Multiproduct agricultural supply response and factor demand estimation in the U.S. : the profit function approach

Abstract

Using a comprehensive multiproduct-multifactor approach to product supply and factor demand analysis, this study analyzes 8 commodity groups and 8 input categories for the post-war (1946-1979) period for 10 farm production regions in the U.S. Product categories include livestock products, feed grains, food grains, oil crops, hay-forage, cotton, tobacco, and vegetable-fruit-sugar crops. Variable input categories are agricultural chemicals, feed-seed-livestock purchases, mechanical power-machinery, taxes-interest, hired labor, and miscellaneous inputs. Family labor and real estate are assumed to be fixed or quasi-fixed in the short-run. Other relevant exogenous variables are weather, government policies, and technology. Own and cross price elasticities of product supply and input demand are computed for each of the 10 regions and for the U.S. (derived from the regional estimates). Sensitivity of the results to alternative functional forms is examined. Predictive accuracy is evaluated both within and outside the data period. Tests are conducted on selected hypotheses about production structure and on implications of the competitive model. The specified system of supply and demand equations are the first derivatives of the indirect restricted profit function. Econometric estimation is accomplished using generalized least squares on the seemingly unrelated system. The normalized quadratic form of the profit function is judged superior to the translog form both in conformity of results to theoretical expectations and in explanatory power of the dependent variables. Own-price input demand parameters more closely approximate competitive expectations than do own-price product supply parameters. Derived U.S. supply and demand elasticities give own-price effects that are more consistent with theoretical expectations than most of the individual regions. Adjusting U.S. elasticities for upward-sloping variable input supply curves has only a modest effect on the implied responsiveness of producers. Explanatory power over the historical data and simulation beyond the data range are both acceptable but not outstanding. Symmetry, homogeneity and convexity in prices of the implied profit function are not supported by the data. Homotheticity in outputs is not rejected for the Texas-Oklahoma region, but weak separability of several subsets is rejected; for the Texas-Oklahoma region, Hick's-neutral technological change is rejected for variable inputs but not for outputs, and Solow-neutral and Harrod-neutral technical change are rejected; nonjointness is rejected in most regions; short-run scale effects are smaller than 1 in all regions.