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Adaptive Markov chain Monte Carlo sampling and estimation in Mata

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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
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    File URL: http://wfs.gc.cuny.edu/Economics/RePEc/cgc/wpaper/CUNYGC-WP003.pdf
    File Function: First version, July 2014
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    References listed on IDEAS

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    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, December.
    2. Arne Risa Hole, 2007. "Fitting mixed logit models by using maximum simulated likelihood," Stata Journal, StataCorp LP, vol. 7(3), pages 388-401, September.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. Erik Figueiredo & Luiz Renato Lima & Gianluca Orefice, 2016. "Migration and Regional Trade Agreements: A (New) Gravity Estimation," Review of International Economics, Wiley Blackwell, vol. 24(1), pages 99-125, February.
    3. 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.
    4. 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.
    5. 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.

    More about this item

    Keywords

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

    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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