生产率与效率分析lecture7--参数方法.ppt

Productivity Analysis Principles For simplicity, assume away joint (multi-output) production. Theoretical model of production in terms of the (single-output) production function y = f(x). Purpose is to estimate f from the data (Y,X). Elements: 1) Specification of empirical model (function form of the production function). 2) Specification of data-generating process (DGP) (error distribution, inefficiencies). 3) Estimation (calibration of model parameters to best fit the data). 1) Specification of production function Select a certain family of functions flexible enough to approximate the true but unknown f. Examples: CD: Translog: Note 1: Translog provides the second-order numerical approximation to an arbitrary function form. Note 2: Additional constraints on parameters can be imposed to enforce particular substitution properties. E.g. CD function exhibits CRS (NIRS, NDRS) if 2) DGP: sources of deviations from f Most generally, it is assumed that deviations from the production function occur for 2 reasons: i) errors, and ii) technical inefficiency. This can be formalized (for firm k) as where vk is the noise term that captures e.g. random measurement errors; TEk is the usual Farrell output efficiency term. (Note: the additive structure preserved by taking logs. E.g. CD 2b) Distribution assumptions A) The noise term: It is typically assumed (following the central limit theorem) that the noise terms B) The inefficiency term: Must be one-sided TEk ? 1 ? uk= - lnTEk ? 0. It is often assumed the transformed inefficiency terms uk are i.i.d. half-normally distributed, i.e. (other one-sided specifications include exponential and gamma distributions) 3) Estimation Traditional approach: Assume away inefficiency (after all, there is no room for that in the world of neoclassical profit maximizing firms). The residual collapses to the noise term, i.e. It is typically assumed (following the central limit theorem) that the noise terms Therefore, the u