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Fitting fully observed recursive mixed-process models with cmp

David Roodman ()

Stata Journal, 2011, vol. 11, issue 2, 159-206

Abstract: 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 mul- tiequation 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 maxi- mum likelihood. Direct maximum likelihood estimation has been made more prac- tical 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, Econometrica 57: 1317–1339; Hajivassiliou and McFadden, 1998, Econometrica 66: 863–896; Keane, 1994, Econometrica 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 un- related 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-information maximum likelihood. If only the final stage or stages are structural, then estima- tion 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, ghk2(), that implements the Geweke–Hajivassiliou–Keane algorithm. Copyright 2011 by StataCorp LP.

Keywords: cmp; ghk2; Geweke–Hajivassiliou–Keane algorithm; recursive mixed-process models; seemingly unrelated regression; conditional mixed-process models (search for similar items in EconPapers)
Date: 2011
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