Reswitching, relative prices and linearity

Ok so only 1000 people in the world understand this and only 10 care about it: economics for the most part has long since given up its empirical pretensions when it comes to its ontological assumptions.  Still I suspect the heterodox world will be interested in this forthcoming publication by Anwar Shaikh antiseptically titled, The Empirical Linearity of Sraffa’s Critical Output‐Capital Ratios.  Here is the conclusion:

Even though Marx initially develops his analysis in Volumes I‐II under the assumption that prices are proportional to labor values, he is adamant that the two must be systematically different. In his famous (and incomplete) transformation procedure in Volume III, he derives prices of production as linear functions whose deviations from values increased with the rate of profit. The first two components of the Sraffian decomposition can be therefore viewed as the vertically integrated equivalent of Marx’s procedure. The data clearly support Marx’s general hypothesis that prices of production deviate smoothly and near‐linearly from values.

Sraffa’s elegant and elliptical text suggests that prices of production are likely to exhibit more complex patterns. He specifically cites the potentially complex behavior of individual sectoral output/capital ratios as being the source of complicated price movements. But at an empirical level, individual output capital ratios turn out to be virtually linear functions of the rate of profit, so that individual prices of production and the aggregate wage‐profit curve are near‐linear.

Such findings clearly support the structural price theories of Ricardo and Marx. While they do not completely exclude reswitching, they certainly relegate it to a secondary role. This does not mean that they rehabilitate neoclassical economics. First of all, the structural determination of relative prices in equation (1.4) is a far cry from the neoclassical theory of marginal cost pricing. Secondly, the difference between classical and neoclassical theories of profit is most evident precisely when prices are equal to labor values. This is the condition under which profit is exactly equal to the surplus value created in production. Even if we further posit an infinite number of co‐existing techniques, timeless technical change, and a host of other non‐classical assumptions, then equality of standard prices and values is also the condition under which an aggregate pseudo (surrogate) production function obtains, in the sense that frontier techniques corresponding to lower rates of profit will have higher (constant) capital‐labor ratios5. But correlation is not causation: both profit‐as‐surplus value and the profit‐rate‐as scarcity‐price coexist in this abstract space because their real theoretical differences lie elsewhere (6).