LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF
LARGE SAMPLE PROPERTIES OF GENERALIZED METHOD OF
复制标题
广义方法的大样本性质
DOI：
--
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
L. Hansen
中科院分区：
文献类型：
--
作者：
L. Hansen
本文研究了一类广义矩量法（GMM）估计的大样本性质，它包含了许多标准的计量经济学估计。为了激发这门课，考虑一个我们希望估计其参数向量的计量经济模型。该模型隐含了一系列正交条件，其中包含我们希望施加或测试的任何经济理论限制。例如，某些方程定义投影或特定变量是预先确定的假设会产生正交条件，其中不可观测干扰和可观测变量函数的预期叉积等于零。启发式地，识别需要至少与待估计的参数向量中的坐标一样多的正交条件。正交条件中的不可观测扰动可以用包含真参数向量和观测变量的等价表达式来代替。利用矩量法，可以对容许参数空间中的任何元素计算期望叉积的样本估计。通过找到参数空间中使样本叉积的线性组合尽可能接近零的元素，获得真实参数向量的GMM估计。在研究GMM估计的强相合性时，我们给出了如何构造一类具有极小值的准则函数，使其几乎必然收敛于真参数向量。由此产生的估计量的解释，使样本版本的人口正交性条件尽可能接近零，根据一些度量或距离的措施。我们使用的度量指标的替代估计。这类估计量包括Amemiya [1，2]，Jorgenson和Laffont [24]以及Gallant [11]等考虑的非线性工具变量估计量。
IN THIS PAPER we study the large sample properties of a class of generalized method of moments (GMM) estimators which subsumes many standard econometric estimators. To motivate this class, consider an econometric model whose parameter vector we wish to estimate. The model implies a family of orthogonality conditions that embed any economic theoretical restrictions that we wish to impose or test. For example, assumptions that certain equations define projections or that particular variables are predetermined give rise to orthogonality conditions in which expected cross products of unobservable disturbances and functions of observable variables are equated to zero. Heuristically, identification requires at least as many orthogonality conditions as there are coordinates in the parameter vector to be estimated. The unobservable disturbances in the orthogonality conditions can be replaced by an equivalent expression involving the true parameter vector and the observed variables. Using the method of moments, sample estimates of the expected cross products can be computed for any element in an admissible parameter space. A GMM estimator of the true parameter vector is obtained by finding the element of the parameter space that sets linear combinations of the sample cross products as close to zero as possible. In studying strong consistency of GMM estimators, we show how to construct a class of criterion functions with minimizers that converge almost surely to the true parameter vector. The resulting estimators have the interpretation of making the sample versions of the population orthogonality conditions as close as possible to zero according to some metric or measure of distance. We use the metric to index the alternative estimators. This class of estimators includes the nonlinear instrumental variables estimators considered by, among others, Amemiya [1, 2], Jorgenson and Laffont [24], and Gallant [11].2 There the