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A General Inferential Framework for Singly-Truncated Bivariate Normal Models with Applications in Economics

Author

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  • Yin Liu

    (Zhongnan University of Economics and Law)

  • Guo-Liang Tian

    (Southern University of Science and Technology)

  • Chi Zhang

    (Shenzhen University)

  • Hong Qin

    (Zhongnan University of Economics and Law)

Abstract

To analyze the singly-truncated bivariate economic data, we establish a class of singly-truncated bivariate normal distributions via stochastically representing the original bivariate normal random vector as a mixture of the singly-truncated part and its complementary components. Aided with the stochastic representaion, we creatively construct two novel unified and simple algorithms—the expectation–maximization algorithm as well as the minorization–maximization algorithm—to calculate the maximum likelihood estimates of the means and covariance matrix for the model of interest. In addition, we also develop a DA algorithm for posterior sampling in Bayesian analysis. Both simulation results and two real data applications in economics, collaborated by comparisons with existing methods, demonstrate the effectiveness and stability of proposed methodologies.

Suggested Citation

  • Yin Liu & Guo-Liang Tian & Chi Zhang & Hong Qin, 2024. "A General Inferential Framework for Singly-Truncated Bivariate Normal Models with Applications in Economics," Computational Economics, Springer;Society for Computational Economics, vol. 64(5), pages 2747-2781, November.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:5:d:10.1007_s10614-023-10525-w
    DOI: 10.1007/s10614-023-10525-w
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    References listed on IDEAS

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    1. 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.
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    3. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    4. A. W. Phillips, 1958. "The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica, London School of Economics and Political Science, vol. 25(100), pages 283-299, November.
    5. Danny D. Dyer, 1973. "On Moments Estimation of the Parameters of a Truncated Bivariate Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 22(3), pages 287-291, November.
    6. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.
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