U.s. Aggregate Agricultural Production Elasticities Estimated by an Arima Factor Share Adjustment Model

In an effort to circumvent the multicollinearwhere 3 = yFt, f1 = 1-y, and et is a stochastic ity problems associated with direct estimation disturbance. Implied equilibrium factor share, of the aggregate agricultural production funcPo/(l-fiP), was postulated to change from tion, many economists have used indirect estidecade to decade by inclusion of dummy varimation procedures. Because in equilibrium the ables, dk, on the intercept, i.e., 3o = Po + IdkDk, partial production elasticities of an industry where k represents a decade index. composed of perfectly competitive firms are Although this work received considerable atequal to their respective factor shares, the lattention and was recognized as an important ter have been used as a means of estimating contribution to agricultural economics literaproduction elasticities. Most researchers have ture,' the theoretical justification for the consimply assumed that actual factor shares are ceptual model was largely ad hoc. A connection equilibrium values (e.g., Griliches; Rosine and between the neoclassical theory of the firm and Helmberger). Substantive contributions refactor share disequilibrium was explored recently have been made in explaining the procently by Shumway, Talpaz, and Beattie. Howcess of factor share adjustment by changes in ever, no rigorous theory of factor share disprices and technology over time (Binswanger; equilibrium has yet emerged. Lianos). However, except for the work nearly Tyner and Tweeten's estimation model is re15 years ago by Tyner and Tweeten (1965), stricted by, among other things, the two asagricultural economics literature is largely sumptions that equilibrium factor shares are silent on the measurement of differences constant for a decade and that only two varibetween actual and equilibrium factor shares. ables, current and lagged factor shares, are It is this issue with which we are primarily connecessary to define the equilibrium share. Alcerned in this article. Therefore, our point of though we do not purport to derive a theory of departure is the work by Tyner and Tweeten. factor share disequilibrium either, we do report Because there is no assurance that current the development of an autoregressive inteeconomic equilibrium is ever actually achieved, grated moving average (ARIMA) model of facTyner and Tweeten imposed a less restrictive tor share adjustment that relaxes the two asassumption than other economists i.e., that sumptions. producers are not necessarily ever in a perfectU.S. factor share data for eight inputs for the ly competitive equilibrium. They assumed that years 1910-1976 are used to estimate equilibproducers adjust toward equilibrium in their rium factor shares by year for the period 1919factor shares following a geometric lag adjust1976. Production function implications during ment, this 58-year period are then explored.