The Estimation of Marginal Product from a Cobb-Douglas Production Function
Cobb–Douglas 生产函数中的边际产出估计AI 解读 ↓
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Cobb–Douglas 生产函数中的边际产出估计
- 研究问题
- 从 Cobb–Douglas 生产函数计算边际产出时，常用估计量具有怎样的偏差、精度与渐近分布，能否通过替代估计改进？
- 方法与思路
- 作者在误差正态分布假设下研究常用估计量的抽样性质，提出降低偏差的替代估计，并构造各类估计量的方差协方差估计。
- 材料陈述的贡献
- 摘要称，替代估计量偏差更小、精度更高，并给出常用估计量的渐近正态性及相关方差协方差矩阵的近似估计。
- 阅读关注点
- 核对边际产出的定义与评价点、正态误差条件、偏差及方差展开的阶数，并检查数值例子是否支持作者所述的小样本用途。
- 阅读边界
- 摘要未说明精度优势的完整适用条件，也未讨论投入内生性或模型误设；仅凭所述数值例子不能判断一般小样本表现。
原文摘要
The sampling properties of the usual estimator of marginal product from a CobbDouglas production function are studied under the assumption of normally distributed errors. The asymptotic normality of these estimators is demonstrated and certain special cases are considered for which the asymptotic distribution is particularly simple. An alternative estimator of marginal product is suggested which has both a smaller bias and greater precision than the usual estimator. Estimators of the variance-covariance matrix of all marginal product estimators mentioned are given. These are accurate to order n-1. A GREAT deal of attention is given nowadays to the statistical properties of estimators of parameters in simultaneous equations models. By contrast, little attention is given to the statistical properties of estimators of parameters in simpler economic models. One such model that has been virtually ignored by statisticians is the Cobb-Douglas production function. The usefulness of this function in the cross section analysis of an industry should not be underrated although, as with all models, care must be taken to ensure that the data to which the function is fitted correspond reasonably well with the assumptions, both economic and statistical, implied by the function. The purpose of the present paper is to consider some of the statistical properties of estimators of marginal product obtained from a CobbDouglas function. Section 2 will discuss the estimator most frequently used (see, for example, Tintner and Brownlee [8] and Heady [4]). The third section will discuss alternative estimators which reduce bias to order n-2 where n is the size of sample. These alternative estimators may be useful when the sample size is small and the variability of observed production about the fitted Cobb-Douglas function is large. The fourth section considers the problem of estimating the variance matrices of the estimators discussed in Sections 2 and 3. A numerical illustration is given in Section 5.