OLS and Frontier Function Estimates of Long-Run Average Cost for Tennessee Livestock Auction Markets

Considerable research has been conducted to exAlthough the frontier function has not been widely plore economies of size in the livestock auction market used by researchers to estimate industry cost funcindustry. Since auction market cost functions are extions, this approach may yield a more appealing estipected to conform to microeconomic theory, conclumate of the LRATC function than the OLS method. sions regarding industry economies of size are often Observations of average cost probably represent firms derived from estimated long-run average total cost operating at various points along numerous short-run (LRATC) functions (French; Stoddard). The LRATC average total cost (SRATC) curves. It is unlikely that function suggests the least-cost firm size, as well as the each firm would be operating at the tangency between structure of size economies for the industry. Previous its SRATC and the industry LRATC during a given economies-of-size research has generally used the least time period. Each observation on SRATC will either squares method or the economic-engineering method be on or above the LRATC, and it is probable that most to estimate LRATC functions (French; Bressler; Poliof the observations will be above the LRATC. Thus, shuk and Buccola; and Johnson). The frontier function cross-section data for an industry would include firms method has been suggested as an alternative to these operating not only with a variety of plant capacities but methods (Bressler; Miller and Nauhein; Seitz). Even also at a variety of volumes for a particular plant cathough use of a frontier function is theoretically appacity. Although many factors may influence average pealing in some cases, its application in economies-oftotal cost in the short run, the LRATC function defines size research has not been widespread (Bressler; the relationship between cost and volume only. Since French; Farrell and Fieldhouse; Lesser and Greene). annual plant volume from a cross section of firms would The purpose of this paper is to evaluate the frontier reflect both shortand long-run factors, one would exfunction method of estimating an LRATC function in pect a range of average total costs to be observed at each contrast to the ordinary least squares (OLS) method. plant volume. Both methods will be applied to evaluate size econOLS estimation of LRATC produces a function omies in the Tennessee livestock auction market inwhich lies as near the mean of the average total costs dustry. for a certain size firm as allowed by the particular functional form used. The OLS estimate is a useful predictor of short-run average cost for a range of plant METHODOLOGY sizes, but would overestimate LRATC at a particular output volume. It is clear from economic theory that, Typically, the OLS method uses cross-section data at any given volume, the firm operating at a lower in a regression of average total cost against output volSRATC is operating nearer the LRATC. Thus, a fronume to estimate an LRATC function. Recent studies tier function fitted to the lower extreme of the scatter utilizing OLS have confirmed that cost economies do of average cost-output volume observations would exist in auction markets (Wootan and McNeely; Grinmore closely approach the theoretical notion of a nell and Shuffett; Grimes and Cramer; Wilson and LRATC function which is envelope to the industry's Kuehn). SRATC curves. A frontier function estimate of LRATC is an enveEven though the frontier function more accurately lope curve fitted to the bottom of the point scatter of resembles the theoretical LRATC curve, if none of the average cost plotted against volume. A frontier funcobserved firms were operating on the LRATC curve, tion may be estimated by several methods (Farrell and the estimated frontier function would overestimate the Fieldhouse; Aigner and Chu; Timmer; Hazell). This actual LRATC curve. Even so, the overestimation bias study incorporates the minimum absolute deviations would likely be less than that of the OLS estimate. Data (MAD) method developed by Hazell. The MAD estimeasurement error could affect the frontier function mate of LRATC at a given output minimizes the sum estimate more than the OLS estimate. The location of of the deviations of estimated average total cost from the frontier function is most dependent on the obserthe observed average total cost, assuming that the esvations with lower SRATC for any given volume. timated average total cost is less than or equal to obThus, errors in measurement in these few observations served average total cost. may disproportionately affect the estimated function.