Fitting fully observed recursive mixed-process models with cmp
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.
Volume (Year): 11 (2011)
Issue (Month): 2 (June)
|Note:||to access software from within Stata, net describe http://www.stata-journal.com/software/sj11-2/st0224/|
|Contact details of provider:|| Web page: http://www.stata-journal.com/ |
|Order Information:||Web: http://www.stata-journal.com/subscription.html|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- William H. Greene, 1998. "Gender Economics Courses in Liberal Arts Colleges: Further Results," The Journal of Economic Education, Taylor & Francis Journals, vol. 29(4), pages 291-300, January.
- Heckman, James J, 1978.
"Dummy Endogenous Variables in a Simultaneous Equation System,"
Econometric Society, vol. 46(4), pages 931-59, July.
- James J. Heckman, 1977. "Dummy Endogenous Variables in a Simultaneous Equation System," NBER Working Papers 0177, National Bureau of Economic Research, Inc.
- Bolduc, Denis, 1999. "A practical technique to estimate multinomial probit models in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 63-79, February.
- Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
- Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
- Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
- Richard Chiburis & Michael Lokshin, 2007. "Maximum likelihood and two-step estimation of an ordered-probit selection model," Stata Journal, StataCorp LP, vol. 7(2), pages 167-182, June.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
- Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
- Alfonso Miranda & Sophia Rabe-Hesketh, 2005. "Maximum Likelihood Estimation of Endogenous Switching And Sample Selection Models for Binary, Count, And Ordinal Variables," Keele Economics Research Papers KERP 2005/14, Centre for Economic Research, Keele University.
- Lorenzo Cappellari & Stephen P. Jenkins, 2003.
"Multivariate probit regression using simulated maximum likelihood,"
StataCorp LP, vol. 3(3), pages 278-294, September.
- Lorenzo Cappellari & Stephen P. Jenkins, 2003. "Multivariate probit regression using simulated maximum likelihood," United Kingdom Stata Users' Group Meetings 2003 10, Stata Users Group.
- Vassilis A. Hajivassiliou & Daniel L. McFadden, 1993.
"The Method of Simulated Scores for the Estimation of LDV Models,"
_023, Yale University.
- Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
- V A Hajivassiliou & DL McFadden, 1997. "The Method of Simulated Scores for the Estimation of LDV Models," STICERD - Econometrics Paper Series /1997/328, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
- William J. Burke, 2009. "Fitting and interpreting Cragg's tobit alternative using Stata," Stata Journal, StataCorp LP, vol. 9(4), pages 584-592, December.
- Mark M. Pitt & Shahidur R. Khandker, 1998. "The Impact of Group-Based Credit Programs on Poor Households in Bangladesh: Does the Gender of Participants Matter?," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 958-996, October.
- James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492 National Bureau of Economic Research, Inc.
- David M. Drukker & Richard Gates, 2006. "Generating Halton sequences using Mata," Stata Journal, StataCorp LP, vol. 6(2), pages 214-228, June.
- Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-85, May.
- Michael Lokshin & Roger B. Newson, 2011. "Impact of interventions on discrete outcomes: Maximum likelihood estimation of the binary choice models with binary endogenous regressors," Stata Journal, StataCorp LP, vol. 11(3), pages 368-385, September.
- Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
- G. S. Maddala & Lung-Fei Lee, 1976. "Recursive Models with Qualitative Endogenous Variables," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 525-545 National Bureau of Economic Research, Inc.
- Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
- Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
- Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
- Richard Gates, 2006. "A Mata Geweke–Hajivassiliou–Keane multivariate normal simulator," Stata Journal, StataCorp LP, vol. 6(2), pages 190-213, June.
- Pagan, Adrian, 1979. "Some consequences of viewing LIML as an iterated Aitken estimator," Economics Letters, Elsevier, vol. 3(4), pages 369-372.
When requesting a correction, please mention this item's handle: RePEc:tsj:stataj:v:11:y:2011:i:2:p:159-206. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)or (Lisa Gilmore)
If references are entirely missing, you can add them using this form.