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Estimation of Heterogeneous Agent Models: A Likelihood Approach

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  • Juan Carlos Parra-Alvarez
  • Olaf Posch
  • Mu-Chun Wang

Abstract

We study the statistical properties of heterogeneous agent models. Using a Bewley-Hugget-Aiyagari model we compute the density function of wealth and income and use it for likelihood inference. We study the finite sample properties of the maximum likelihood estimator (MLE) using Monte Carlo experiments on artificial cross-sections of wealth and income. We propose to use the Kullback-Leibler divergence to investigate identification problems that may affect inference. Our results suggest that the unrestricted MLE leads to considerable biases of some parameters. Calibrating weakly identified parameters allows to pin down the other unidentified parameter without compromising the estimation of the remaining parameters. We illustrate our approach by estimating the model for the U.S. economy using wealth and income data from the Survey of Consumer Finances.

Suggested Citation

  • Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    • Handle: RePEc:ces:ceswps:_6717
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    1. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
    2. Jess Benhabib & Alberto Bisin & Shenghao Zhu, 2011. "The Distribution of Wealth and Fiscal Policy in Economies With Finitely Lived Agents," Econometrica, Econometric Society, vol. 79(1), pages 123-157, January.
    3. Marco Cagetti & Mariacristina De Nardi, 2006. "Entrepreneurship, Frictions, and Wealth," Journal of Political Economy, University of Chicago Press, vol. 114(5), pages 835-870, October.
    4. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2006. "Idiosyncratic production risk, growth and the business cycle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1095-1115, September.
    5. Jess Benhabib & Alberto Bisin, 2018. "Skewed Wealth Distributions: Theory and Empirics," Journal of Economic Literature, American Economic Association, vol. 56(4), pages 1261-1291, December.
    6. Canova, Fabio & Sala, Luca, 2009. "Back to square one: Identification issues in DSGE models," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 431-449, May.
    7. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    8. Brant Abbott & Giovanni Gallipoli & Costas Meghir & Giovanni L. Violante, 2013. "Education Policy�and Intergenerational Transfers in Equilibrium," Cowles Foundation Discussion Papers 1887, Cowles Foundation for Research in Economics, Yale University.
    9. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    10. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2018. "Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 108(3), pages 697-743, March.
    11. Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
    12. Arlene Wong, 2016. "Population aging and the transmission of monetary policy to consumption," 2016 Meeting Papers 716, Society for Economic Dynamics.
    13. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    14. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    15. Burkhard Heer & Alfred Maußner, 2024. "Dynamic General Equilibrium Modeling," Springer Texts in Business and Economics, Springer, edition 3, number 978-3-031-51681-8, December.
    16. Brant Abbott & Giovanni Gallipoli & Costas Meghir & Giovanni L. Violante, 2019. "Education Policy and Intergenerational Transfers in Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2569-2624.
    17. Jess Benhabib & Alberto Bisin & Mi Luo, 2019. "Wealth Distribution and Social Mobility in the US: A Quantitative Approach," American Economic Review, American Economic Association, vol. 109(5), pages 1623-1647, May.
    18. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    19. Heer, Burkhard & Trede, Mark, 2003. "Efficiency and distribution effects of a revenue-neutral income tax reform," Journal of Macroeconomics, Elsevier, vol. 25(1), pages 87-107, March.
    20. Cagetti, Marco & De Nardi, Mariacristina, 2008. "Wealth Inequality: Data And Models," Macroeconomic Dynamics, Cambridge University Press, vol. 12(S2), pages 285-313, September.
    21. Mi Luo & Simon Mongey, 2019. "Assets and Job Choice: Student Debt, Wages and Amenities," NBER Working Papers 25801, National Bureau of Economic Research, Inc.
    22. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    23. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    24. Ríos-Rull, José-Víctor & Schorfheide, Frank & Fuentes-Albero, Cristina & Kryshko, Maxym & Santaeulàlia-Llopis, Raül, 2012. "Methods versus substance: Measuring the effects of technology shocks," Journal of Monetary Economics, Elsevier, vol. 59(8), pages 826-846.
    25. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    26. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    27. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    28. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    29. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    30. Thomas Winberry, 2018. "A method for solving and estimating heterogeneous agent macro models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1123-1151, November.
    31. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    32. Robert Shimer, 2005. "The Cyclical Behavior of Equilibrium Unemployment and Vacancies," American Economic Review, American Economic Association, vol. 95(1), pages 25-49, March.
    33. Díaz-Giménez, Javier & Pijoan-Mas, Josep, 2011. "Flat Tax Reforms: Investment Expensing and Progressivity," CEPR Discussion Papers 8238, C.E.P.R. Discussion Papers.
    34. George-Marios Angeletos, 2007. "Uninsured Idiosyncratic Investment Risk and Aggregate Saving," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(1), pages 1-30, January.
    35. Serdar Ozkan & Kurt Mitman & Fatih Karahan & Aaron Hedlund, 2016. "Monetary Policy, Heterogeneity and the Housing Channel," 2016 Meeting Papers 663, Society for Economic Dynamics.
    36. R. F. Engle & D. McFadden (ed.), 1986. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 4, number 4.
    37. Gomme, Paul & Rupert, Peter, 2007. "Theory, measurement and calibration of macroeconomic models," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 460-497, March.
    38. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Identification and estimation of heterogeneous agent models: A likelihood approach," CREATES Research Papers 2017-35, Department of Economics and Business Economics, Aarhus University.
    39. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    40. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
    41. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, Decembrie.
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    Cited by:

    1. Khieu, Hoang & Wälde, Klaus, 2023. "Capital income risk and the dynamics of the wealth distribution," Economic Modelling, Elsevier, vol. 122(C).
    2. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    3. Balbus, Lukasz & Dziewulski, Pawel & Reffett, Kevin & Wozny, Lukasz, 2022. "Markov distributional equilibrium dynamics in games with complementarities and no aggregate risk," Theoretical Economics, Econometric Society, vol. 17(2), May.
    4. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    5. Laura Liu & Mikkel Plagborg-M{o}ller, 2021. "Full-Information Estimation of Heterogeneous Agent Models Using Macro and Micro Data," Papers 2101.04771, arXiv.org, revised Jun 2022.
    6. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    7. Fischer, Thomas, 2019. "Determinants of Wealth Inequality and Mobility in General Equilibrium," Working Papers 2019:22, Lund University, Department of Economics.
    8. Laura Liu & Mikkel Plagborg‐Møller, 2023. "Full‐information estimation of heterogeneous agent models using macro and micro data," Quantitative Economics, Econometric Society, vol. 14(1), pages 1-35, January.
    9. Laura Liu & Mikkel Plagborg-M{o}ller, 2021. "Full-Information Estimation of Heterogeneous Agent Models Using Macro and Micro Data," Papers 2101.04771, arXiv.org, revised Jun 2022.
    10. Glawion, Rene & Puche, Marc & Haller, Frédéric, 2020. "A General Equilibrium Model of Earnings, Income, and Wealth," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224580, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    heterogeneous agent models; continuous-time; Fokker-Planck equations; Kullback-Leibler divergence; maximum likelihood;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E24 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity

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