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Adaptive Markov chain Monte Carlo sampling and estimation in Mata

Author

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  • Matthew J. Baker

    (Hunter College and Graduate Center, City University of New York)

Abstract

I describe algorithms for drawing from distributions using adaptive Markov chain Monte Carlo (MCMC) methods, introduce a Mata function for performing adaptive MCMC, amcmc(), and a suite of functions amcmc *() allowing an alternative implementation of adaptive MCMC. amcmc() and amcmc *() may be used in conjunction with models set up to work with Mata’s [M-5] moptimize( ) or [M-5] optimize( ), or with stand-alone functions. To show how the routines might be used in estimation problems, I give two examples of what Chernozukov and Hong (2003) refer to as Quasi-Bayesian or Laplace-Type estimators - simulation-based estimators employing MCMC sampling. In the first example I illustrate basic ideas and show how a simple linear model can be estimated by simulation. In the next example, I describe simulation-based estimation of a censored quantile regression model following Powell (1986); the discussion describes the workings of the Stata command mcmccqreg. I also present an example of how the routines can be used to draw from distributions without a normalizing constant, and in Bayesian estimation of a mixed logit model. This discussion introduces the Stata command bayesmlogit.

Suggested Citation

  • Matthew J. Baker, 2014. "Adaptive Markov chain Monte Carlo sampling and estimation in Mata," Working Papers 3, City University of New York Graduate Center, Ph.D. Program in Economics.
  • Handle: RePEc:cgc:wpaper:003
    as

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    File URL: http://wfs.gc.cuny.edu/Economics/RePEc/cgc/wpaper/CUNYGC-WP003.pdf
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    References listed on IDEAS

    as
    1. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    2. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    4. Arne Risa Hole, 2007. "Fitting mixed logit models by using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 7(3), pages 388-401, September.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Matthew J. Baker, 2023. "Using bayesmixedlogit and bayesmixedlogitwtp in Stata," Papers 2302.01775, arXiv.org.
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    4. Tu D. Q. Le & Thanh Ngo & Tin H. Ho & Dat T. Nguyen, 2022. "ICT as a Key Determinant of Efficiency: A Bootstrap-Censored Quantile Regression (BCQR) Analysis for Vietnamese Banks," IJFS, MDPI, vol. 10(2), pages 1-15, June.
    5. BELAÏD, Fateh & Elsayed, Ahmed H. & Omri, Anis, 2021. "Key drivers of renewable energy deployment in the MENA Region: Empirical evidence using panel quantile regression," Structural Change and Economic Dynamics, Elsevier, vol. 57(C), pages 225-238.
    6. Fateh Belaid & Ahmed H. Elsayed, 2019. "What drives renewable energy production in MENA Region? Investigating the roles of political stability, governance and financial sector," Working Papers 1322, Economic Research Forum, revised 21 Aug 2019.
    7. O.S. Mariev & N.B. Davidson & O.S. Emelianova, 2020. "The Impact of Urbanization on Carbon Dioxide Emissions in the Regions of Russia," Journal of Applied Economic Research, Graduate School of Economics and Management, Ural Federal University, vol. 19(3), pages 286-309.
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    10. Pourya Valizadeh & Travis A Smith, 2020. "How Did The American Recovery and Reinvestment Act Affect the Material Well‐Being of SNAP Participants? A Distributional Approach," Applied Economic Perspectives and Policy, John Wiley & Sons, vol. 42(3), pages 455-476, September.
    11. Andrew Myburgh & Jordi Paniagua, 2016. "Does International Commercial Arbitration Promote Foreign Direct Investment?," Journal of Law and Economics, University of Chicago Press, vol. 59(3), pages 597-627.
    12. Ryan A. Fitch & Julie M. Mueller & Rebecca Ruiz & Wade Rousse, 2022. "Recreation Matters: Estimating Millennials’ Preferences for Native American Cultural Tourism," Sustainability, MDPI, vol. 14(18), pages 1-11, September.
    13. Mallela, Keerti & Singh, Sunny Kumar & Srivastava, Archana, 2023. "Remittances, financial development, and income inequality: A panel quantile regression approach," International Economics, Elsevier, vol. 175(C), pages 171-186.
    14. Baker, Matthew J. & George, Lisa M., 2024. "The news hour: Welfare estimation in the market for local television news," International Journal of Industrial Organization, Elsevier, vol. 94(C).
    15. Panagiotidis, Theodore & Printzis, Panagiotis, 2021. "Investment and uncertainty: Are large firms different from small ones?," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 302-317.
    16. Cuadros, Ana & Martín-Montaner, Joan & Paniagua, Jordi, 2019. "Migration and FDI: The role of job skills," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 318-332.
    17. Valizadeh, Pourya & Smith, Travis A., 2017. "How Did the American Recovery and Reinvestment Act (ARRA) Impact the Material Well-being of SNAP Participants? A Distributional Approach," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258496, Agricultural and Applied Economics Association.

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    More about this item

    Keywords

    Stata; Mata; Markov chain Monte Carlo; drawing from distributions; mixed logit Bayesian estimation; bayesmlogit; mcmccqreg;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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