all of this? One possibility would be to tackle the common ownership itself. But what if we cannot do that? In that case, government spending can increase output and employment. (We show this formally in the model without capital.)
18/ The interesting thing is that the mechanism through which government employment increases output is not Keynesian, but "Kaleckian": government employment reduces the monopsony power of the private sector (Kalecki wrote on "The political economy of full employment").
19/ By employing people directly, the government reduces the effective MHHI in the labor market, and therefore reduces equilibrium markdowns and the economy moves up the labor supply curve towards full employment.
20/ To the extent that antitrust policy doesn't fully eliminate market power, there is room for the government to do this. Thus, antitrust and government employment are policy substitutes.
21/ It would be interesting to think about what is the analogue of this "Kaleckian" government policy in the capital market. We haven't done it formally, but my guess is it would be government borrowing to invest in public capital. Again, mechanism would be less market power.
22/ Another interesting thing to think about: why does the model overpredict the fall in the capital share? (i) maybe there is more overlap between the class of savers and the class of owners, due to indexing. (ii) maybe it's, to some extent, being close to the zero lower bound.
23/ That's basically it. One nice feature of this model is that the markdown is different for labor and capital. The markdown of each factor has two wedges: a product market wedge that is the same for both factors, and a factor market wedge. /end
