A constrained maximum-likelihood approach to estimating switching regressions

It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameter...

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Bibliographic Details
Published inJournal of econometrics Vol. 48; no. 1; pp. 241 - 262
Main Author Phillips, Robert F.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.04.1991
Elsevier
North-Holland Pub. Co
Elsevier Sequoia S.A
SeriesJournal of Econometrics
Subjects
Algorithms
Econometrics
Economic models
Economic statistics
Economic theory
Estimating techniques
Exact sciences and technology
Mathematics
Probability and statistics
Regression analysis
Sciences and techniques of general use
Statistics
Studies
Switching
Utility functions
Regression equation
Regression model
Asymptotic normality
Gaussian distribution
Maximum likelihood
Timing
EM algorithm
Switching
Variance
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Summary:It is widely known that the likelihood function for the switching-regression model is unbounded if the error variances are unconstrained. This paper shows that a constrained maximum-likelihood formulation makes the likelihood function bounded. Relatively mild constraints are imposed on the parameters, and if the true parameters satisfy the constraints, there is a global maximizer of the likelihood function on the constrained parameter space which is consistent, asymptotically normal, and efficient. A well-known EM algorithm is modified in order to compute constrained maximizers of the likelihood function.
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ISSN:0304-4076
1872-6895
DOI:10.1016/0304-4076(91)90040-K