“Price Formation of Fish,” A.P Barten & L.J. Bettendorf (1989)

I came across this nice piece of IO in a recent methodological book by John Sutton, which I hope to cover soon. Sutton recalls Lionel Robbins’ famous Essay on the Nature of Significance of Economic Science. In that essay, Robbins claims the goal of the empirically-minded economist is to estimate stable (what we now call “structural”) parameters whose stability we know a priori from theory. (As an aside, it is tragic that Hurwicz’ 1962 “On the Structural Form of Interdependent Systems”, from which Robbins’ idea gets its modern treatment, is not freely available online; all I see is a snippet from the conference volume it appeared at here). Robbins gives the example of an empiricist trying to estimate the demand for haddock by measuring prices and quantities each day, controlling for weather and the like, and claiming that the average elasticity has some long-run meaning; this, he says, is a fool’s errand.

Sutton points out how interesting that example is: if anything, fish are an easy good to examine! They are a good with easy-to-define technical characteristics sold in competitive wholesale markets. Barten and Bettendorf point out another interesting property: fish are best described by an inverse demand system, where consumers determine the price paid as a function of the quantity of fish in the market rather than vice versa, since quantity in the short run is essentially fixed. To the theorist, there is no difference between demand and inverse demand, but to the empiricist, that little error term must be added to the exogenous variables if we are to handle statistical variation correctly. Any IO economist worth their salt knows how to estimate common demand systems like AIDS, but how should we interpret parameters in inverse demand systems?

Recall that, in theory, Marshallian demand is a homogeneous of degree zero function of total expenditures and prices. Using the homogeneity, we have that the vector quantity demand q is a function of P, the fraction of total expenditure paid for each unit of each good. Inverting that function gives P as a function of q. Since inverse demand is the result of a first-order condition from utility maximization, we can restate P as a function of marginal utilities and quantities. Taking the derivative of P, with some judicious algebra, one can state the (normalized) inverse demand as the sum of moves along an indifference surface and moves across indifference surfaces; in particular, dP=gP’dq+Gdq, where g is a scalar and G is an analogue of the Slutsky matrix for inverse demand, symmetric and negative semidefinite. All we need to do know is to difference our data and estimate that system (although the authors do a bit more judicious algebra to simplify the computational estimation).

One more subtle step is required. When we estimate an inverse demand system, we may wish to know how substitutable or complementary any two goods are. Further, we want such an estimate to be invariant to arbitrary monotone increasing changes in an underlying utility function (the form of which is not assumed here). It turns out that Allais (in his 1943 text on “pure economics” which, as far as I know, is yet to be translated!) has shown how to construct just such a measure. Yet another win for theory, and for Robbins’ intuition: it is hopeless to atheoretically estimate cross-price elasticities or similar measures of substitutability atheoretically, since these parameters are determined simultaneously. It is only as a result of theory (here, nothing more than “demand comes from utility maximizers” is used) that we can even hope to tease out underlying parameters like these elasticities. The huge numbers of “reduced-form” economists these days who do not understand what the problem is here really need to read through papers of this type; atheoretical training is, in my view, a serious danger to the grand progress made by economics since Haavelmo and Samuelson.

It is the methodology that is important here; the actual estimates are secondary. But let’s state them anyway: the fish sold in the Belgian markets are quite own-price elastic, have elasticities that are consistent with demand-maximizing consumers, and have patterns of cross-price elasticities across fish varieties that are qualitatively reasonable (bottom-feeders are highly substitutable with each other, etc.) and fairly constant across a period of two decades.

Final version in EER (No IDEAS version). This paper was in the European Economic Review, an Elsevier journal that is quickly being killed off since the European Economic Association pulled out of their association with Elsevier to run their own journal, the JEEA. The editors of the main journal in environmental economics have recently made the same type of switch, and of course, a group of eminent theorist made a similar exit when Theoretical Economics began. Jeff Ely has recently described how TE came about; that example makes it quite clear that journals are actually quite inexpensive to run. Even though we economists are lucky to have nearly 100% “green” open access, where preprints are self-archived by authors, we still have lots of work to do to get to a properly ungated world. The Econometric Society, for example, spends about $900,000 for all of its activities aside from physically printing journals, a cost that could still be recouped in an open access world. Much of that is for running conferences, giving honoraria, etc, but let us be very conservative and estimate no income is received aside from subscriptions to its three journals, including archives. This suggests that a complete open access journal and archives for the 50 most important journals in the field requires, very conservatively, revenue of $15 million per year, and probably much less. This seems a much more effective use of NSF and EU moneys that funding a few more graduate research assistants.


One thought on ““Price Formation of Fish,” A.P Barten & L.J. Bettendorf (1989)

  1. plw says:

    “In the present context the quantities are treated as exogenous variables.
    Consequently, their covariance with the current or lagged disturbance terms
    is taken to be zero.”

    Right or wrong, this phrase alone would make this paper essentially unpublishable under the current empirical regime.

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