Why Does The Labor Theory Of Value Work Empirically As A Theory Of Prices?

Anwar Shaikh On The Transformation Problem

Lots of empirical work shows that prices tend to be proportion to the labor embodied in commodities. My references in this article document this claim. Furthermore, empirical wage-rate of profits curves tend to be close to straight lines. This is not what, say, Sraffa' mathematical economics would lead me to expect. What explains these surprising empirical findings?

Almost 34 minutes in, in the above video, Shaikh makes the above point about the contrast between theory and empirical findings. He concludes with speculation, including with comments on Bertram Schefold's work with input-output matrices formed out of random matrices.

I offer some speculations myself in this post. I do not have much theory to back these suggestions up.

The Leontief matrices obtained from National Income and Product Accounts (NIPAs) are still highly aggregated. The empirical results on the LTV are obtained with matrices that have on the order of, say, 100 industries. One of these industries, if disaggregated, might contain commodities that are produced with a high Organic Composition of Capital (OCC) and a low OCC. Their prices of production would deviate more from labor values than an average combining them both. The extremes would be cancelled out in forming an average.

In my examples of pattern analysis, I also suggest that Sraffa effects could be difficult to see, in that they arise in a transition from one very long run position to another. But I concoct those examples to make a point about possibilities. I do not want to insist on any empirical point here.

Technical progress, despite how I usually model it, is endogenous. If in process of production adopted in some industry, some input is noticeably more expensive than others, managers of firms will seek out and research processes in which that input is reduced or some other cheaper input is substituted for it. Perhaps after a couple of centuries of rapid technical change under these incentives, empirical Leontief input-output matrices will have the properties Schefold highlights for random matrices. I suppose one could confirm this by showing wage-rate of profits curves are closer to affine functions for more highly developed economies. I have done some empirical work along these lines.

Aside: Here is another YouTube video with Anwar Shaikh. He sounds a lot like he accepts Milgate and Eatwell's critique of "imperfectionism". Actually existing capitalism is to be analyzed by a theory that accepts empirical reality, not by deviations from a neoclassical utopia that could never exist in any conceivable world.