Brian is doing what to me seems like some of the most interesting work on competition analysis that I've read in a long time, and I'm a fan of the suggestion of adopting OP-covariance. But I do want to point out a limiting principle that seems important.
Brian treats OP-covariance primarily as a diagnostic tool, but his policy framing also makes it a candidate target, not just a candidate measure. Used as a target, the measure pushes us toward a potentially pathological optimum. Covariance is bounded above by the product of the standard deviations of market share *and* productivity, so maximizing it requires collapsing one of those variances. A regulator steering toward high covariance steers toward a state in which either all firms cluster at the frontier (Albrecht's own frontier-clustering caveat) or a single productive firm captures the market (what we might call a "covariance singularity"). This second path forecloses the nascent-competitor concern that Lemley and others have pressed on predatory acquisitions: if the acquirer is the most productive observed firm and the target is low-share, then the acquisition raises covariance *even as* it destroys the option value of a future alternative. And in markets where horizontal variety is itself a consumer good (think food, books, film, software) the optimum annihilates the thing the market is supposed to deliver. OP-covariance works much better as a thermometer than as a thermostat. It's a *much* better thermometer than what we're using now anyway. I just think reform efforts would be easier if we acknowledged its limitations. It's not a "set it and forget it" to optimize for. (To be clear, I don't read Brian as suggesting that; but I also haven't seen him acknowledge the "covariance singularity" I'm concerned about here.)
To make this more concrete, I think the case of Columbia is illustrative. Pre-reform Colombia had low covariance and low variety. Post-reform had higher covariance and much higher variety. Brian reads this as OP-covariance *correctly* tracking welfare. But I could argue that the co-movement there is incidental to the reform mechanism: Tariff removal happened to raise *both* simultaneously because the reform opened the market to new kinds of cars, not just more productive producers of the same cars. The Colombia case doesn't test what OP-covariance would do in a mature, already-open market where the policy lever is merger review rather than tariff reduction, which is the one we should care about if we're going to use OP-covariance to guide us on M&A.
I don't have a great solution to this limitation on OP-covariance, but I can say that I've been pushing on Lemley for years to acknowledge the obverse problem of wasteful investment in too many different distribution platforms. Acquisitions that look predatory may not be when there are enough different potential acquirers, each of which has its own platform for reaching consumers, each of which provides a different bundle of opportunities. Do we need 20 different app stores, for example? If the "predatory" acquisition is of a technology that improves the quality of consumer experience with a given platform and the target and other potential acquirers had a fair opportunity to transact, thenI don't know that we need to worry. If, on the other hand, the "predatory" acquisition is of a source of information/content that doesn't improve the quality of the consumer experience with a given platform per se, but rather the value of the platform as a source of information/content, then maybe the scare quotes should be removed?
Brian is doing what to me seems like some of the most interesting work on competition analysis that I've read in a long time, and I'm a fan of the suggestion of adopting OP-covariance. But I do want to point out a limiting principle that seems important.
Brian treats OP-covariance primarily as a diagnostic tool, but his policy framing also makes it a candidate target, not just a candidate measure. Used as a target, the measure pushes us toward a potentially pathological optimum. Covariance is bounded above by the product of the standard deviations of market share *and* productivity, so maximizing it requires collapsing one of those variances. A regulator steering toward high covariance steers toward a state in which either all firms cluster at the frontier (Albrecht's own frontier-clustering caveat) or a single productive firm captures the market (what we might call a "covariance singularity"). This second path forecloses the nascent-competitor concern that Lemley and others have pressed on predatory acquisitions: if the acquirer is the most productive observed firm and the target is low-share, then the acquisition raises covariance *even as* it destroys the option value of a future alternative. And in markets where horizontal variety is itself a consumer good (think food, books, film, software) the optimum annihilates the thing the market is supposed to deliver. OP-covariance works much better as a thermometer than as a thermostat. It's a *much* better thermometer than what we're using now anyway. I just think reform efforts would be easier if we acknowledged its limitations. It's not a "set it and forget it" to optimize for. (To be clear, I don't read Brian as suggesting that; but I also haven't seen him acknowledge the "covariance singularity" I'm concerned about here.)
To make this more concrete, I think the case of Columbia is illustrative. Pre-reform Colombia had low covariance and low variety. Post-reform had higher covariance and much higher variety. Brian reads this as OP-covariance *correctly* tracking welfare. But I could argue that the co-movement there is incidental to the reform mechanism: Tariff removal happened to raise *both* simultaneously because the reform opened the market to new kinds of cars, not just more productive producers of the same cars. The Colombia case doesn't test what OP-covariance would do in a mature, already-open market where the policy lever is merger review rather than tariff reduction, which is the one we should care about if we're going to use OP-covariance to guide us on M&A.
I don't have a great solution to this limitation on OP-covariance, but I can say that I've been pushing on Lemley for years to acknowledge the obverse problem of wasteful investment in too many different distribution platforms. Acquisitions that look predatory may not be when there are enough different potential acquirers, each of which has its own platform for reaching consumers, each of which provides a different bundle of opportunities. Do we need 20 different app stores, for example? If the "predatory" acquisition is of a technology that improves the quality of consumer experience with a given platform and the target and other potential acquirers had a fair opportunity to transact, thenI don't know that we need to worry. If, on the other hand, the "predatory" acquisition is of a source of information/content that doesn't improve the quality of the consumer experience with a given platform per se, but rather the value of the platform as a source of information/content, then maybe the scare quotes should be removed?