A Dual Approach to Estimation With Constant Prices

In a recent paper, Mundlak assumes that the price-taking, risk-neutral and profit-maximizing entrepreneur makes his decisions on the basis of a planning model that maximizes expected profit using expected prices. In the same paper, the author asserts that when there is no sample price variation across competitive firms, it is impossible to estimate the supply and factor demand functions from cross-section data using a dual approach. In a famous paper, titled “To Dual or not to Dual,” Pope asserted a similar opinion. This paper shows that, using Mundlak’s assumption about planning decisions based upon expected profit, it is possible to use a dual estimator to estimate supply and factor demand functions. This objective is achieved by using Mundlak’s assumption about the individuality of the firm’s expectation process. A two-phase procedure is suggested to obtain consistent estimates of the expected quantities and prices which are then used, in phase II, in a nonlinear seemingly unrelated equations problem to obtain efficient estimates of the technological parameters.