Flexible Specification and Robust Estimation of Input Demand Systems

Cost function and factor demand estimation and measurement are among the most useful tools in economic analysis. This paper defines cost function flexibility in a new way that extends results and concepts from consumer demand theory to models of joint production. This applies to production models where input demand equations can be represented in terms of input prices, quasi-fixed inputs, and cost. The model’s flexibility is determined by the rank of a matrix of price functions and the number and functional form of a vector of cost functions. The new model is particularly useful when outputs are subject to measurement errors, perhaps due to production risk. Input demands obtained with this approach are robust to the form of the decision maker’s risk preferences. An empirical application to state-level annual time series data on U.S. agricultural input use in the 48 contiguous states over the period 1960-1999 demonstrates the flexibility, generality, and value of this new approach to production economics. The model is estimated by a new semiparametric generalized method of moments method to address measurement errors in outputs, endogenous regressors, technical change, heterogeneous production, heteroskedasticity, and spatial-temporal error correlations. The estimated model is economically regular at almost all (96 percent) observations, reflects a cross-sectional distribution of technologies and economic responses, and the stochastic process for the residuals is stationary across space and time. Full rank three is supported by the data. Common functional forms such as the translog and quadratic are rejected.