Fitting fully observed recursive mixed-process models with cmp
Fitting fully observed recursive mixed-process models with cmp
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DOI：
10.1177/1536867x1101100202
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发表时间：
2011-01-01
期刊：
影响因子：
4.8
通讯作者：
Roodman, David
中科院分区：
文献类型：
--
作者：
Roodman, David
许多计量经济学模型的核心是线性函数和正态误差。示例包括经典的小样本线性回归模型以及概率、有序概率、多项概率、tobit、区间回归和截断分布回归模型。由于正态分布具有自然的多维概括，因此可以将此类模型组合成多方程系统，其中误差共享多元正态分布。文献历来关注于拟合混合模型的多阶段程序，这些程序在计算上比最大似然更有效，尽管在统计上不太有效。通过更快的计算机和用于估计高维累积正态分布的模拟似然方法，直接最大似然估计变得更加实用。这种模拟似然方法包括Geweke-Hajivassiliou-Keane算法(Geweke，1989，Econometrics 57：1317-1339；Hajivassiliou和McFadden，1998，Econometrics 66：863-896；Keane，1994，Econometrics 62：95-116)。最大似然还有助于推广到切换、选择和其他模型，其中方程的数量和类型随观察而变化。 Stata 命令 cmp 适合这个大家族看似无关的回归模型。它的估计量对于递归系统也是一致的，其中所有内生变量都出现在观察到的右侧。如果所有方程都是结构性的，那么估计就是全信息最大似然。如果只有最后一个或多个阶段是结构性的，那么估计就是有限信息最大似然。 cmp 可以模仿大量内置和用户编写的 Stata 命令。它也适用于以前难以估计的一系列模型。然而，异方差性可能会导致 cmp 不一致。本文解释了 cmp 和相关 Mata 函数 ghk 2 () 的理论和实现，该函数实现了 Geweke-Hajivassiliou-Keane 算法。
At the heart of many econometric models are a linear function and a normal error. Examples include the classical small-sample linear regression model and the probit, ordered probit, multinomial probit, tobit, interval regression, and truncated-distribution regression models. Because the normal distribution has a, natural multidimensional generalization, such models can be combined into multiequation systems in which the errors share a multivariate normal distribution. The literature has historically focused on multistage procedures for fitting mixed models, which are more efficient computationally, if less so statistically, than maximum likelihood. Direct maximum likelihood estimation has been made more practical by faster computers and simulated likelihood methods for estimating higher-dimensional cumulative normal distributions. Such simulated likelihood methods include the Geweke-Hajivassiliou-Keane algorithm (Geweke, 1989, Econometrics 57: :1317-1339; Hajivassiliou and McFadden, 1998, Econometrics 66: 863-896; Keane, 1994, Econometrics 62: 95-116). Maximum likelihood also facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata command cmp fits seemingly unrelated regressions models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous variables appear on the right-hand sides as observed. If all the equations are structural, then estimation is full-inforrnation maximum likelihood. If only the final stage or stages are structural, then estimation is limited-information maximum likelihood. cmp can mimic a score of built-in and user-written Stata commands. It is also appropriate for a panoply of models that previously were hard to estimate. Heteroskedasticity, however, can render cmp inconsistent. This article explains the theory and implementation of cmp and of a related Mata function, ghk 2 (), that implements the Geweke-Hajivassiliou-Keane algorithm.