To answer this question completely would take a whole tome. The short answer is that the empirical estimates of the "production function" are meaningless barring stringent assumptions. Suppose, just for a minute, that there really is "perfect competition" neoclassical style and that there really is a constant-returns-to-scale production function (required for NC PC). In this case, ANY CRS (i.e., linearly homogeneous) production function has the property that Y(k,l) = k * dy/dk + l * dy/dl , so that all you are really estimating empirically is the marginal products of labor and capital and the labor and capital shares of the economy, regardless whether the underlying production function is Cobb-Douglas or not. Anwar Shaikh has a sharp and typically obnoxious piece on this in the Palgrave volume on capital theory. Now, relax the perfect competition assumption and replace it with monopolistic competition. It turns out that the parameter estimates on k and l are not equal to dy/dk and dy/dl, but with dy/dk(1-Q) and dy/dl(1-Q), where Q is the elasticity of demand. Therefore the coefficients adding up to one is not necessarily a sign of CRS. A good mainstream advanced macro textbook like Blanchard and Fischer will probably have something on this. Suppose further that income distribution affects product demand, and that in particular workers consumer a higher percentage of their income than capitalists. In this case, the marginal product of labor is determined only _after_ the aggregate wage level is determined, i.e., there is (what you might have seen called in your econometrics books) simultaneity bias. Drop the assumption of constant returns to scale and this bias will be amplified. Again, see the Palgrave on capital theory and look in particular at the bits on post-Keynesianism and the Cambridge controversy. Hope this helps. Don't let the PC police (perfect competition, that is) get you down. Best wishes from a lowly PhD student, Tavis On Fri, 13 Sep 1996, Ted Kuster wrote: > I, a lowly master's degree student, seek enlightenment. The > macro course I took last semester was based on a new text by > Alan Auerbach (UC Berkeley) and Lawrence Kotlikoff (NBER), who > present a version of "generational accounting" that rests on a > master Cobb-Douglas production function for the whole economy > which you can tinker with by manipulating returns to capital or > labor or the technology level or some other things. (The book > includes a software package to let you do this.) I have been > trying to figure out a context to place this stuff in, but am > confused. (A&K, faithful to pedagogical tradition in econ, offer > no context at all but just wade right into the math.) My best > guess is that this is basically an updated version of an > aggregate production function a la Wicksell (what Robinson > called a "pseudo-production function") which was supposed to > restore general equilibrium after Keynes, with a lot of bells > and whistles and ASCII spreadsheets worked in. Robinson's > critique, if I understand it, was that this kind of thing did > nothing to save general equilibrium from Walras-style > timelessness, because it gave no convincing mechanism for the > central relationships to work through, and time, if anything, > ran at right angles to the page, as I think she put it. Is > anyone familiar enough with this stuff to help me figure out > what is going on here? > > Ted Kuster > >
