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On the Role of Jacobian Terms in Maximum Likelihood Estimation

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  • James G. MacKinnon

Abstract

Because of the presence of Jacobian terms, determinants which arise as a result of a transformation of variables, many common likelihood functions have singularities. This fact has several implications for maximum likelihood estimation. The most interesting of these is that singularities often correspond with economically meaningful restrictions, and can be used to impose the latter. Several applications of this principle are presented. They suggest that maximum likelihood should be preferred to other estimation schemes not only because of its optimal large-sample statistical properties, but also because of its ability to incorporate certain a priori restrictions from economic theory.

Suggested Citation

  • James G. MacKinnon, 1978. "On the Role of Jacobian Terms in Maximum Likelihood Estimation," Working Paper 304, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:304
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    References listed on IDEAS

    as
    1. Beach, Charles M. & MacKinnon, James G., 1978. "Full maximum likelihood estimation of second- order autoregressive error models," Journal of Econometrics, Elsevier, vol. 7(2), pages 187-198, June.
    2. 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.
    3. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
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