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请问计量中什么是delta方法？我在看文献过程中，有三个方程，方程1、方程2、方程3，方程3是通过将方程1带入方程2得到的，三个方程各变量的系数可以用一个式子表示出来，文章在对方程3回归后得到方程3各系数的估计值后，说通过delta方法就可以得到方程1和方程2的系数及其标准误，那么什么是delta方法？如何使用delta方法来达到上述的目的?

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关键词：Delta del ELT 如何使用 标准误 文章 如何

你可以看greene的《计量经济分析》；
《计量经济理论和方法》_戴维森_麦金农
《微观经济计量学  方法与应用》 卡梅伦；
Principles of Econometrics 4th-R.Carter Hill，William E. Griffiths，Guay C. Lim



这些书上有介绍


http://www.stata.com/support/faqs/statistics/delta-method/
What is the delta method and how is it used to estimate the standard error of a transformed parameter?

Title		Explanation of the delta method
Author		Alan H. Feiveson, NASA
Date		December 1999; minor revisions May 2005

---

The delta method, in its essence, expands a function of a random variable about its mean, usually with a one-step Taylor approximation, and then takes the variance. For example, if we want to approximate the variance of G(X) where X is a random variable with mean mu and G() is differentiable, we can try

        G(X) = G(mu) + (X-mu)G'(mu)        (approximately)

so that

        Var(G(X)) = Var(X)*[G'(mu)]2      (approximately)

where G'() = dG/dX. This is a good approximation only if X has a high probability of being close enough to its mean (mu) so that the Taylor approximation is still good.

This idea can easily be expanded to vector-valued functions of random vectors,

        Var(G(X)) = G'(mu) Var(X) [G'(mu)]T

and that, in fact, is the basis for deriving the asymptotic variance of maximum-likelihood estimators. In the above, X is a 1 x m column vector; Var(X) is its m x m variance–covariance matrix; G() is a vector function returning a 1 x n column vector; and G'() is its n x m matrix of first derivatives. T is the transpose operator. Var(G(X)) is the resulting n x n variance–covariance matrix of G(X).

Acknowledgments

Nicholas Cox of Durham University and John Gleason of Syracuse University provided the references.

ReferencesOehlert, G. W. 1992.A note on the delta method. American Statistician 46: 27–29.Rice, John. 1994.Mathematical Statistics and Data Analysis. 2nd ed. Duxbury.

蓝色 发表于 2015-4-4 19:42
你可以看greene的《计量经济分析》；
《计量经济理论和方法》_戴维森_麦金农
《微观经济计量学  方法与应 ...

非常感谢！那在stata中如何使用delta方法来估计系数组合的标准误呢？

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