Expectations and the Regression Fallacy In Estimating Cost Functions - Walters, A. A. (The Review of Economics and Statistics, 1960)
M ETHODS used to fit cost functions either to time series or cross-section data have been extensively criticized.' In a recent article Johnston2 has reexamined some of these criticisms and has to some extent succeeded in reestablishing the validity of the two major findings, i.e., (i) constant marginal cost, (2) decreasing long-run average cost. There are, however, criticisms made by Friedman (and Stigler) which Johnston is less successful in countering. The first which we shall consider here is a version of the classical regression fallacy. Friedman expresses this as follows: a firm produces a product the demand for which has a known two year cycle, so that it plans to produce ioo units in year one, 200 in year two, ioo in year three, etc. Suppose also that the best way to do this is by an arrangement that involves identical outlays for hired factors in each year (no 'variable' costs). If outlays are regarded as total costs, average cost per unit will obviously be twice as large when is ioo as when it is 200. If, instead of years one and two, we substitute firms one and two, a cross section study would show sharply declining average costs. When firms are classified by actual output, essentially this kind of bias arises. The firms with the largest outputs are unlikely to be producing at an unusually low level; on the average they are clearly likely to be producing at an unusually high level, and conversely for those that have the lowest output (page 236). And Stigler says: that three firms on average (over say a decade) produce ioo units each per year at an average cost of $io. In any one year because of weather, catastrophe, illness or death of a salesman, regional differences in business, etc. ('chance fluctuations') the firms will have sales (outputs) above or below the decade average of i0o. Suppose firm A sells only 8o units in a given year, firm B, Ioo units and firm C, I20 units. Suppose further that for each firm costs include (I) $500 of fixed costs plus (2) $5 of variable costs per unit of output. Tabulating the results: