I have written a working paper about my Stata command -cmp- (stands for "conditional mixed process"). It is similar to my "How to Do xtabond2" paper in mixing theory, pedagogy and command documentation.
The paper is at:
http://www.cgdev.org/content/publications/detail/1421516
Comments welcome.
Abstract:
At the heart of many econometric models is 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 multi-equation systems in which the errors share a multivariate normal distribution. The literature has historically focussed on multi-stage procedures for estimating mixed models, which are more efficiently computationally, if less so statistically, than maximum likelihood (ML). But faster computers and simulated likelihood methods such as the Geweke, Hajivassiliou, and Keane (GHK) algorithm for estimating higher-dimensional cumulative normal distributions have made direct ML estimation practical. ML also facilitates a generalization to switching, selection, and other models in which the number!
and types of equations vary by observation. The Stata module cmp fits Seemingly Unrelated Regressions (SUR) 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-information maximum likelihood (FIML). If only the final stage or stages are, then it is limited-information maximum likelihood (LIML). cmp can mimic a dozen built-in Stata commands and several user-written ones. It is also appropriate for a panoply of models previously hard to estimate. Heteroskedasticity, however, can render it inconsistent. This paper explains the theory and implementation of cmp and of a related Mata function, ghk2(), that implements the GHK algorithm.
--David
David Roodman
Research Fellow
1776 Massachusetts Avenue NW
Washington, DC 20036
Center for Global Development
Independent Research and Practical Ideas for Global Prosperity
Phone: 1 202 416-0723
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