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Fitting fully observed recursive mixed-process models with cmp

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  • David Roodman

    (Center for Global Development)

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.

Suggested Citation

  • David Roodman, 2011. "Fitting fully observed recursive mixed-process models with cmp," Stata Journal, StataCorp LP, vol. 11(2), pages 159-206, June.
    • Handle: RePEc:tsj:stataj:v:11:y:2011:i:2:p:159-206
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    References listed on IDEAS

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