Some Econometric Options for Dealing with Unknown Functional Form

Economic theory often provides information on the variables to be included in economic relationships (e.g., demands are functions of prices) and sometimes provides information on the signs and magnitudes of firstand second-order derivatives (e.g., homogeneity and concavity information). However, it rarely provides information concerning functional forms. In the absence of this information, it is common to assume a specific functional form (e.g., translog) and subsume errors of approximation into a disturbance term. Unfortunately, the estimated parameters of these approximating relationships do not consistently estimate the economically-relevant characteristics of the true relationship unless the latter is of the approximating class (White, 1980). Practical econometric solutions to the problem are now becoming available. This paper discusses kernel regression (KR), flexible least squares (FLS), generalized restricted least squares (GRLS) and latent class (LC) estimators. The empirical performance of all four estimators is assessed using an artificially-generated data set. Three of the estimators are then used to estimate characteristics of a labour demand function for US agriculture. 1 Paper presented to the 50 Annual Conference of the Australian Agricultural and Resource Economics Society, 8-10 February, 2006.